Reactive and Membrane-Assisted Separations. Process Intensification: by Reactive and Membrane-assisted Separations [2nd, Revised Edition] 9783110720464, 9783110720457

Table of contents :
Preface
Contents
List of contributing authors
1 Introduction to process intensification and synthesis methods
2 Hybrid separation processes
3 Thermodynamics for reactive separations
4 Modeling concepts for reactive separations
5 Reactive distillation
6 Reactive absorption
7 Reactive extraction
8 OSN-assisted reaction and separation processes
9 Pervaporation and vapor permeation– assisted reactive separation processes
Index

Citation preview

Process Intensification

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Process Intensification by Reactive and Membrane-assisted Separations Edited by Mirko Skiborowski, Andrzej Górak 2nd Edition

Editors Prof. Dr. Mirko Skiborowski Hamburg University of Technology Institute of Process Systems Engineering Am Schwarzenberg-Campus 4 C 21073 Hamburg Germany [email protected] Prof. Dr. Andrzej Górak Łódź University of Technology Faculty of Process and Environmental Engineering ul. Wólczańska 175 90-924 Łódź Poland [email protected]

ISBN 978-3-11-072045-7 e-ISBN (PDF) 978-3-11-072046-4 e-ISBN (EPUB) 978-3-11-072060-0 Library of Congress Control Number: 2021953287 Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. © 2022 Walter de Gruyter GmbH, Berlin/Boston Cover image: Scimat Scimat/Science Source/gettyimages Typesetting: Integra Software Services Pvt. Ltd. Printing and binding: CPI books GmbH, Leck www.degruyter.com

Preface Chemical products like basic, commodity and specialty chemicals, as well as pharmaceuticals, life science and consumer products are all of essential importance for every day’s life in modern society. However, as one of the most energy demanding industrial sectors the chemical processing industries are facing an increasing need to improve energy efficiency and sustainability. The latter also demands a transition of raw materials from those largely based on fossil resources to one that builds on recycling strategies in a circular economy and the use of renewable resources. Yet, production processes still have to be reliable, efficient and economically viable in rapidly changing markets with global competition. Generally speaking, the necessary development requires an increase in the efficiency of existing processes, based on an optimal selection of raw materials, solvents and energy improvements, as well as innovative technologies and totally new processing pathways. One important toolset to successfully face these challenges in the chemical process industry is process intensification. The current graduate level textbook provides an overview over the various process intensification technologies for fluid separations. The basic thermal separation processes, which have been utilized for more than two centuries, are responsible for more than half of the energy demand in the chemical industry and consequently need substantial improvements and intensification. The technologies covered in this book have been selected as the most important means for process intensification in fluid separations, covering front running technologies, such as reactive distillation, absorption and extraction, as well as various membrane-assisted reactions and reactive separations. Prior to the specific chapters on the individual technologies, first an introduction to process intensification and hybrid separation processes is provided, as well as a fundamental introduction to the thermodynamic modelling of reactive multiphase systems and a conceptual discussion on modelling of reactive separation processes. The overall motivation for this textbook is to provide a fundamental introduction to process intensification technologies for fluid separation processes and to demonstrate their evolution and development together with a model-based assessment and process design tools. We also illustrate the links of the individual technologies with the general strategies of process intensification to motivate young researchers to develop new intensified equipment or technologies and to implement process intensification in industry. Therefore, each chapter on the individual technologies classifies them in the context of process intensification at different scales, presents important and current applications, as well as information on modelling and design with selected case studies. Finally, each chapter ends with a brief summary of take-home messages and a quiz and exercises. This second edition of the book on Reactive and Membrane-Assisted Separations extends the scope of the preceding first edition to a broader range of Process Intensification technologies. While we decided to add two general chapters on the https://doi.org/10.1515/9783110720464-202

VI

Preface

thermodynamics of reactive multiphase systems and modelling concepts for reactive separations, the previously addressed centrifugally enhanced vapor/gas-liquid separations are no longer covered in this book. Instead, a full second book has been added to this compendium on process intensification, which addresses the basics and various applications of rotating packed beds as a major representative of HiGEE technology.

Contents Preface

V

List of contributing authors

IX

Mirko Skiborowski, Daniel Sudhoff 1 Introduction to process intensification and synthesis methods Mirko Skiborowski, Andrzej Górak 2 Hybrid separation processes

49

Moreno Ascani, Christoph Held 3 Thermodynamics for reactive separations Eugeny Y. Kenig 4 Modeling concepts for reactive separations Anton A. Kiss 5 Reactive distillation

265

Anna-Katharina Kunze 6 Reactive absorption

323

127

205

Robin Schulz, Thomas Waluga 7 Reactive extraction 363 Stefan Schlüter, Patrick Franke 8 OSN-assisted reaction and separation processes

397

Johannes Holtbrügge, Jerzy R. Pela 9 Pervaporation and vapor permeation–assisted reactive separation processes 473 Index

567

1

List of contributing authors Moreno Ascani TU Dortmund University Laboratory of Thermodynamics 44227 Dortmund, Germany Chapter 3 Patrick Franke Covestro Deutschland AG 50769 Dormagen, Germany Chapter 8

Anna-Katharina Kunze Evonik Operations GmbH 63457 Hanau-Wolfgang, Germany Chapter 6 Jerzy R. Pela Łódź University of Technology Faculty of Process and Environmental Engineering 90-924 Łódż, Poland Chapter 9

Andrzej Górak Łódź University of Technology Faculty of Process and Environmental Engineering 90-924 Łódź, Poland Chapter 2

Stefan Schlüter TU Dortmund University Laboratory of Fluid Separations 44227 Dortmund, Germany Chapter 8

Johannes Holtbrugge Henkel Strategic Business Solutions BV 1081LA Amsterdam, The Netherlands Chapter 9

Robin Schulz Julius Montz GmbH 40723 Hilden, Germany Chapter 7

Christoph Held TU Dortmund University Laboratory of Thermodynamics 44227 Dortmund, Germany Chapter 3

Mirko Skiborowski Hamburg University of Technology Institute of Process Systems Engineering 21073 Hamburg, Germany Chapter 1, 2

Eugeny Y. Kenig Paderborn University Chair of Fluid Process Engineering 33098 Paderborn, Germany Chapter 4

Daniel Sudhoff Evonik Operations GmbH 45772 Marl, Germany Chapters 1

Anton A. Kiss TU Delft Department of Chemical Engineering & Biotechnology 2629HZ Delft, The Netherlands Chapter 5

https://doi.org/10.1515/9783110720464-204

Thomas Waluga Hamburg University of Technology Institute of Process Systems Engineering 21073 Hamburg, Germany Chapter 7

Mirko Skiborowski, Daniel Sudhoff

1 Introduction to process intensification and synthesis methods 1.1 Introduction The intermediates and consumer products generated by the chemical, specialty, and pharmaceutical industries are essential for modern society. While the intermediates produced by the chemical industry may not be widely known to the general public, they are present in almost every item handled on an everyday basis in some processed form. These manufacturing industries are generally faced with challenges resulting from continuously developing markets, demanding innovative products [1]. Furthermore, they need to address the pressing need for a more sustainable production based on renewable resources by more sustainable, more efficient and more economical processes to fight climate change. Especially, the bioeconomy has been identified as a strategic development target. In this regards, many industrial countries have set very ambiguous objectives, with the EU aiming for 25–30% of all chemicals and other industrial products as well as 5–10% of transportation fuels being bio‐based by 2030 [2]. In order to face climate change, initially a reduction of greenhouse gas (GHG) emission in the EU by 2020 by at least 20% below those in 1990 carbon dioxide emissions was targeted by the United Nations Framework Convention on Climate Change in 2011. While this ambitious target was not fulfilled, it is still planned and considered of vital importance that GHG emissions are reduced by 80–95% below 1990 levels by 2050, through investment in clean technologies and low-carbon energy. While the transition to renewable energy in residential and transportation applications are of major importance for these efforts, the industrial sector contributes to an almost equivalent share as these publicly recognized sectors, with an overall contribution to the national energy consumption in the range of 25–30% in the EU and United States, whereas separation processes account for almost half of the energy demand of this sector [3]. Especially, energy integration has been a strength of the chemical industry, which has managed to extend the production rate by 85% while cutting energy consumption by almost 60% during the period of 1990–2015 [4]. Despite these impressive results, the objective of an envisioned carbon neutrality by 2050 calls for further reaching and innovative measures to realize drastic savings and a transition to plant operation based on renewable energies. As a consequence, new types of reaction routes, based on improved or completely novel catalysts (e.g., biocatalysts), solvents, and operations are required to increase

Mirko Skiborowski, Hamburg University of Technology Daniel Sudhoff, Evonik Operations GmbH https://doi.org/10.1515/9783110720464-001

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Mirko Skiborowski, Daniel Sudhoff

efficiency in terms of the consumption of raw materials, solvents, and energy. The need for innovative solution for meeting these challenges mandates the improvement of the design of existing as well as the development of innovative novel processes that extend beyond the toolbox of conventional process units. One important and potentially necessary tool to meet these future challenges in the process industry is process intensification (PI) [5]. The high relevance of PI is not only highlighted by a steadily increasing number of publications but especially through the creation of new research centers, such as the Rapid Advancement in Process Intensification Deployment Institute, which was established in 2016 by the U.S. Department of Energy (DoE). DoE funding of $70 million and additional funds contributed by more than 75 industrial members result in total project spending exceeding $140 million.1

1.2 Background on process intensification 1.2.1 Definitions of PI While the first use of the term “process intensification” can be traced back to a publication in polish journal from 1973 [6], the first general understanding of PI has been shaped in the early 1980s with the work on HiGee technology by Ramshaw [7], who primarily defined the key purpose of PI as the reduction of capital costs and volumes [8]. Since these first definitions, a variety of extensions and alternative definitions have been proposed which also extend the scope of PI. An exemplary selection of definitions is provided in Tab. 1.1. In 2003, Tsouris and Porcelli [11] expanded the definition, stating that “The term PI refers to technologies that replace large, expensive, energy-intensive equipment or processes with ones that are smaller, less costly, more efficient or that combine multiple operations into fewer devices (or a single apparatus).” This definition combines the objectives of size, energy, and cost reduction, with the functional integration. Moulijn et al. [5] moved away from the essential size reduction and stated that “PI tries to achieve drastic improvements in the efficiency of chemical and biochemical processes by developing innovative, often radically new types of equipment and/ or processes and their operations,” while Becht et al. [12] broadened the definition even more, claiming that “PI stands for an integrated approach for process and product innovation in chemical research and development, and chemical engineering in order to sustain profitability even in the presence of increasing uncertainties.” Recently, Van Gerven and Stankiewicz [9] proposed a more fundamental definition, which specifies four explicit goals of PI:

1 http://energy.tamu.edu/texas-lead-modeling-simulation-140m-rapid-modular-processintensification-institute/.

1 Introduction to process intensification and synthesis methods

3

(1) Maximize the effectiveness of intra- and intermolecular events. (2) Optimize the driving forces at every scale and maximize the specific surface area to which these forces apply. (3) Maximize synergistic effects. (4) Give each molecule the same processing experience. According to Stankiewicz et al. [15], these goals can be achieved through four domains, which are the spatial, functional, thermodynamic, and temporal domain. By crossing these domains, PI reaches beyond chemical engineering into disciplines such as chemistry, catalysis, energy technology, applied physics, electronics, and materials science [10]. Because the desired behavior of a process or unit operation is characterized by its performance and attained by the interaction of the involved Tab. 1.1: Selected definitions of PI in literature (extended from [9, 10]). Process intensification

Reference

[Is the] devising exceedingly compact plant which reduces both the “main plant item” and the installations costs.

Ramshaw and Arkley []

[Is the] development of innovative apparatuses and techniques that offer drastic improvements in chemical manufacturing and processing, substantially decreasing equipment volume, energy consumption, or waste formation, and ultimately leading to cheaper, safer, sustainable technologies.

Stankiewicz and Moulijn []

Refers to technologies that replace large, expensive, energy-intensive equipment or process with ones that are smaller, less costly, more efficient or that combine multiple operations into fewer devices (or a single apparatus).

Tsouris and Porcelli []

“Tries to achieve drastic improvements in the efficiency of chemical and biochemical processes by developing innovative, often radically new types of equipment processes and their operation.”

Moulijn et al. []

“Stands for an integrated approach for process and product innovation in chemical research and development, and chemical engineering in order to sustain profitability even in the presence of increasing uncertainties.”

Becht et al. []

“Is a process development/design option which focuses on improvements of a whole process by [adding/] enhancing of phenomena through integration of unit operations, integration of functions, integration of phenomena and/or targeted enhancement of a phenomenon within an operation.”

Lutze et al. []

“Is an holistic overall process based intensification (i.e. global process intensification) in contrast to the classical approach of process intensification based on the use of techniques and methods for the drastic improvement of the efficiency of a single unit or device”

Portha et al. []

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Mirko Skiborowski, Daniel Sudhoff

phenomena, the goals of PI can also be related to the enhancement of the involved phenomena inside those four domains.

• Existing equipment • Integration of process flows and utilities

Scales of process intensification

Process & plant

Equipment related: • Material, • Operational, • Dimensional, ...

Operation & equipment

Phase & transport

Fundamental & molecular

Interface Driving Force

R1 N+ N R2 O N– O S N F3C O O CF3

N N C– N– R

Transfer phenomena: • Master transfer • Energy transfer • Momentum transfer • Thermodynamics • Materials • Catalysts • Reaction

Boundaries / limitations targeted by PI

Therefore, one particularly practical definition of PI is that it is a tool for the targeted enhancement of the involved phenomena at different scales to overcome bottlenecks and limitations in performance and to achieve a targeted benefit based on a set of performance criteria. Following the definition of Freund and Sundmacher [16], PI can be accomplished on four scales, which are (i) fundamental and molecular; (ii) phase and transport; (iii) equipment and operation; and (iv) process and plant. These scales have further been addressed in the development of process design methodologies [13, 17] and are schematically presented in a hierarchical structure in Fig. 1.1.

Fig. 1.1: Conceptual illustration of PI across the different scales, in accordance with [16].

A multitude of different ways exists to intensify processes and reach a certain target. Several articles and textbooks provide excellent overview of PI and the different related aspects [10, 13, 15, 16, 18]. The review paper of Keil [10] provides an excellent overview of prominent PI technologies, especially addressing the top three scales, covering processes, equipment, and energy fields. Figure 1.2 provides an exemplary selection of prime examples for intensified reactor designs. Reactive distillation, which also has been termed the frontrunner of PI [19], is likely the best-known example of functional integration and illustrated in Fig. 1.2(a). The multifunctional unit performs a multiphase reactive separation, which allows for replacing several unit operations by a single piece of equipment, as best illustrated for the methyl acetate process [20]. This specific example is further described in Section 1.3.2. Considering the

1 Introduction to process intensification and synthesis methods

5

application of innovative catalysts and reactive internals, reactive distillation virtually covers all four scales illustrated in Fig. 1.1. The heat exchanger reactor concept, illustrated in Fig. 1.1(b), specifically addresses the equipment and the transport scales, improving reactor performance by improved heat transfer. An overview of such reactor concepts is provided by Anxionnaz et al. [21]. The same scales are addressed by oscillatory baffled reactors, as indicated in Fig. 1.1(c), or static mixer reactors, which both improve mixing and thereby provide a more narrow residence time distribution [10]. The recent review article of Kiss et al. [22] summarizes further intensification potentials for reactive distillation covering the different scales, including hybridization with membrane separations, functional integration toward reactive dividing wall columns (DWCs), external force fields through application of microwaves and ultrasound, as well as novel concepts for catalyst immobilization. Finally, note that even new and specialized definitions of PI are being developed, such as dynamic PI [23], which addresses the dynamic operation, which is, for example, prominently displayed by cyclic distillation columns [24]. While PI does truly cover a broad range of technological developments, it is important to differentiate it from general process improvement and, for that purpose, the above definitions of the four scales, as well as the four fundamental domains provide an excellent basis on which PI measures can be characterized.

Fig. 1.2: Three examples of developed PI reactors: (a) reactive distillation; (b) heat exchanger reactor; and (c) oscillatory baffled reactor.

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1.2.2 Performance indicators for PI Although PI should not be confused with general process improvements, PI does of course seek to improve process performance and performance metrics are required to evaluate alternative technologies. In the past, economic criteria primarily drove decisions in choosing and implementing a particular chemical process. However, during the last decade, the use of sustainability metrics has become increasingly important [25]. Considering the objective to essentially become emission-free until 2050 and rising CO2 taxes in the process, process economics and sustainability become more and more aligned. Besides these economic and environmental metrics, safety and intrinsic intensified metrics should ideally be incorporated into decisionmaking [26]. Thus, frequently quoted performance indicators evaluating PI include economics, safety (often associated with a decrease in volumes), environmental (e.g., energy efficiency, emissions and waste generation), and intrinsic metrics (e.g., volume, process simplification in terms of the number of units) [13]. These performance metrics are usually considered for PI on the process and plant scale. However, PI on the lower scales is usually evaluated by other performance metrics. On the operation and equipment scale, the targeted performance metrics are usually conversion, selectivity, and yield in the context of reactors, or energy requirements in the context of separations. Improved controllability as well as flexibility are additional performance metrics in that context. Extending the operating range can enable the production of entirely new components or following previously infeasible reaction routes [27]. At the phase and transport scale, the targeted performance metrics are homogeneity, interfacial area, as well as heat and mass transfer coefficients, which are to be maximized through innovative phase contacting and improved mixing. Membrane contactors, for example, do provide extraordinary high volume-specific geometric surface areas for phase contacting, while simultaneously decoupling the hydrodynamics of the individual phases [27, 28]. At the fundamental and molecular scale, new solvents and catalysts allow for the development of new processing routes on a molecular level by exploiting molecular interactions. However, finally, the performance metrics on the lower scales need to translate to improved performance metrics on the process and plant scale.

1.3 Scales and principles behind process intensification While the previous sections clarified that various definitions for PI have been proposed, fewer attempts have been made to classify PI. Stankiewicz and Moulijn [1] classified PI technologies into “equipment” and “methods.” While equipment covered various technologies for chemical reactions and other operations apart from

1 Introduction to process intensification and synthesis methods

7

chemical reactions, methods were subdivided into multifunctional reactors, hybrid separations, alternative energy sources, and other methods. This early classification led to the later classification into the four domains (spatial, functional, thermodynamic, and temporal) [15]. Apart from the definition of these domains, the definition of the four scales, as introduced by Freund and Sundmacher [16], has gained traction and allows for a well interpretable classification of PI technologies.

1.3.1 PI at different scales As already illustrated in Fig. 1.1, PI can be achieved across different scales and a single PI technology can include intensification on different scales. For example, reactive distillation performed in a novel type of column with an innovative catalyst, deployed in a novel form of catalytic packing may combine intensification on all four scales. The following paragraphs address different options for PI on the individual scales.

Process and plant The process and plant scale covers individual subprocesses or whole production plants, which convert substrates to desired products in a desired quality and quantity. These processes usually consist of a set of interconnected unit operations. On this level, PI can primarily be achieved through improved integration. Examples are the external integration of a reactor with an initial separation step or the external integration of two different unit operations to fulfill one separation task, which is also defined as hybrid separation process [29]. Figure 1.3 shows a number of illustrations of exemplary hybrid distillation processes, which might be used for the separation of an azeotropic mixture, combining distillation with extraction, decantation, crystallization, or a membrane separation. For a more detailed description of hybrid separation processes, refer to Chapter 2 of this book.

Fig. 1.3: Examples of different hybrid separations.

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While pinch analysis and the design of heat exchanger networks have been established as tools for heat integration [30, 31] they are not considered PI. However, the implementation of innovative process configurations by means of heat pumps, such as in mechanical vapor (re)compression, enables energy transformation and can provide significant energy savings for PI of distillation processes. Figure 1.4 illustrates three alternative configurations for mechanical vapor (re)compression, which either perform a direct compression of the top vapor of the column (left), bottoms flashing (center), or utilize an external working fluid in a closed cycle (right). Since the distillation unit is effectively not altered when applying mechanical vapor (re)compression, it can be considered as a measure for PI on the process and plant scale.

Fig. 1.4: Different forms of mechanical vapor recompression for application in distillation.

Another option for PI on the process and plant scale is the external integration of a reactor and a separation unit, which may help to improve efficiencies and yields without the need to exactly match the operating windows of the individual units [32]. Possible examples include the external integration of a side reactor with a distillation column or a membrane, which are supposed to extract a target product, while the remaining fluid is subsequently fed back to the reactor. As described by Baldea [33], the size of the recycle stream provides an excellent indicator to decide for the relevance of further internal integration of the unit operations, which would result in PI on the operation and equipment scale. Finally, similar unit operations can also be integrated, for example, as conducted in thermal coupling of distillation columns. The Petlyuk configuration is probably the best-known example of thermal coupling and results from the integration of a sequence of three individual distillation columns, as illustrated in Fig. 1.5. By replacing the individual heat exchangers and recycle streams with bidirectional vapor/liquid transfer streams, the process gets more integrated and requires less energy by avoiding mixing of already-separated components on feed trays. As will be explained in the subsequent section, further integration of the Petlyuk configuration results in the equipment-integrated DWC. Additional options for PI on the process and plant scale are described in the article of Freund and Sundmacher [34].

1 Introduction to process intensification and synthesis methods

9

Fig. 1.5: Three-column sequence for the separation of a ternary mixture (left) and conversion toward the fully thermally coupled Petlyuk configuration (right).

Operation and equipment Following a task-oriented approach, for example, promoted by Siirola [35], each process can be understood as a connection of tasks, which are to be performed by selected equipment. Such tasks can be reaction, separation, mixing, and energy supply, while a specific piece of equipment, such as a continuously stirred tank or plug flow reactor already represent more distinct operations, for which furthermore different pieces of equipment are available. A task can be realized by one or multiple pieces of equipment, and/or multiple tasks can be realized in a single piece of equipment. The transformation from tasks to equipment is also reflected in the transition from basic block flow diagrams to process flow diagrams in the hierarchical process design approach [36]. At the operation and equipment level, PI does not alter the tasks of an equipment, but affects the way these tasks are accomplished. Examples of PI at this scale include structuring and miniaturization in order to provide a more homogeneous experience to the processed molecules and improve the involved phenomena, such as heat and mass transfer. Yet, the general task of the processing step or the involved transport phenomena are not altered. For example, a micro heat exchanger intensifies the efficiency of heat transfer by providing a narrower residence time distribution and increased volumetric surface area compared to conventional heat exchangers. Different internals for increasing the specific surface area in a reactor or contactor are listed in Tab. 1.2. Nature-inspired concepts, such as the fractal injector for gas injection have not yet found widespread application, but show great promise for PI on this scale and scalability in general [37, 38].

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Mirko Skiborowski, Daniel Sudhoff

Tab. 1.2: Specific surface areas of different reactor internals [39, 40]. Catalytic packing

Surface area/volume a (m−)

Glass spheres dp =  mm



Glass spheres dp =  mm



Raschig rings, ceramic



Raschig rings, metal



Hollow ceramic cylinders



Full ceramic cylinders



Structured packing (wide Sulzer Katapak)



Structured packing narrow channels

,

Monolith

>,

Foam

>,

While thermal coupling of distillation columns has been introduced as PI at the process level in the previous section, equipment integration into a DWC allows for further reduction of the number of pieces of equipment as well as the related investment costs. DWC can be applied to the separation of zeotropic mixtures as well as azeotropic mixtures, when considering the addition of a suitable mass separating agent and the respective recycle. Fig. 1.6 illustrates the fully thermally coupled DWC, which is thermodynamically equivalent to the Petlyuk configuration illustrated in Fig. 1.5, as well as a DWC for an extractive distillation process. Refer to the referenced literature for more detailed descriptions of DWC [41, 42] as well as further options of PI on the operation and equipment scale [43].

Fig. 1.6: Dividing wall column for the separation of a ternary zeotropic mixture (left) and for the separation of a binary azeotropic mixture by means of extractive distillation (right).

1 Introduction to process intensification and synthesis methods

11

Fig. 1.7: Principle of a heat-integrated distillation column (HIDiC) and an internally heat-integrated distillation column (iHIDiC).

Another example for improved PI on the operation and equipment scale is the heat-integrated distillation columns (HIDiC), in which heat transfer between the rectifying and stripping sections of a distillation column is realized within a single device, by operating the rectifying section at a sufficiently higher pressure than the stripping section [44]. This improved heat pump-assisted distillation concept is schematically illustrated in Fig. 1.7. The HIDiC design approaches a diabatic distillation process and thereby allows improving the thermodynamic efficiency of the distillation process. Similar to the DWC, further PI can be established when integrating the rectifying and stripping section in a single column shell, resulting in the so-called internally heat-integrated distillation column. Unlike the DWC, which have been established several hundred times in industry [45], there is so far only one known industrial implementation of a HIDiC configuration, which only applies few discrete heat exchangers for the integration of the rectifying and stripping section [46].

Phase and transport While PI on the operation and equipment scale builds on the optimal design and control of the individual local processes inside the process units, PI on the phase and transport scale primarily builds on the manipulation of the individual phases in a chemical process [43, 47]. Thus, the major tools at this scale address phase equilibrium and mass transfer kinetics. Within any space in the process unit, one or multiple phases may be present depending on the operating conditions, such as temperature and pressure, as well as the composition of the processed mixture. Each individual phase conserves mass, energy, and momentum, and transfers these quantities when in contact with other phases. On this scale, PI can be achieved through targeted combination of individual phases and selective transport between these phases. The prime example of such a targeted combination are reactive

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Mirko Skiborowski, Daniel Sudhoff

separations, in which a second phase is brought in contact with a reactive phase, such that one or more products are selectively removed from the reactive phase, continuously shifting the equilibrium, in case of equilibrium limited reactions. A specific example of this concept is the combination of a reactive liquid phase and a vapor phase that is richer in the products. A single stage contacting of these phases results in a reactive flash, while countercurrent multistage contacting results in a reactive distillation. Depending on the specific phases that are brought in contact, different concepts for reactive separations are feasible and an overview illustration is provided in Fig. 1.8. Through continuous removal of a product, equilibrium limitations are effectively overcome, enabling higher conversion and selectivity, while phase transition allows for an effective internal heat integration. A second phase can furthermore act as a distribution phase for delivering substrates in case of limited solubility of the substrate in the reactive phase. Such internal integration of mixing, reaction, and separation can have substantial benefits in terms of energy and cost, as highlighted by the aforementioned reactive distillation process for methyl acetate production, which spares almost 80% of the process costs [19]. However, the potential for PI on the phase and transport scale is usually tightly connected to the operation and equipment scale, as the operating windows of the individual processes (reaction and separation) need to match with each other and with the type of equipment they are supposed to be implemented in [32]. In contrast to the external integration, which was described as major PI tool on the process and plant scale, the internal integration results in less degrees of freedom, which besides a more complicated scale-up may result in a more complex process control task. However, these limitations may not be significant and are oftentimes outweighed by the economic benefits [48]. Besides the integration of different phases, the targeted enhancement of transport phenomena is also a valid tool for PI on the phase and transport scale. One example is the improvement of mixing by oscillatory pumping of the fluid (see Fig. 1.1 (c)) to increase reaction rates or enable a continuous crystallization process. Another example of the targeted enhancement of transport phenomena as well as momentum is the use of HiGee technology, such as in centrifugally enhanced separation or reaction systems, building on the superimposition of a centrifugal field. Of course, this is another example for which PI on the phase and contacting scale penetrates the operation and equipment scale. HiGee reactors include centrifugally enhanced trickle bed reactors [50], as well as spinning disc reactors [51], which both are advantageous for mass transfer limited reactions and reactions which depend on improved micromixing [27]. Rotating packed beds, which also exploit centrifugal forces for intensified mass transfer have also been shown to provide benefits for separation processes, especially in case of reactive separations [52, 53]. This technology is covered in detail in Part II of this book. Cyclic operation is another PI tool on the phase and transport scale that can enhance mass transfer and increase reaction rates. Cyclic distillation is a specific

13

1 Introduction to process intensification and synthesis methods

Liquid Reactive absoprtion/ stripping reactive distillation (homogeneous catalyst)

Reactive extraction

Gas/ vapour Reactive absoprtion/ stripping reactive distillation (homogeneous catalyst), reactive membranes, membrane reactors

Liquid

Reactive adsorption

Solid

Fig. 1.8: Reactive separations in relation to involved phases, in accordance with Schmidt-Traub and Górak [49].

example, in which the vapor flow and transfer of liquid to a subsequent tray are separated into individual cycles, whereby back mixing is reduced, and hydrodynamic limitations are overcome, leading to higher plate efficiencies and capacities [24, 54]. Further examples include cyclic transient gas membranes that exploit different diffusivities of components [55], and the cyclic operation of trickle bed reactors for the reduction of mass transfer resistance to the catalyst and intensified mixing of the liquid phase [56].

Fundamental and molecular While PI on the phase and transport scale is primarily determined by the contacting of individual phases and the enhancement of transport phenomena, the fundamental and molecular scale focuses even further on the chemical system and the individual molecules. As such, PI at the fundamental and molecular scale focuses primarily on the thermodynamics and reaction kinetics. The major tools for PI at this scale address the reaction routes and catalyst development, as well as the targeted tuning of solvents, in order to improve the reaction or separation [16]. Application of tailored catalysts, like enzymes optimized by protein engineering, and multistep catalysis by enzymatic or chemo-enzymatic reaction cascades are one option for PI on the molecular scale providing significant potential for

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improved selectivity, turnover numbers and sustainability [57]. Furthermore, tailored immobilization of the enzymes in mesoporous structures may even result in increased activity [58]. Also, local manipulation of molecular conditions realized by electromagnetism or photochemical induction can be applied to broaden the reactivity of molecules by absorbing light as an additional “reagent.” Dielectric heating of a molecule by microwaves enables the remote activation of reactions. The energy absorbed by the molecules leads to local overheating of the reagents or catalysts [15]. Tailored selection or even design of solvents can drastically improve both reactions, as well as separations [59]. Ionic liquids are a specific example of tunable solvents composed of an anion and cation, which are liquid below 100 °C with a negligible vapor pressure. Through careful selection and combination of both, the properties of the solvent, such as selectivity and capacity, can be tuned for a specific application. Deep eutectic solvents follow a similar idea, but are considered less expensive and more sustainable [60]. On the other hand, supercritical solvents possess several interesting characteristics combining high solubility of liquids with low viscosities and high diffusion coefficients, similar to gases. These solvents have been proposed for the extraction of substances with high boiling temperatures and recovery of these valuable substances by lowering pressure. A well-known example is the decaffeination of coffee, in which supercritical CO2 is used at approximately 10–100 °C and 50–300 bar, while applications such as the extraction of bioactive compounds from natural plant material are also relevant [61].

Integrative character between scales It is important to note that PI is manifold and not an “either–or” option. Different PI tools at different scales align and improve benefits, thus requiring simultaneous consideration of the different scales for evaluating the feasibility and prospect. This was already indicated for several of the aforementioned examples. There are several cases which practically perform PI on all of the four scales. For example, the enzymatic reactive distillation in a DWC, as presented by Egger and Fieg [62], illustrated in Fig. 1.9, presents a highly integrated process, comprised in a multifunctional equipment that implements thermal coupling and reactive distillation, while exploiting a highly selective biobased catalyst. For some ways of intensifying a process, multiple scales are involved naturally. When introducing an additional solvent for extraction of a targeted compound the phase and transport scale as well as the fundamental and molecular scale are involved when choosing an optimal solvent. Considering solvent recovery and the implementation of the process, even the operational and equipment as well as the process and plant scale will be involved in the evaluation, even though PI happens on the lower scales.

1 Introduction to process intensification and synthesis methods

15

Fig. 1.9: Reactive dividing wall column.

1.3.2 Principle behind process intensification Processes are composed of process units that are connected to achieve a desired target. Each of the process units is supposed to fulfill one or multiple tasks, while the performance of each unit depends on the interaction of the adjacent units and the involved functions within the equipment and its operation. The performance of the involved functions in the individual units are described by the underlying transport phenomena, bound to the fundamental description through thermodynamics or reaction kinetics and to the operation within the equipment (see Fig. 1.1). In general, the rate of change can be defined as follows: rate = rate constant × dimension × driving force Therefore, PI can improve the rates by altering the rate constants, dimension, and/ or driving forces (cf. Fig. 1.10). The elementary phenomena, which govern this process, include transport phenomena, kinetics, and thermodynamics [63]. The transport phenomena include mass transfer, energy transfer, and fluid dynamics or

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momentum transfer. All these are grounded in the conservation laws within the system and are subject to driving forces (thermodynamics, including reactions) as well as limitations, such as equipment boundaries, equipment fabrication boundaries, and material-bound boundaries. The general driving force of each system is the difference in the chemical potential, which assures that transport within systems only occurs to minimize Gibbs free energy. More specifically, this is achieved through differences in concentration, temperature, pressure, partial pressure, and so on. Examples of mass transfer phenomena are diffusional and (or) convective mass transport, and energy transport phenomena consist of conductive, convective and radiative energy transport. Momentum transport can be exemplified by the friction a viscous liquid experiences while traveling through equipment, leading to a decrease in pressure and velocity. An excellent overview on the concept of transfer phenomena is provided in the book of Bird et al. [64]. Transport phenomena often occur simultaneously in a volume element of equipment when a common operating window exists. For example, when two phases are in contact with each other, heat and mass transfer occur simultaneously during phase transition. Therefore, knowledge of the general flow of each phase, as well as the distribution of component concentrations and temperature in the two-phase mixing zone, is important. Furthermore, the phase contact, that is, the provision of surface area or specific surface area (surface area per volume) for interfacial transfer, needs to be known. In general, knowledge of thermodynamics is necessary to identify whether a positive driving force is available that enables the transfer of components or energy between the phases. Consequently, the different scales are highly integrated, as already illustrated in Fig. 1.1. While the final benefits of PI on the lower scales only becomes apparent when evaluated on the process and plant scale, any modification on a lower will always influence the upper scale, while the requirements of a solution are reported from top to bottom.

Fig. 1.10: Relationship and difference between the transport phenomena for two contacting phases [63, 65].

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This may be more obvious when looking at a specific example. Consider an exothermic reaction performed in a tubular reactor, which can be safely operated to reach high conversion and product yield. However, due to slow kinetics, a larger residence time is required, which is primarily reflected by high investment costs on the process level. In order to reduce the required residence time and further improve the selectivity, a new catalyst is designed providing PI on the molecular scale. Implementation of the catalyst in the previous reactor tubes does however result in a considerable heat development which can no longer be efficiently removed through cooling the reactor surface. Furthermore, internal mixing also limits the performance. Thus, further PI at the phase and transport scale is required to exploit the improved catalyst. Increasing the surface-to-volume ratio and introducing internal structuring, for example, including a static mixer into the tubes allows overcoming these limitations. As illustrated by this example, PI might require analysis and actions on multiple scales to identify and overcome existing limitations. Further examples for PI on the different scales and related elementary phenomena are listed in Tab. 1.3. Tab. 1.3: Interactions of scale, process performance limitations, and elementary phenomena. Scale

Example of PI technologies

Possible process bottlenecks/limitations

Improvement(s) of elementary phenomena

Process and plant

Hybrid separations

An azeotrope or distillation boundary limits product quality by distillation

Thermodynamics, mass transfer

Reactor(s) externally integrated with a separator

Unfavorable reaction equilibrium

Thermodynamics, mass transfer

Vapor recompression

High energy demand of distillation

Energy transfer

Microtechnology (change of A/V)

Energy supply/removal is not Energy and mass sufficient transfer

structuring

Maldistribution leading to low product quality

Mass transfer

Reactor(s) internally integrated with a separator (e.g., reactive distillation)

Unfavorable reaction equilibrium

Thermodynamics (reaction equilibrium), mass transfer

One-pot synthesis reactors

Unfavorable reaction equilibrium of first reaction

Thermodynamics (reaction equilibrium), mass transfer

Equipment and operation

Phase and transport

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Tab. 1.3 (continued) Scale

Example of PI technologies

Fundamental Catalyst tuning and Solvent selection/tuning molecular

Possible process bottlenecks/limitations

Improvement(s) of elementary phenomena

Reaction is too slow

Kinetics

Solvent has low capacity

Mass transfer, thermodynamics

1.3.3 Process intensification within this textbook As pointed out in the previous sections, PI is usually achieved across the different scales in various types of equipment, mostly by combining different PI principles. This graduate level book focuses on a selection of PI technologies in the area of fluid separations which primarily build on the integration of different technologies in form of either hybrid separation process or integrated reactive separation process, including specifically reactive distillation, reactive absorption, reactive extraction, and membrane-assisted reaction and separation processes. Furthermore, the second part of this book provides a detailed introduction to HiGee technology and rotating packed beds in specific. While reactive distillation has already been proclaimed as the front runner in PI [19], the other technologies are gaining increasing importance, especially due to the high energy demand of chemical processes and the need for a sustainable production that has to be realized within the work life of the current generation of engineers. Chapter 2 focuses on the synthesis and design of hybrid separation processes and as such primarily addresses various options for PI on the process and plant scale, exploiting synergies through purposeful external integration of different process units. Chapters 3–7 further focus on reactive separations and thus the internal integration of reaction and separation, which is primarily related to PI on the operation and equipment, as well as the phase and transport level. However, the tailored design of solvents and catalysts also enables PI on the fundamental and molecular scale for these reactive separations. Chapters 3 and 4 address the fundamental aspects of the thermodynamics of reactive separations as the different possibilities to model reactive separations. Chapter 5 focuses on reactive distillation and presents further options for PI, including thermal coupling, alternative forms of energy and hybridization [22]. Focusing on gas-liquid, rather than vapor-liquid separation, reactive absorption is further addressed in Chapter 6, which also illustrates the importance of solvent selection and the possible use of catalysts. Liquid-liquid separation in combination with reactions is further addressed in Chapter 7, considering different methods for reactive extraction, as well as the integration of multistage enzymatic reactions. Finally, Chapters 8 and 9 focus on the combination of reactive separation and hybrid separation

1 Introduction to process intensification and synthesis methods

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processes in form of membrane-assisted reaction and separation processes. While Chapter 8 considers solvent stable nanofiltration membranes for the separation of organic mixtures, which is of particular interest in the area of homogeneously catalyzed reactions, Chapter 9 deals with pervaporation-assisted reaction and separation processes. Although both chapters inherently tackle PI from the process and plant scale down to the phase and molecular scale, designing a membrane with optimal properties could furthermore be considered as PI on the fundamental and molecular scale. The second part of this book series deals with HiGee technology and rotating packed beds in specific. As such it focuses on PI from the operation and equipment scale down to the fundamental and molecular scale, covering the design of the packing, the contacting of different phases for reactive separations, as well as the application of an external force field to improve the kinetics of the process.

1.4 Process synthesis/design As outlined in the previous sections, PI is a multiscale approach that provides tremendous opportunities with a steadily increasing set of tools. It bears the potential for significant improvements and possible paradigm shifts for the development of safer, more sustainable, and economic processes. However, it also brings significant challenges for process engineers, as they have to handle a steadily increasing portfolio of options, as PI promotes highly integrated process configurations with interconnected design decisions across multiple scales. The need for simulation and scale-up capabilities as well high-level process synthesis methods for PI was pointed out as two of the major obstacles for the technical implementation of PI technologies in industrial practice [66]. While the suitability of PI tools should always be evaluated by multidisciplinary teams that cover all different aspects related to the implementation, it is important to enable the identification of relevant PI technologies already in the conceptual design or retrofit of processes, requiring an extension of existing systematic process synthesis and modeling methods [5]. Yet, it is not only an extension of the scope that is required, but also an increase in efficiency, which allows for an evaluation of classical and intensified process units and concepts without an extensive increase in time and resources. Therefore, “not only the process has to be intensified but also the process design methodology” as conveniently summarized by Gourdon et al. [67]. Apart from the toolset required to foster the synthesis and design of PI technologies, the introduction of PI technologies in an early phase of conceptual design requires a departure from the classical unit operation cantered approach that has been introduced more than 100 years ago and is still the established approach in chemical engineering curricula [68]. While this concept is still of relevance and has practically and effectively connected various disciplines, PI education requires

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rather a functional approach that addresses the multiscale and multifunctional nature of most PI technologies. For that purpose, a multidisciplinary group of researchers has recently conducted a broader study of the objectives and opportunities for PI education, proposing several options for introducing PI in the chemical engineering curricula and highlighting the possible contributions of PI for achieving the sustainable development goals of the UN [68, 69]. In order to effectively transfer PI to industrial application, the fundamental understanding of PI and the necessary toolsets for evaluating PI technologies need to align. This necessitates a symbiosis between PI and process systems engineering (PSE) [5]. Efficient process synthesis and design tools can facilitate the identification and evaluation of integrated process configurations, innovative equipment, solvent and catalyst selection, as well as improved transport phenomena, while enabling the evaluation of performance metrics representing the overall process performance. Therefore, PSE can aid in local/unit intensification as well as global/ plant intensification, as defined by Ponce-Ortega [70] and Portha [14]. However, there is and likely will not be a single tool that addresses all possible means for PI. Especially, the multiscale nature of these problems presents significant challenges that rather mandate tailored approaches for individual PI technologies. Yet, the availability and application of such tools can significantly foster the application of PI in industrial practice. Different tools and methods have been proposed to target and/or achieve PI during conceptual process design. As indicated in Fig. 1.11, these can again be classified based on the different scales of PI, covering the external

Scales of process intensification

• PI equipment selection tool • Process synthesis tools based • on PI equipment, function, tasks, etc.

Operation & Equipment

• Process synthesis based on phenomena • Detailed modelling of phenomena

Interface

Phase & Transport

Driving Force

Fundamental & Molecular

+ R1 N N R2

O N– O S N F3C CF3 O O

N N C– N– R

• Solvent section • Reaction path selection • Predictive modelling of thermodyanmic and pure component properties

Fig. 1.11: Set of tools and methods to achieve PI at different scales [79].

Examples of PSE Tools &methods for PI

• Equipment selection tools • Process synthesis methods for integration of conventional units (incorpating e.g hybrid operations) • Process bottleneck anlysis

Process & Plant

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integration of conventional unit operations for PI at the process and plant scale, internal integration in PI equipment at the operation and equipment scale, as well as phenomena-based methods at the phase and transport scale and methods for solvent and catalyst tuning and selection or reaction pathway identification at the fundamental and molecular scale. The most general methods build are on an abstract representation of the design problem, based on tasks [71], mass and heat building blocks [72], reactor/mass exchanger building blocks [73], or phenomena [63, 74]. However, PSE contributions to PI have been manifold, covering advanced separation, reaction and reactive separation technologies, as well as alternative energy sources with contributions to modeling, simulation and design optimization. This is well reflected by the recent review article of Tian et al. [75], which covers almost 900 references. Several other recent review articles are focusing on more specific aspects of PSE for PI [23, 76–78]. While these review articles are highly recommended, the remainder of this section will focus specifically on process synthesis methods and specifically those enabling PI. In general, process synthesis is concerned with the identification of a feasible and potentially optimal process for a predefined problem specification with the given system boundaries. The specific problem specification and definition of system boundaries depends on the individual scale, which is considered for a given problem. On the process and plant scale, the system boundary may cover a complete process flow sheet with the objective to convert raw materials to the final product, at given specifications with minimum waste production, use of utilities, and related costs. At this scale process, synthesis involves the identification of the optimal path from a given starting point to reach a desired product of desired quality and quantity while subject to defined constraints on the process, while the objective functions cover economic and/or environmental criteria. On lower scales, the system boundary may just span individual separation or reaction sections, or single tasks within these sections. In any way, the feasibility of processes depends inherently on the thermodynamics and kinetics of the processed systems and the identification of feasible and potentially optimal solutions is by no means a simple or intuitive task. However, despite the challenges that come with the complexity and scale of the decision space in process synthesis, the vast creativity that comes along with this challenge makes process synthesis “very much the fun part of engineering” [80]. Independent of the coverage of PI technologies, process synthesis methods can mostly be classified in three categories [20, 81]: 1. Systematic generation methods 2. Methods based on evolutionary modification 3. Optimization-based methods

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1.4.1 Systematic generation methods Systematic generation methods are probably the most established tools. They usually build on hierarchical decomposition of the overall flow sheet and the application of heuristic rules as well as dedicated algorithms to generate and evaluate alternatives for the individual subproblems.

Hierarchical decomposition Probably, the most established systematic generation method is the hierarchical decomposition of the overall flow sheet design problem, following the concepts proposed by Douglas [82] or the onion model of Smith and Linnhoff [83], which have also been transferred to renewable energy systems [84]. The hierarchical approach is still at the core of almost every process design course. The structured method considers the overall synthesis problem as a hierarchy of subproblems, which build on a decomposition of the overall process into an aggregation of individual subprocesses that are finally composed of elementary processes. Both methods place the design of the reaction section at the core of the development process, while synthesis of the separation section and the energy/utility system are individual subproblems that are tackled subsequently. Consequently, all subproblems are solved separately. Thus, these methods are inherently incapable of considering most of the aforementioned PI technologies, which build on a strong integration of these subsections and the exploitation of synergies between them.

Process synthesis based on heuristics The individual subsections are further designed based on algorithmic or heuristic methods. Heuristics can be considered a set of rules that are supposed to compress expert knowledge. While heuristics provide suggestions for potentially favorable options, rather than a quantitative evaluation of options, they remain an important tool in industrial practice. They can be encompassed in simple if-then-else statements, such as suggested for the selection of unit operations for liquid and gas separations by Barnicki and Fair [85]. Further examples of this class of heuristics for separation systems are available for the chemical industry [71, 86] and bioprocesses [87]. Such guidelines enable a fast selection of potentially suitable technologies, based on limited knowledge of the system, such as relative volatilities or distinctive property differences, like differences in molecular size or polarity.

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Such differences in pure and mixture properties are also the basis for the selection of process units in the thermodynamic insights approach proposed by Jaksland et al. [88] (cf. Section 2.2.2). Herein, the suitability of specific unit operations is linked to the ratios of individual physicochemical properties of pure components, as well as mixtures properties. The suitability of distillation is for instance evaluated based on a sufficient boiling point difference and the absence of an azeotropic point, while sufficient differences in the solubility parameters indicate the suitability of liquid-liquid extraction the application of dense membranes for nanofiltration or pervaporation. Consequently, thermodynamic insight may be used for the synthesis of alternative hybrid separation processes, considering that more than one unit operation is suitable for the same separation task. Suitable combinations of these unit operations may be determined by means of an analysis of the driving forces for varying compositions [89] or a more detailed model-based evaluation [90]. The thermodynamic insight approach has further been extended for the consideration of selected reactive and hybrid separation processes [91], allowing for the synthesis of candidate flow sheets including DWCs, membrane-assisted hybrid distillation and reactive distillation processes. The tool was illustrated for the separation of a fermentation supernatant and the production of ethyl lactate. While thermodynamic insight enables a quick selection of potentially feasible process units, including selected PI technologies, several limitations remain. The methodology is limited to a database of potential process units, and individual tasks are evaluated as suitable based on simplified criteria that primarily build on pure component properties and the evaluation of binary splits. Apart from the thermodynamic insight approach, there are only few specialized heuristics that cover certain PI technologies. Shah et al. [92] proposed heuristic guidelines for the application of reactive distillation, which also build on knowledge of physicochemical properties, as well as information on the reaction kinetics, in terms of rate and equilibrium constants, as well as Dalton and Hatta numbers. Kiss et al. [93] further describe a framework for the selection of energy efficient PI distillation technologies, including different heat pumps, HiDiC, cyclic distillation, and thermally coupled distillation columns, based on boiling point differences, pressure, relative volatility, and product distribution. While heuristic rules provide only qualitative suggestions that may contradict each other and do not allow for a reliable ranking of alternatives, such as quantitative evaluations, their value should not be underestimated. Art Westerberg [80] aptly formulated “We need heuristics to solve many of the problems industry poses. Without them we need to formulate problems that are too difficult to converge and/or too large to search.” Accordingly, heuristics help to narrow down the design space and foster the traceability of the synthesis problem, while they should not be used as a single tool for decision-making. In order to automate the application of heuristics several expert tools have been developed [94, 95]. One particular interesting approach has been implemented in the software PROSYN, which combines heuristics and numerical computations in a system of distributed expert systems, which are concerned with individual

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tasks, such as reactor design, solvent selection, or the separation of azeotropic mixtures and heat integration [96–99]. This software is still developed and in use.2

Process synthesis based on algorithms While PROSYN already follows a mixed heuristic-numeric approach, also a number of purely algorithmic methods have been proposed for the process synthesis in the context of PI. Especially, the synthesis of thermally coupled distillation processes has received a lot of attention. Most recently, Madenoor Ramapriya et al. [100, 101] have introduced a six-step approach to synthesize all DWCs for any potential thermally coupled configuration, including those that avoid vapor splits, allowing for improved controllability. The method builds on the matrix method proposed by Shah and Agrawal [102] and provides stepwise guidance on how to transform the basic sequence into a DWC. Other algorithmic methods pursue a similar objective [103, 104]. Agrawal et al. [105, 106] further introduced an enumeration-based global optimization approach that allows evaluation of the whole set of feasible options based on energy consumption and economic performance. The approach builds on a reformulation of the Underwood equations, by means of a set of bilinear inequalities, enable the evaluation of several thousands of configurations in a fraction of the time required for a simulation-based approach. Yet, it has to be considered that application of the Underwood equations relies on assumptions of constant relative volatility and molar overflow. Further algorithmic tools have been proposed for the automatic synthesis of distillation-based processes for the separation of azeotropic mixtures [107–109], or the automatic screening of solvents [110, 111]. While these algorithmic tools oftentimes build on the automatic enumeration of a finite, but large set of alternatives, they do generally compete with optimization-based methods that mostly operate on a superstructure model of these alternatives. The latter are addressed in Section 1.4.3. Algorithmic and optimization-based methods build on a model-based problem formulation and apply computational methods for the solution, such that the lines between these methods are kind of blurry. Yet, they clearly differ in the approach followed for the solution of the individual problems.

1.4.2 Methods based on evolutionary modification While systematic generation methods try to generate new solutions from scratch, evolutionary modification methods start with an existing solution and perform targeted modifications of this solution in order to define a superior design [20]. This approach

2 https://www.process-design-center.com/home.html.

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25

is obviously more representative of retrofit design, than grassroot design, but it has been proposed for either of these tasks. A vast variety of evolutionary modification methods has been proposed in literature, following different strategies. Commenge and Falk [112] proposed a heuristic-based framework for the selection of PI equipment. Based on an initial analysis of bottlenecks of a given process, a set of PI strategies is selected from matching matrices between limitations and PI strategies as well as PI strategies and PI technologies. The matching matrices rank the impact a specific PI strategy has on a certain limitation, as well as the suitability of a certain PI technology on a scale of 0 to 5 and thus foster a simple qualitative ranking of alternatives. However, such a heuristic database can further be combined with an algorithmic assessment of PI technologies, as proposed in the decomposition-based multistep solution approach by Lutze et al. [65]. The method does also start with a simulation-based analysis of an existing process, while a number of suitable PI technologies are further evaluated from a database of options, resulting in a portfolio of PI-based alternatives that are further evaluated in a sequence of screening steps, before the remaining alternatives are further evaluated by means of process simulation or optimization to determine an optimal intensified process. The method was initially demonstrated for the chemo-enzymatic synthesis of N-acetyl-D-neuraminic acid [65] and was further illustrated for the intensification of the industrial 4,40-methylenedianiline process at Huntsman B.V. in the Netherlands [113]. Barecka et al. [114, 115] further proposed a modification of the method and demonstrated the application on ethylene oxide and ethylene glycol production. An overview of the different steps of the methodology, with indications of associated tools, is provided in Fig. 1.12. Instead of targeting specific bottlenecks of a given process, the whole process can be decomposed into a set of required tasks that can be rearranged to create novel and potentially intensified alternatives. The hierarchical means-ends analysis approach presented by Siirola [35] was the first approach that proposed the exploitation of an increased level of abstraction from the unit operation thinking for process synthesis. Siirola [35] himself classified the approach as a systematic generation approach, but practically illustrated it for the methyl acetate process, for which the original process flow sheet was analyzed for task identification, while the final reactive distillation design was derived through rearrangement and combination of the individual tasks. Figure 1.13 illustrates the task-based and unit operation-based representation of the resulting reactive distillation column for the methyl acetate production process. Rearrangement of the tasks effectively reduced the number of unit operations from ten to one and the resulting costs by almost 80% [19]. This approach is also classified as rule-based approach by Tula et al. [116], since a set of rules is applied in an iterative refinement process. However, a general list and documentation of these rules for the identification and variations of tasks and the identification of unit operations has not been published. Thus, the task-based synthesis has rather been a theoretical

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Fig. 1.12: Schematic of the evolutionary modification approach followed by Lutze et al. [65] and Barecka et al. [114, 115].

construct that fosters the understanding of multifunctional units, than providing a practical approach for process synthesis. However, the idea of achieving PI through the abstraction of a given reference process has been further developed in the context of phenomena-based process synthesis methods. The idea of retrofitting and designing process flow sheets by means of a phenomena-based approach was first described by Tanskanan et al. [117] with similar ideas later presented by Hauan et al. [118] and Rong et al. [119]. Unlike tasks, which are rather related to a specific purpose, phenomena are the fundamental mechanisms, which any chemical process is based on. The relationship and dependency between tasks and phenomena is indicated in Fig. 1.14 in the context of the functional and systems approach toward process modeling [74]. In this context, phenomena include mixing, reaction, energy transfer, phase change, phase contact, phase transition, phase separation, and stream splitting. As most phenomena cannot be manipulated in an isolated form phenomena-based process synthesis methods usually build on aggregated phenomena building blocks (PBB), which already present a combination of different phenomena that usually are linked together, such as mass and heat transfer in case of phase contacting. Arizmendi-Sánchez and Sharratt [74] first published a library of PBB and illustrated the generation of a phenomena-based

27

1 Introduction to process intensification and synthesis methods

MeAc

HOAc

Separation (Purify MeAc) By differences in relative volatility MeAc

Separation (Remove H2O) By differences in relative volatility and solubility HOAc

Separation (Remove MeOH) By full reaction of MeOH due to excess of HOAc Separation main reaction till equilbrium

MeOH

Rectifying section

Catalytic section

Separation (Remove HOAc) By full reaction of HOAc due to excess of MeOH

MeOH

Separation (Remove MeAc) By differences in relative volatility and solubility

Stripping section

(Remove MeOH) By differences in relative volatility and solubility

H2O H2O

(a)

(b)

Fig. 1.13: (a) Task-based and (b) unit-operation-based representations of the production of methyl acetate.

Fig. 1.14: Illustration of the relationship and dependency of tasks and phenomena in the context of functional and systems approaches, according to Arizmendi-Sanchez et al. [74].

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process representation of the case study of a well-mixed cooled reactor with competing reactions. However, they neither used the approach to derive an intensified design, nor did they propose a specific approach for synthesis of PI technologies. Such an approach was first proposed by Lutze et al. [63], presenting an extension of the former unit operation-based approach [65]. The method still begins with the analysis of a given base case process design, which if nonexisting is first generated by means of a classical process synthesis approach. This design is subsequently transposed into a PBB-based representation, forming the basis for subsequent intensification. The method builds on a database of PBB, from which phenomena-based flow sheet variants are generated by a series of screening steps and connection rules. Since various algorithmic and optimization-based tools are integrated in the workflow, the method can also be classified as a hybrid approach [116]. The concept of the phenomena-based representation is illustrated for an aerobic fermenter in Fig. 1.15. The unit operation-based representation consists of a single stage in which reactions, mixing and/or separation occur in multiple phases. In the fermenter, the substrate and oxygen are fed to achieve cell growth, which results in the formation of a product and side products that are continuously removed. The fermenter is assumed to operate in semibatch mode, and perfectly mixed throughout the whole vessel. The phenomena-based representation considers a variety of simultaneously occurring phenomena: – one-phase mixing: solid, liquid, gas; – two-phase mixing: solid-liquid (S-L); – two-phase mixing: gas-liquid (G-L); – phase contact (G-L); – phase transition (G-L) for oxygen absorption into the water and for side product (CO2) stripping into the air; – phase separation (G-L); – phase contact (S-L); – phase transition (S-L) for substrate supply to the cell in which the reaction occurs; – a divider for removal of a suspension of cell material, substrate, and product(s). The phenomena-based approach of Lutze et al. [63] was further developed by Babi et al. [120–122] who extended the method by the translation of phenomena-based flow sheets to innovative designs and an additional sustainability analysis, considering grouping of the PBB to simultaneous phenomena building blocks (SPB), applying combination rules on the basis of the thermodynamic insights approach of Jaksland et al. [88]. Tula et al. [116, 123–125] further extended the approach with intermediate layers, introducing basic structures to foster the transformation of SPB to intensified equipment. While the general workflow, building on an initial problem definition, base-case selection and analysis, and final multiscale synthesis of PI options remained very similar, further elements and tools were integrated in the

1 Introduction to process intensification and synthesis methods

Fig. 1.15: A fermenter represented in the unit operation, as well as the phenomena-based representation in accordance with Lutze et al. [63].

29

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overall workflow, which was consolidated in the computer-aided software tool ProCAFD, which is linked to several support tools in an overall software framework offered by the company PSE for SPEED.3 Figure 1.16 presents an overview of the three major design stages and the integrated set of tools and methods, which are linked to the ProCAFD. The phenomena-based intensification mainly takes place in the third and so-called innovation stage.

1.4.3 Optimization-based methods While the previously described methods for process synthesis also integrated to some extent optimization-based tools for certain subtasks, the current section addresses optimization-based methods for a direct process synthesis, which does not rely on the refinement of an initial reference process. These methods build on some mathematical definition of the overall design space and the solution of a respective optimization problem with either gradient-based deterministic or stochastic optimization methods. Such optimization-based methods bare the advantage that the best process flow sheet is determined on a purely quantitative basis. However, the generation of a suitable superstructure, an appropriate model formulation, and computational solution, including necessary initialization, require sufficient knowledge and limit current use of such tools [126–128]. Nevertheless, optimization-based methods provide the potential to effectively extend the search space for PI, while simultaneously enabling a more efficient evaluation of the best solutions.

Process synthesis methods focusing on reactor (network) design Instead of selecting a specific type of reactor from a database of potential options, process synthesis methods for PI in reactor design build on a suitable level of abstraction. The concept of elementary process functions (EPF) proposed by Freund and Sundmacher [17] optimizes the time-dependent path of a well-mixed fluid element by means continuous manipulation of mass and energy fluxes. Thereby, it considers an arbitrary modification of the thermodynamic state vector of a respective fluid element on the phase level through consideration of molecular reactions as well as mass and energy fluxes with respect to time. Optimization of the EPF represents the most general form of a targeting method [129], which allows for the determination of equipment-independent best possible reaction products. The EPF concept has further been the basis for the development of a multilevel reactor design (MLRD) methodology [130, 131], which translates the abstract representation of

3 https://www.pseforspeed.com/.

Synthesis stage

Design & Analysis stage

Innovation stage

Step 4 : Process analysis (base case)

Sizing methods, ECON, SustainPro, LCSoft

Fig. 1.16: Overview of the integrated computer-aided software tool ProCAFD and the interconnection to additional support tools [116].

Step 8 : Verification of alternatives

Aspen plus, PRO/II, Sizing methods, ECON, SustainPro, LCSoft

More sustainable flowsheet

Intensified flowsheet alternatives

Step 7 : Generation of alternatives

Phenomena base synthesis method

Tasks, database, Phenomena database

Initial list of phenomena

Base case flowsheet

Process hotspots, Design targets

Economic, Sustainability, Safety & LCA indicators.

Operational design parameters, Simple mass and energy balance results

Base case flowsheet

Input compounds, output compounds, reaction data, Flowrate, Pressure, Temperature, Processspecifications, Constraints

Data flow

Step 6 : Identification of tasks & phenomena

Step 5 : Identification of process hotspots & design targets

Step 3 : Process design (base case)

Step 2 : Generation of base case

ProCAFD, SUPER-O, Patents/ literature search

Aspen plus, PRO/II

Step 1 : Problem definition

compound database, reaction system database, literature search

Methods & Tools

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the optimal processing route into a specific implementation through discretization and approximation. The concept is illustrated in Fig. 1.17. Apart from various applications, recent advances have demonstrated the applicability to multiphase reaction systems, with complex reaction networks, in the context of the full process [132] and mass transfer limited reactions [133], as well as the consideration of catalyst deactivation [134] and tolerant reactors that can process variable feedstocks [135]. The review article of Freund et al. [136] provides an overview of the various applications and extensions of the method.

Fig. 1.17: Illustration of the concept of elementary process functions, as well as the multilevel reactor design approach by Freund and Sundmacher [63].

While the MLRD method is well developed and demonstrated on multiple problems, there are further methods that build on an abstract problem representation for reactor design. The optimization of a superstructure consisting of reactor building blocks was recently proposed by Zivkovic and Nikacevic [46], while the systematic design framework proposed by Kokossis and co-workers [137–139] also allows for the synthesis of nonconventional reactor designs, through a combination of a network superstructure and generic unit representations that link different phases through mass transfer facilitated by a shadow reactor concept.

Process synthesis methods on generalized building blocks Extending beyond the consideration of reactor design, the generic unit representation model of Kokossis and co-workers can also be applied for the synthesis of reactive separation processes, considering mass transfer between different phases [140, 141]. The superstructure optimization can even be extended to cover larger flow sheets, whereas separation processes were simply modeled as ideal separators. The generalized modular framework (GMF) developed by Pistikopoulos and co-workers [72, 142, 143] also performs process synthesis by means of a superstructure optimization on building blocks. Starting from the synthesis of separation processes, the building blocks are multipurpose mass/heat transfer modules, for which an optimal connection is determined by means of superstructure optimization. The application

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has been demonstrated for various distillation-based separation processes [144, 145], as well as reactive separation processes [146, 147], and more recently to include safety and operability considerations [148]. An important feature of the GMF approach is the use of a general form of driving force constraint, based on Gibbs free energy, which allows for the simplification of the model of the individual building blocks. The driving force constraints add significant variability to the mathematical problem formulation and avoids detailed modeling of the individual transport, but also requires subsequent validation of the feasibility of the GMF-based flow sheets. Building on a more rigorous model formulation of the individual building blocks, Kuhlmann and Skiborowski [81, 149] proposed an optimization-based process synthesis approach, which combines the concept of PBB from Lutze et al. [63] with a general state space superstructure [150]. The individual PBB are selected from a library including (reactive) vapor-liquid (VL) and liquid-liquid (LL) contacting, as well as reactor network and pervaporation/vapor permeation blocks. The major difference to the aforementioned building blocks is the rigorous modeling of mass transfer, by either rate-based differential models or multistage countercurrent cascades for VL and LL PBB. Thus, feasibility of the generated process configurations is guaranteed by the model formulation. However, the added complexity requires a multistage hybrid stochastic-deterministic solution approach. The proposed process synthesis framework further promotes a subsequent translation into equipmentbased flow sheets by means of a rate-based model formulation and a database of operating constraints and performance indicators. The state-space superstructure, as well as an indicative PBB-based flow sheet, and a corresponding equipment-based flow sheet for the case study of ethanol dehydration are illustrated in Fig. 1.18. The method has further been illustrated for a larger case study with reactive separation and the synthesis of a membrane reactor [149, 151]. Another optimization-based process synthesis approach has been presented by Hasan and co-workers [152]. The innovative 2D-block superstructure model allows for the general definition and connection of the abstract building blocks (ABB), which are characterized by three types of boundaries to the adjacent blocks and physical attributes, for example, temperature, pressure, and phase. While a single ABB can, for example, represent a mixed zone in which a reaction takes place, two adjacent blocks can, for example, represent an individual vapor-liquid equilibrium stage, or a membrane separation. Thus, the individual ABB can represent various types of phenomena and perform different tasks. The approach has been demonstrated for various applications, such as reactive separations [152], heat and mass integration of existing flow sheets [153], work and heat exchanger networks [154], as well as reaction and separation flow sheets [155, 156]. This illustrates the extreme versatility of the ABB-based block-superstructure. However, it needs to be considered that either the individual models need to be simplified (Fenske–Underwood model for distillation column in flow sheet optimization [155]) or the superstructure needs to be restricted for largescale applications (predefined structure and types of ABB for DWC design [157]).

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Fig. 1.18: Illustration of the state-space superstructure (left), a resulting PBB-based flow sheet (center) and the translated equipment-based flow sheet including membrane modules and a rotating packed bed [81].

Nature-inspired synthesis/design methods While most of the previous synthesis methods build on mathematical programming techniques because of the efficiency and reliability of these mathematical tools, a number of nature-inspired techniques, mainly population-based metaheuristics, such as evolutionary algorithms and swarm optimization methods are also available. These techniques have demonstrated their potential for several applications

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and may also be valuable tools for PI and process synthesis. One of the most prominent examples for evolution-based synthesis methods is directed protein evolution, a protein engineering approach that won the Nobel Prize in 2018 [158]. The method enables the evolution of enzymes for reaction invented by chemists, improving both turnover numbers as well as selectivity, and opens up possibilities to generate completely new synthesis routes to bonds previously unknown in biology. Thus, it can very much be considered as a tool for PI on the fundamental and molecular scale. Evolutionary methods show large prospect whenever the fundamental process that is to be optimized is not fully understood, or highly nonlinear and multimodal. While evolutionary methods have regularly been applied to process design problems [159], most of these methods depend on a predefined superstructure. The generic development of process flow sheets by means of evolution has only been addressed in the work of Neveaux [160]. A similar and somewhat related approach that builds on reinforcement learning has recently been presented by Göttl et al. [161]. Yet, both of these methods have so far only been demonstrated for simple reaction and separation sequences without any recycles and PI.

1.5 Take-home messages – PI can be considered as a tool, which allows for the improvement of different performance metrics by means of the targeted enhancement of involved phenomena at different scales, ranging from the fundamental and molecular scale, over the phase and transport scale to equipment and operation scale, and finally covering the process and plant scale. – There are various PI technologies available and under development, resulting in intensified equipment and processes. The selection of the most suitable technologies is an important task for process synthesis and design that should be based on quantitative performance measures. – Process synthesis involves the identification of the optimal path from a given starting point to reach a desired product of desired quality and quantity that is subject to defined constraints on the process. Several methods incorporating PI have been developed to date, which enable the identification of the most suitable PI solutions from a pool of potential solutions as well the identification of novel process configurations. Nevertheless, the identification of the best options is still a major challenge and requires further progress.

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1.6 Quiz 1.6.1 General PI Question 1. Can you name the four different scales of PI? Question 2. What are possible performance metrics by which PI is frequently evaluated?

1.6.2 Process and plant: hybrid separation process Question 3. How do we define hybrid separation processes? Question 4. Can you propose an exemplary hybrid separation process for the separation of an azeotropic mixture by exploiting the differences in relative volatility and in melting points?

1.6.3 Operation and equipment: dividing wall columns Question 5. Can you provide an explanation of the benefits of a DWC compared to the application of a simple side stream column for the separation of a zeotropic threecomponent mixture based on the composition profiles in the different columns?

1.6.4 Phase and transport: equilibrium reaction Question 6. Consider a reaction of type A + B ⇌ C + D in which D is the final product and C is a by-product. Due to the equilibrium reaction limitation, a full conversion of both substrates is infeasible. Can you propose PI technology options on the phase and transport level which potentially enable full conversion for an equimolar feed of both substrates?

1.6.5 Fundamental and molecular: equilibrium reaction Question 7. Considering the same equilibrium reaction as described in the previous question, can you propose alternative PI options at the fundamental and molecular level?

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1.7 Solutions The respective solutions to the above questions, which cannot be found within the preceding sections of this chapter, are explained in the subsequent paragraphs. Solution to Question 4: The separation of an azeotropic mixture by exploiting the differences in relative volatility and in melting points has been exemplarily illustrated Fig. 1.3 (b). Assuming a mixture with a minimum boiling azeotrope the distillation column is applied to purify one of the components as bottoms product, while the top product is (close to) the azeotropic composition and fed to a crystallization process which purifies the other component based on the difference in melting points. Refer to Chapter 2 for a more detailed description of hybrid separation processes, as well as their synthesis and design. Solution to Question 5: While the simple side stream column and the DWC have the same number of feed and product streams, the DWC has a considerably larger number of column sections. The side stream column, as illustrated in Fig. 1.19 has only three individual column sections, which are the rectifying and stripping section, close to the top and bottoms product, as well as an intermediate middle section, between the feed and the side stream. Depending on the relative volatilities between the different components, the side stream configuration cannot provide all three products at high purity. Usually, a compromise needs to be made between the side product and the end product that is on the respective end of the side product. In contrast to the side stream column, the DWC with the central partitioning wall, as illustrated in Fig. 1.20, has six individual column sections. In addition to the rectifying and stripping section adjacent to the top and bottom products, the column has two sections on each side of the partitioning wall, separated by the feed (prefractionator side) and the side stream (main column side). These additional column sections allow for the separation of all three individual products at high purity, while enabling energy savings due to a fully thermally coupled separation. The better separation performance of the DWC is indicated by the composition profiles of the individual components A, B, and C in Figs. 1.19 and 1.20. Solution to Question 6: Possible PI technologies on the phase and transport scale include: – Addition of a second phase which selectively removes one or both of the products C and D from the reaction phase. This would constantly shift the reaction equilibrium toward the reactant side, meaning that continuously A and B are transformed to C and D until no more reactant is present. The respective challenge is to find a phase based on the properties of the mixture, in which the substrates are preferentially unsolvable, while the products preferentially distribute to this phase. Since partition coefficients are usually limited, oftentimes multistage reactive separations

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such as reactive distillation, reactive extraction, or reactive absorption are applied, depending on the added phase. – Addition of a second reaction which further transforms component C, the byproduct, also shifting reaction equilibrium to the product side.

Fig. 1.19: Concentration profile in a side stream column with the sides stream above the feed.

Solution to Question 7: One option to PI on the fundamental and molecular scale is the development of a new or tuned catalyst. However, this will not overcome the equilibrium limitation as the catalyst has no influence on the reaction equilibrium. Yet, reaction equilibrium generally depends on the activities, rather than the concentrations, such that manipulation of the activities by selection of an optimal solvent does indeed affect the equilibrium compositions. Therefore, selection tools or targeted solvents such as ionic liquids can be beneficial. Furthermore, new reactions within reactive solvents may again help to remove the by-product C efficiently.

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Fig. 1.20: Concentration profile in a dividing wall column with a central partitioning wall.

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Mirko Skiborowski, Andrzej Górak

2 Hybrid separation processes 2.1 Introduction As already introduced in Chapter 1, hybrid separation processes are one important example of process intensification (PI) at the process and plant scale, which similar to reactive separation processes facilitate PI at the functional level [1]. Following the definition provided by Franke et al. [2], hybrid separation processes are defined as the combination of at least two different, externally integrated unit operations, which contribute to one and the same separation task by means of different physical phenomena. Hybrid separation processes are characterized by a mutual interdependency of the different unit operations and overcome the limitations of the single unit operations by exploiting synergetic effects [3]. The maximization of these synergetic effects improves the performance of the hybrid separation process and cannot only facilitate economic benefits, but also result in smaller, cleaner, and safer processes [4]. There are two important differentiations that need to be pointed out. Unlike reactive separations, hybrid separation processes are no multifunctional units. Therefore, processes such as membrane distillation, membrane absorption, or adsorptive distillation do not belong to the class of hybrid separation processes, even though they are sometimes referred to as hybrid separations [5]. According to the classification of PI the latter addresses the operation and equipment scale, rather than the process and plant scale (see Section 1.3.1). This can be illustrated by e.g. membrane absorption, for which the membrane serves as a permeable barrier between the gas and liquid phase that facilitates operation independent of gas and liquid flow rates, without entrainment, flooding, channeling, or foaming [5]. Implementation in form of spiral-wound or hollow-fiber membrane modules creates large mass transfer areas in particularly compact equipment. All features for PI on the operation and equipment level. Unlike multifunctional units, which target an equipment integrated form of two or more unit operations pursuing multiple tasks, hybrid separation processes represent externally integrated equipment pursuing a common separation task. The integration, which mandates recycles in the hybrid separation process, is of essential importance and results in the differentiation from a simple sequence of unit operations. The discrimination between a simple sequential connection of unit operations and a hybrid separation process, according to the above definition, is illustrated in Fig. 2.1 for the combination of a membrane separation and a distillation column. In the sequential configuration (Fig. 2.1 (a)) the membrane performs the separation of Mirko Skiborowski, Hamburg University of Technology Andrzej Górak, Łódź University of Technology https://doi.org/10.1515/9783110720464-002

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component C from the ternary mixture ABC and the distillation column separates the remaining binary mixture into the pure components A and B. In the hybrid configuration (Fig. 2.1 (b)), both, the distillation column and the membrane, contribute to the separation of the binary mixture AB. If the separation performance of each potential unit operation is limited, either by a separation boundary, or because of negligible driving forces, a hybrid separation process might be the only solution for a given separation task. However, even if a separation in a single unit operation is feasible, a hybrid separation process can result in improved performance due to the previously mentioned synergetic effects. For example, the hybrid separation process in Fig. 2.1 provides the potential for substantial capital and energy savings in case of the separation of a binary azeotropic or close boiling mixture. Fig. 2.2 illustrates the regions in which the distillation column and the membrane process should be operated for the hybrid configuration, shown in Fig. 2.1 (b).

Fig. 2.1: Illustration of simple sequential connection (a) and hybrid separation process (b).

The dehydration of ethanol (see also Section 2.4.3) is the most prominent example for the application of a hybrid separation process, as illustrated in Fig. 2.1 (b). Nowadays more than one hundred such configurations, based on the combination of distillation and pervaporation, have been installed for solvent dehydration [6]. While such a hybrid separation process was first proposed by Binning & James in 1958 [7], the first implementation was achieved much later, in the late 1980s [8]. This illustrates that the concept of hybrid separation processes has already been known for several decades, but it took some time until they were recognized and implemented in larger scale. This is a common feature of PI technologies, as e.g. also illustrated by the concept of a dividing wall column, which was patented by Wright in 1949 [9], while the first industrial application was not reported before 1985 [10].

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Fig. 2.2: Illustration of the vapor-liquid equilibrium of an azeotropic mixture and the regions in which the distillation column and the membrane process operate for the hybrid separation process illustrated in Fig. 2.1 (b).

A lot of processes classified as hybrid separation processes according to the above definition, are already established in industry and are often considered as promising options during process design. Figure 2.3 provides an exemplary selection of representative configurations of hybrid separation processes, including heteroazeotropic distillation (a, f), which is a combination of distillation and decantation; distillation combined with crystallization (b); adsorption (c) or liquid-liquid extraction (e); adsorption interlinked with a membrane process (d); as well as a combination of distillation, a membrane process and adsorption (g). All these configurations have been investigated and implemented in various processes, but an even larger number of configurations can be synthesized in accordance with the given definition of a hybrid separation process. These hybrid separation processes can be divided into three categories, which is also the reason for heteroazeotropic distillation being illustrated twice. The first two configurations (a, b) perform the separation based on the mixture properties without the addition of an auxiliary component, a so-called mass separating agent (MSA). The second two configurations (c, d) make use of an additional but immobilized MSA, the adsorbent in the adsorption columns, e.g. a zeolite, and the membrane material, e.g. a polymer. The separation performance depends on the interactions between the molecules of the mixture and the zeolite or membrane. The hybrid separation process (g), which is based on a combination of distillation, a membrane process and adsorption, also belongs to this second category, as both the membrane material and the adsorbent material have to be determined. In a quite similar way the third pair of configurations (e, f) makes use of a non-immobilized MSA. The solvent in liquid-liquid extraction represents the transfer phase, which should selectively extract one type of molecule from the feed mixture and which has to be regenerated afterwards to be reused and to purify the product. A MSA can also be added to an azeotropic mixture in order to introduce a liquid immiscibility that is exploited in a heteroazeotropic distillation configuration as illustrated in Fig. 2.3 (f). The selection of the MSA provides an important additional degree of freedom for the design of these processes, which

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Fig. 2.3: Exemplary selection of the most prominent hybrid separation processes.

considerably increases the complexity and mandates computer-aided methods for process synthesis and design. For example, several hundred zeolites may be considered in the design of an efficient pressure-swing adsorption process [11] and several thousand molecules may be considered as potential solvents for a liquid-liquid extraction process [12, 13]. The choice of an optimal MSA may well be the key to an economic and energy-efficient performance of the final process. Thus, while hybrid separation processes obviously exploit synergetic effects between the single unit operations on the process and plant scale, the proper design of hybrid separation processes also requires knowledge and optimization on the lower scales (cf. Fig. 1.1 and Section 1.3.1). For example, introducing an additional phase requires PI on the phase and transport scale, while the selection of materials or solvents allows for PI on the fundamental and molecular scale. This once more highlights the integrative character between the different scales of PI that was already emphasized in Chapter 1. Nevertheless, it also results in a substantial increase in the complexity of the design of hybrid separation processes, compared to classical sequential processes [14]. In addition to the selection of unit operations and their interconnection, which already represents a tremendously large number of alternatives, the selection of MSA, like a solvent, a membrane material or an adsorbent, further increases the search space for determining a suitable and potentially optimal process variant. This is one of the main reasons why hybrid separation

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processes are seldom considered by default in the conceptual design of new processes. However, the chemical industry is well aware of the potential benefits offered by hybrid separation processes [15, 16]. In order to implement them as a default option in the design of separation processes, efficient and systematic methods for process synthesis and design are required. The following sections present an introductory overview of the different options for considering hybrid separation processes during process synthesis (Section 2.2) and conceptual design (Section 2.3), highlighting the complexities and providing efficient means to handle them. The design of hybrid separation processes is finally illustrated in Section 2.4 for a selection of exemplary applications. Further applications and details concerning modeling and design are provided for membrane-assisted processes considering organic solvent nanofiltration in Chapter 8 and pervaporation and vapor permeation in Chapter 9.

2.2 Synthesis of hybrid separation processes Since a general overview of process synthesis methods for PI was already presented in Section 1.4, this section will present different tools that are available for process synthesis with an emphasis on hybrid separation processes. We focus on distillation-based hybrid separation processes due to the dominate role of distillation with about 40,000 existing distillation columns in the U.S. [17, 18], being used for about 95% of all fluid separation and still considered as one of the default options for fluid separations. Separation processes do not only account for approximately 50% of all manufacturing costs [19], but also account for about 50% of the energy consumption of the overall industrial sector, which again contributes to one third of the U.S. total energy consumption [20], highlighting the importance of separation processes also in the context of climate change. The majority of these energy requirements are in fact related to thermal separations, especially distillation, but also drying and evaporation. However, while it is oftentimes claimed that cold separations, such as pressure-driven membrane processes, have the potential to perform these separations with 90% less energy than distillation [20], such high energy savings are rarely achieved. On the one hand side, the superiority of alternative separation processes in terms of thermodynamic efficiency generally drops significantly or vanishes once high recoveries and purities are targeted for both products [21]. On the other hand distillation is not inherently inefficient, as it is oftentimes claimed [22]. It is important to consider the various means for energy integration of thermal separation processes in order to correctly judge the efficiency of distillation-based separation processes. Hybrid separation processes offer the potential to exploit both, the superiority of separation technologies, such as membrane processes, for separations that do not simultaneously require high product recoveries and purities, as well as the high reliability and possible energy-integration of thermal separation processes.

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2.2.1 Systematic generation methods Different flowsheet design variants are regularly generated based on the existing knowledge and intuition of experienced process engineers. In order to make this knowledge further available, it has been compiled into heuristic rules, providing initial guidance for sequencing of separation steps [23], i.e. corrosive or reactive materials should be separated first or difficult separations, like the separation of closeboiling and azeotropic mixtures, should be performed last. The information from such heuristic rules and expert systems [24] is certainly valuable and should always be considered in designing a process. However, only few heuristic guidelines have been proposed for the design of hybrid separation processes and basically all heuristic rules are qualitative by nature, resulting in contradicting suggestions that further need to be resolved. Consequently, most approaches for the synthesis of hybrid separation processes focus on the use of thermodynamic insights, as well as visual analysis of graphical representations of thermodynamic equilibrium data.

Thermodynamic insight Knowledge about the physicochemical properties of a mixture, like the boiling temperatures of pure components or the existence of azeotropes and miscibility gaps, provides first insights into the nature of the mixture and reveals limitations of certain separation technologies. The existence of azeotropes indicates possible distillation boundaries (DB) and thus limitations for distillation, while the existence of a miscibility gap is a prerequisite for the application of liquid-liquid extraction, as well as heteroazeotropic distillation. Thus, knowledge of these mixture properties allows for the determination of potentially suitable separation techniques, while hybrid separation processes can be determined by combining the individual operations in an optimal fashion. Physicochemical properties can be determined on the basis of available databases, experimental evaluation, or property predictions. Experimental data from available databases is always the preferred option since the accuracy of an experimental investigation is usually higher than the accuracy of computational methods for property predictions. Nevertheless, property predictions are usually much cheaper and faster than experimental investigations, if they need to be performed specifically for the conducted study. Consequently, they are a viable option in the early phase of process synthesis, especially for the screening of larger sets of alternative MSA (see e.g. [11–13]). Missing property data is estimated by means of group contribution methods [25], quantitative structure-property relationships (QSPR) [26], predictive methods based on statistical associating fluid theory (SAFT)-type state equations [27], or quantum-chemical methods like COSMO-RS [28]. All these methods finally link physical properties to molecular structure and play an important role in Computer Aided

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Molecular Design (CAMD), which is a mathematical programming approach for the determination of a suitable MSA (see Section 2.2.2). More recently also machine learning methods for computer-aided molecular design have been proposed [29], including graph neural networks, which mimic the molecular structure of the individual molecules [30]. Once all available physicochemical properties are compiled and missing data is estimated, process synthesis based on thermodynamic insight allows for an easy and quick assessment and selection of likely feasible separation methods and hybrid separation processes. The determination of the single separation techniques can be performed based on the analysis of pure and mixture properties, while the final synthesis and analysis of the feasibility of hybrid separations requires graphical analysis or an algorithmic approach by mathematical programming as illustrated in Section 2.2.2.

Analysis of pure and mixture properties The knowledge about the physicochemical properties of the individual components in the process is the key information for the synthesis of separation processes, as e.g., described in the thermodynamic insight approach proposed by Jaksland et al. [31]. In a first step pure component properties are compiled from known databases or estimated by property prediction methods. Table 2.1 presents an exemplary selection of such different structural, chemical, physical, and transport properties of pure components, as well as their dependency on temperature (T) and pressure (p). Since separation processes are in general based on the exploitation of differences between physicochemical properties, the knowledge of these properties can in reverse be used to determine suitable separation processes. Structural properties like the kinetic diameter for instance are important properties for the separation of gases by molecular sieve adsorption [31]. As the suitability of a certain separation technique is usually not related to a single property, Jaksland et al. [31] proposed a list of relationships between pure component properties and separation techniques. Table 2.2 presents an exemplary selection that includes most of the separation techniques introduced in Section 2.1. If the ratios of the single properties of two individual components fall in between lower and upper bounds, the separation technique is considered potentially feasible for the separation of these two components. As previously stated, for all separation techniques that require MSA, process feasibility strongly depends on the availability of a suitable MSA. Yet, the associated pure component properties can also be used for the selection of the MSA, searching for a suitable component in available databases or making use of mathematical programming approaches as described in Section 2.2.2. For those properties which are depending on the operating conditions, the consistency of these values has to be guaranteed

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Tab. 2.1: Selection of pure component properties (adopted from Jaksland et al. [31]). Classification

Property

Function of (T, p)

Structural

Kinetic diameter

No

Molecular weight

No

Dielectric constant

Yes

Molar volume

Yes

Gibbs free energy

Yes

Boiling point

Yes

Melting point

Yes

Critical T & p

No

Solubility parameter

Yes

Viscosity

Yes

Chemical

Physical

Transport

Tab. 2.2: Relationships between pure component properties and separation processes (adopted from Jaksland et al. [31] and Holtbruegge et al. [32]). Separation type

Separation technique

Important pure component properties

Gas separation

Absorption

Solubility parameter

Gas membrane

Critical temperature, van der Waals volume

Micro- & ultrafiltration

Kinetic diameter, molecular weight

Nanofiltration

Solubility parameter, molecular weight

Liquid-liquid extraction

Solubility parameter

Supercritical extraction

Solubility parameter, critical T & p

Distillation

Vapor pressure, heat of vaporization, boiling point

Pervaporation

Molar volume, solubility parameter, dipole moment

Crystallization

Melting point and heat of fusion

Adsorption

Solubility parameter, kinetic diameter

Liquid separation

Liquid-liquid separation

Vapor-liquid separation

Solid-liquid separation

when evaluating certain splits. However, if data on these properties is available at different operating conditions, estimates for suitable operating conditions, like e.g., the temperature for a liquid-liquid extraction, can be determined by evaluating the ratio of the relevant pure component properties for the different components.

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Hybrid separation processes are an option whenever more than one type of separation is at least partially feasible. They are especially of interest if the single separations are expected to be complicated or limited, indicated by small differences between the associated property values. However, identification of suitable combinations to overcome these limitations requires knowledge of mixture properties, like the existence of azeotropes or eutectic points and miscibility gaps. Looking back at the example of the membrane-assisted distillation process for ethanol dehydration, which is illustrated in Fig. 2.1, separation by means of distillation is indicated by a boiling point difference of more than 20 K, while the difference in molar volume and solubility parameters of water and ethanol indicates the suitability of pervaporation (PV) or vapor permeation (VP). As illustrated in Fig. 2.2, distillation is limited by an azeotropic point at about 89 mol% (96 wt%) of ethanol. Besides this distinct limitation the mixture shows little variation in relative volatility above and closely below the azeotropic point, while relative volatilities above 10 are reached at low ethanol compositions. Thus, distillation requires little effort for low ethanol compositions, but becomes infeasible at the azeotropic point. PV or VP is not limited by the vaporliquid equilibrium (VLE) and especially hydrophilic membranes are commercially available, which enable water/ethanol selectivities larger than 200 and 2,000 for polymeric and zeolite membranes respectively [33]. Therefore, PV and VP both enable the purification of ethanol, by selective removal of water. However, permeating large quantities of water requires high membrane areas, as well as heat for evaporation in case of PV (see Chapter 9). As a consequence, the hybrid process depicted in Fig. 2.1 combines the advantages of both separation processes, exploiting the large relative volatilities of the mixture at low ethanol compositions by distillation, while overcoming the azeotropic point at high ethanol compositions, exploiting highly selective membranes. As the membrane separation does not enable high purity and recovery of the ethanol, the permeate stream is recycled to the stripping section of the distillation column, in order to warrant high purities of both product streams of the hybrid process. Section 2.4.3 presents a detailed example of the ethanol dehydration case. The analysis of the pure component and mixture properties facilitates a thorough screening of potential separation processes for binary splits. The analysis extends to multicomponent mixtures with the concept of key components, like a low and a heavy boiling key component for distillation, assuming that there is a distinct order between the present components. However, one should be aware that this is not necessarily straightforward. Azeotropic multicomponent mixtures can exhibit multiple distillation regions (DR), in each of which the boiling order can change. The DR are separated by DB, which originate from so-called saddle azeotropes. The feasible product compositions depend on the composition of the individual feed. Consequently, feasibility of process variants generated on the basis of pure component and mixture properties only cannot be guaranteed. Either a graphical analysis of the multicomponent mixture properties, or a model-based assessment by means of simulation or optimization of the potential process variants has to be performed.

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Graphical analysis Each process is a connection of tasks that can be illustrated by means of mass balance (MB) lines in the composition space. This visualization is feasible for binary to quaternary mixtures. Yet, it is most prominently applied to binary and ternary mixtures. Please refer to some of the excellent textbooks on thermal separation technologies for the basic principles of the different separation technologies [34–36]. Building on these principles, we elegantly depict the performance of distillation columns at the limiting cases of total reflux by either residue curves (RC) or distillation lines (DL) and can nicely illustrate DR for azeotropic mixtures, as well as the limiting DB in the composition diagrams [37]. While the existence of a distillation boundary can be derived from the knowledge of azeotropes, residue curve maps (RCM) or distillation line maps (DLM) facilitate the localization of these DB. As illustrated for the ethanol dehydration example such limitations are key indicators for the identification of hybrid separation processes. Figure 2.4 illustrates the RCM for the ternary mixture of acetone, isopropanol, and water at 1 atm. The composition space is obviously separated into two DR by the DB emanating from the minimum boiling azeotrope between isopropanol and water. Having a selective hydrophilic membrane for pervaporation facilitates the separation of the ternary mixture in either a sequential configuration (left side of Fig. 2.4) or a hybrid configuration (right side of Fig. 2.4) with the membrane connected to a distillation column via a side stream. This example already illustrates the synthesis of hybrid separation processes by means of visual insight. As for the ethanol dehydration, a separation which is not possible by means of distillation alone becomes feasible by combining distillation with a membrane separation process. Refer to the article of Scharzec et al. [38] for a more detailed evaluation for this case study. Graphical illustrations of thermodynamic equilibrium data can facilitate the generation of various kinds of hybrid separation processes in the same way. The remainder of this section presents several examples for utilizing visual insights for the synthesis of hybrid separation processes. However, let us first go one step back and take a closer look at the graphical illustration of thermodynamic equilibrium data for binary mixtures. Most useful for the analysis of process limitations is a purely composition-based graphical representation, such as the y-x diagrams for the VLE behavior illustrated in Fig. 2.5. While a wide boiling mixture (a) can be easily separated by means of distillation, a partially narrow boiling mixture (b) mandates high reflux ratios and associated energy and cost requirements for obtaining a high purity product A, while an azeotropic mixture (c) cannot be separate by means of a single distillation column. The grey areas in these diagrams highlight the composition range in which distillation should be replaced/augmented with another separation technique in a hybrid separation process. Figure 2.6 illustrates possible membrane and distillation process configurations for the separation of such binary mixtures, assuming a highly selective membrane exists for the separation of the two components. As for the case of ethanol

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Fig. 2.4: Illustration of the RCM for the ternary mixture of acetone, isopropanol, and water at 1 atm, with the MB lines for a sequential configuration of a distillation column and a pervaporation membrane (left side) as well as a hybrid configuration of the same unit operations (right side).

Fig. 2.5: Illustration of different types of VLE behavior in y-x diagrams: wide boiling system (a), narrow boiling system close to pure A (b), and azeotropic mixture (c).

dehydration, the separation of a mixture which shows an azeotrope or is just narrow boiling at high concentration of component A, like type (b) in Fig. 2.5, can be performed with a hybrid configuration of type (I) illustrated in Fig. 2.6. The membrane separation purifies the top product of the distillation column and recycles the impurities to the distillation column, which purifies the bottom product. For the separation of an azeotropic mixture, where the azeotrope is located closer to an equimolar composition, like type (c) in Fig. 2.5, a hybrid configuration of type (II) can be utilized for the separation. The hybrid process performs the purification of both products by the individual distillation columns, while the intermediate membrane separation breaks the azeotrope.

Fig. 2.6: Illustration of membrane-assisted hybrid distillation processes for the separation of azeotropic and close boiling mixtures.

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While high membrane selectivities are advantageous they are not mandatory for this configuration. The dehydration of isopropanol is one example for which this configuration is applied, which together with the dehydration of ethanol accounts for the majority of the applications of pervaporation-based hybrid distillation processes [39]. Configuration (III) in Fig. 2.6 can be applied for the intensification of the distillation of a close-boiling mixture. While distillation columns require high reflux ratios and equilibrium trays for relative volatilities close to one, high purities of both product streams are usually not viable for a membrane separation due to large membrane areas and multi-stage configurations. The hybrid separation process exploits larger separation factors of the membrane process for the bulk separation, while achieving high purities of products by means of distillation. Refer to Roth et al. [40] and Lutze & Górak [41] for a more elaborate comparison of the merits of the standalone processes and the benefits of the hybrid configurations. Membrane processes cannot only be applied in combination with distillation, but also intensify other separation techniques like liquid-liquid extraction or adsorption [4, 8, 42]. Besides the consideration of selected physicochemical properties (cf. Tab. 2.2), membrane screening mostly relies on expert knowledge, potentially supported by databases and mostly relying on experimental evaluation [38, 43]. So far, only few model predictions have been proposed for flux and selectivity predictions [44–46]. Other hybrid configurations for the separation of complex binary mixtures build on the exploitation of intrinsic differences in phase behavior. If an intermediate azeotrope is located in a miscibility gap, a complete fractionation of a binary mixture is feasible in a heteroazeotropic distillation process, which is a hybrid process combining distillation and decantation. The feasibility of this process becomes apparent from the y-x diagram illustrated in Fig. 2.7 (a). Similar to configuration (II) in Fig. 2.6 the distillation columns purify the products, while the decanter exploits the miscibility gap in order to break the azeotrope by splitting the top products of each column into the two liquid phases with composition xIA and xAII . The individual phases of the decanter are recycled as reflux streams to the two columns. In case the miscibility gap extends sufficiently to one of the products, one of the columns may be spared. The synergies used by this process are again obvious. While the decanter easily overcomes the azeotrope, it is limited by the size of the miscibility gap, governed by the liquid-liquid equilibrium (LLE). Thus, the decanter cannot produce high purity products, which is however feasible in the individual distillation columns that are limited by the azeotrope. Since decantation allows for an easy and cheap separation, such hybrid separation processes are extensively used in industry, e.g. for the separation of mixtures of water with organic compounds like toluene, benzene, chloroform, heptane, butanol, or nitromethane [36]. Note, while the feasibility of such a hybrid separation process becomes directly apparent from the y-x diagram illustrated in Fig. 2.7 (a), this requires the calculation of the vapor-liquid-liquid equilibrium (VLLE). However, since

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Fig. 2.7: Illustration of heteroazeotropic distillation processes for the separation of a binary azeotropic mixture with y-x diagram (a) and the respective process configuration (b).

the LLE and as such the size of the miscibility gap is usually quite sensitive to temperature, operation of the decanter should be evaluated for different temperatures. In this case intermediate heat exchangers should not be forgotten. Hybrid processes based on the combination of distillation and crystallization can also be evaluated well based on the analysis of the VLE and solid-liquid equilibrium (SLE) behavior. Crystallization is a technically proven separation method for purification used in the chemical, pharmaceutical, and food industry [47]. It is a very selective separation method often considered for close boiling or azeotropic mixtures and is also suitable for thermally sensitive compounds due to the low operating temperatures. Specifically, the combination of distillation and melt crystallization, the crystallization of organics without addition of further components [47], is relatively well known for separation of close boiling mixtures and azeotropes, resulting in significant benefits. Such hybrid separations have found industrial application for the separation of isomers of xylenes, dichlorobenzenes, carbon acids, and diphenylmethanediisocyanates [48–50]. For synthesis of such hybrid processes the feasibility of the individual unit operations is usually evaluated by analysis of T-x diagrams, such as illustrated in Fig. 2.8 (a). The illustrated T-x diagram indicates a minimum boiling azeotrope xAz A , as well as . More than 53% of all organic compounds form such a eutectic a eutectic point at xEu A type of SLE [51]. In such a case hybrid processes are of interest, since the eutectic point that limits separation by means of crystallization can be overcome by means of distillation, while the azeotropic point can be overcome by crystallization. Several hybrid separation processes can be synthesized based on the visual insight from the T-x diagram (see Fig. 2.8 (b–d)). Depending on the feed composition, crystallization can

Fig. 2.8: Illustration of T-x diagram (a) and different hybrid distillation-crystallization process configurations (b–d) for the separation of a binary azeotropic and eutectic mixture.

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be used to purify either one of the components. Hybrid separation process variants (b) and (c) can be used for the separation of a feed mixture with xA < xAz A , while process variant (d) can be used for the separation of a feed mixture with xA > xEu A . While this selection of hybrid separation processes illustrates the possible process synthesis by means of visual insight, it does not provide a complete representation of all potential topologies for the presented phase equilibria (VLE, LLE, and SLE). Yet, it should facilitate a basic understanding of how to interpret and utilize the phase equilibrium representations for this purpose. Before moving to the analysis of phase diagrams for ternary mixtures we briefly discuss the driving force approach of Bek-Pedersen et al. [52] as another approach for graphical analysis of binary systems. The method builds on the idea of using a general driving force representation and identifying the most suitable separation technique for a certain concentration range, as the one which shows the highest driving force. Figure 2.9 presents an illustration of such a diagram and an according separation process, whereas the difference in the composition of the two phases separated by the corresponding separation technique is considered as the driving force. The driving-force-based approach has been demonstrated for different hybrid processes and was also applied to multicomponent mixtures, making use of the concept of key components [52, 53]. However, the actual choice of a suitable driving force is not straightforward. While the general driving force for all separation processes is the difference in chemical potential of the individual phases that are brought into contact (see Chapter 3) the difference in retentate and permeate composition for the depicted membrane separation depend on the different fluxes, which are the product of permeance and actual driving force.

Fig. 2.9: Illustration of a driving-force diagram and a corresponding separation process.

Care should also be taken in general in applying the concept of key components, as the behavior of multicomponent mixtures, like the relative volatility, can change

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significantly throughout the composition space for complex multicomponent mixtures. As described by Kiva et al. [54] the terms “light,” “intermediate,” and “heavy” component have generally little meaning for nonideal and azeotropic mixtures. This will become apparent from the following analysis of ternary and quaternary mixtures in composition space, for which we start by analyzing the RCM for feasible product regions for a single distillation column, assuming a limiting operation at total reflux. These regions are bound by the MB lines through the feed, the RC through the feed and potential DB. While the product compositions have to be connected by an RC, the feed composition may be situated in a different DR. The product regions for the separation of a given feed are illustrated in Fig. 2.10 for a zeotropic (left) and an azeotropic ternary mixture (right).

Fig. 2.10: Illustration of feasible product regions for the RCM of zeotropic mixture (left) and an azeotropic mixture with a strongly curved DB (right). The mixture consists of a low boiling (LB), intermediate boiling (IB) and heavy boiling (HB) component. The azeotropic mixture exhibits a minimum azeotrope between IB and HB, which is heavier boiling than LB.

The latter highlights the additional limitations introduced by the DB and the feasible product regions in the DR that does not contain the feed. These bottom products are feasible due to the strongly curved DB, since the low boiling component LB can be obtained as the top product in both DR. Despite these potential boundary crossing splits, it is important to note that the composition space is partitioned into two DR, divided by the DB, and the both DR differ in the boiling order of the components HB and IB. While depending on the feed composition, exploitation of the curved DB might allow for a full separation of the mixture in a two-column process with recycle, a hybrid separation process, like the membrane-assisted process illustrated in the Fig. 2.5, would facilitate such a separation.

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Synthesis of such hybrid separation processes can be performed for ternary mixtures in a similar fashion, as previously introduced for the binary y-x diagrams. The subsequent paragraphs illustrate this for hybrid separation processes based on distillation and decantation, analyzing the VLE and LLE behavior of a mixture. A transfer to crystallization is principally straightforward, taking into account the SLE instead of the LLE [55, 56]. The feasibility of a heteroazeotropic distillation process can be based on the VLLE (or VLE and LLE) behavior as illustrated in Fig. 2.11. The feed stream, which is located in the right DR, can be separated into all three components by combining either two distillation columns with a decanter, as illustrated by the MB lines in the composition space and the first hybrid configuration in Fig. 2.11, or by just one distillation column and a decanter connected to the distillation column in the side stream. In the latter configuration, the composition profile inside the distillation column is located completely in the left DR.

Fig. 2.11: Illustration of a ternary mixture with a minimum boiling heterogeneous azeotrope between component B and C and two feasible processes based on distillation and decantation.

Depending on the VLE and LLE behavior various types of hybrid configurations are possible, such that the visual analysis should always be performed prior to proposing a specific process configuration. Refer to the article of Kiva et al. [54] for a review of the different possible topologies of ternary VLE diagrams, as well as the article by Pham & Doherty [57] and the book by Doherty & Malone [58] for an analysis of the different topologies of VLLE diagrams. Even if a mixture does not exhibit a miscibility gap, a hybrid separation process based on the combination of distillation and decantation can be a feasible and favorable option if a suitable MSA is available. In general, it should be possible to find a suitable entrainer if the original mixture consists of hydrophobic and hydrophilic organic components, such as ethanol and water. While entrainer candidates can be screened on the basis of physicochemical properties, making use of databases or CAMD tools (see Section 2.2.2), visual analysis of the resulting VLLE

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diagrams can be used to confirm the feasibility or synthesize appropriate process configurations. Figure 2.12 illustrates the VLLE diagram and the heteroazeotropic distillation configuration for the example of ethanol dehydration using the established entrainer cyclohexane [59]. In the first column a mixture of the ethanol-water feed (EW) and the recycle stream, which is the cyclohexane lean stream from the decanter is separated into a purified water bottom product and an enriched ethanol top product. The latter is separated into a purified ethanol bottom product and the recycle stream. Note that the composition profile inside the column proceeds inside the ethanol rich DR.

Fig. 2.12: Illustration of the VLLE diagram for the ternary mixture of ethanol, water, and cyclohexane, as well as a heteroazeotropic distillation process for the separation of a binary ethanol-water feed, using cyclohexane as entrainer.

Note that this process cannot be anticipated by the analysis of physicochemical property data for the pure components and binary mixtures, since the minimum boiling ternary VLLE azeotrope is actually the key to the separation process. Yet, the feasibility of the process can be determined elegantly based on the visual analysis of the VLLE diagram. As visual representations are limited to threedimensional space, quaternary mixtures are the natural limit to visual analysis, and even though these representations are possible, such visual analysis is complex, as illustrated in Fig. 2.13 for the quaternary mixture of water, n-butyl acetate, n-butanol, and acetic acid. This mixture exhibits four homogeneous and three heterogeneous azeotropes, with a miscibility gap that extends from the pure water vertex into the quaternary composition space. There are multiple DB that extend into the quaternary composition

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Fig. 2.13: Illustration of the VLLE diagram for the quaternary mixture of water, n-butyl acetate, n-butanol, and acetic, as well as a heteroazeotropic distillation process for the dehydration of a quaternary feed mixture.

space, resulting in several DR, which are not further highlighted, since the diagram would no longer be comprehensible. Refer to the work of Kraemer et al. [60] and Skiborowski et al. [61] for a more detailed analysis and model-based evaluation of this complex example.

2.2.2 Model-based approaches and mathematical programming While thermodynamic insight and graphical analysis are important tools for the synthesis of process configurations application to multicomponent mixtures with five or more components is only possible through component lumping. By translating the criteria for a feasible separation that were illustrated for the graphical analysis into mathematical constraints, geometrical model-based approaches and mathematical programming techniques can be applied to generate and evaluate suitable process configurations. Another important application of mathematical programming techniques for process synthesis is in computer-aided molecular design (CAMD) approaches, which allow for synthesis and screening of suitable MSA based on molecular building blocks. This is specifically important for hybrid separation processes involving decantation or liquid-liquid extraction, for which the process performance is highly dependent on the selected MSA.

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Synthesis of hybrid separation processes Model-based methods for the synthesis of separation processes have been under development for almost 50 years, especially focusing on the synthesis of distillation trains for the separation of zeotropic mixtures [62, 63]. For this task all basic and thermally coupled configurations can be derived automatically by means of a simple matrix method [64] and the approach has more recently been extended to cover all possible types of dividing wall columns [65, 66]. However, process synthesis for the separation of azeotropic mixtures is not as straightforward, and only few methods have been proposed for the synthesis of hybrid separation processes. These methods build on the knowledge and geometrical modeling of DB for VLE-based separations, binodal curves or hypersurfaces for LLE-based separations and eutectic boundaries for SLE-based separations. Having a mathematical description of these boundaries or building directly on suitable thermodynamic models it is possible to address process synthesis independent of the number of components in a specific mixture. Large efforts were made in the development of expert systems that resulted in software implementations such as MAYFLOWER [67], SPLIT [68], or DISTIL [69], which were support systems for conceptual design. However, split feasibility of a specific separation technique was pursued either by graphical analysis, or by means of rigorous simulation model [70], which may be one reason why these tools are not available any more. In order to effectively address multicomponent mixtures that impede a graphical analysis a more abstract approach has to be taken, which builds on a so-called topological analysis. The most important and initial information for the topological analysis for distillation-based processes is the calculation and characterization of all azeotropes, which is not a trivial task, especially in case of heterogeneous mixtures. Refer to Bonilla-Petriciolet et al. [71] and Skiborowski et al. [72] for an explanation of the complexities and potential methods for azeotrope calculation. Luckily, most process simulators do at least allow for azeotrope computation. Yet, they do not necessarily provide a characterization. However, for further analysis it is important to characterize all singular points, which are azeotropes and pure components, classifying them as stable node, unstable node or saddle, based on the nonlinear dynamics in the vicinity of these points. Considering RC as the reference, a stable node represents a singular point which is a terminal of the surrounding RC, while an unstable node is the origin of the surrounding RC. A saddle is approached by RC from some direction, which are however deflected into another direction before they reach the singular point. Refer to the articles of Westerberg et al. [73] and Kiva et al. [54] for a more detailed description. Based on this characterization, the topology of the mixture can be analyzed utilizing the concept of adjacency (A) and reachability matrix (R), as introduced by Knight & Doherty [74]. Both matrices are upper triangular matrices with binary values, indicating if a singular point SPi is directly adjacent to another singular point SPj (ai,j = 1) or if it is generally possible to reach one from the other by means of a residue curve (ri,j = 1). The topological DR

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are exemplarily illustrated in Fig. 2.14 together with the adjacency and reachability matrix for a complex ternary azeotropic mixture. These matrices can efficiently be computed with the algorithms introduced by Rooks et al. [75]. Based on that knowledge feasible product specifications for a distillation column can be derived for general multicomponent mixtures.

Fig. 2.14: Illustration of the topological DR, as well as the adjacency and reachability matrices for a ternary azeotropic mixture.

While most of the work on topological analysis was performed in the early 2000s, Sasi et al. [76] have recently extended the existing methods for the development of an automatic process synthesis approach, which was also applied to the generation of heteroazeotropic distillation processes [77]. Nevertheless, commercial process simulators still only support graphical analysis, potentially requiring component lumping [31] as well as trial and error studies by means of rigorous simulation or optimization.

Selection of MSA MSA such as solvents play a crucial role in many separation processes, like absorption, liquid-liquid extraction, heteroazeotropic distillation, extractive distillation, or organic solvent nanofiltration (cf. Chapter 8). In a similar way as defined in Section 2.2.2, suitable solvents may be preselected based on the specification of favorable physicochemical properties. A list of suitable solvents may be determined from a database of component property data, derived from literature or from a process simulator, which usually contains such information in form of an incorporated library. Considering possible constraints for the specific application and the effort for solvent recovery, usually more than one important property has to be considered. For an affinity driven process, such extractive distillation or liquid-liquid extraction, Jaksland

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et al. [31] propose an initial evaluation of potential solvents based on pure component properties like dipole moment, solubility parameter, dielectric constant, surface tension, or the refractive index, in order to select components that resemble the properties of one molecule, while distinguishing from the properties of the other molecule, for a binary separation. The resulting list of potential solvents is further evaluated for additional criteria, considering thermal and chemical stability, low viscosity and freezing points, nontoxicity, or even commercial availability [78]. From the resulting list, a final selection is performed in subsequent steps based on solvent power and selectivity, as well as distribution coefficients, which can be determined based on group contribution methods [31]. Yet, even if a solvent has outstanding solvent power and selectivity it might be difficult to recover, resulting in an inefficient process [31]. Predicting the respective thermodynamic equilibria does however enable the evaluation of the single unit operations and in combination the overall process performance. As illustrated in Fig. 2.15, knowledge of the size of the miscibility gap and the orientation of the liquid-liquid tie lines allows for the computation of the minimum entrainer to feed ratio (E/F)min, required for specified product purity and recovery, while full LLE and VLE models allow for the computation of the minimum heat requirement (QB,min) for thermal regeneration of the solvent, or the cost related to the combined hybrid process. Given efficient computational tools and shortcut methods (see Section 2.3.2) these metrics can be evaluated in just a few hours for more than 1,000 potential solvents [12, 79].

Fig. 2.15: Illustration of the relation between property prediction and process performance in the context of solvent selection.

Apart from the selection of solvents from a well-established candidate set, potential solvents can also be rigorously synthesized from molecular building blocks by means of CAMD, which directly and systematically identifies solvents with desirable properties, such as favorable selectivities or distribution coefficients for the solutes [80], or even process performance metrics [13]. For this purpose, an inverse problem is solved by performing a mathematical optimization that considers a variable molecular structure linked to an objective function representing the former metrics (see Fig. 2.16). Further criteria, such as limiting boiling or melting points,

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Process performance Property prediction Molecular structure

Molecular design inverse problem

Screening direct problem

toxicity, or cost, can be implemented as additional constraints. The CAMD problem can be solved either by means of enumeration, applying a so-called generate-and-test procedure [81] or by formulating and solving a MINLP optimization problem [82]. Refer to the article of Gertig et al. [83] for a recent status report on CAMD and process design. The prominent CAMD tool ICAS, which is based on group-contribution methods and was primarily developed at the DTU [84], is nowadays available through the newly founded company PSEforSPEED in ProCAPE framework.1

Fig. 2.16: Differentiation between solvent screening and computer-aided molecular design in accordance with [83].

While CAMD facilitates an efficient screening of a vast number of potential solvents, the accuracy of the property predictions is a limiting factor and necessitates experimental validation. Nevertheless, despite the limitation in absolute accuracy, the predicted ranking of solvent candidates has been confirmed in several experimental validation studies [85, 86].

2.3 Conceptual design of hybrid separation processes After or during synthesis of potentially feasible process configurations, these configurations have to be validated and evaluated in order to rank them concerning some performance criteria. Most of the time this is some economic criteria, as e.g., the total annualized cost (TAC) or operating cost. If the specific equipment has not been fixed oftentimes auxiliary criteria regarding the required energy for certain separation techniques, sustainability indicators, or alternative measures are applied.

2.3.1 Process synthesis framework If feasible, all possible process configurations would be combined in a generic superstructure, building on the most accurate process models, and providing the best solution by means of deterministic global optimization, thus providing a mathematical guarantee that the best solution has been determined. However, this is likely to remain

1 https://www.pseforspeed.com/ .

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a far-fetched fantasy, at least for the next decades. This is not only due to current limitations in problem size and complexity for global optimization solvers, but also due to limited data and limited accuracy of available models in the early phase of process development. Generally, a lot of different options are screened initially with simplified models that maintain significant uncertainty. Focusing on a smaller number of selected options, effort is placed on improving model accuracy and the level of detail with which promising process options are modeled. Consequently, evaluations of a suitable process structure and a more detailed design are usually performed by models on different scales, considering the limited availability of data and resources. The reduction of potential process variants and model-based analysis also facilitate the determination of targeted experiments that can further reduce the experimental demand. Process synthesis and design should consequently be integrated with the necessary experimental analysis of the chemical system that needs to be separated and the unit operations that are considered for process design. Figure 2.17 illustrates a systematic approach for process synthesis and design, introduced by Marquardt et al. [87] and further extended by Skiborowski et al. [88] in the context of the conceptual design of distillation-based hybrid separation processes. Building on an initial knowledge and thermodynamic analysis, variant generation follows the methods described in Section 2.2. Thermodynamic equilibrium and physicochemical property calculations enable the application of so-called shortcut models for a rapid screening of the entire set of process variants. Suitable shortcut methods make use of simplifying assumptions in order to facilitate a numerically robust and efficient screening. The result of the screening is a selection of the most promising variants according to a performance indicator, like the total energy requirement (Qtot). The selected variants are investigated further by means of more detailed conceptual design models. By means of MESH models2 based on rigorous thermodynamics and in combination with additional equations for sizing and costing, the process configurations can already be optimized for an estimate of the TAC to evaluate the potential economic performance. Finally, a detailed equipment design can be determined based on rate-based engineering models, which require information on heat and mass transfer to allow for a reliable sizing of the final process. The idea of the process synthesis framework is therefore to transfer only the most promising process variant to this final level and to perform targeted experiments based on the results from the previous conceptual design step. In order to efficiently address the various degrees of freedom for process design on the different levels the application of optimization-based design methods is recommended. While structural degrees of freedom, like the interconnection of different unit operations or the number of separation stages, and operational degrees of freedom, like pressure levels and heat duties, can be determined based on systematic variations

2 MESH = Mass balances, equilibrium and summation constraints and enthalpy balances.

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Generation of variants

Rapid screening with shortcut models

Optimization-based design with conceptual models

Optimization-based design with rate-based engineering models

Generation of process variants

Feasibility check and determination of separation cost

Simultaneous optimization of operating points and unit specif cations

Simultaneous optimization of operating points and detailed unit design

Cost-optimal process

Cost-optimal process

Tree of variants Selection of promising variants

Knowledge of mixture properties

Estimated or validated equilibrium and physicochemical property models

Validated heat and mass transfer models for selected equipment

Cost-optimal process

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Number of process variants Model complexity

Fig. 2.17: Process synthesis framework with iterative refinement adapted from [88].

in simulation studies, optimization-based methods allow for their simultaneous determination. As nicely phrased in the article of Biegler [89] “Don’t search for the optimal solution! Instead, solve for the optimum directly from the KKT conditions.”3 This is of special importance in the design of hybrid separation processes, due to the high level of interconnection and interdependency, which severely complicates an iterative search. A concise overview of recent advances in process optimization can be found in the articles by Biegler [89, 90] while more elaborate descriptions are given in various textbooks (e.g. Edgar et al. [91] and Kallrath [92]). The remainder of this section presents an introduction to process evaluation and optimization on the different levels of the process synthesis framework (cf. Fig. 2.17). The upcoming sections will present more information on the different modeling approaches for integrated and hybrid separation processes.

2.3.2 Shortcut methods The term shortcut is not clearly defined and is used for simple performance models/ methods making use of predefined split factors, as well as for sophisticated and

3 Karush-Kuhn-Tucker conditions are the first-order necessary conditions for a solution in nonlinear programming to be optimal.

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thermodynamically sound models. Well-known examples for separation processes include the separator model in Aspen Plus, plainly using split factors, the wellknown Kremser equation, assuming a constant slope of the operating and equilibrium line, the Underwood method [93], which assumes constant relative volatility and molar overflow, as well as the graphical McCabe-Thiele method [94]. All of the above shortcut methods apply different degrees of assumptions to simplify rigorous equilibrium tray models, which are further classified as conceptual design models (cf. Section 2.3.3). One of the least restrictive assumptions underlies the so-called pinch-based shortcut models, which take into account the limiting state of a vanishing driving force that results in the requirement of an infinite number of equilibrium stages to perform a desired separation. This is the same principle that applies for heat transfer in the well-known pinch analysis for heat exchanger networks [95]. Figure 2.18 illustrates two exemplary pinched separations for distillation (left) and extraction (right). The left part of the figure illustrates a feed pinch situation for a binary distillation in a y-x diagram. Here both operating lines intersect with the equilibrium curve at the composition of the feed stage, requiring an infinite number of stages in both column sections, due to the vanishing driving force in the vicinity of the feed stage. The same principle applies to multicomponent systems, for which the composition profile of tray-to-tray calculation shows little to no progress in the vicinity of a pinch point. However, unlike for binary mixtures, multiple pinch points may occur along the composition profile of a distillation column for the separation of a multicomponent mixture [96].

Fig. 2.18: Illustration of pinched separations for a binary distillation and a ternary extraction.

The right part of the Fig. 2.18 illustrates a feed pinch situation for a liquid-liquid extraction process. While all the MB lines for the extraction column intersect in the

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difference point (PD), the MB line at the top, where the feed (F) enters and the extract phase (E) leaves the column, is colinear with the liquid-liquid tie-line, such that the driving force for mass transfer vanishes. While there are further types of pinches, especially for multicomponent mixtures, pinch-based shortcuts have the advantage of limiting the necessary calculations to the specific pinch-points, allowing for a direct computation of a design with limited driving force, providing the thermodynamic minimum energy demand (MED) for distillation or the minimum solvent required for a liquid-liquid extraction. The well-known Underwood method [93], which is also part of the DSTWU shortcut method in ASPEN Plus®, is also a pinch-based shortcut method, which furthermore builds on the assumptions of constant molar overflow and relative volatilities. These assumptions are however not valid for nonideal mixtures, which are most relevant in the context of hybrid separation processes. For distillation various shortcut methods for nonideal mixtures, like the boundary value method (BVM) [97] or the rectification body method (RBM) [98] have been proposed. Refer to the book chapter of Skiborowski et al. [96] for a detailed introduction and overview. It is crucial to know and understand the underlying assumptions when selecting a suitable model for a specific application, as the reliability of the results tremendously depends on these assumptions. This does of course apply to modeling in general as illustrated in Chapter 4. For the shortcut evaluation of hybrid separation processes, suitable shortcut models of the single unit operations are aggregated and the process is evaluated for an appropriate indicator. The indicator should generally be a representative value for the major share of the process costs and depends on the type of process under investigation. The cost of hybrid distillation-extraction processes is mostly determined by the energy requirement for solvent recovery. The minimum solvent flow rate in the extraction column is often used as a suitable indicator for the separation effort and provides a good indication for the discrimination of solvent candidates. However, the MED of the recovery column provides an even better indicator, since it takes into account the amount of entrainer and the ease of recovery. This has been confirmed by Minotti et al. [99], who demonstrated the relevance of solvent recovery in designing distillation-extraction hybrids. A graphical analysis of the minimum solvent flowrate (cf. Fig. 2.18 (right)) was first introduced by Hunter & Nash [100] and can be applied for ternary systems. In order to consider multicomponent mixtures with more than three components and to take into account impurities in the solvent recycle, numerical shortcut models have been proposed. Several pinched-based shortcut methods for extraction columns have been proposed [101–103]. Kraemer et al. [104] have furthermore demonstrated the combination of a pinch-based distillation [60] and extraction column model [99] to identify the MED by means of an equation-oriented model of the hybrid separation process. Without consideration of a closed recycle, Scheffczyk et al. [12] demonstrated the use of the individual shortcut models for screening more than 1,000 potential solvents from a database of molecules.

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Hybrid distillation- crystallization processes are presented by quite similar configurations to distillation-extraction hybrids. While crystallization itself presents an energy-efficient separation method, the operating cost may significantly impact the process economics [105]. A shortcut method for the determination of the MED for melt crystallization was first proposed by Wellinghoff & Wintermantel [106]. The shortcut method does not rely on SLE calculations. However, it requires the specification of a feasible MB with respect to the melting temperature and the eutectic behavior. It is based on the melt enthalpy of the involved components in combination with empirical factors to account for cooling and heating. Wallert et al. [107] and Franke et al. [50] successfully evaluated a variety of hybrid distillation-crystallization flowsheet variants by making use of this method. In order to account for impurities in melt-layer crystallization and to increase the accuracy of the shortcut evaluation, multiple crystallization steps are necessary to achieve satisfactory separation. An appropriate modeling approach represents the product concentration as a function of the subcooling temperature and introduces an additional mixture-dependent parameter determined from experiments [108]. Section 2.4.1 presents more details on the design of hybrid distillation-crystallization processes in the context of a case study. Heteroazeotropic distillation processes are often presented by strongly integrated configurations. In the standard configuration the top vapor from the distillation column is condensed and split in two liquid phases in the decanter, one of which being recycled to the distillation column (cf. Fig. 2.13). This configuration can already overcome the limitations that would be valid for the standalone unit operations. Determining the MED of such heteroazeotropic distillation process requires sophisticated shortcut models, which account for three-phase solutions (VLLE) and possible liquid phase splitting in the column [109]. Shortcut methods are either based on tray-to-tray calculations, such as the BVM [110, 111] or the shortest stripping line method (SSLM) [112], or pinch-based shortcut methods, which avoid the additional specifications but require the correct computation of pinch points in the homogeneous and heterogeneous regions. Kraemer et al. [60] present a detailed review of the applicability of the various pinch-based shortcut methods to the design of heteroazeotropic distillation processes. Because pinch-based shortcuts rely on some linear approximation of the concentration profile, MED estimates, the strongly nonideal behavior of the heterogeneous mixture may result in larger deviations, which are avoided by specifically modified shortcut methods [60, 109]. Hybrid distillation-membrane processes are often composed of sequential configurations with recycle streams, but can also represent highly integrated configurations like the side stream configuration illustrated in Fig. 2.4. Even a shortcut model for a membrane separation requires a model for mass transfer through the membrane. Due to the significant experimental effort for characterizing membrane separation, typically only few membrane materials are considered in process synthesis and a simple enumeration of the resulting types of process alternatives is employed. The first shortcut models for hybrid distillation-membrane processes were

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based on simple performance models [113, 114]. For binary mixtures a graphical analysis based on the McCabe–Thiele diagram [115] can be performed (cf. Fig. 2.2) to analyze the potential of different hybrid configurations [116]. However, for multicomponent mixtures a numerical model is required and for membrane processes like pervaporation, for which flux and selectivity strongly depend on composition, temperature, and pressure, a suitable model has to reflect this by at least some semi-empirical correlation. Yet, shortcut models for membrane processes generally assume perfect mixing on both retentate and permeate side, and ignore additional flux-reducing effects like concentration or temperature polarization and pressure drop. Bausa & Marquardt [117] introduced a more sophisticated shortcut method combining the pinch-based RBM for distillation with a one-dimensional isothermal model of a pervaporation membrane employing a semi-empirical, local flux model. The hybrid separation process was assessed on the basis of a cost estimates using the two target values, MED and minimum membrane area. Nevertheless, even without the known existence and model of a specific membrane, a shortcut-based evaluation can be used to evaluate the potential of a membrane-separation or hybrid separation process. This is illustrated in Fig. 2.19 for the example of ethanol dehydration, following the work of Scharzec et al. [38]. The figure illustrates the individual energy requirements of three process alternatives, building on the assumption of a perfectly selective hydrophilic membrane. Just the heat of evaporation deems a purely PV or VP-based process most energy intensive, while depending on the composition of the top vapor in the distillation column, the hybrid PV-assisted distillation requires considerably less energy than the alternative heteroazeotropic distillation process (cf. Fig. 2.12). As this evaluation does not account for the required membrane area, it is advisable to concentrate the top vapor as much as possible without exceeding the MED of the reference process, resulting in the indicated range of feed compositions for the membrane separation. These computations therefore allow for an initial evaluation of a membrane independent potential of the membrane or membrane-assisted process, as well as some restriction of the operational conditions of interest, to limit resource requirements for experimental investigations. Similar arguments also hold for pressure-driven membrane processes, especially exploiting new membrane technologies, such as organic solvent nanofiltration (OSN). The large experimental effort for membrane screening and characterization is usually considered as a prerequisite for process evaluation and oftentimes a roadblock that results in discarding the technology as long as other, conventional unit operations such as distillation are feasible. Initial model-based computations allow for an evaluation of the potential given different performance metrics (see e.g. [118, 119]). This evaluation either provides incentive for further experimental efforts, while narrowing down the design space and operating range, sparing many superfluous experiments with unsuitable membranes, or provides quantitative arguments for discarding the technology. Refer to Section 2.4.2 for an example on organic solvent nanofiltration and distillation.

Qtot [MW - kmol-1.s-1]

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50

25

feed concentrations of interest 0,70

0,75

0,80

0,85

0,90

XD,Ethanol [mol%] PV stand alone

Heteroaz. dest. with cyclohexane

PV-based (90 mol% H20)

PV-based (100 mol% H20)

Fig. 2.19: Illustration of minimum energy demand of three alternative separation processes for the dehydration of an aqueous ethanol feed with a perfectly selective hydrophilic membrane, according to Scharzec et al. [38].

2.3.3 Methods based on conceptual design models Conceptual design models can be distinguished from the previously presented shortcut models by the degree of simplifying assumptions. While a clear distinction is not easy, we restrict the term “conceptual design models” to those models which rely on rigorous thermodynamics, mass and energy balances and which are not limited to a specific mode of operation. The model of a countercurrent cascade of equilibrium stages, as represented in the RadFrac model of ASPEN Plus® for distillation columns, is the classic example of such a conceptual design model. It provides the necessary information for validating thermodynamic feasibility and an economic evaluation of process performance by combining the model with additional equations for equipment sizing, assuming suitable hydrodynamic conditions. To obtain physically relevant design results deviations from thermodynamic equilibrium are usually considered by means of either Murphree efficiencies for tray columns or HETP values for packed columns [94]. The design of separation processes based on conceptual design models, even those based purely on distillation, requires the evaluation of a multitude of fully specified processes, including structural (number of stages and position of feed and side stream stages) and operational degrees of freedom (heat duties and potential heat integration). Optimization-based approaches relying on a superstructure that captures all structural and operational degrees of freedom allow for a simultaneous determination for an optimal process design. Figure 2.20 provides an illustration of the superstructure for a curved-boundary process, which the respective MBs illustrated in the adjacent Gibbs diagram.

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Fig. 2.20: Illustration of a superstructure and composition profiles for a ternary distillation process for the separation of an azeotropic mixture by exploiting the curved boundary.

Note that the process structure itself is fixed, while the superstructure allows for variable tray numbers in the individual column sections. The first column produces pure C as bottoms product and a distillate with a composition D1 close to the distillation boundary (DB), which is separated into pure A as top product of the second distillation column. The bottoms product B 2 of that column is further separated in the third column to obtain pure B as bottoms product and recycling the binary azeotrope back to column 1. Process optimization determines the individual tray numbers in each section, as well as heat duties of each column and the intermediate product compositions, through minimization of some objective function, such as TACs. For this purpose, a mathematical formulation of the superstructure model is required. For distillation columns these models were first introduced by Viswanathan & Grossmann [120] and later extended to nonideal distillation by Bauer & Stichlmair [121]. In contrast to shortcut models, complex column configurations with side streams and multiple feed streams are straightforward extensions of the superstructure. The resulting optimization problems can be formulated as either general disjunctive programming (GDP) or mixed-integer nonlinear programming (MINLP) problems [122]. They are particularly difficult to solve, due to the combinatorial complexity and the strong nonlinearity [123]. Either deterministic gradient-based algorithms [90, 124] or a metaheuristic, such as evolutionary algorithms or simulated annealing, can be combined with a process simulator for flowsheet optimization [125, 126]. Gradient-based approaches provide computationally efficient and proven locally optimal solutions. In contrast, metaheuristics are oftentimes phrased as global search strategies are not limited to local optimization. They can easily exploit existing simulation models, as in commercial process simulators. However, depending on the size of the search space, they may require tremendous computational effort, a successful application requires proper parametrization of the methods and

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depends on the convergence of the associated process simulator [127]. While the combination of a metaheuristic and a process simulator requires the least effort, tailored optimization models are usually more efficient and computationally robust. Metaheuristics and gradient-based optimization methods can also be combined in hybrid optimization so-called memetic optimization approaches, which just like hybrid processes can combine the benefits of both methods [125, 126, 128]. Conceptual design models for hybrid distillation-extraction processes are based on a superstructure of equilibrium stage cascades for both, distillation and liquid-liquid extraction columns. Several general superstructures for multicomponent liquid-liquid extraction and related hybrid process configurations have been proposed in combination with deterministic approaches [129, 130], as well as metaheuristics [131]. The extractor configurations that can result from these superstructure formulations include single contact, repeated contact, and solvent distribution over several stages. A superstructure for such a hybrid distillation-extraction process for the separation of a close boiling mixture of components A and C, using B as solvent is illustrated in Fig. 2.21. Application of such a model has been presented by Glanz & Stichlmair [130] for the separation of a binary mixture of acetic acid and water by means of methyl-tert-butyl-ether (MTBE). Kruber et al. [79] apply such models for the final evaluation of a selected number of alternatives from the over 1,000 solvents evaluated by the shortcut screening of Scheffczyk et al. [12].

Fig. 2.21: Illustration of a superstructure for a hybrid distillation-extraction process.

Superstructures for hybrid distillation- crystallization processes can be formulated in a similar fashion, modeling the crystallization unit as a countercurrent cascade of SLE stages. Such superstructures and the respective MINLP problems for distillation-crystallization hybrid processes have been applied for the separation of a ternary mixture of isomers with minimum TAC [50, 132]. Figure 2.22 illustrates the superstructure of one of the potential configurations that can be used to determine

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the number of stages and the feed stage in each crystallization and distillation step within the sequence. The design of such a hybrid distillation-crystallization process is further be illustrated in Section 2.4.1.

Fig. 2.22: Illustration of a superstructure for the separation of a close boiling mixture of para (p), meta (m), and ortho (o) isomers.

The extension of a distillation column superstructure to a heteroazeotropic distillation column superstructure is also straightforward. While rigorous modeling and simulation of these well-known hybrid configurations has been performed since the 1970s [133], setting up and initializing the respective simulation models in a commercial process simulator is not straightforward [134, 135]. Mathematical optimization is even more challenging due to the transition from two-phase VLE to three-phase VLLE models when the composition profile enters or leaves a miscibility gap [61]. For an accurate description of the composition profile, it is however indispensable to determine phase stability correctly for each equilibrium stage [136]. By combining a metaheuristic with a commercial process simulator, the problem can be addressed by an iterative procedure of simulation and phase stability testing [137, 138], while an equation-oriented simultaneous approach requires an integrated phase stability test, e.g. through solution of a bilevel optimization problem [139, 140]. Skiborowski et al. [61] present a thorough review of the different approaches to the conceptual design of heteroazeotropic distillation processes and propose a novel approach for a deterministic optimization of these processes, encapsulating the complex equilibrium calculations and the phase stability testing in form of implicit functions.

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For distillation-membrane processes at least a simple rate-based model of the membrane process has to be combined with an equilibrium model of the distillation columns. In order to account for a reliable feasibility and cost estimate driving force limiting effects, such as temperature and concentration polarization or pressure drop should be accounted for in conceptual design [119]. Apart of that, a comprehensive superstructure has to be formulated that is composed of the distillation column superstructures and a membrane network superstructures. The network can be composed of several membrane modules, possibly even of different membrane types, which are interconnected in different stages and usually include additional equipment, such as intermediate heat exchangers in the case of PV or pumps in case of pressure-driven membrane processes. The optimal design of the membrane network is accomplished by decisions regarding the optimal interconnection of the membrane and distillation units as well as the configuration of the distillation column(s) and the individual sizes. Figure 2.23 illustrates the superstructure of a pressure swing distillation process with an integrated and intermediate membrane process. The first two of the three sequential membrane stages can be bypassed and the feed and recycle streams can be introduced on various column stages.

Fig. 2.23: Illustration of a superstructure for a hybrid distillation-membrane process with up to three membrane stages and two distillation columns operated at different pressure.

Several optimization-based methods relying on different objectives have been presented to design such membrane networks. The article of Skiborowski et al. [141] provides an overview of the different approaches and a detailed presentation of a deterministic optimization approach for the conceptual design of membraneassisted distillation processes, focusing on PV and VP. Since membrane processes are usually not available in commercial process simulators, various customized model formulations have been proposed in literature. Membrane separation models coded in FORTRAN, MATLAB®, and gPROMS® and integrated in process simulators like ASPEN PLUS® or HYSIS® facilitate a simulation-based design [142–144].

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2.3.4 Methods based on detailed rate-based models While shortcut and conceptual design models are used to determine the most promising process configuration from a variety of different options, they do not provide a detailed insight into mass and heat transfer phenomena taking place inside of the involved unit operations. In order to determine a detailed design that can be utilized for engineering and scale-up, equilibrium-based calculations usually do not suffice and more sophisticated process models have to be applied, directly modeling fluid dynamics, mass and heat transfer. While most of the presented shortcut and conceptual design models build on equilibrium-based calculations, necessitating only a thermodynamic model for the chemical systems, rate-based models assume a continuous transfer of mass and energy between both phases in contact, requiring individual models for fluid dynamics and transport properties as well as equipment specific correlations. Application of these models provides an increased level of detail, which might be indispensable for sufficiently accurate equipment design but also necessitates the specification of the type of equipment (type of internals, material, etc.) and the knowledge of the necessary properties and correlations. Further information on rate-based models is presented in Chapter 4, as well as excellent textbooks by de Haan & Bosch [94], Taylor & Krishna [145], Bird et al. [146], and Keil [147]. Despite the simplifying assumptions underlying the equilibrium-based model, it is often assumed to be adequate for the design of distillation columns. Yet, several authors demonstrate severe shortcomings and highlight the necessity of non-equilibrium models to accurately describe the mass transfer phenomena in distillation columns (refer to [145]). Rate-based distillation models are available in several commercial simulators, e.g. as a rate-based version of the RadFrac model in ASPEN PLUS®. These models can be applied to design optimization by means of metaheuristic, similar to the previous conceptual design models. The design of heteroazeotropic distillation processes by means of rate-based models is however still not feasible in commercial simulators. While non-equilibrium models for heterogeneous systems were already presented in the literature some time ago, these models differ in their assumptions of which phases are in direct contact [148] and although experimental results suggested the need for rate-based modeling [149], adjustment of the equipment-specific mass transfer correlations for three-phase operation may be necessary to obtain sufficiently accurate results [150]. Especially for liquid-liquid extraction in hybrid distillation-extraction processes, the equilibrium assumption rarely provides sufficient accuracy for design calculations due to significant mass transfer limitations determined by droplet size, coalescence behavior, and diffusive mass transfer resistance. There are different designs for industrial liquid-liquid extractors, being either static or making use of mechanical agitation or pulsation to intensify the mass transfer [34]. The specific type of equipment should be carefully selected taking into account the number of required theoretic stages determined by the conceptual design model as well as

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throughput and physical properties of the processed media. More information on the different contacting equipment for liquid-liquid extraction is provided in Chapter 7. Further detail beyond the level of a continuous non-equilibrium model, can be achieved by means of population-balance models that build on mass transfer data from single-droplet experiments and account for the major kinetic phenomena that determine extraction column performance [151]. Such a Monte Carlo-type simulation model can result in excellent performance predictions but is computationally demanding and has not yet been considered for optimization-based design. Knowledge about the kinetics is also highly important for the design of crystallizers in distillation-crystallization processes. Especially the major kinetic effects, such as nucleation and crystal growth for melt crystallization but also breakage and aggregation, have to be taken into account in the case of suspension crystallization. The formation of the layer in melt crystallization has to cover the entrapment of impurities in addition to the representation of the overall dynamic behavior of the crystallizers. In case of suspension crystallization, also the solid-liquid separators have to be accounted for. These considerations result in complex models requiring the use of mixing theory, computational fluid dynamics, and population balance modeling (Jones et al. 2005). Nevertheless, and probably due to the complexity, design calculations are often performed based on the same methods used for conceptual design, such as the method of Wellinghoff & Wintermantel [106]. Refer to the textbook by Mersmann [36] for more detail on crystallization processes and detailed modeling. Distillation-membrane processes require rate-based models for the membrane separation at any level of detail, but especially for final equipment design fluid dynamics and polarization effects have to be accounted for. Pressure losses on feed and permeate side, concentration polarization and transport resistance within the porous support providing mechanical stability but not determining selectivity, can have a severe effect on mass transfer, while temperature polarization can affect heat transfer across the membrane. Depending on the type of membrane separation all of these effects might be important and consequently modeling them can be mandatory for an accurate description of membrane separation performance on a technical scale. In order to accurately model separation performance, the type and geometry of the module also have to be considered as well as the flow pattern for the specific application. Consequently, the mathematical models for describing permeation in hollow-fiber and spiral-wound membrane modules show different characteristics if they are derived from rigorous mass, energy, and momentum balances [152]. Depending on the type of module and flow pattern even a resolution in two spatial dimensions might be necessary, resulting in a partial differential algebraic equation system for a single membrane module, which is integrated into a larger membrane network connected to a rate-based distillation model. Despite the severe complexity of the resulting process model, simulation models have been developed and successfully optimized by means of evolutionary optimization approaches, aiming at improved operating conditions and equipment parameters (e.g. [153]).

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This should be fully sufficient, since the optimal process structure can be determined by means of the shortcut-based screening and the optimization-based design calculations on the conceptual design level. The application of detailed rate-based engineering models results in an improvement of the design accuracy and a detailed equipment design. Further information on the detailed modeling and design of membrane-assisted distillation processes is presented in the subsequent chapters on hybrid and reactive separations involving organic solvent nanofiltration (Chapter 8) pervaporation and vapor permeation (Chapter 9).

2.4 Illustration of exemplary applications of hybrid separation processes This section illustrates the application of process synthesis and design methods for different examples of energy-efficient distillation-based hybrid separations. Three case studies are discussed. In the first case study, a combination of distillation and melt crystallization is used to separate a complex ternary mixture, while in the second case study a heavy boiling impurity is separated from a wide boiling mixture combining organic solvent nanofiltration and distillation. The third case study deals with the investigation of several distillation-based hybrid separation processes for the dehydration of bioethanol.

2.4.1 Case study 1: distillation and melt crystallization Separation task: As an industrial case study the separation of a mixture of ortho, meta and para isomers containing less than 1% of the low boiling meta component (M), about 66% of the intermediate boiling para component (P) and about 33% of the high boiling ortho component (O). For each product stream a purity of 99% is required. The design of a hybrid crystallization and distillation process is performed in accordance with the process synthesis framework (cf. Section 2.3.1), which reduces to a three-step procedure in this case, leaving out the rate-based design optimization (cf. [50, 87]).

Generation of process alternatives Since the isomers do not form azeotropes, separation by means of distillation alone is generally feasible but economically unattractive due to the low relative volatilities (cf. Tab. 2.3), with the P/O separation being particularly difficult.

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Tab. 2.3: Separation factors αi,j for the isomer mixture (ratio of the vapor pressures) [50]. i/j

M

P

O

M



.

.



.

P O



Graphical analysis of the SLE in Fig. 2.24 reveals multiple eutectic points (E) for the isomer mixture, but also indicates that melt crystallization enables almost pure products in few stages with very high separation factors if limited yields can be accepted. Eutectic troughs connect the binary eutectic points (E1 – E3) with the ternary eutectic point (E4) and subdivide the composition space into three saturation regions in each of which only one pure product can be obtained. For the feed composition (F) illustrated in Fig. 2.24 the intermediate boiler P can be crystallized, whereas crystallization of the other components can be enabled through distillation, mandating a hybrid process. The solid product S, the feed F, and the melt residue R lie on the balance line of the initial crystallization unit. By lowering the crystallization temperature, the intermediate boiler P precipitates and the residue composition R moves along the crystallization path F–BE until it reaches the eutectic trough. From this point a second component crystallizes which is undesired. In the present case study the composition at the point BE is called eutectic composition and the temperature at this point will be referred to as eutectic trough temperature. In order to further generate flowsheet alternatives, the following set of heuristics are applied: 1. A maximum of four unit operations are allowed in each process flowsheet. 2. No stream splitting is allowed. 3. Only products which satisfy the purity specifications are allowed to leave the process. Streams that satisfy the product specifications are not recycled. 4. Only simple distillation columns with one feed and two product streams are considered. 5. Distillation is used either to obtain product(s) or for pre-concentration of a crystallization. Based on these rules, 19 feasible sequences are synthesized, including an indirect (18) and direct (19) column sequence based on distillation alone. Figure 2.25 shows the remaining 17 hybrid processes. As first separation step the feed mixture is either separated by distillation of the components O or M (sequences 1–11) or by crystallization of component P (sequences 12–17). Process streams that contain only components that have already been obtained as products in previous separation steps are recycled. Note, that these recycle streams are not shown in Fig. 2.25.

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Fig. 2.24: Representation of melt crystallization in polythermal ternary diagram and corresponding phase diagram (M: meta isomer, P: para isomer, O: ortho isomer, Ei: eutectic points, F: feed, R: residue, BE: point on eutectic trough, L: liquid phase, S: solid phase) [50].

Shortcut screening based on the minimum energy consumption of the variants As described for the process synthesis framework in Section 2.3.1, a shortcut screening is performed for the full set of generated process variants. The melt crystallization shortcut model relies on the following assumptions: – The desired crystal product is pure and obtained in a single stage. – The crystallization temperature is equal to the eutectic trough temperature. – The cooling energy is assumed to be equal to the energy for crystallization. The detailed model is described in the article by Franke et al. [50]. The cooling energy is estimated by means of the equation of Wellinghoff & Wintermantel [106].

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The minimum energy duty for distillation is determined by the well-known Underwood equations [93]. The results of are listed in Tab. 2.4. According to these results sequence 15 has the lowest energy demand, but the difference between sequence 15 and sequences 12, 13, 14, 16, and 17 is less than 5%. Tab. 2.4: Ranking of sequences after shortcut optimization [50]. Variant

QD − 1 Qtot, min

QD − 2 Qtot, min

Qc − 1 Qtot, min

Qc − 2 Qtot, min

Qtot Qtot, min





.

.

.

.

.





.

.

.

.

.





.

.

.

.

.





.

.

.

.

.





.

.

.

.

.





.

.

.

.

.





.

.

.

.

.





.

.

.

.

.





.

.

.

.

.





.

.

.

.

.





.

.

.

.

.





.

.

.

.

.





.

.

.

.

.





.

.

.

.

.





.

.

.

.

.





.

.

.

.

.





.

.

.

.

.





.

.

.

.

.





.

.

.

.

.

Rank

As apparent from Fig. 2.25 these sequences have in common that they purify the intermediate boiler P by crystallization. If heavy boiler O is separated by distillation first or the intermediate boiler P is not crystallized the energy demand is increased by at least 50%. The distillation sequences are ranked 13th and 16th with more than twice the energy demand. Based on these results variant 12 to 17 are selected for rigorous optimization with conceptual design models cutting the number of variants by two thirds. However, to validate the results of the shortcut screening

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Fig. 2.25: Developed hybrid distillation/melt crystallization sequences (bold letters: product on specification, italic letters: change of saturation region) according to [50]. Configuration 18 and 19 are the indirect and direct distillation sequence, which are not shown in the Figure.

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variants 1, 6, 18, and 19 are also evaluated by rigorous optimization in order to check if the MED is a reasonable criterion to select promising alternatives. Selection of the best process variant based on rigorous optimization of conceptual models Depending on the ratio of the non-crystallizing components in the feed, i.e. impurity, a second component precipitates when the crystallization path hits the eutectic trough. For example, in Fig. 2.26 the crystallization path intersects the eutectic

Fig. 2.26: Multi-stage crystallization with 3 stages (purification stage (1), feed stage (2), and stripping stage (3)) as well as phase composition and temperature depicted in the polythermal ternary diagram and phase diagram.

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trough E3–E4 and therefore component O crystallizes. This is illustrated for a threestage crystallization process. For process optimization a superstructure of the crystallization unit with a maximum number of five stages is considered as illustrated in Fig. 2.27. The conceptual melt crystallization model considers the trapping of impurities in the crystal phase. This complicated physical behavior is expressed in a very simplified way by a distribution coefficient which is the ratio between the impurity concentration in the solid and liquid phase (see [154], p. 93). For the distillation columns a superstructure based on a detailed MESH model is considered, as described in Section 2.3.3. A maximum number of 150 stages is allowed to avoid columns over 80 m or column splitting. Process optimization is performed by a MINLP approach minimizing TACs [50].

Fig. 2.27: Superstructure of the crystallizer for modeling different feed positions and number of stages (a) and reduced design resulting from optimization (b) [50].

The flowsheet of the economically best performing process configuration (variant 16) is illustrated in Fig. 2.28. The residue streams of the crystallizers C-1 and C-2 represent eutectic compositions and both crystallizers require few stages. C-1 involves one feed, one rectifying and one stripping stage, while crystallizer C-2 has only one feed and one stripping stage. On the other hand, the distillation columns require a tremendous number of stages. Column D-1 involves 136 stages with feed stage 64, while column D-2 requires 82 stages with feed stage 76. As expected from the large number of stages, both columns operate close to minimum reflux, with reflux ratios of 18.1 and 41.7.

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Fig. 2.28: Flowsheet of sequence 16 (the upper and lower numbers refer to the flow rates, feed stages, number of stages and reflux ratios before and after optimization, respectively) [50].

The results of the economic optimization of all considered variants are listed in Tab. 2.5. Variant 16, ranked 5th in the shortcut screening, is slightly more economically favorable over sequence 15 that was ranked 1st in the shortcut screening. However, while the ranking of the first six sequences has obviously changed the differences in economic performance is lass than 3% and they remain superior to the four sequences included for validation. Consequently, the proposed approach according to the process synthesis framework in Section 2.3.1 proves to be a systematic and reasonable approach for the fast and reliable design of hybrid separation processes. Yet, variants with low performance differences in the shortcut screening should be passed to the conceptual design stage. According to the computations the hybrid crystallization-distillation processes are expected to spare almost 75% of the costs of the direct and indirect distillation sequences.

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Tab. 2.5: Total annualized costs (TAC) of the rigorously optimized sequences [50]. CD − 1 Ctot, min

CD − 2 Ctot, min

Cc − 1 Ctot, min

Cc − 2 Ctot, min

Ctot Ctot, min



.

.

.

.

.



.

.

.

.

.



.

.

.

.

.



.

.

.

.

.



.

.

.

.

.



.

.

.

.

.



.

.

.

.

.



.

.

.

.

.



.

.

.

.

.



.

.

.

.

.

Variant

2.4.2 Case study 2: distillation and organic solvent nanofiltration Separation task: This case study considers the separation of heavy boilers from the product mixture of a hydroformylation reaction of long chained aldehydes. A feed stream of 4,500 kg/h composed of 70 wt.% light boiler (solvent in the reaction), 25 wt. % of the intermediate boiling product dodecanal and a small amount (5 wt.%) of a heavy boiling aldol condensation by-product. The separation shall produce a mixture with a maximum amount of 0.5 wt.% of heavy boilers and a recovery of decane/dodecanal should of 99%. The heavy boiling aldol condensates are represented by hexacosane, an n-alkane with the molecular weight of 367 g/mol. The design of a hybrid membrane-assisted distillation process follows the process synthesis framework (cf. Section 2.3.1), with some modifications, accounting for the experimental effort that is related to the screening and characterization of a suitable membrane. In order to integrate the experimental investigations in the early process development stage, a four-step design method according to Fig. 2.29 can be applied, in which model-based process analysis is applied prior to detailed experimental studies in order to perform directed experiments and reduce the experimental effort [119]. The approach can be extended to include further PI options [38].

95

2 Hybrid separation processes

Fig. 2.29: Modified four-step design approach for membrane-assisted hybrid processes [119].

Generation of process alternatives The generation of process variants begins with an analysis of the pure component properties that are listed in Tab. 2.6. Based on the differences in boiling points, molecular weight and melting points, distillation, nanofiltration, and crystallization are candidate separations. Especially given the large difference in boiling points and the absence of azeotropes, this wide-boiling mixture can be separated rather easily by means of distillation. However, the specific separation requires 95 wt.% of the feed to be separated as top product and the large temperature difference between top and bottoms product complicates direct energy integration, leaving distillation energy intensive. This however holds only true for the individual separation and might be rated differently if the heat duties can be integrated elsewhere in the overall process [22]. Focusing on the single separation, nanofiltration is an interesting option for a hybrid separation process, as temperatures below zero are avoided. For this separation solvent resistant membranes and a so-called organic solvent nanofiltration process is required. Tab. 2.6: Pure component properties of the chemical components considered [119]. Component

Formula

Molecular weight

Melting point

Boiling point

n-Decane

CH

 g/mol

− °C

 °C

n-Dodecanal

CHO

 g/mol

 °C

 °C

Hexacosane

CH

 g/mol

 °C

 °C

Besides a single distillation column (option I), or membrane separation process (option II), several hybrid configurations can be generated even for this two-product separation problem. The five considered process variants considered in this study are illustrated in Fig. 2.30. In combination with distillation OSN can be applied as a polishing step at the bottom of the column (option III), as pre-concentration prior to the column (option IV) or as purification step at the top of the column (option V). Because of the recovery of

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Fig. 2.30: Alternative process variants for the separation of the heavy boilers [119].

99%, which means that the hexacosane-rich stream has to be concentrated to more than 97 wt.%, not only the driving force for solvent flux is decreasing, resulting in large membrane areas, but also precipitation at the membrane may occur due to limited solubility. Consequently, despite the possible membrane separation such high concentrations cannot be reached with OSN at low temperatures and therefore options II and III can be eliminated as infeasible without further process evaluation, leaving option IV and V as possible hybrid process configuration. In option IV the feed stream processed by the distillation column can be dramatically reduced and thus the necessary heat duty. On the contrary, option V would result in an increased feed stream due to the retentate recycle. Since the separation in the distillation column is rather simple and the heat duty is dominated by the evaporation of the top product, the required heat duty will be higher than that of standalone distillation and option V can also be eliminated for this case study, leaving only option IV to be benchmarked with the single distillation column. Even though the order of the unit operations is fixed, the hybrid process still has many degrees of freedom, especially considering that the OSN separation is potentially performed in a multistage process. Here, a three-staged process, as illustrated in Fig. 2.31, is considered, a variable number of parallel pressure vessels in each stage and a variable number of up to eight membrane modules in each pressure vessel. Furthermore, interstage recycling of retentate is considered as an additional degree of freedom for each stage to ensure sufficient crossflow velocities and minimize concentration polarization.

Fig. 2.31: Illustration of flexible OSN membrane cascade model [119].

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A priori process analysis In accordance to the workflow depicted in Fig. 2.29 an a-priori process analysis is performed prior to experimental investigations, based on the assumption of a solutiondiffusion-based transport through the membrane. The flux Ji of a component i can be described as the product of the permeance Pi and the driving force ΔDFi (see eq. (2.1)). Ji = Pi · ΔDFi ,

i = 1, . . . , nc .

(2:1)

Here the driving force depends on the concentration and transmembrane pressure, while the permeance Pi is a lumped parameter representing sorption and diffusion characteristics that is generally determined experimentally for each membrane and chemical system. Based on the values of the component specific permeance values the permselectivity αsolvent, solute =

Psolvent, membrane Psolute, membrane

(2:2)

can be determined. While it is not influenced by changes in the driving force it provides an indicator of the selectivity of the membrane separation. Refer to Chapter 8 for further detail on modeling of OSN processes. Instead of experimentally determining the permeance and permselectivity values for a set of membranes first, a model-based screening is performed, in order to evaluate suitable ranges of these values for which a hybrid separation process can be superior to the benchmark process. Therefore, those values of permeance and permselectivity are determined, for which the hybrid process is economically compatible to the distillation processes. As expected form the large boiling point difference, a distillation column with only two theoretical stages is sufficient to reach both purity and recovery. The specific costs for this separation are evaluated as 5.9 €/t, whereas the largest cost contribution originates from the required heat duty (531 kW), which makes up more than 75% of the overall costs. The cost of the OSN-assisted process (option IV) is further determined in dependency of the unknown model parameters: – permeability of decane (Pdecane) – permselectivity (αdecane/hexacosane) – permselectivity (αdecane/dodecanal) The higher the permeability of decane, the less membrane area will be required and the higher the permselectivity αdecane/hexacosane, the higher the purity of the permeate stream. However, the results indicate that the permselectivity αdecane/dodecanal also plays a vital role, which is larger than intuitively expected. Optimization of the OSN-assisted process with varying αdecane/hexacosane, indicate costs from 5.9 to 5.1 €/t, for a permeslectivity for decane and dodecanal of 10, as illustrated in Fig. 2.32.

98

8

Stand alone distilation

CPT [€/t]

6

4

2

0

Energy demand reboiler [kW]

Mirko Skiborowski, Andrzej Górak

600

450

300

150

0 0

25

50

75

100

Permselectivity decan/hexacosane [–]

0

25

50

75

100

Permselectivity decan/hexacosane [–]

Fig. 2.32: Influence of αdecane/hexacosane on CPT (left) and energy demand (right) for αdecane/dodecanal = 1.1 ( ) and for αdecane/dodecanal = 10 ( ), compared to standalone distillation [119].

Only in the worst case does the OSN-assisted process result in slightly higher costs than the standalone distillation. In this case only decane is passing preferentially through the membrane and both, hexacosane and dodecanal are rejected. Given the large potential ranges of permeance and permselectivity for which the OSN-assisted process outperforms the standalone distillation the subsequent experimental investigations of possible membranes are justified. The a-priori process analysis indicates that membranes that reject hexacosane but are highly permeable for both decane and dodecanal should be chosen, and that the experiments should be performed up to a concentration of 10% of hexacosane, as this was the highest concentration in the retentate for the optimized processes.

Experimental investigation of membrane performance Only commercially available membranes suitable for nonpolar solvents are to be considered, and an according pre-selection is made based on the manufacturer data. The chosen membranes their material, and data concerning temperature stability are given in Tab. 2.7 [119]. Based on initial screening experiments the GMT ONF 1 membrane was selected for detailed experimental investigations, showing highest rejection for hexacosane and the second best flux. Separation experiments for the binary system of decane and hexacosane and the ternary system of decane, dodecanal and hexacosane were performed at different temperatures (20–40 °C) with resulting flux and rejection data presented in Fig. 2.33. Empirical correlations for the permeances of each component were determined on the experimental data with an additional term accounting for temperature dependence:

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Tab. 2.7: Membranes used in the experimental work [119]. Membrane

Company

Material

Maximal temperature

GMT ONF 

Borsig

PDMS

 °C

GMT ONF 

Borsig

PDMS

 °C

GMT NC 

Borsig

PDMS

 °C

Puramem™

Evonik

Polyimide

 °C

Puramem™S

Evonik

Silicon-coated polyimide

 °C

Pdecane = 944.4 · expð0.0181 · TÞ, Phexacosane = 17.8 · expð0.0362 · TÞ,

(2:3)

Pdodecanal = 38.3 · expð0.0392 · TÞ. As illustrated in Fig. 2.34, the identified model can describe total flux with less than 20% error, while rejection is described with less than 10% error. The developed model can further be used in the last step of the workflow (see Fig. 2.29) for process optimization. 100

64

90 Rejection [%]

48 32 16 0 15.0

80 70 60

22.5 30.0 37.5 Temperature [°C]

45.0

50 15.0

22.5

30.0 37.5 Temperature [°C]

45.0

Fig. 2.33: Influence of temperature on flux (left) and rejection (right) for: binary decane and hexacosane mixtures (2.5 wt.% hexacosane in feed ( ) 6.5 wt.% hexacosane in feed ( )) and ternary mixtures (6.5 wt.% hexacosane, 7.6 wt.% dodecanal in feed ( )) [119].

Process optimization In the final step of the workflow an optimal process design is determined based on detailed models. For the OSN separation a hierarchical and modular process model is utilized, that accounts for the different levels of detail described in Sections 2.3.3

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54 –20% 36 18 0 0

54 18 36 Flux experiments [kg h–1m–2]

Rejection simulation [%]

Flux simulation [kg h–1m–2]

1.00 +20%

+10% 0.75 –10% 0.50 0.25 0.00 0.00

0.25 0.50 0.75 1.00 Rejection experiments [%]

Fig. 2.34: Comparison between simulated and experimental flux (left) and rejection (right) for binary decane and hexacosane mixtures (sheet I ( ) and sheet II ( )) and ternary decane, hexacosane, and dodecanal mixtures ( ) [119].

and 2.3.4. The different elements of the model are further illustrated in the visualization in Fig. 2.35. The OSN-process model is based on the segregation of a single OSNstage into a number of parallel connected pressure vessels, consisting of a number of membrane module elements. It is assumed that the feed is distributed equally between the pressure vessels, and the total retentate in a stage is the sum of retentate streams of all pressure vessels. To account for local variations in pressure, temperature, concentration, and flow rate, a membrane module is discretized into equidistant intervals [155]. Additional models for the evaluation of membrane geometry and thermodynamic models are required to determine the performance of the membrane separation for a specific membrane material and module type. Further details concerning the OSN model can be found in the article by [119]. For the economic evaluation, the investment costs of the OSN separation are determined based on the required membrane area, assuming module costs of 200 €/m2 and a membrane price of 400 €/m2. The operating costs for the OSN process are composed of membrane replacement, assuming a lifetime of four years, and the costs for liquid compression. However, membranes costs and lifetime are further considered as uncertain parameters and a specific annual membrane price costmemb,ann [€/m2/a] is defined in order to investigate the effect of varying economic assumptions. Figure 2.36 shows that the resulting costs of the OSN-assisted separation for different assumptions, covering a range between 5.50 and 6.20 €/t. The OSN-assisted separation process is deemed economically attractive if the annual membrane price is less than 125 €/m2. However, even for low membrane prices of 50 €/m2 possible savings are not high and a decision-maker may prefer distillation due to higher reliability or better control properties. The information gained in this study forms a solid basis for an educated decision on the choice of process to be further

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Flowsheet level Membrane stage can be connected with other membrane stages or unit operations via streams in flowsheet

Membrane stage level Specification of number of pressure vessels and membrane elements cost calculation

Pressure vessel level Pressure vessel level is discretised in 2D elements

Discrete membrane element In each element, flux and driving force reducing effects are calculated

Flux Databank membrane

Aspen properties

Databank membrane modules

Fig. 2.35: The hierarchal structure of the OSN-model [119].

developed. A similar study has been conducted by Werth et al. [156, 157] for solvent recovery and deacidification in the refinement of non-edible and waste-cooking oils.

2.4.3 Case study 3: Distillation with vapor permeation and/or adsorption Separation task: The final case study focusses again on the dehydration of an aqueous ethanol stream from a fermentation broth that is first concentrated in a beer column. Due to the toxic effect of ethanol on the microorganisms [158], the fermentation produces a stream with a maximum ethanol content of 10 wt.%. Considering different applications, the purification of ethanol is to be evaluated for three ethanol mass fractions of the beer column top product with 45, 80 and 92 wt.% and production capacities of 25 000 and 250 000 m3/year. Furthermore, two product purities for the final ethanol

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Fig. 2.36: Influence of the specific annual membrane price on the cost of the OSN-assisted hybrid separation compared to standalone distillation [119].

product of 99.6 and 99.95 wt.% are to be considered. Thus, overall 12 different cases are to be evaluated, considering a product at atmospheric pressure and a temperature of 25 °C, considering all necessary auxiliary equipment, such as heat exchanger, and compressor. The design approach does again follow the process synthesis framework (cf. Section 2.3.1) considering a larger number of possible combinations. Unlike the previous two examples, the process variants are directly evaluated by means of detailed rate-based engineering models. While this skips the possible effort savings by means of shortcut and conceptual design models, it illustrates the applicability of the fourth level of the process synthesis framework.

Generation of process alternatives Evaluation of the pure component properties of ethanol and water listed in Tab. 2.8 suggests the suitability of distillation, based on the difference in boiling points, PV or VP membranes, based on the differences in the solubility parameter and dipole moment, crystallization, based on the difference in melting temperature, as well as adsorption, based on different kinetic diameters. The difference in solubility may as well be exploited in a solvent-based separation, such as heteroazeotropic or extractive distillation. The latter was already considered in the brief example in Section 2.3.2 (see Fig. 2.19). Further comparison with a PV-based process is provided in

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the article of Scharzec et al. [38], while Waltermann et al. [159] further evaluate the potential for energy integration for both extractive and heteroazeotropic distillation. The following discussion will focus on the combination of distillation, which is already applied for the pre-concentration in the beer stripper, with VP and adsorption. The latter being of special importance for reaching very high purities, such as the 99.95 wt.%, as the results of this case study will reveal. Tab. 2.8: Selected pure component properties of ethanol and water [38]. Pure component property

Ethanol

Water

Molecular weight [g/mol]





Boiling temperature [°C]





Melting temperature [°C]

−



Dipole moment [D]

.

.

Solubility parameter [MPa.]

.

.

Kinetic diameter [Å]

.

.

In combination with the beer stripper, these separation technologies are combined to yield five hybrid processes, which are further illustrated in Fig. 2.37. The first hybrid process is a combination of distillation and adsorption (D/Ad), in which an additional distillation column concentrates the ethanol close to the azeotropic composition (95.57 wt.% ethanol) [160], while purification is performed by adsorption using zeolites with a pore diameter of 3 Å, selectively adsorbing water. An operation as pressure swing adsorption (PSA) with a purge stream is considered to regenerate the zeolites. This is further considered as an established benchmark process [161]. The second hybrid process results from replacement of the adsorption with VP, resulting in the combination of distillation and vapor permeation (D/VP). A hydrophilic membrane processes the top vapor stream from the distillation column, purifying the ethanol as the retentate, while the permeate stream is recycled to the distillation for an economic operation. Despite several industrial applications [8, 162, 163] this kind of process is often viewed with skepticism, mainly because of the necessary large membrane area and doubts about membrane lifetime and robustness. The third hybrid process is combination of vapor permeation and adsorption (VP/Ad) in which the concentration column is replaced by the VP membranes, while the final dehydration that comes with vanishing driving forces for the membrane separation, is again performed by adsorption. Such a combination of membrane separation and adsorption is oftentimes used for the recovery of organic vapors [164].

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The fourth hybrid process replaces both the concentration column and the adsorber with vapor permeation (VP) resulting in a VP-assisted beer stripper. This bears the advantages of the energy efficiency of the VP, but retains the problem of the large membrane areas and high capital costs required to produce ethanol with the desired purity. Finally, the fifth hybrid process presents a combination of all three technologies by the integration of the vapor permeation into an existing distillation and adsorption process (D/VP/Ad). While it is the most complex configuration, it can result in an increase of energy efficiency and/or production capacity. The compact membrane modules can be positioned between the distillation and adsorption process, only concentrating the top product from the distillation above the azeotropic point, prior to the adsorption. As a result, a higher throughput for the adsorption column can be achieved in order to increase the production capacity. Distillation & adsorption

Vapour permeation & adsorption Ethanol Ethanol Ethanol water

Distillation Ethanol water Ethanol water

Recycle Recycle

Fermentation broth

Recycle VP/Ad&VP

Water

Distillation & vapour permeation Ethanol

Ethanol water

Recycle

Vapour permeation Ethanol water

Ethanol

Recycle Distillation & VP & adsorption Ethanol

Ethanol water

Recycle

Fig. 2.37: Hybrid processes for the dehydration of ethanol (Roth et al. [40]).

Process modeling and optimization All processes are modeled in ASPEN Custom Modeler™ (ACM), with distillation columns modeled as packed columns by means of a non-equilibrium model, as presented by Klöker et al. [165]. The VP model is based on the solution-diffusion model as described by Kreis & Górak [166], fitted to and validated against experimental data presented by Roth & Kreis [167]. A dynamic adsorption model is implemented for the PSA, based on the linear driving force approach [168]. For the simulation of the hybrid processes auxiliary equipment, such as heat exchangers, coolers, and

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105

compressors, is included. Further modeling detail and the assumptions on utilities, as well as the economic objective function for process optimization can be found in the article of Roth et al. [40]. While the D/VP and VP process variants are optimized by means of the combination of an evolutionary algorithm with process simulation models in ACM, those hybrid process configurations that include PSA are optimized manually based on a detailed process analysis by means of simulation studies, due to the complexity of the dynamic PSA model. The following paragraphs provide a brief discussion on the results for the individual hybrid processes, before presenting a final comparative process evaluation at the end.

Distillations and adsorption The combination of distillation and adsorption (D/Ad) is considered as the benchmark process and is illustrated in more detail in Fig. 2.38. This process requires no recycle to the beer stripper. Of special importance for the optimization of the hybrid process are the transfer variables between the distillation column and the PSA process. Specifically, the temperature, pressure, flow rate, and composition of the distillate and the recycle stream form the PSA.

Fig. 2.38: Flowsheet of the hybrid process distillation/adsorption [40].

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For process analysis an evaluation was performed for an ethanol mass fraction of 80 wt.% from the beer stripper, as well as both product purity specifications and capacities. An ethanol mass fraction of 1 wt.% in bottom and of 92 wt.% in distillate [169], an adsorption pressure of 3 bar and a purge ratio of 20% were assumed. Desorption pressure is determined by the lowest value that cooling water that can be used for the condensation of the purge. The heat exchanger superheats the vapor coming from the distillation to 130 °C to enhance the endothermic desorption process. The cycle time was set to 6 min based on literature values [161]. The resulting operating costs for the different scenarios are summarized in Fig. 2.39. Since PSA can achieve very high product purities with a moderate increase of adsorbent mass the increase in costs with higher product purity is negligible. However, increasing production capacity can significantly reduce the operating costs by up to 20%. The major contributor to the total energy consumption is beer stripper upstream of the D/Ad process, accounting for about 35%of the total energy consumption. Energy integration is therefore an important factor. Integrating the condenser of the distillation column and the product condenser of the PSA process with the reboiler of the beer stripper leads to a cost reduction of 20–24%.

Fig. 2.39: Operating costs of the D/Ad process for a feed ethanol mass fraction of 80 wt.% [40].

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107

Vapor permeation The VP process is modeled as a single stage process with multiple parallel membrane modules, as illustrated in Fig. 2.40. The process is optimized for all 12 different scenarios concerning the ethanol composition of beer stripper stream, product compositions, and capacities. The optimization determines use of and operating targets of an optional compressor, membrane feed, and permeate pressure, as well as the superheating temperature of the membrane feed. Independent of product purity and production capacity, the lowest operating costs are obtained for the pre-concentration by the beer stripper resulting in a mass fraction of 80 wt.% in the VP feed stream. Reducing the pre-concentration in the beer stripper to an ethanol mass fraction of 45 wt.% reduces the required energy consumption but increases the necessary membrane area and the capital costs significantly.

Fig. 2.40: Flowsheet of VP process for the dehydration of ethanol [40].

Increasing the pre-concentration in the beer stripper to 92 wt.% results in significantly increased energy consumption, while the membrane area can be moderately decreased. This is due to the reduction in relative volatility close to the azeotropic composition, which results in a considerable increase in the necessary reflux ratio for the beer stripper. The minimum operating costs are determined for the pre-concentration

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up to 80 wt.% and D to be 6.15 € cent/l for product purities of 99.6 wt.% and 6.67 € cent/l for product purities of 99.95 wt.%.

Distillation and vapor permeation Introducing the additional distillation column for pre-concentration between the beer stripper and the VP process (D/VP process), as illustrated in Fig. 2.41, provides additional degrees of freedom.

Fig. 2.41: Flowsheet of the hybrid process of distillation/vapor permeation [40].

Besides the design degrees of freedom of the VP process the optimization further determines the operating pressure of the distillation column, the column height, the feed and recycles position, as well as the reflux ratio. The results show that the distillation column and the VP process operate at the maximum operating pressure for the membrane to minimize the necessary number of membrane modules avoiding the need for a compressor. The permeate pressure is determined as the minimum pressure that allows for the utilization of cooling water such that the utilization of more expensive cooling brine is avoided. Superheating is applied only to the extent necessary to avoid condensation in the VP process. The total operating cost minimum of 6.28 € cent/l is obtained for the production capacity of 250 000 m3/year and a product purity of 94 99.6 wt.% ethanol. With

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increasing product purity, the total membrane area increases significantly and the total operating costs increase to 6.74 € cent/l. Thus, the additional distillation column does not provide a considerable benefit.

Vapor permeation and adsorption Based on the results for the previous three process configurations, the VP/Ad process, which is illustrated in Fig. 2.42, is expected to have a large potential for performance improvements. This process is again analyzed for a fixed ethanol mass fraction of 80 wt.% by means of simulation studies, considering the different product specifications and capacities. Again the main focus is placed on the transfer variables. The pressure, temperature, mass flow, and composition of the retentate and the recycle stream determine the required total membrane area, adsorbent mass, and ethanol yield, which is defined as the ratio between ethanol mass flow in product and in feed. The recycle stream is composed of the mixed permeate and purge streams.

Fig. 2.42: Flowsheet of the hybrid process of vapor permeation/adsorption [40].

Analogous to the results of the D/Ad process, high purities can be obtained without a significant cost increase, since only a small increase of adsorbent mass is necessary to achieve the high product purities. By increasing production capacity, the costs can be reduced by up to 20%, exploiting the effects related to the economy of scale for the distillation column and the PSA process. Energy integration can further reduce the costs by utilizing the hot product stream as heat source for the reboiler of the beer stripper, resulting in a further cost reduction of up to 10%. The energy requirements and total operating costs of the D/Ad, VP, D/VP, and VP/Ad process are compared in Fig. 2.43. The individual bars illustrate the relative

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energy consumption or operating costs in comparison to the D/Ad configuration, which was selected as benchmark. Especially the VP and VP/Ad process can significantly reduce the energy consumption by up to 30%. However, due to increased capital costs under the given assumptions, these energy savings result only in minor cost savings. For high capacities and high product purities only the VP/Ad process is economically attractive in comparison with the D/Ad process. However, this might change if the costs for energy increase, or the costs and lifetime for the membranes decrease.

Fig. 2.43: Comparison of resulting energy consumption and total operating costs for the optimized process designs for the D/Ad, VP, D/VP, and VP/Ad configurations [40].

Distillation, vapor permeation and adsorption Finally, the integration of VP membrane separation into an existing D/Ad process is investigated. A flowsheet of the D/VP/Ad process is shown in Fig. 2.44. While this configuration is not competitive as a new process, a retrofit might be interesting to increase the performance in terms of energy efficiency and/or capacity. Therefore, the scenario with 80 wt.% ethanol feed composition, 96 wt.% product purity, and 25 000 m3/year is investigated. The addition of the VP separation allows to reduce the reboiler duty of the column by 34% compared to the D/Ad process. However, since less heat is available for heat integration, the total energy consumption for a heat integrated design increases by 0.1 MW compared to the D/Ad process, also resulting in increased operating costs. Nevertheless, the product purity can be increased to 99.99 wt.% by increasing the ethanol mass fraction in the adsorption feed. On the other hand, the capacity can be nearly doubled, without compromising product purity.

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Fig. 2.44: Flowsheet of the hybrid process of distillation, vapor permeation, and adsorption [40].

Process evaluation The energy-based and economic comparison of the different membrane-assisted hybrid processes with the benchmark D/Ad process leads to the following conclusions: – While the membrane-assisted processes (VP and VP/Ad) provide a limited potential for cost reduction, they provide a significant potential for improving energy efficiency. The latter might result in cost savings in case energy costs rise or membrane costs drop. The effect of such changing prices can again be evaluated by the presented models and optimization approaches. – Overall, the best processes operate based on a pre-concentration in the beer stripper up to 80 wt.% of ethanol, do operate without expensive cooling brine or a compression prior to the VP process and make use of energy integration. – The results emphasize the advantage of the PSA process as end-of-pipe technology in order to produce highly purified ethanol with a small increase in adsorbent mass. The VP/Ad process is a promising alternative to the conventional process, while the process does not benefit from an additional distillation column.

2.5 Take-home messages – Hybrid separation processes are defined as the combination of at least two different, externally integrated unit operations, which contribute to one and the same separation task by means of different physical phenomena and which overcome the limitations of the single unit operations by means of synergetic effects. – Hybrid separation processes are potentially viable options in case separation by single unit operation is limited, due to separation boundaries or insufficient driving

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forces, but also offer potential performance improvements if a separation by means of an individual unit operation or a simple sequence is feasible, but expensive. – The selection of potential unit operations and their combination in form of hybrid separation processes can be accomplished by an identification of generally suitable options and bottlenecks of the individual separation techniques. Thermodynamic insight, based on the analysis of chemical, physical, and transport properties and visual analysis of the equilibrium behavior are important tools for process synthesis of hybrid processes. – Mathematical tools for the identification of separation boundaries, miscibility gaps, and solvent selection (CAMD) further enable the synthesis of hybrid separation processes for the complex multicomponent mixtures and the identification of suitable process configurations and MSA. – Due to the complexity of hybrid separation processes conceptual process design should be separated into a hierarchy of steps, taking into account the increasing information requirements and availability for an increasing level of modeling detail. While shortcut and conceptual design models can be used to narrow down the number of potential process variants a final equipment design should always be based on detailed (rate-based) engineering models.

2.6 Quiz 2.6.1 Hybrid separation processes Question 1. In which way are hybrid separation processes distinguished from simple sequences and multifunctional units? Provide an illustrating example. Question 2. On which scales is process intensification performed by means of hybrid separation processes?

2.6.2 Synthesis of hybrid separation processes Question 3. What is the general idea of using thermodynamic insight for the synthesis of separation processes? Question 4. What kind of hybrid separation process might be suitable for the separation of a ternary mixture of acetone, isopropanol, and water, taking into account the properties listed in Tab. 2.9?

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Tab. 2.9: Pure and mixture properties for acetone, isopropanol and water. Acetone

Isopropanol

Molecular weight (g/mol)

.

.

Boiling point (°C)







Melting point (°C)

−

−



Dipole moment (D) Solubility (MPa Azeotropes Miscibility

/

)

.

.

.

.

Water .

. .

minimum azeotrope at  atm (./.) fully miscible

Question 5. Propose two different hybrid separation processes based on the T-x diagram in Fig. 2.45.

Fig. 2.45: T-x diagram for a hypothetical binary azeotropic mixture.

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Question 6. Propose a hybrid separation process for the ternary mixture, for which the residue curve map is illustrated in Fig. 2.46.

Fig. 2.46: Residue curve map for a hypothetical ternary azeotropic mixture.

2.6.3 Conceptual design of hybrid separation processes Question 7. What are the different levels of the presented process synthesis framework and what is the idea behind this structured approach to conceptual process design? Question 8. What is most important when selecting a suitable model for a specific application? Question 9. What is the benefit of optimization-based design methods and why are they of special importance for the design of hybrid separation processes? Question 10. What are the different methods for process optimization and in which way do they differ? Question 11. What is the major difference between conceptual design and rate-based engineering models?

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2.7 Solutions 2.7.1 Hybrid separation processes Solution to Question 1: Hybrid separation processes are externally integrated, which distinguishes them from internally integrated separations and they are characterized by a mutual interdependency of the involved unit operations, which distinguishes them from sequential configurations. An illustrating example is given in Fig. 2.47 for a separation process based on a distillation column and a membrane separation. The separation of A, B, and C is fully decoupled between the membrane and the distillation column in the sequential configuration, while both are depending on each other in the hybrid configuration. In the internally integrated separation, the membrane separation is performed by exchanging part of the stripping section with a membrane module.

Fig. 2.47: Illustration sequential configuration (left), hybrid configuration (center), and internally integrated configuration (right) of a distillation column and a membrane separation.

Solution to Question 2: Since hybrid separation processes combine different unit operations, they primarily perform process intensification on the process and plant scale. However, any hybrid separation process that makes use of an additional auxiliary 101 compound, like heteroazeotropic distillation and hybrid liquid-liquid extraction and distillation processes, or that makes use of a separating material, like adsorption or membrane-assisted distillation processes, also addresses the phase and transport scale, as well as the fundamental and molecular scale.

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2.7.2 Synthesis of hybrid separation processes Solution to Question 3: The general idea of using thermodynamic insight is to evaluate pure component and mixture properties, such as the existence of azeotropes and miscibility gaps, in order to determine potentially suitable separation techniques and combine those in an optimal fashion, maximizing the synergies between them. Solution to Question 4: Taking into account that there are no miscibility gaps and that there is only one binary azeotrope between isopropanol and water, hybrid separation processes like heteroazeotropic distillation and the utilization of liquidliquid extraction require an additional solvent and are therefore initially discarded. Since there is no azeotrope which limits the separation of acetone from the ternary mixture and since the boiling points are considerably different, the separation of acetone is considered by distillation, leaving the separation of isopropanol and water to be further determined. According to the melting points, water might be separated by means of crystallization, but only at high costs due to the requirement of a refrigerant. Due to the different molecular weights and the difference in the solubility parameters, membrane separations like organic solvent nanofiltration and pervaporation are potential options. Consequently, the sequential configuration and the hybrid separation process illustrated in Fig. 2.4 can be proposed as potentially suitable separation processes based on the properties listed in Tab. 2.7. Solution to Question 5: The mixture illustrated in Fig. 2.45 is similar to the one presented in Fig. 2.8 and consequently the potential hybrid separation processes are quite similar to the ones illustrated in Fig. 2.8. The difference between the two mixtures relates to the binary azeotrope, which is now a maximum boiling azeotrope at low composition of component A. The two different hybrid separation processes based on the combination of distillation and crystallization are illustrated in Fig. 2.48.

Fig. 2.48: Illustration of two potential hybrid distillation-crystallization processes for the hypothetical binary azeotropic mixture.

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Solution to Question 6: The ternary mixture, for which the RCM is illustrated in Fig. 2.46, is characterized by one homogeneous minimum boiling azeotrope between components A and B, and by one heterogeneous minimum boiling azeotrope between components B and C. The large miscibility gap can be utilized to cross the illustrated distillation boundary by means of liquid phase splitting. Consequently, a hybrid separation process by means of distillation and decantation presents a suitable process variant. This feed mixture can therefore at first be separated in a simple column, producing pure A as distillate and a binary mixture of B and C as bottoms product. The bottoms product can further be processed in a sequence of two stripping columns and a decanter, in which the decanter performs the liquid-liquid separation of the top vapor streams of both strippers, which each perform the purification of B and C on opposite sides of the azeotrope, similar to the configuration shown in Fig. 2.7. Further integrating this configuration results in the configuration presented in Fig. 2.49, in which a distillation column with a decanter in a side stream configuration is extended by an additional stripper, which performs the purification of component B. This configuration can be interpreted as an extension of the configuration presented for a slightly different mixture in Fig. 2.11.

Fig. 2.49: Residue curve map (RCM) and mass balance lines for a hypothetical ternary azeotropic mixture and a potential hybrid separation process.

2.7.3 Conceptual design of hybrid separation processes Solution to Question 7: The presented process synthesis framework is composed of four sequential levels: (i) generation of variants, (ii) rapid screening with shortcut models, (iii) optimization-based design with conceptual models, and (iv) optimizationbased design with rate-based engineering models. The general idea behind this

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structured approach is to account for the usually limited availability of data and resources by using simplified shortcut methods for a rapid screening of promising process variants, before evaluating these variants in further detail by means of conceptual and rate-based models. Solution to Question 8: When selecting a suitable model, it is crucial to know and understand the underlying assumptions, since the reliability of the results tremendously depends on these assumptions. Solution to Question 9: Optimization-based design methods allow for a simultaneous determination of structural degrees of freedom, like the interconnection of different unit operations, or the number of separation stages, and operational degrees of freedom, like pressure levels and heat duties. This is of special importance in the design of hybrid separation processes, due to the high level of interconnection and interdependency. Solution to Question 10: Process optimization can either be performed by means of a deterministic gradient-based algorithm, or by means of a metaheuristic, like an evolutionary or genetic algorithm, combined with a process simulator. While the former approach is computationally efficient and provides locally optimal solutions, the latter is not limited to local optima and can directly be connected to existing simulation models, as in commercial process simulators, but may require considerably larger computational effort without providing any mathematical guarantees of optimality. Solution to Question 11: Conceptual design models mostly rely on equilibriumbased calculations for performance estimation, coupled with sizing calculations for cost estimation based on empirical correlations and values like the height equivalence of a theoretical plate (HETP) for packed distillation columns. Detailed ratebased models assume a continuous transfer of mass and energy between both phases in contact, which in addition to thermodynamic equilibrium, also requires knowledge of transport properties like viscosity, diffusivity, surface tension, and thermal conductivity in order to quantify mass and heat transfer. Application of the latter models provides an increased level of detail, which might be indispensable for sufficiently accurate equipment design. However, it also necessitates the specification of the type of equipment and the knowledge of the necessary properties and correlations.

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Moreno Ascani, Christoph Held

3 Thermodynamics for reactive separations 3.1 Fundamentals Thermodynamics is historically the science of energy transformation [1]. It provides a rigorous mathematical framework that establishes the direction and extent of the evolution of every spontaneous process. The principles of classical thermodynamics, generalized in the first and second law of thermodynamics, allow engineers to design processes and machines for heat transfer or to convert heat in work, such as steam or combustion engines, heat exchangers, evaporators, dehumidifiers, or condensers. The first law of thermodynamics imposes the conservation of energy in each process by stating that the change of the internal energy, U, stored in a system is equal to the sum of heat, Q, and work, W, transferred through the system boundaries (see Section 3.1.2). The second law restricts the direction in which processes can occur by stating that each process in an isolated system must evolve in the direction of entropy maximization (see Section 3.1.2). However, several systems of great scientific interest are composed by multiple components, which can lead to a homogeneous phase or split in different phases: examples are the air in contact with the blood in animal’s lungs, the dissolution of solid pharmaceuticals in the digestive system, crystal precipitation from a supersaturated solution, or sugar leaching from beets. Furthermore, multicomponent mixtures are ubiquitous in the chemical industry, and knowledge of their thermodynamic behavior plays a central role in the design of separation processes. In multicomponent mixtures, besides heat and work, matter too can be exchanged and transformed: components can be transferred across the phase boundaries; they can split into different phases, and even react into new substances with different physicochemical properties. The principles of classical thermodynamics, although generally valid, lack the formalism to describe the behavior of multicomponent chemical systems [2]. This problem was conceptually solved by J.W. Gibbs [3] through the introduction of the number of moles ni of each component, i = 1,2, . . .,N as further state variables, and of the chemical potential μi of a component, i, to express the dependence of the internal energy on ni (see Sections 3.1.2–3.1.5). The formalism introduced by Gibbs and the principle of entropy maximization allow the definition of useful equilibrium conditions, which correspond to the most stable internal configuration (number and composition of all coexisting phases, value of caloric properties, and state variables in each phase) of a system, with respect to external constraints. Yet, the same thermodynamic framework that is more than 100 years old, coupled with advanced thermodynamic models (Section 3.2), is now used in every simulation package to calculate the stable phases, their composition, and other state variables (such as pressure, density, or even heat capacity) at equilibrium of process streams in each apparatus of a chemical plant. The thermodynamic framework is the basis of https://doi.org/10.1515/9783110720464-003

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many of the modeling and design methods explained in the chapters of this book. The equilibrium stage model, formulated for classic and reactive separation processes assumes that two or more streams (gaseous, liquid, or even solid) within a unit operation reach thermodynamic equilibrium after contacting each other (see Chapter 4 for an exhaustive description). Graphical and algorithmic tools for inspection of potential separation processes (see Chapters 2 and 4–7) such as phase diagrams, reactive and nonreactive residual curve maps (RCM) or distillation line maps (DLM) are generated by computing the mass balance, together with the phase and chemical equilibrium conditions described in the present chapter. Modeling the density is required, for instance, for modeling of two-phase flows (see Section 3.3 of the book Rotating Bed Separation), and can be accomplished using an appropriate thermodynamic model (see Section 3.2). Even nonequilibrium processes such as kinetically controlled reactions and diffusion can be formulated using a thermodynamics-based approach, since the chemical potential (or better, its gradient) represents the driving force of a chemical reaction and of mass transfer (see Chapters 6–9) and Sections 2.1.1 and 8.3.1 of the book Rotating Bed Separation. For a more fundamental understanding, this section introduces the framework of phase-equilibrium thermodynamics. In Section 3.1.1, general (but also more specific) formulations of the phase-equilibrium problem are introduced, whereas Section 3.1.2 applies the first and second laws of thermodynamics to derive equilibrium conditions of a homogeneous closed system. Starting from an isolated (adiabatic isochoric) system, three further thermodynamic functions are introduced in Sections 3.1.2 to treat other systems of interest, namely the adiabatic isobaric, the isothermal isobaric, and the isothermal isochoric. In Section 3.1.3, equilibrium conditions in a heterogeneous system are derived as well as the Gibbs phase rule. In Section 3.1.4, two ideal systems, namely the ideal-gas mixture and the ideal mixture of liquids will be defined, and the phase-equilibrium conditions will be reformulated, based on two further thermodynamic functions: the fugacity and the activity. In Section 3.1.5, the equilibrium condition of chemical reacting systems will be introduced. In Section 3.2, the most relevant thermodynamic models are introduced, which are needed to obtain a quantitative solution of the phase equilibria and of the chemical equilibrium problem.

3.1.1 The phase-equilibrium problem Figure 3.1 resumes the essence of the phase-equilibrium problem of a general multicomponent system. The system of interest is enclosed by boundaries through which the system can exchange heat, work, and, in some cases, matter, with its environment. In the interior of the system, one or multiple homogeneous phases can coexist at contact and can interchange matter and energy (heat and work) to each other. To simplify the mathematical treatment of the investigated system, the effect of external force fields (gravitational, centrifugal, electrostatic, or magnetic fields) as well as the

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effect of phase boundaries through interfacial tensions are (usually) neglected, and only bulk properties of each phase are considered. For a discussion about including further types of work in the thermodynamic treatment, refer to the work of Alberty [4]. At thermodynamic equilibrium, there is no net flux of work, heat, or matter through the system boundaries as well as from one phase to the other; the amount of each phase and the value of each intensive property (composition, density, internal energy, enthalpy, entropy, etc.) within each phase attain a constant value [2]. Furthermore, temperature and pressure, which are, respectively, the driving forces for heat and mechanical work, assume a constant value within the entire system.

Fig. 3.1: Abstraction of a real system: each phase (1, . . ., π) is treated as a homogeneous system, which can exchange work, heat, and matter with other phases in the interior of the system. Furthermore, energy (in the form of heat or work) and matter can be transferred through the system boundaries. The phase-equilibrium problem is solved by determining the pressure, temperature, and the number of moles of each component in each phase.

The phase-equilibrium problem of a multiphase mixture of N components is solved, once the number of stable phases and N + 2 state variables for each phase at equilibrium (see Sections 3.1.2 and 3.1.3) are determined. Although the choice of state variables is arbitrary, usually N mole numbers (one for each component) plus the temperature and pressure are chosen. The advantage of choosing temperature and pressure, compared to other state variables, is their easy accessibility by measurement and because their value at equilibrium should be the same for each phase (conditions of thermal and mechanical equilibrium, see Section 3.1.3). All the other thermodynamic properties of each phase (density, internal energy, enthalpy, entropy, etc.) can then be calculated using exact mathematical relationships given by the thermodynamic framework, provided that a thermodynamic model is available (Section 3.2). If only the intensive properties of the system are of interest, then N + 1 state variables (Temperature, pressure, and N − 1 concentrations) at equilibrium should be provided for each phase (the “extension” or “size” of the system is, then, not considered).

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Through the abstraction given by Fig. 3.1, several systems of industrially relevant interest can be modeled, for example: – The two-phase vapor-liquid system in each tray of a distillation column (see reactive distillation in Chapter 5). – The two-phase system of a flue gas in contact with the solvent in an absorption column (see reactive separations in Chapter 4). – Two liquid phases in contact in an extraction column (see Chapter 6). – The solid-liquid equilibrium in a crystallizer (see hybrid processes in Chapter 2). – A three-liquid phase water–monomer–polymer polymerizing emulsion. The minimal amount of information about the system, which should be known in advance to solve the phase-equilibrium problem, is given by the Gibbs phase rule (Section 3.1.3). Some formulations of the phase-equilibrium problem that thermodynamics seeks to solve are, for example: – Given the composition ðz1 , z2 , . . . , zN Þ of a feed stream of N components at given conditions (temperature and pressure), find the number of stable phases π which are present at equilibrium, their amount Φj and their equilibrium composition, ðx1 , x2 , . . . , xN Þj , j = 1, 2, . . . , π. This problem is also known as flash calculation. – Given the composition of a liquid mixture, ðx1 , x2 , . . . , xN Þ and pressure of a liquid phase, find the boiling temperature T LV and the composition of the vapor phase, ðy1 , y2 , . . . , yN Þ in equilibrium with the liquid mixture at T LV . This problem is also known as bubble-point calculation. – Given a solid compound at a given temperature, T, and pressure, p, and a liquid mixture, ðx1 , x2 , . . . , xN Þ, find the maximal solubility of this compound in the given mixture at the given condition. – Given a chemical reactor containing a homogeneous mixture at a given temperature, T, pressure, p, and initial composition, ðz1 , z2 , . . . , zN Þ with one or more
 ongoing chemical reactions, find the equilibrium composition, z1* , z2* , . . . , zN* . Process simulation may require performing a flash or bubble-point calculation thousands of times within a specific unit operation. This requires robust numerical approaches to guarantee reliable convergence and computational efficiency at the same time. The focus of this chapter lies, however, on the thermodynamic fundamentals, which are the basis of all the phase-equilibrium formulations. For choosing the most appropriate numerical procedure to solve a specific problem, refer to the specific literature [5, 6].

3.1.2 Fundamental relation of the internal energy The first and second laws of thermodynamics provide limitations about the extent and the direction in which every spontaneous process occurs. Ultimately, they allow

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formulating general conditions of thermodynamic equilibrium of any system. According to the second law, the equilibrium state of an isolated system is characterized by a global maximization of its entropy, S. Thus, it follows that at equilibrium, two necessary (but for the global maximum, not sufficient) conditions should be satisfied, characterized mathematically by eqs. (3.1) and (3.2). dS = 0

(3:1)

d2 S < 0

(3:2)

The first condition imposes that the entropy does not change spontaneously at equilibrium. The second condition is a “stability requirement,” that is, the system is stable toward infinitesimal perturbations from the equilibrium condition. Although defined for an isolated system, the second law can be applied to every system, if in eqs. (3.1)–(3.2), the sum of the entropy of system Ssys and environment Senv are considered (eq. (3.3)). The entropy change of the system is related to the heat transferred to the system δQ and the irreversible work δW irr at the temperature T as shown in eq. (3.4): S = Ssys + Senv dS =

δQ + δW irr T

(3:3) (3:4)

The first law for a closed and homogeneous system is defined, in differential form, as follows: dU = δQ + δW

(3:5)

The total work δW performed by or to the system is given as the sum of reversible, dW rev and irreversible δW irr work. By combining eqs. (3.4) and (3.5) and expressing the infinitesimal reversible work as dW rev = − pdV, eq. (3.6) can be obtained, which relates the state variables internal energy, U, entropy, S, and volume, V, of a closed homogeneous system. dU = TdS − pdV

(3:6)

Equation (3.6) can be extended to open systems (such as each of the single phases in Fig. 3.1) by introducing the mole number of each component as an additional state variable. The exchange of matter through the system boundaries of a homogeneous system is related to the change of the internal energy through the chemical potential μi of each component, i. This is defined, for a generic component, i, as the change of internal energy upon introducing or removing one mole of the component i, at constant conditions and by keeping all the other natural variables of the
 internal energy S, V, n j ≠ i constant. In differential form, this is formulated as

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∂U Þ = μi ðS, V, n ∂ni

 (3:7) S, V, nj ≠ i

Using the chemical potential, eq. (3.6) can be extended to open, homogeneous systems in the form of the Gibbs fundamental equation (eq. (3.8)): dU = TdS − pdV +

N X

μi dni

(3:8)

i=1

Equation (3.8) is a very important equation, since it couples the first and second law in a homogeneous system, which can exchange matter and energy with its environment. After defining the Gibbs fundamental equation for open systems, we turn our attention again to the equilibrium conditions provided by eqs. (3.1) and (3.2). In fact, further useful equilibrium conditions can be derived by imposing constant values of one or more state variables (this will also be shown in Section 3.1.2). From the second law of thermodynamics (dS ≥ 0 in each spontaneous process) it can be shown that, at equilibrium, if the natural variables of the internal energy Þ are maintained constant, then the internal energy of the system must be ðS, V, n globally minimized (mathematical derivation not shown here). At the global minimum of the internal energy, eqs. (3.9) and (3.10) (which are also necessary but not sufficient conditions) hold: ðdUÞS, V, n = 0
2  d U S, V, n > 0

(3:9) (3:10)

Due to the equilibrium conditions (3.9) and (3.10), the internal energy is also called thermodynamic potential. Other thermodynamic potentials will be introduced in the following paragraphs of this section. Through the Gibbs fundamental equation, derived from the first law and the definition of entropy, the internal energy of a system is defined as function of N + 2 independent state variables (entropy S, volume V, and N mole numbers ni ) by eq. (3.11). However, the molar internal energy, u (eq. (3.12)) is a function of N + 1 intensive variables (molar entropy s, molar volume, v and N−1 molar fractions xi ) and independent of the extension of the system: the corresponding extensive internal energy is simply rescaled through the overall mole number n (see eq. (3.12)): U = U ðS, V, n1 , n2 , . . . , nN Þ u=

U S V ni = uðs, v, x1 , x2 , . . . , xN − 1 Þ, s = , v = , xi = n n n n

(3:11) (3:12)

By knowing the functional dependence of the internal energy on N + 2 state variables of a system (only N + 1 by considering only intensive properties), all the other thermodynamic properties are uniquely fixed and can be calculated. For instance,

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if a function of the internal energy U as well as the value of its functional variables Þ are known, then the pressure, p, and temperature, T, of the system can be ðS, V, n calculated as partial derivatives of the internal energy:     ∂U ∂u = (3:13) T= ∂S V, n ∂s v, x     ∂U ∂u = (3:14) −p= ∂V S, n ∂v s, x Further thermodynamic potentials The fundamental relation of the internal energy (eq. (3.8)) condenses the information of the first and second laws of thermodynamics and allows defining an equilibrium condition of a homogeneous system at constant value of the respective state variables of the internal energy (eqs. (3.9)–(3.10)). However, it contains the volume and the entropy as state variables, which are not easily accessible. Most of the natural processes, for instance, occur at constant pressure (or the system pressure is, at least, known) while the volume can change, without its exact value over time being known. For this reason, a further thermodynamic potential, the enthalpy (denoted by the letter, H), was introduced. The enthalpy is defined, starting from the internal energy, by transforming the Þ into ðS, p, n Þ through partial Legendre transcorresponding variable space ðS, V, n formation [4, 7], which is expressed as follows: H ≡ U + pV

(3:15)

From eqs. (3.15) and (3.8), the fundamental relation of the enthalpy can be defined (eq. (3.16)): dH = TdS + Vdp +

N X

μi dni

(3:16)

i=1

Like the Gibbs fundamental relation for the internal energy, eqs. (3.8) and (3.16) contain the entire information of the first and second law of thermodynamics. However, as opposed to the internal energy, the enthalpy is a function of the state variables entropy, pressure, and number of moles of all components: Þ H = H ðS, p, n

(3:17)

The chemical potential is also defined for the enthalpy (eq. (3.18)) as the change of the extensive enthalpy of the system upon adding one mole of component, i, in the system at values of all the other natural variables (entropy, pressure, and constant mole number of all components, except i):

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∂H Þ = μi ðS, p, n ∂ni

 (3:18) S, p, nj ≠ i

Necessary equilibrium conditions analogue to eqs. (3.9) and (3.10) for a homogeneous system can be derived for the enthalpy when the corresponding natural variÞ are kept constant: ables ðS, p, n ðdHÞS, p, n = 0
2  d H S, p, n > 0

(3:19) (3:20)

The advantage of using the enthalpy instead of the internal energy (which would naturally follow from the first law) to balance real systems is that the pressure is, in general, easier accessible than the volume, whereas the term, TdS, in eq. (3.16) maintains the meaning of the sum of exchanged heat and irreversible work as in eq. (3.8). The change in enthalpy of a system can be directly measured as the heat absorbed or released by the system in a reversible process occurring under isobaric conditions. Thus, the standard enthalpy (i.e., the enthalpy change at tabulated conditions, usually at constant, T and p) is reported for many processes: examples are the enthalpy of vaporization, the melting enthalpy, or the reaction enthalpy. Analogous to the enthalpy, two more thermodynamic potentials, the Gibbs energy and the Helmholtz energy (denoted, respectively, by G and A) were introduced as partial Legendre transformation of the enthalpy and internal energy, respectively: G ≡ H − TS

(3:21)

A ≡ U − TS

(3:22)

Based on eqs. (3.21) and (3.22) the corresponding fundamental equations for G and  and T, V, n ) follow: A and their respective functional variables (T, p, n dG = − SdT + Vdp +

N X

μi dni

(3:23)

i=1

Þ G = GðT, p, n dA = − SdT − pdV +

(3:24) N X

μi dni

(3:25)

i=1

Þ A = AðT, V, n

(3:26)

, the temperIn case of the Gibbs energy, the state variables are the mole number, n ature, T, and the pressure, p. That is, the state variable entropy, S (which is also very difficult to quantify) in the enthalpy expression is substituted by the far more practical temperature, T. In phase-equilibrium calculations, the Gibbs energy is, by far, the most important and mostly used thermodynamic potential. The reason is

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that in almost all practical phase-equilibrium problems, the temperature and pressure are known, and they are assumed (independent on the considered phases) to be constant values within the system. The equilibrium condition of a system at isothermal and isobaric conditions is that its Gibbs energy reaches its global minimum, at which the following equations hold: ðdGÞT, p, n = 0
2  d G T, p, n > 0

(3:27) (3:28)

Mathematically, the equilibrium conditions stated by eqs. (3.27)–(3.28) correspond to the state of the system at which the entropy of the system and the environment is maximized, according to the second law (eqs. (3.1)–(3.2)). However, the reformulation based on the minimization of the Gibbs energy allows deriving equilibrium conditions based exclusively on the properties of the system, without taking the entropy of the environment explicitly into account (which would be rather impossible to quantify).

3.1.3 Equilibrium of a heterogeneous closed system In the previous sections, different equivalent conditions for thermodynamic equilibrium of closed homogeneous systems were derived, based on the first and second law of thermodynamics. Each of the derived equilibrium conditions (adiabatic isochoric (eqs. (3.9)–(3.10)), adiabatic isobaric (eqs. (3.19)–(3.20)), isothermal isobaric (eqs. (3.27)–(3.28))) is valid at constant value of the functional variables of the respective thermodynamic potential. The next step is to consider internal rearrangements. As introduced in Section 3.1, most relevant systems in real life are not homogeneous: a liquid can, under certain conditions, split into two liquid phases, a solute can crystallize, and a vapor phase can appear or disappear. As a result, the specification of N + 2 state variables is not sufficient, since each phase is characterized by different thermodynamic properties, among which the concentration of each component also differs. However, the global minimization of the Gibbs energy (eqs. (3.27)–(3.28)) as equilibrium criterion holds for every closed system at given temperature, T, and pressure, p, independent of the internal rearrangement (the same holds, of course, for the other thermodynamic potentials, when the respective functional variables are kept constant). The solution of the phase-equilibrium problem of a multicomponent multiphase system described in Section 3.1.1 can be obtained by considering each single phase as an open homogeneous system, which can be described independently by the thermodynamic functions introduced in Section 3.1.2. By considering a heterogeneous closed system under isobaric and isothermal conditions, the Gibbs energy of each homogeneous phase, (j), is related to the chemical potential of each component, i, as follows [7]:

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Gð jÞ =

N X i=1

ð jÞ

ni

 ð jÞ  ∂G ∂ni T, p, n

= j≠i

N X i=1

ð jÞ ð jÞ

ni μi

(3:29)

Therefore, the overall Gibbs energy of a closed heterogeneous system is given as the sum of the Gibbs energy of each homogeneous subsystem represented by the single phases. For a system containing π phases, the Gibbs energy is given as follows: G = Gð1Þ + Gð2Þ +    + GðπÞ =

π X N X j=1 i=1

ð jÞ ð jÞ

ni μi

(3:30)

Each single phase is considered as open homogeneous system in contact with the other phases. Each phase can exchange matter with other phases, while the overall mole number of each component remains constant within the system: π X j=1

ð jÞ

ni = const ∀i = 1, . . . , N

(3:31)

Temperature and pressure are assumed to be constant within the entire system (in other words, thermal and mechanical equilibrium are already attained). The task, now, is to find the most stable configuration, which means the value of mole numð jÞ ber ni of each component, i, in each phase, j that minimizes the value of the Gibbs energy given by eq. (3.30), while satisfying the mass balance constraints (eq. (3.31)). The phase-equilibrium calculation is, thus, reformulated as a constrained optimization problem, which is represented as follows: min G =

π X N X

ð jÞ ð jÞ

ni μ i

(3:32)

ni = 0 ∀i = 1, . . . , N

(3:33)

ni ≥ 0 ∀i = 1, . . . , N ∀j = 1, . . . , π

(3:34)

n

s.t. ni, tot −

j=1 i=1 π X j=1

ð jÞ

ð jÞ

The previous optimization problem can be directly implemented and solved using a simulation program, once a thermodynamic model to calculate the chemical potenð jÞ tials μi is provided. A necessary (but, again, not sufficient) condition that should be fulfilled at the global minimum can be derived by solving the previous optimization problem, using the method of undetermined Lagrange multipliers. The result is given as follows: β

μαi = μi ∀α, β = 1, . . . , π ∀i = 1, . . . , N

(3:35)

Equation (3.35) builds, together with the equality of temperature and pressure in each phase (eqs. (3.36)–(3.37)), the necessary condition of phase equilibrium of a closed heterogeneous system:

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137

T α = T β ∀α, β = 1, . . . , π

(3:36)

pα = pβ ∀α, β = 1, . . . , π

(3:37)

The chemical potential represents the driving force for transfer of matter between different regions of spaces. Thus, the condition given by eq. (3.35) is also called condition of chemical equilibrium, since for each component, the net flow of matter between different regions of the system becomes zero and is, in general, valid independently of which state variables are kept constant (they are also valid for adiabatic isochoric, adiabatic isotherm, or isotherm isochoric systems). Equation (3.35), coupled with the mass balance constraint (eq. (3.31)), can also be solved directly with a thermodynamic model for the chemical potentials to calculate the equilibrium composition of a multiphase multicomponent system. Calculation methods that are based on the direct minimization of the Gibbs energy (eqs. (3.32)–(3.34)) are called Gibbs free energy minimization approaches, whereas methods for solving a system of nonlinear equations based on the equality of the chemical potential (eq. (3.35)) and the mass balance (eq. (3.31)) are called equation-solving approaches [6, 8]. Equation-solving approaches are, in general, faster and less computation-demanding than solving the optimization problem given by eqs. (3.32)–(3.34). However, since they exploit only a sufficient condition for phase-equilibrium, they are prone to converge to solutions that do not correspond to the global minimum of the Gibbs energy (such as the trivial solution with the same concentration in both phases, α and β) imposed by eqs. (3.32)–(3.34). Convergence to the real solution of the phase equilibrium problem using local methods requires very good initial values, which can be provided, for instance, using a phase-stability analysis [9, 10].

The Gibbs phase rule As stated in Section 3.1.2, a homogeneous system is completely characterized, once the number of moles of each component, i = 1, . . . , N, as well as two state variables (usually, temperature, T and pressure, p) are provided. An equal statement can be derived starting from mathematical considerations, for a system consisting of π phases. As discussed in Sections 3.1.1 and 3.1.3, a heterogeneous system can be treated using the same thermodynamic relationships derived in Section 3.1.2, by considering each phase as a homogeneous subsystem that can exchange matter and energy with each other. Therefore, N + 2 variables should be provided for each phase to uniquely characterize the system, or N + 1 for each phase, if only intensive properties are considered. Thus, by considering only intensive properties, the number of variables NV is given as follows: NV = π · ðN + 1Þ

(3:38)

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If thermodynamic equilibrium is attained, the equilibrium condition given mathematically by eqs. (3.35)–(3.37) should be fulfilled. The equality of the chemical potential provides ðπ − 1Þ · N equations; the uniformity of pressure and temperature gives 2 · ðπ − 1Þ equations. The number of independent equations that can be set up is given as follows: NEq = ðπ − 1Þ · ðN + 2Þ

(3:39)

Therefore, only F variables (F is also called number of degrees of freedom of the system) given by the difference NV − NEq must be provided in order to uniquely characterize a general multiphase multicomponent system: F=2− π+N

(3:40)

Equation (3.40) is also called Gibbs phase rule and holds for a nonreactive system. The extension of eq. (3.40) to multiphase multicomponent reactive systems will be discussed in Section 3.1.5. In Example 1 at the end of this chapter, the Gibbs phase rule will be applied to determine the number of degrees of freedom of a few real multiphase multicomponent systems.

3.1.4 Fugacity and activity In Section 3.1.2, the chemical potential of a generic component, i, was introduced, which describes the change of the respective extensive thermodynamic potential (U, H, G, or A) of the system upon adding or removing one mole of component, i, at given conditions (T, p, x). In Section 3.1.3, it was shown that the temperature, pressure, as well as the chemical potentials of each component, should be the same in all phases at equilibrium (eqs. (3.35)–(3.37)). From a theoretical point of view, the phase-equilibrium problem is uniquely formulated with the introduction of the chemical potential [2]. However, it remains an abstract function, which exactly defines equilibrium conditions but can hardly relate to real or measurable properties. For this reason, new useful functions were introduced to describe the thermodynamic behavior of real substances. These functions do not solve the phase-equilibrium problem stated by eqs. (3.35)–(3.37). However, they allow reformulating it, starting from well-known reference system, which simplifies the phase-equilibria representation. For this purpose, two further thermodynamic functions, the fugacity and the activity, will be introduced, as well as two important reference states: the ideal gas and the ideal mixture of liquids.

3 Thermodynamics for reactive separations

139

Fugacity and fugacity coefficients Fugacity was introduced by Lewis [1] starting from the expression of the pressure dependence of the chemical potential of an ideal gas at constant temperature, T. For a pure component, 0i, as an ideal gas, the differential change of the molar Gibbs energy g0i with pressure at constant temperature is given as follows: id dg0i = RT

dp p

(3:41)

Equation (3.41) can be derived from eq. (3.23) by expressing the volume using the ideal gas law. Equation (3.41) can be integrated from a reference pressure to the actual pressure. The molar Gibbs energy of the pure component 0i at actual conditions (T, p) is given, after integration as follows: id id ðT, pÞ = g0i ðT, p + Þ + RT ln g0i

p p+

(3:42)

From eq. (3.42), the fugacity, f, is introduced as a corrected pressure, p, which represents the chemical potential, μ, of a real substance, even far away from ideal-gas behavior. Since μ0i = g0i holds for a pure component 0i, the final expression of the chemical potential of a component, i, at given conditions, is given as follows: + μ0i ðT, pÞ = μid 0i ðT, p Þ + RT ln

f0i ðT, pÞ p+

(3:43)

Since the fugacity describes properties of a real substance, it is a function of pressure and temperature. The ratio between the fugacity of a pure substance at given conditions (T, p) and the corresponding pressure is a measure of the deviation of the real thermodynamic behavior of the component, i, from that of an ideal gas. This ratio is called fugacity coefficient and is defined by the symbol, φ. For a pure substance, the fugacity coefficient and the resulting expression for the chemical potential are given as follows: φ0i ðT, pÞ =

f0i ðT, pÞ p

+ μ0i ðT, pÞ = μid 0i ðT, p Þ + RT ln

p + RT ln φ0i ðT, pÞ p+

(3:44) (3:45)

If the same pressure is chosen for the actual and the reference state, p + = p, then the fugacity coefficient describes a residual property, that is, the difference between the real property and that of the corresponding substance as an ideal gas and at the same conditions, ðT, pÞ. Analogously to the pure component, the chemical potential can be expressed for a mixture of ideal gases or real substances, using the fugacity.

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Equation (3.42) can be extended to a mixture of ideal gases starting from the pure component at pressure p + as reference state using the following equation: + xÞ = μid μid i ðT, p. 0i ðT, p Þ + RT ln

p + RT ln xi p+

(3:46)

Using the same pressure for the actual and the reference state, the chemical potential of component, i, in a mixture of ideal gases is related to the chemical potential of the pure component as ideal gas at the same conditions as follows: xÞ = μid μid i ðT, p. 0i ðT, pÞ + RT ln xi

(3:47)

For a mixture of real substances, the fugacity of a component in the mixture and the corresponding chemical potential are given by fi ðT, p, xÞ = pi φi ðT, p, xÞ = pφi ðT, p, xÞxi p + RT ln φi ðT, p, xÞxi p+ fi ðT, p, xÞ + = μid 0i ðT, p Þ + RT ln p+

(3:48)

+ μi ðT, p, xÞ = μid 0i ðT, p Þ + RT ln

(3:49)

By expressing the chemical potential of a component, i, using the fugacity, the equality of the chemical potential (eq. (3.35)) can be reformulated as equality of the fugacities of all components between two generic phases, α and β (isofugacity criterion, eq. (3.50)) since the reference chemical potential of component, i, in the ideal-gas state is independent of the specific phase and cancels out in the following equation: β

fiα = fi ∀i = 1, . . . , N ∀α, β = 1, . . . , π

(3:50)

Equation (3.50) is equivalent to eq. (3.35). The advantage of using eq. (3.50), besides avoiding the reference chemical potential, is that the fugacity coefficient (and therefore, the fugacity according to eq. (3.48)) can be directly calculated using a fluid model in the form of an equation of state (EoS) (Section 3.2.2).

Ideal mixture of real liquids Most of the unit operations in the chemical industry handle liquid mixtures of organic and inorganic compounds. Although the fugacity and fugacity coefficient are universally defined, condensed phases show a strongly pronounced deviation from the ideal gas model, and using the fugacity to represent the real behavior of such mixtures can be impractical (depending on the adopted model). For a long time, no model was available to correctly represent the real behavior of the vapor and liquid phase, and thus, the approach described in the previous section was limited to gas

3 Thermodynamics for reactive separations

141

mixture. In order to describe the phase behavior of liquid systems, the chemical potential can be reformulated from another reference state as that of an ideal gas, which is assumed by the fugacity: dμi ðT, p, xÞ = RT

dfi ðT, p, xÞ = RTd ln fi ðT, p, xÞ fi

(3:51)

Starting from the definition of fugacity in differential form (eq. (3.51)), the chemical potential μi of component, i, in a mixture of N components at given conditions ðT, p, xÞ can be obtained by integrating eq. (3.51) from an arbitrary reference state (defined at a reference pressure p + and composition x + at the actual temperature, T) to the actual state: μi ðT,ðp, xÞ μ + ðT, p + , x + Þ i

~i = RT dμ

lnfi ðT, ð p, xÞ

f dlnf i

(3:52)

fi ðT, p, xÞ + ðT, p + ,  x+ Þ

(3:53)

lnf + ðT, p + , x + Þ i

μi ðT, p, xÞ = μi+ ðT, p + , x + Þ + RTln

fi

Since many of the encountered components of industrially relevant systems are subcritical at the temperature of the system, T (and thus, they can be condensed at a pressure, p, greater than the vapor pressure, pLV 0i ðT Þ), the reference state of pure liquid component, (x0i = 1), is usually employed: μi ðT, p, xÞ = μL0i ðT, p + Þ + RTln

fi ðT, p, xÞ f0iL ðT, p + Þ

(3:54)

Equation (3.54) can be further developed in a more useful expression by introducing the mole fraction of component, i, in the right-hand side of eq. (3.54) and choosing the system pressure as reference pressure (p + = p). The final expression is given as follows: μi ðT, p, xÞ = μL0i ðT, pÞ + RTlnxi + RTln

fi ðT, p, xÞ xi f0iL ðT, pÞ

(3:55)

If the last term of eq. (3.55) becomes equal to zero, an expression similar to eq. (3.47) is recovered. Equation (3.47) denotes the chemical potential of a component, i, in a mixture of ideal gases. Analogously, an ideal mixture of real fluids can be defined as follows: μi ðT, p, xÞ = μL0i ðT, pÞ + RTlnxi

(3:56)

The pure liquid component at the system conditions, μL0i ðT, pÞ represents a useful reference state to describe the thermodynamic behavior of most of the encountered

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Moreno Ascani, Christoph Held

substances in liquid mixtures. Equation (3.56) holds, in general, with good approximation for component, i, in a mixture of chemically similar components with similar size (i.e., hydrocarbon mixtures of similar chain length) and becomes exact at the limit of pure component (for xi ≈ 1). However, it becomes impractical for describing components that are hardly definable as “pure liquid” at the system conditions. To such components belong, for instance, ionic components, sugars and many other biomolecules, as well as supercritical components (CO2, CH4, O2), which can take part in phase-equilibria involving mixtures with liquid solvents. For those components, an equivalent reformulation of the chemical potential as given in eq. (3.55) can be obtained by starting from the opposite concentration range, namely, the limit of infinite dilution of component, i, in a reference system at hypothetical unit molar fraction of component, i (xi* = 1 and thus fi* = φ*i = φ∞ i ). By choosing a reference solvent, j, and applying the same procedure in eqs. (3.52)–(3.53) with p + = p, eq. (3.57) can be obtained to describe the chemical potential of component, i: μi ðT, p, xÞ = μ*i ðT, pÞ + RTlnxi + RTln

fi ðT, p, xÞ xi fi* ðT, pÞ

(3:57)

Analogously, if the last term of eq. (3.57) becomes equal to zero, the chemical potential of component, i, in an ideal mixture of fluids can be expressed, starting from the reference state of infinite dilution at unit molar fraction as follows: μi ðT, p, xÞ = μ*i ðT, pÞ + RTlnxi

(3:58)

Equation (3.58) is fulfilled at the limit of component, i, at infinite dilution (xi ≈ 0). Although the thermodynamic behavior of an ideal mixture of real fluids described by eqs. (3.56) or (3.58) is restricted to very specific conditions (pure component or infinite dilution), it represents a useful concept from which a framework to describe the phase-equilibrium of real mixtures can be developed. This will be done in the following paragraphs.

Activity and activity coefficients As discussed in the previous section, the concept of ideal mixture of real fluids can be used to develop a useful framework to describe the thermodynamic behavior of liquid mixtures. The Gibbs energy of a liquid mixture at given conditions ðT, p, xÞ can be represented as a sum of two contributions: a contribution Gid which describes the thermodynamic behavior according to the hypothetical ideal mixture of real fluids and the last GE , called excess term, which gives the contribution of nonideality in real mixtures:

3 Thermodynamics for reactive separations

GðT, p, xÞ = Gid ðT, p, xÞ + GE ðT, p, xÞ

143

(3:59)

Due to the relationship between the extensive Gibbs energy and the chemical poP tential of each component i, G = Ni= 1 ni μi , an analogue term separation can be obtained for the chemical potential: xÞ + μEi ðT, p, xÞ μi ðT, p, xÞ = μid i ðT, p, 

(3:60)

The ideal contribution to the chemical potential is given, depending on the chosen reference state, by either eqs. (3.47) or (3.58). By comparing eq. (3.60) with eqs. (3.55) or (3.57), the excess contribution can be given explicitly as a function of the fugacity fi of component, i, at the system condition and of component, i, at the reference state, fi0 : μEi ðT, p, xÞ = RTln

fi ðT, p, xÞ xi fi0 ðT, p, x + Þ

(3:61)

The term in the logarithm in eq. (3.61) is called activity coefficient of the component, i, and is denoted by the symbol γi whereas the product of activity coefficient and concentration is called activity and denoted by ai : γi ðT, p, xÞ =

fi ðT, p, xÞ xi fi0 ðT, p, x + Þ

ai ðT, p, xÞ = γi ðT, p, xÞxi =

fi ðT, p, xÞ 0 fi ðT, p, x + Þ

(3:62)

(3:63)

The value of the activity coefficients depends on the choice of the reference state, fi0 . If the pure component, i, at the system conditions (T, p) is chosen, the activity coefficient is called symmetric and is denoted by the symbol, γi . At concentration close to that of pure component, i, the symmetric activity coefficient tends to the value 1: γi ! 1 for xi ! 1

(3:64)

The value of γi at the limit of zero concentration of component, i ðxi ≈ 0Þ is called infinite dilution activity coefficient and is denoted by the symbol, γ∞ i . If the reference state of component, i, at infinite dilution and unit molar fraction in the pure solvent, j, at the system conditions (T, p) is chosen, the activity coefficient is called asymmetric or rational, and is denoted by γ*i . It approaches a value of γ*i = 1 at the
 limit of infinite dilution in the pure solvent, j xi ! 0, xj ! 1 : γ*i ! 1 for xi ! 0, xj ! 1

(3:65)

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The symmetric activity coefficient can be converted to the asymmetric, using the following equation: γ*i =

γi γ∞ i

(3:66)

The right choice of the reference state depends on the nature of the components, as discussed in the previous paragraphs. Using the activity and the activity coefficient defined in eqs. (3.62) and (3.63), the chemical potential of component, i, in the liquid phase can be rewritten, depending on the chosen reference state, as given by μi ðT, p, xÞ = μL0i ðT, pÞ + RTlnai ðT, p, xÞ = μL0i ðT, pÞ + RTlnγi ðT, p, xÞxi

(3:67)

μi ðT, p, xÞ = μ*0i ðT, pÞ + RTlna*i ðT, p, xÞ = μ*0i ðT, pÞ + RTlnγ*i ðT, p, xÞxi

(3:68)

Through its definition, the activity can be viewed as an “effective” concentration for the thermodynamic behavior of a component in a mixture. The lower the activity coefficient (i.e., the stronger the intermolecular interaction in the mixture compared to the reference state), the lower the activity and stable is the component in the liquid phase, at the given conditions. Due to the usefulness of the activity-based reformulation of the chemical potential, several models were developed for calculating the excess Gibbs energy GE and excess chemical potential μEi of liquid components. Those so-called gE-models will be discussed in Section 3.2.1.

Phase equilibrium: φ–φ, γ–γ, and γ–φ concepts The fugacity was introduced in the previous paragraphs to describe the temperature, pressure, and composition dependence of the chemical potential of a generic component, i. It was shown that the phase-equilibrium problem can be reformulated, for each component, i, based on the equality of the fugacity in all phases. Then, the fugacity and activity coefficients were introduced, which describe the thermodynamic behavior of a component, i, in a mixture as deviation, respectively, from the reference state of ideal-gas mixture and the reference state of ideal mixture of real fluids. The relation between fugacity coefficient, the activity coefficient, and the fugacity is given by γi ðT, p, xÞ =

fi ðT, p, xÞ fi ðT, p, xÞ = f0i ðT, p, xÞ xi fi0 ðT, p, x + Þ

φi ðT, p, xÞ =

fi ðT, p, xÞ idG fi ðT, p, xÞ

=

fi ðT, p, xÞ xi · p

(3:69)

(3:70)

Therefore, by means of eqs. (3.69)and (3.70), the isofugacity criterion (eq. (3.50)) can be expressed using the fugacity coefficient, the activity coefficient, or both of

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145

them. If the fugacity in both generic phases is expressed using the fugacity coefficient, this reformulation of the isofugacity criterion is called φ–φ concept. If the fugacity in both phases is expressed using the activity coefficient, then the γ–γ concept is employed. If both reformulations are employed, i.e., the activity coefficient is used to describe the fugacity of component, i, in one phase and the fugacity coefficient for the fugacity of component, i, in the other phase, then the γ–φ concept is used. In the following, these three concepts will be used to derive useful expressions to describe two relevant phase-equilibrium problems: the liquid-liquid equilibrium (LLE) and the vapor-liquid equilibrium (VLE).

Liquid-liquid equilibrium (LLE) The partial mixing of liquid mixtures at given conditions (T, p) has a thermodynamic explanation also based on the principle of Gibbs energy minimization (eqs. (3.27) and (3.28)). According to eqs. (3.56) and (3.59), an ideal mixture always has zero excess Gibbs energy, gE and only an ideal contribution to the overall Gibbs energy, given by eq. (3.71) in terms of molar properties: gðT, p, xÞ = gid =

N X

xi μ0L i ðT, pÞ + RT

i=1

N X

xi ln xi

(3:71)

i=1

The first contribution to gid in eq. (3.71) is simply the average value of the pure-liquid Gibbs energies of all the mixture components (the Gibbs energy of the nonmixed system). The second contribution gives the change of Gibbs energy due to P mixing the components into the ideal mixture, Δgid = RT Ni= 1 xi ln xi . Since all the MIX

molar fractions in the natural logarithm of eq. (3.71) are lower than 1, the contribution of ideal mixing is always negative and, therefore, an ideal mixture will always mix completely. A real mixture, however, has an excess contribution to the Gibbs energy, which represents the differences in size and interaction between unlike molecules. The complete expression of the Gibbs energy of a real mixture is given by gðT, p, xÞ = gid + gE =

N X i=1

xi μ0L i ðT, pÞ + RT

N X i=1

xi ln xi + RT

N X

xi ln γi ðT, p, xÞ (3:72)

i=1

where the excess Gibbs energy, gE, is expressed using the activity coefficients of all P the components in the mixture, (gE = RT Ni= 1 xi ln γi ). Figure 3.2 represents the Gibbs energy of a binary mixture as a function of the concentration for two different mixtures: an almost ideal mixture (left diagram) and a mixture with a strong positive excess contribution (right diagram). In the mixture on the left diagram, the Gibbs energy curve is convex, and the homogeneous mixture at the given feedpoint (F) always corresponds to the global minimum of the Gibbs energy (for the fixed feed composition, x1, and without chemical reactions).

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Fig. 3.2: Gibbs plot of two binary mixtures. The curve of the molar Gibbs energy (g) is represented as a sum of an ideal (gid) and an excess contribution (gE) according to eq. (3.58). Due to a strong positive excess contribution, the feed point (F) of the mixture in the bottom diagram splits into two phases (P1 and P2), since the inhomogeneous system has a lower Gibbs energy than the homogeneous one. The composition of both phases is given by the tangent construction (green line).

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However, for the mixture in the right diagram, the configuration of homogeneous mixture (F) at the given feed composition, x1, is not at the lowest value of Gibbs energy. If the feed is allowed to separate into two phases (P1) and (P2), a more stable configuration can be approached. The composition of both phases corresponding to the most stable configuration that can be found graphically (when no more than two components are present) by drawing a tangent line touching the two compositions below the Gibbs energy curve (see Fig. 3.2). The criterion for instability of the mixture is the appearance of two saddle points in the Gibbs energy curve (eq. (3.73)), indicating that a concentration range exists in which the second derivative of the Gibbs energy becomes negative [1]: 

∂2 g ∂x2

 =0

(3:73)

T, p

The calculation of the equilibrium between two phases is generally accomplished using the same thermodynamic model to describe the thermodynamic behavior of each component in both (two or multiple) liquid phases P1 and P2. This can be either a gE-model, from which the activity coefficients (eq. (3.69)) can be calculated, or an EoS, from which the fugacity coefficients can be obtained (eq. (3.70)). Moreover, using an EoS, the activity coefficients can be calculated from the fugacity coefficients of each component, i, in the reference state φ0i ðT, p, x + Þ and in the mixture φi ðT, p, xÞ as follows: γi ðT, p, xÞ =

φi ðT, p, xÞ φ0i ðT, p, x + Þ

(3:74)

By using the γ–γ concept to describe LLE, the isofugacity criterion can be rewritten:

 0 0 xP1 xP1 x + Þ = γP2 xP2 xP2 x+ Þ γP1 i T, p,  i fi ðT, p,  i T, p,  i fi ðT, p, 

(3:75)

If the same reference state fi0 ðT, p, x + Þ is used, the fugacity of the reference state will have the same value on both sides of the equation and can be eliminated. Thus, the LLE expressed through the γ–γ concept reduces to

 P2 xP1 xP1 xP2 xP2 γP1 i T, p,  i = γi T, p,  i

(3:76)

By using the φ–φ concept, the fugacity in each phase can be rewritten as follows:

 φP1 xP1 xiP1 = φP2 xP2 xiP2 i T, p,  i T, p, 

(3:77)

The pressure in eq. (3.44) was already eliminated by deriving eq. (3.77), since it is uniform in the whole system at equilibrium.

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Vapor-liquid equilibrium (VLE) VLE can be represented by using the φ–φ or the γ–φ concept. Using the φ–φ concept leads to the same equilibrium expression obtained for LLE, where one phase is liquid and the other is vapor:

 φLi T, p, xL xiL = φVi T, p, xV xVi

(3:78)

Using the γ–φ concept implies that two different models (a gE-model and an EoS) are used to represent the thermodynamic behavior of each component in the liquid and the vapor phase. The derivation of a useful expression of the VLE problem will be shown in this section by using both the symmetric and the asymmetric activity coefficients to describe the thermodynamic behavior of the components of real mixtures. The symmetric activity coefficient is the usual choice for mixtures of subcritical components, i.e., for components which can exist as pure liquid at the system temperature. Starting from the isofugacity criterion (eq. (3.79)), this leads to the following equation:


fiL = fiV


 γi T, p, xL xiL f0iL ðT, pÞ = φVi T, p, xV xiV p

(3:79) (3:80)

In eq. (3.80), the fugacity of the hypothetically pure liquid component f0iL ðT, pÞ at the system T and p should be provided explicitly. In order to simplify further derivations, the reference fugacity will now be related to that of a pure liquid under satu
 ration condition at the system temperature, f0iL T, pLV 0i ðT Þ , which is only a function of the temperature, T, once a function of the pure-component vapor-pressure curve, pLV 0i ðT Þ is provided. The pressure dependence of the fugacity of a generic component, i, at given condition (T, p, x) is related to the partial molar volume of the same component, i, as given by [11]   vi ðT, p, xÞ ∂lnfi = (3:81) ∂p T, x RT For a pure component, 0i, the partial molar volume becomes equal to the pure-component molar volume, vi = v0i . Therefore, by applying eq. (3.81) to the reference fugacity of the pure liquid at given p and T, eq. (3.82) is obtained:   ∂lnf0iL v0i ðT, pÞ = ∂p T RT

(3:82)

This can be integrated at constant temperature T, between the vapor pressure at the given system, T, and the system pressure, p, to obtain the following equations:

3 Thermodynamics for reactive separations

f L ðT, pÞ ln L
0i LV  = f0i T, p0i ðT Þ
L

f0iL ðT, pÞ = f0i

ðp

~Þ v0i ðT, p ~ dp RT

pLV ðT Þ 0i

0 ðp  B LV T, p0i ðT Þ · exp@

149

(3:83) 1

~Þ C v0i ðT, p ~A dp RT

(3:84)

pLV ðT Þ 0i

The term on the right-hand side in eq. (3.84) is called Poynting factor and is denoted by the symbol, Π0i . It is a function of pressure and temperature and can be understood as a correction factor, which accounts for the pressure dependence of the reference fugacity, f0iL ðT, pÞ. The usefulness of eq. (3.84) becomes clear by expressing
 the fugacity, f0iL T, p* ðT Þ of the pure component at the temperature, T, and saturated condition p* ðT Þ using the fugacity coefficient:

 LV f0iL T, p* ðT Þ = φL0i T, pLV (3:85) 0i ðT Þ · p0i ðT Þ Since the fugacity coefficient of a pure component in the vapor and liquid phases must be the same, in eq. (3.85), it must hold that φL0i = φV0i . Therefore, the fugacity
 coefficient φL0i T, pLV 0i ðT Þ in eq. (3.85) can be calculated using the same EoS used to describe the vapor phase in eq. (3.80). The vapor pressure pLV 0i ðT Þ is known for most of the common substances and is usually accessible by the Antoine equation. Therefore, eq. (3.80) can be rewritten as follows:
 LV

 V xV xiV p γi T, p, xL xLi φL0i T, pLV 0i ðT Þ · p0i ðT Þ · Π0i ðT, pÞ = φi T, p, 

(3:86)

Equation (3.86) is the general formulation of the VLE problem for a multicomponent system using the γ–φ concept. In general, it can only be solved numerically even for binary systems, because of the high nonlinearity with respect to the composition in the models used to calculate the activity and fugacity coefficients. In case the liquid mixture behaves nearly ideally according to eq. (3.56) (γLi ≈ 1), if the vapor phase can be described by the ideal gas law, (φVi ≈ 1 → φL0i ≈ 1), and the Poynting factor can be neglected (for instance, the Poynting factor of water at T = 70 °C changes from 1.0006 to 1.0065 if the value of p-pLV 0i changes from 100 to 1,000 bar [1]; so at low pressure, its value can be set to 1), eq. (3.86) simplifies to the Raoult’s law V xiL · pLV 0i ðT Þ = xi p

(3:87)

Although this is called a “law,” eq. (3.87) is nearly never appropriate for the description of real mixtures. If one or more components in the liquid mixture are supercritical at the temperature of the system, the previous description will be impractical due to the poor definition of the reference state of pure liquid. Therefore, an alternative representation of the VLE is used, based on the choice of the reference state of

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infinite dilution at unit molar fraction. Starting again from the isofugacity criterion, eqs. (3.88) and (3.89) can be obtained: fiL = fiV

(3:88)



 γ*i T, p, xL xLi fi* ðT, p, x + Þ = φVi T, p, xV xVi p

(3:89)

The fugacity of the reference state fi* can be expressed using the Henry’s constant Hi, j [1]. The Henry constant Hi, j is reported for many relevant binary systems and is defined as the ratio between the fugacity fi of the gas solute, i, in the solvent, j, and the molar fraction xiL of component, i, in the liquid phase, at the limit of zero concentration of i (eq. (3.90)): Hi, j ðT Þ =

fi xi

lim xi ! 0

(3:90)

xj ! 1 p ! pLV 0j ðT Þ Since the Henry constant is defined at infinite dilution of component, i, in solvent, j, it is automatically defined at the vapor pressure of the solvent pLV 0j ðT Þ at the system temperature, T. However, the value of the Henry constant can be adjusted to the system pressure once an expression for the partial molar volume v∞ i of component, i, at infinite dilution in j as a function of pressure and temperature is provided. The relation between Hi, j and v∞ i is given by 

∂lnHi, j ∂p

 = T

v∞ i ðT, pÞ RT

(3:91)

Thus, by integrating eq. (3.88), the value of the Henry constant can be obtained, depending on the system pressure: ln

Hi, j ðT, pÞ  = ð T Þ Hi, j T, pLV 0j

ðp

~ v∞ i ðT, pÞ ~ dp RT

(3:92)

pLV ðT Þ 0j

0 ðp   B LV B Hi, j ðT, pÞ = Hi, j T, p0j ðT Þ · exp@

1 ~ v∞ i ðT, pÞ RT

C ~C dp A

(3:93)

pLV ðT Þ 0j

Using the Henry constant, the fugacity fiL of component, i, in the liquid phase (eq. (3.88)) can be given explicitly, using the asymmetric activity coefficient to correct for the deviation from infinite dilution assumed in eq. (3.90). The final representation of the VLE based on the reference state of infinite dilution is given as follows:

3 Thermodynamics for reactive separations



 γ*i T, p, xL xiL Hi, j ðT, pÞ = φVi T, p, xV xiV p

151

(3:94)

In case the liquid mixture and the vapor phase behave near ideally (γ*i ≈ 1, φVi ≈ 1) and the Henry constant remains nearly constant with pressure, eq. (3.94) simplifies to the Henry’s law: xiL Hi, j ðT Þ = xVi p

(3:95)

As many gases are poorly soluble in liquids (xiL ! 0, γ*i ≈ 1Þ, Henry’s law is a good assumption for some real mixtures; however, it should be noted that the Henry coefficient is a binary property, which is often misused in the literature for the description of higher systems. Comparison of experimental VLE and predicted VLE (with the Henry’s and Raoult’s laws) can be found in Examples 2 and 3.

3.1.5 Chemical equilibrium In Section 3.1.3, necessary conditions for phase equilibrium in a nonreactive system were formulated, based on the minimization of the Gibbs energy with the constraint of constant total number of moles of each component in the system. The same principle applies to systems in which one or more components can undergo a change in the chemical structure by a chemical reaction. This causes the formation of one or more chemical components with different physicochemical properties, until the Gibbs energy of the system reaches its global minimum. This allows formulating necessary conditions for reactive systems, comparably to what has been shown in Section 3.1.3 for nonreactive multiphase systems. However, further concepts need to be introduced, allowing a mathematical description of the chemical equilibrium to derive useful equilibrium conditions. Those concepts are the reaction stoichiometry, the reaction coordinate, and the key reactions. After that, equilibrium condition of single and multiphase reactive systems can be derived, and the Gibbs phase rule for a reactive system can be formulated.

Stoichiometry and reaction coordinate Chemical reactions lead to disappearance of a given amount of reactants and to the generation of a given amount of products, and the number of reactants and product species can vary, depending on the considered reaction. However, the quantity of each species has to satisfy the element mass balance, which means that the overall mass of each element present in the components involved in all the reactions will remain constant. Therefore, the element mass balance uniquely fixes the ratio at

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which products and reactants can participate in the reaction. A general chemical reaction involving n reactants, Ri and m products, Pj is written as follows [12]:         νR R1 + νR R2 +    + jνR jRn = νP P1 + νP P2 +    + jνm jPm (3:96) 1

2

n

1

2

Conventionally, the reactants are written on the left-hand side, and products on the right-hand side. The symbols νi are called stoichiometric coefficients. They are positive for the products and negative for the reactants and give the exact molar proportion on which each component can participate in the reaction. For instance,   to eq. (3.96), then a number of moles of if νRi  moles of reactant Ri react according     each product species Pj given by νPj  would be produced, j = 1, . . . , m. At the same   time, the stoichiometry requires that νRk  moles of the other reactant species, Rk ðk = 1, . . . , n, k ≠ i) must take part at the reaction. By considering infinitesimal changes of the number of moles, it can be observed that the ratio of the infinitesimal change of mole numbers over the stoichiometric coefficient of each component must be constant [12]: dnR1 dnR2 dnRn dnP1 dnP2 dnPm = =  = = = =  = νR1 νR2 νRn νP1 νP2 νPm

(3:97)

This means that the proceeding of the reaction (i.e., the change of composition with the reaction) can be tracked by a single variable, which is represented by λ and is defined as follows: dni = dλ νi

(3:98)

The variable λ is called reaction coordinate and characterizes the extent of a chemical reaction with respect to the initial composition [12]. It connects the differential change of the number of moles dni of each component with its stoichiometric coefficient. By integrating eq. (3.98) from an initial state to a state after an arbitrary extent of reaction, the actual number of moles of each component can be obtained: ni = ni0 + νi λ

(3:99)

If more than one chemical reaction occurs in the system, then one distinct reaction coordinate for each reaction should be introduced. If NR chemical reactions occur, the actual number of moles of each component will be described as follows: ni = ni0 +

NR X

νi, j λj

(3:100)

j=1

In eq. (3.100), νi, j represents the stoichiometric coefficient of component i in reaction j and λj the reaction coordinate of reaction j. At this point, it is important to note that a chemical reaction is simply a schematic representation of a chemical

3 Thermodynamics for reactive separations

153

transformation in a reacting system, which aims neither at making any statements about the reaction mechanism nor the reaction kinetics. However, it allows deriving chemical equilibrium conditions and calculating the equilibrium composition in a reactive system. In Example 4, the mass balance of all reacting components as a function of the reaction coordinate will be explained. The kind and minimal number of chemical reactions required to completely describe a reacting system are described in the following section.

Minimal number of independent key reactions As previously explained, a chemical reaction is a schematic representation of the chemical transformation going on in a reactive mixture, which aims at representing the mass balance of the reactive mixtures; it does not correspond to the real reaction mechanism going on at the molecular level. In general, different equivalent chemical equations in the form of eq. (3.96) can be written for the same reactive system. In this section, rules will be derived for the minimal number and type of chemical equations in the form of eq. (3.96), which must be written in order to balance unambiguously reactive systems. A general chemical reaction, k, involving N components Ai ði = 1, . . . , N Þ, as depicted in eq. (3.96), can be written in compact form as a sum of all the single components multiplied by the respective stoichiometric coefficient [13]: N X

νki Ai = 0

(3:101)

i=1

A chemical reaction is formulated in such a way that the number of atoms of each element building up all the components does not change over the reaction. The conservation of each element is therefore implicitly formulated in eqs. (3.96) and (3.101) [14]. The formation reaction of each component Ai from its constituent elements Ej can also be written as a chemical reaction: Ai =

Ne X

εi, j Ej

(3:102)

j=1

where Ne is the total number of elements in the reacting system, and εi, j denotes the number of atoms of element Ej contained in the molecule of component Ai . To calculate the number of independent reactions, the number of independent equations among the N formation reactions eq. (3.102) should be found. The system of equations described by eq. (3.102) for each component, Ai (i = 1, . . .,N) can be written in vector-matrix form as follows:   = εE A

(3:103)

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The number of independent formation reactions is equal to the rank of the compo
 nent-element matrix, ε (eq. (3.104)), which has a dimension, dim ε = N × Ne : 0 1 ε1Ne ε11 ε12  B C ε2Ne C B ε21 ε22 B C ε =B (3:104) .. .. .. C B . . . C @ A εN1 εN2    εNNe Therefore, the minimal number of independent key reactions, NR , which must be written for the reactive system is given as follows:
 NR = N − rank ε

(3:105)

In principle, the type of key reaction can be freely defined. To prove the linear independence of a chosen set of NR key reactions, the rank of the stoichiometric matrix, v (eq. (3.106)), of the NR reactions described algebraically by eq. (3.101) has to be equal to NR : 0 1 ν1N ν11 ν12    B C ν2N C B ν21 ν22 B C v =B (3:106) .. .. .. C B C . . . @ A νNR 1 νNR 2    νNR N Example 5 will clarify the methodology for determining the number and type of key reactions.

Reaction equilibrium In the previous paragraphs, the basic concepts for the mathematical characterization of a reacting system consisting of N components were introduced. These concepts allow not only balancing a reacting system, but also reformulating the equilibrium condition of a reactive system as an optimization problem (as done in Section 3.1.3 for a nonreacting system); the problem is solved by seeking a solution for the state of the system that corresponds to the global minimum of the Gibbs energy at given conditions (pressure, temperature, and initial composition). The procedure is shown here for a homogeneous closed system, (π = 1), of N components and a single reaction [12]. For this system, at constant T and p, with given initial mole numbers, the Gibbs energy can be reformulated as a function of the reaction coordinate λ with the actual mole number of all components ni expressed by eq. (3.99). The final expression is given as follows:

3 Thermodynamics for reactive separations

GðλÞ =

N X

ðni0 + νi λÞμi

155

(3:107)

i=1

If the system is not at chemical equilibrium, the chemical reaction, described by λ, must lead to a decrease of the Gibbs energy. The dependence of the Gibbs energy on λ is illustrated in Fig. 3.3.

Fig. 3.3: Gibbs energy plot of a reactive mixture of reactant A (component 1) and product B (component 2). Starting from an initial point, xs.p., (with λ = 0), the composition changes according to the stoichiometry, until the equilibrium composition, x* (with λ = λ *) is attained. At this point, the Gibbs energy has reached its global minimum.

There is one value of the reaction coordinate λ* which corresponds to the global minimum of the Gibbs energy in Fig. 3.3 and satisfies eqs. (3.27) and (3.28). Equilibrium conditions at this point can be found by differentiating eq. (3.107) with respect to λ at constant T and p and setting this partial derivative to zero: 

 N X ∂G = νi μi = 0 ∂λ T, p i = 1

(3:108)

Therefore, the problem of finding the state of equilibrium of a reactive system reduces to finding an equilibrium composition, x* that satisfies eqs. (3.27) and (3.28). This 0 . equilibrium composition depends on the initial number of moles in the system, n However, for a single reaction, the final composition only depends on the value of λ* at equilibrium, according to eq. (3.109), once initial mole numbers are provided:

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Moreno Ascani, Christoph Held

ni0 + νi λ* = PN
* * k = 1 nk k = 1 nk0 + νk λ

n* xi* = PN i

(3:109)

It can be shown that the results derived for a single reaction in a homogeneous closed system holds for the general case of a closed multiphasic system with multiple reactions at constant T and p. If a reactive system consisting of π phases and N components can be described by NR independent key reactions at constant T and p, the equilibrium conditions require that eq. (3.108) must be satisfied for each reaction, k, in each phase, π, together with the equality of the chemical potential of each component, i, in all phases, according to the following equations: N X i=1

ð jÞ

νki μi = 0 β

μαi = μi

k = 1, . . . , NR j = 1, . . . , π i = 1, . . . , N α, β = 1, . . . , π

(3:110)

(3:111)

The reactive phase-equilibrium problem reduces to finding the component distribu* , which satisfies eqs. (3.110) and (3.111) simultaneously. tion in each phase, n

Reaction equilibrium constant In the previous section, necessary conditions for chemical equilibria (eqs. (3.110) and (3.111)) were reformulated, based on the stoichiometry of the key reaction(s) and the minimization of the system’s Gibbs energy. It was shown that eq. (3.108) holds for all the reacting components of each key reaction at equilibrium. However, a formulation of chemical equilibrium based on the chemical potential alone is impractical, for the reasons mentioned in Section 3.1.4; thus, it is usually not used in equilibrium calculations. Much more useful is a reformulation of the chemical potential in eq. (3.108), based on the fugacity or the activity: fi ðT, p, xÞ p+

(3:112)

μi ðT, p, xÞ = μ0i ðT, p + Þ + RTlnγi ðT, p, xÞxi

(3:113)

+ μi ðT, p, xÞ = μid 0i ðT, p Þ + RT ln

The derivation of an expression of the equilibrium condition based on the fugacity of each reacting component will be presented here. Considering only one reaction, by using eq. (3.112) and insertion into eq. (3.108), the condition of chemical equilibrium can be reformulated:   N N X X fi ðT, p, xÞ νi + ln =− νi μid (3:114) RT 0i ðT, p Þ + p i=1 i=1

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157

Due to the equality, μ0i = g0i , the term on the right-hand side of eq. (3.114) represents the change of Gibbs energy by the complete reaction of νiR moles of reactants into νiP moles of products, with all components in the reference state of pure, ideal gases at the system temperature and at a standard pressure, p + . This term is called standard Gibbs free energy of reaction and is denoted by ΔR g0 . Due to the definition of the reference state for each component, the standard Gibbs energy of reaction depends only on the temperature, and neither on the system pressure nor on the composition (i.e., on a specific solvent or impurity in the system). By expressing the fugacities using the fugacity coefficients, the molar fractions, and the pressure, eq. (3.114) can be rewritten in a more useful form: 

p p+

N P νi Y N i=1



 ΔR g0 ðT Þ ðφi xi Þ = exp − RT i=1 νi

(3:115)

The exponential term only contains ΔR g0 and the RT term and is also only a function of temperature. It is called equilibrium constant and is denoted by the symbol, Q K f . Two further symbols, K φ and K x , are used to represent the product, Ni= 1 ðφi xi Þνi , defined by Kφ =

N Y

ðφi Þνi

(3:116)

ðxi Þνi

(3:117)

i=1

Kx =

N Y i=1

P The sum of the stoichiometric coefficients Ni= 1 νi in the exponent of the pressure ratio p=p + in eq. (3.115) is represented by the symbol ΔR ν and denotes the change of the overall number of moles of reacting components due to the reaction progress. For gas-phase reactions with nearly ideal behavior (Kφ ≈ 1), the ΔR ν has a great impact on the pressure dependence of the equilibrium composition (given by Kx ) at given temperature, T (see examples (6) and (7)). Finally, the equilibrium condition can be rewritten as given by  Kf ðT Þ = Kφ ðT, p, xÞ · Kx ðT, p, xÞ ·

p p+

ΔR ν (3:118)

Due to the high nonlinearity of the fugacity coefficients, eq. (3.118) can only be solved numerically for the general case to obtain the equilibrium composition, (Kx ), at given conditions. However, for ideal behavior and low number of components, an analytical solution can be found (see examples (6) and (7)). For reactions occurring in the liquid phase, an equivalent condition of chemical equilibrium is usually derived by expressing the chemical potentials using the activity. By choosing the pure component in the liquid state at the system pressure

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Moreno Ascani, Christoph Held

and temperature as the reference state to calculate the activity coefficients (this reference state is often chosen; however, other reference states can also be employed), the final expression is given by Ka ðT, pÞ = Kγ ðT, p, xÞ · Kx ðT, p, xÞ

(3:119)

In eq. (3.119), Kx has the same definition as in the expression for Kf given by eq. (3.118), and Kγ is defined using the activity coefficients of each component by Kγ =

N Y

ðγi Þνi

(3:120)

i=1

The activity-based equilibrium constant, Ka , is now dependent on the temperature and (due to choosing the reference state) also on the pressure of the system. Ka is related to the standard Gibbs energy of reaction by   ΔR g0 (3:121) Ka ðT, pÞ = exp − RT ΔR g0 ðT, pÞ =

N X

νi μL0i ðT, pÞ

(3:122)

i=1

The standard Gibbs energy of reaction ΔR g0 represented in eq. (3.122) is the change in Gibbs energy by the complete reaction of νiR moles of reactants into νiP moles of products, with all components in the reference state being the pure liquid at the system temperature, T, and pressure, p.

Gibbs phase rule for reacting systems The number of degrees of freedom of a reacting system according to the Gibbs phase rule can be obtained, as done for a nonreacting system, starting from the number of variables in the system and the number of mathematical equations that can be written for the system. The total variables in a system consisting of π phases and N components are the pressure, the temperature, and N mole fraction in each phase. The total number of variables, NV, is therefore given by NV = 2 + π · N

(3:123)

The mathematical equations that can be written are the normalization of the mole fractions, which provides π equations, the equality of the chemical potential of each component in all phases, which provides ðπ − 1Þ · N equations, and NR independent key reactions for a reactive system. The total number of equations NEq is therefore given by

3 Thermodynamics for reactive separations

NEq = π · N − N + π + NR

159

(3:124)

The number of degrees of freedom in a reactive system, determined as the difference between the number of variables NV and the number of equations NEq is given by F = 2 + N − π − NR

(3:125)

Equation (3.125) is reduced from the number of degrees of freedom in a nonreactive system (cf. eq. (3.40)) by the number of independent key reactions, NR . In Example 8, the calculation number of the degrees of freedom in a reactive system will be shown.

3.2 Thermodynamic models In Section 3.1, the thermodynamic framework for equilibrium calculations was introduced. The mathematical relationships between the thermodynamic potentials, ðU, H, G, AÞ and all the macroscopic state variables of a homogeneous system, , cP , cV , . . .Þ, as well as the conditions of physical and chemical equilibðT, p, V, S, x, μ rium are exact, and nowadays are not objects of discussion in the scientific community. However, although exactly defined, the thermodynamic framework requires an input function, which allows obtaining numerical results for the phase-equilibrium problem. More in general, for a system containing N components, a quantitative relationship between N + 2 state variables must be available, in order to use the thermodynamic framework for making useful calculations. Such a relationship is the EoS already introduced in the previous sections and usually provided in terms of the state variables temperature, pressure, specific volume (or density), and composition: f ðT, p, v, xÞ = 0

(3:126)

The form of eq. (3.126) suggests that an EoS, in general, can be implicit in one or more variables. Obtaining a relationship in the form of eq. (3.126), which can accurately describe the T, p, v behavior of a real fluid (or a fluid mixture) in the gas and liquid state is still one of the main topics of research in chemical engineering thermodynamics. This section aims at introducing the most important thermodynamic models used to perform equilibrium calculations, without going into their mathematical derivation. Almost all of them are based on a molecular model, which assumes a given structure and a given interaction potential among the molecules present in the system. However, several models are semi-empirical in nature; thus, they maintain a general physical significance, while introducing empirical correlations to correct for inaccuracies of the physical model (for instance, to improve the description of the temperature dependence). The goodness of a given model is mostly determined by the “similarity” between the molecular model and the chemical

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character of the considered molecule, which makes the choice of the right model a system-specific task. Models useful for describing the thermodynamic behavior of a specific class of compounds are not always accurate when applied to other systems. In Section 3.2.1, gE models will be introduced, with particular emphasis on the four most relevant models, Wilson, NRTL, UNIQUAC and UNIFAC. Section 3.2.2 introduces the most important EoS, beginning with cubic EoS, widely used in the chemical and petroleum industry [15], and subsequently addresses more advanced EoS.

3.2.1 gE models As mentioned in the introduction of this section, a thermodynamic model relating N + 2 state variables is needed to obtain quantitative results of equilibrium problems. Historically, EoS in the form of eq. (3.126) were mainly limited to the description of the low density (i.e., gas phase) region of the T, p, v diagram of some simple real fluids, and the description of the liquid phase was possible (to some extent, the problem is still not completely solved nowadays) only for nonpolar or slightly polar fluids, such as hydrocarbon mixtures. On the other hand, the liquid phase is the main source of nonideality, while the gas phase of several mixtures can be described reasonably well with the ideal gas law at low pressures (one exception to this behavior are associating compounds, like carboxylic acids). For this reason, and also to calculate phase equilibria of pure condensed systems (LLE and SLE) at low pressure, several thermodynamic models were developed ad hoc to describe the thermodynamic behavior of an N-component liquid mixture upon mixing up the components [15], leading to the γ–φ concept (see Section 3.1.4). Those models are expressed in term of excess Gibbs energy gE : gE = gE ðT, p, xÞ

(3:127)

gE = g − gid

(3:128)

The reference state of the ideal mixture of real fluid, upon which the phase- and chemical equilibrium calculations using models is based, was described in Section 3.1.4. To apply the framework to real mixtures, the activity coefficients of the mixture components should be computed from the gE model, using the following equation:  E ∂G (3:129) ln γi = RT ∂ni T, P, n i≠j

Due to the form of eq. (3.129), gE models can only be used to describe mixing properties but not to calculate absolute properties, such as the overall density or heat capacity of the liquid mixture. However, whereas the density is not required for phase equilibrium calculations, other properties (such as the vapor pressure of the

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single components, fugacity coefficients, or the specific volume in the Poynting factor) must be estimated using appropriate correlations or an EoS. Because of the mathematical relation between the Gibbs energy, the enthalpy, and the entropy (eq. (3.21)), the excess Gibbs energy is related to the excess enthalpy and the excess entropy through the following equation: gE = hE − TsE

(3:130)

Equation (3.130) helps make distinctions between different models. In many cases, only one of the two contributions (enthalpic hE or entropic sE ) is the dominant effect in the nonideality of a liquid mixture. For mixtures containing components similar in size, the enthalpic term, hE (which arises from the different interaction energies between the different components in the solution) dominates, whereas in mixtures containing component very different in size, the entropic term, sE (which arises from the nonrandomness in the solution) can prevail. Therefore, neglecting the influence of one of the two terms (i.e., setting gE = hE or gE = TsE ) and, thus, to simplify, a model might be reasonable. A further common characteristic of the available models is that the excess volume vE of the mixture is neglected, which is a reasonable assumption for condensed phases at low pressure. This implies an independence of the liquid phase of the pressure. All the available gE models can be basically divided into two categories [15]: the oldest “random mixing models” and the modern “local composition models (LC),” which, nowadays, are the most popular in phase equilibria calculation. For this reason, the discussion in this section will be only limited to this category. Furthermore, the concept of LC will be first introduced. Then, the three most important models in chemical engineering – the Wilson, NRTL, and UNIQUAC (as well as its Group Contribution variant, UNIFAC) will be described.

Local composition (LC) models The LC concept is based on a molecular picture, which considers the molecules not randomly distributed in the solution (as assumed by earlier models) but rather show a local “nonrandomness” caused by intermolecular forces between the mixture components. This leads to a “local composition” in the mixture, which differs from the macroscopic “bulk” composition, a feature of real mixtures; this can be described in a first approximation by the Boltzmann statistics: −

gij

xij xi e kB T = xjj xj − kgjjT e B

(3:131)

In eq. (3.131), the term xi denotes the average or “bulk” molar fraction of component, i, whereas xij denotes the local mole fraction of component, i, around a central

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molecule of component, j. The exponential functions in the numerator and denominator of eq. (3.131) denote an enhanced (or reduced) probability of finding a molecule of component, i (or j), around a central molecule, j, and the terms, gij and gjj are proportional to the interaction energy, respectively, between molecule, i or j, and the central molecule, j (see Fig. 3.4).

Fig. 3.4: Representation of the concept of local composition (LC). The local concentration, xij of molecule, i, around molecule, j, is determined through the interaction energy, gij, via the Boltzmann statistics (eq. (3.131)).

Another important contribution to the improvement of the physical picture of (some) gE-models comes from polymer solution thermodynamics and is the Flory– Huggins theory [16–20]. The necessity for mentioning the Flory–Huggins model at this stage arises from the fact that numerous models adopted the basic idea to account for the difference in molecular size of the components. According to eq. (3.130), the Flory–Huggins theory considers athermal mixtures for which the enthalpic contribution hE is set to zero (i.e., gE = − TsE ). The model fluid behind the Flory–Huggins theory involves a lattice structure in the mixture (see Fig. 3.5) with the following assumptions: – The molecules have different sizes and are divided into segments. All segments have the same size and occupy only one definite lattice cell. Large molecules (such as polymers) consist of a large number of linearly joint segments, whereas small molecules consist of a few or even one segment only. Thus, the number of segments account for the different size of the molecules. – Segments are freely interchangeable in the lattice structure (not molecules). However, the interchangeability of polymer segments is restricted by their connection in the same polymer molecule (they must remain connected). Through the definition of the lattice model fluid and the assumption of zero enthalpy contribution, the question of calculating the entropic term (and thus, the excess Gibbs energy) reduces to a pure combinatorial problem: the entropy of the system, S, is related to the number of microstates (each is equally probable) in which the molecules can rearrange themselves into the lattice, W:

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Fig. 3.5: Picture of the lattice structure and the model fluid of single and multiple jointed segments, which is described by the Flory–Huggins theory.

S = kB ln W

(3:132)

Without going into the derivation details, the resulting excess Gibbs energy gE according to the Flory–Huggins theory, is given by gE = − RT

N X

xi ln

i=1

xi vL Φi = PN i L i = 1 x i vi

Φi xi

(3:133)

(3:134)

where the term Φi denotes the volume fraction of component i in the mixture at composition x and vLi denotes the molar liquid volume of pure component, i [21]. Although the LC concept is adopted by the most successful gE-models, only the Wilson (implicitly), UNIQUAC, and UNIFAC (explicitly) make use of the structural information in their derivation, similar in spirit to the Flory–Huggins theory. One of the greatest merits of LC models, which is closely related to their physical significance, is the possibility of formulating mixing properties of liquid mixtures containing more than two components, using only binary interaction parameters. This offers the great advantage of modeling phase equilibria of ternary and higher mixtures from data obtained exclusively from binary mixtures, thus reducing the experimental effort needed to obtain phase-equilibrium data to design separation units [21]. In the following, the four most successful and used gE-models (Wilson, NRTL, UNIQUAC, and UNIFAC) will be explained.

The Wilson model The Wilson model was the first gE-model derived using the LC concept in the pioneering work of Grant Wilson [22]. To derive an expression for the excess Gibbs energy,

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gE, of a real mixture, Wilson started from eq. (3.131) for the local concentration of a generic component, i, around a molecule of generic component, j. Then, Wilson redefined the Flory–Huggins expression (which assumes equal probability of each microstate due to neglecting energetic effects) by defining the local volume fraction, ξ i (eq. (3.135)), when the molecules are subjected to intermolecular interactions described by the parameters, gij : gii

xi vLi e − RT

ξi = P N

(3:135)

g

ik L − RT k = 1 xk vk e

The parameters gij are related to the parameters Λji defined by Λij =

vLj vLi

e−

gij − gii RT

=

vLj vLi

Δgij

e − RT

(3:136)

Introducing eqs. (3.135) and (3.136) into eq. (3.133), we can recover the final expression of the Wilson equation for gE (eq. (3.137)) and for the activity coefficients: ! N N X X gE xi ln xj Λij =− (3:137) RT i=1 j=1 ln γi = − ln

N X j=1

!

xj Λij + 1 −

N X j=1

xj Λji

PN

k = 1 xk Λjk

!

(3:138)

Besides the very attractive feature of having binary interaction parameters defined only between pair of components (Δgij = gij − gii ), the Wilson equation has a built-in temperature dependence (see eq. (3.136)), which allows predicting properties at a certain temperature from parameters obtained from another temperature not too far away [21]. By considering Δgij as being temperature independent, the Wilson model requires only two binary interaction parameters for each pair of components in the mixture. Those can be estimated using, for instance, VLE data of the binary subsystems. The correlation capability of the Wilson model is excellent for binary and multicomponent systems containing water, polar solvents (such as ketones or alcohols), or nonpolar components such as hydrocarbons [21]. However, the main drawback of the Wilson model is its complete inadequacy in modeling LLE. This is due to the intrinsic mathematical property of the Wilson model: the Gibbs energy of mixing, calculated with the Wilson model, is convex over the whole concentration range, whereas the condition of instability requires that it should become nonconvex (i.e., its second derivative must become negative) in a certain concentration range. Furthermore, the Wilson model cannot predict maxima or minima of activity coefficients in alcohol–chloroform mixtures [15]. Those problems were solved a few years after the original publication, with the development of the NRTL model.

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The NRTL equation The NRTL (not-random two-liquid) model was derived by Renon and Prausnitz [23] in a similar way as the derivation of the Wilson model. The local composition expression (eq. (3.131)) is used with a further binary parameter, αij , the so-called nonrandomness parameter (see eq. (3.139)), which has the physical significance of an inverse of coordination number (αij has a value between 0.1 and 0.3), and it holds that αij = αji [15]): αij gij

xij xj e − RT = αij gii xii xi e − RT

(3:139)

However, the gE expression of the Flory–Huggins theory is not integrated in the model as done for the Wilson model. Instead, the authors obtained an expression for gE from eq. (3.139) and the two-liquid theory of Scott [24]. The generalized expression of gE for a multicomponent system is given by PN N gE X j = 1 τji Gji xj xi PN = RT i = 1 j = 1 Gji xj

(3:140)

The parameters τji and Gji in eq. (3.140) are given, respectively, by gji − gii Δgij = RT RT vj Gji = e − αji τji vi

τji =

(3:141) (3:142)

Furthermore, for the parameters τji and Gji it holds that τji = 0 and Gji = 0, if i = j. The activity coefficient of a component, i, is calculated from the NRTL model, using the following equation: ! PN PN N X xj Gij j = 1 τji Gji xj k = 1 τkj Gkj xk + τij − PN (3:143) ln γi = PN PN j=1 j = 1 Gji xj k = 1 Gkj xk k = 1 Gkj xk Thus, three binary interaction parameters are required for each binary pair, when using the NRTL model: the two Δgij and one nonrandomness parameter, αij . The absence of any structural and size information of the molecules in the mixture (either from the Flory–Huggins or from any other theory) makes the NRTL model a pure excess enthalpy equation (i.e., gE = hE ). Nevertheless, it shows at least the same correlation capability as the Wilson model for modeling multicomponent VLE. NRTL has a great advantage over the Wilson model in that it is possible to model LLE, and it remains one of the most used models in phase-equilibrium modeling and process simulation, nowadays.

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The UNIQUAC equation The UNIQUAC (UNIversal QUAsi-Chemical) model, developed by Abrams and Prausnitz [25], solved the (at least, theoretical) deficiency of NRTL of completely excluding the entropic contribution in eq. (3.130), while, at the same time, retaining, or even improving, its powerful capabilities. Indeed, other than the Wilson model, UNIQUAC explicitly considers the structural information from the size and shape of the molecules. The contribution to gE is split into two parts: a residual (energetic) and a combinatorial (entropic) term: gE = gE, R + gE, C

(3:144)

The final expression of gE is derived from the Guggenheim quasi-chemical theory [26], extended using the LC concept of Wilson (eq. (3.131)), thus applying the name UNIQUAC to the theory. The final expression of the combinatorial term is given by gE, C = RT

N X

xi ln

i=1

N Φi ZX ϑi + RT qi xi ln xi Φi 2 i=1

(3:145)

Z is set to 10 in the original publication [25], and ϑi is the average area fraction of component, i, in the mixture at the given composition, x. The average area fraction ϑi is related to the structural parameter qj (a model parameter of UNIQUAC, which is proportional to the external surface area of component i) of each component j and all the molar fractions xj by xi qi ϑi = PN j = 1 xj qj

(3:146)

The first term in the combinatorial term (eq. (3.145)) is the same as the entropic contribution of the Flory–Huggins theory (eq. (3.134)), but the volume fraction is expressed as a function of the structural parameter, ri (which is related to the volume of molecule, i) through the following equation: xi ri Φi = PN j = 1 xj rj

(3:147)

The parameters qi and ri are also called, respectively, van der Waals area and volume and are not regressed but estimated through a group-contribution method [27], which is usually integrated in process simulators. The residual term is given by gE, R = − RT

N X i=1

xi qi ln

N X j=1

ϑj τji

(3:148)

3 Thermodynamics for reactive separations

ln γi = qi 1 − ln R

N X

ϑj τji −

j=1

N X j=1

ϑj τji

PN

k=1

ϑk τkj

167

! (3:149)

with the parameter τji given by τji = e −

Uji − Uii RT

Uji

= e − RT

(3:150)

Thus, the UNIQUAC model only contains two parameters (ΔUji and ΔUij ) for each binary pair, both of which are present in the residual (energetic) contribution.

The UNIFAC group-contribution method The UNIFAC method was developed from the UNIQUAC model using the groupcontribution (GC) concept. The basic idea of the GC concept is that, whereas there can be millions of relevant components in the chemical industry, those components are made by less than a hundred functional groups [28]. If it is possible to describe the properties of a molecule as the sum of the properties of the single functional groups, this increases the flexibility of the model, by allowing making predictions when experimental data are scarce or absent. Although, in general, the assumption behind a GC is necessarily an approximation (functional groups are not expected to give the same contribution, regardless of the structure of the different molecules in which it can be present), it represents an attractive tool for supporting the design engineer during the decision-making process, when information on the thermodynamic behavior of a mixture is lacking. Like the UNIQUAC model, UNIFAC also describes the excess Gibbs energy (and thus, the activity coefficients) of components in a liquid mixture as the sum of a residual and a combinatorial contribution (eq. (3.144)). The original UNIFAC method [28] retains the same combinatorial term gE, C as the original UNIQUAC (which is estimated, in UNIQUAC, by a GC method [27]). However, the residual term gE, R is estimated through the so-called solution of groups concept [29]. According to the solution of groups concept, a multicomponent mixture can be viewed as a mixture of the functional group that builds up the single components of the real system in the same proportion as they appear therein (see Fig. 3.6). Thus, by assuming additivity of the properties of the single functional group, the properties of the mixture can be estimated. Based on the solution of groups concept, the residual contribution to the activity coefficients ln γi R estimated by UNIFAC is given by ln γi = R

N ðiÞ X k=1

ðiÞ

vk



ðiÞ

ln Γk − ln Γk

 (3:151)

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Fig. 3.6: The concept of solution of groups applied exemplary to an equimolar mixture acetic acidbutanol. Both components are split into their respective functional groups, and the property of the mixture is taken as the average property of the groups.

where Γk denotes the activity coefficient of group, k, of molecule, i, in the mixture, ðiÞ Γk denotes the activity coefficient of the same group in the pure fluid i (which must ðiÞ refer to the same reference state as Γk ) and vk is the number of functional groups of type k contained in the molecule, i. The sum in eq. (3.151) is made over all funcðiÞ tional groups N ðiÞ in molecule, i. The group activity coefficient ln Γk and ln Γk are given by an expression similar to eq. (3.149) for UNIQUAC, but involving only group quantities (see [15] for the complete final expression). The group interaction parameter Ψmn which appears in the expression of ln Γk is defined between each pair of groups, m and n, by  a  mn Ψmn = exp − (3:152) T Thus, the parameter amn defines the only two adjustable parameters between pairs of groups in UNIFAC (since amn ≠ anm ). Within a narrow temperature range, the original UNIFAC method shows reliable prediction capabilities toward calculation of vapor-liquid equilibria [30] even for azeotropic points [31]. For this reason, UNIFAC was implemented in different process simulators [32]. Since the first publication, several UNIFAC variants followed, which will not be discussed in detail, here. The main reason for the development of further UNIFAC variants is the improvement of the prediction of specific properties, among which are the following: – Extension to polymer solutions (free-volume (FV) UNIFAC, [33]) – Prediction of LLE (achieved by introducing LLE data sets in the original UNIFAC [34]) – Description of infinite dilution activity coefficients, γi ∞ , heat of mixing hE and asymmetric systems (through the so-called Dortmund modification of UNIFAC [35]) – Description of water-hydrocarbon systems, prediction of octanol-water partition coefficients [36, 37]

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3.2.2 EoS As explained in the introduction of this section, the thermodynamic framework can be used to calculate all the state variables of a homogeneous system and to set up exact equilibrium relationships among different phases in a multiphase system, provided that a quantitative mathematical relationship between N + 2 state variables is available. One class of such mathematical relationship, developed ad hoc for liquid mixtures, is given by gE-models, which were explained in the previous section. The other class is the already introduced EoS, which are much more general than gE-models and represent (at least, conceptually) the complete essence of the thermodynamic behavior of pure fluids and fluid mixtures.

Fig. 3.7: pvT diagram of pure propane, calculated using the SRK-EoS. Dashed lines represent isotherms (the pressure as function of the molar volume at a given temperature). The area below the bell describes the vapor-liquid region (where vapor and liquid coexist), whereas outside the bell, one single phase (either vapor, liquid, or supercritical gas) exists. Once the pvT behavior can be represented, all the other thermodynamic properties can be calculated.

The simplest EoS was already introduced in the last section and is that of an ideal gas, which describes the T, p, v behavior of a substance (or mixture) at the limit of zero density (ρ ! 0 or v ! ∞). It works fairly well for describing the thermodynamic behavior of simple molecules at low pressure and, therefore, in many cases, can be successfully used within the γ − φ approach to calculate VLEs. The Van der Waals EoS [38] presented in 1873, was the first EoS that could predict the coexistence of a liquid and a vapor phase [39]. For a long time, however, a complete description of the T, p, v behavior over the whole density range (from gas to liquid) was only possible for hydrocarbon mixtures with or without light gases,

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and mixtures of very slight polar components, using EoS derived from the Van der Waals EoS (so-called cubic EoS), cf. Figure 3.7. An improvement in the description of the thermodynamic behavior of complex fluid mixtures was possible, in the last 30 years, with the advent of more sophisticated statistical mechanics theories and the increase in computational power, which allowed to compare the theory with rigorous calculations [40] (see subsequent discussion on SAFT-based EoS in Section 3.2.3). In contrast to gE-models that allow describing the nonideality in the liquid phase of a large variety of components at low pressure (ranging from simple hydrocarbons to strong polar mixtures like chloroform-acetone and, even, mixtures containing polymers), EoS are high-pressure models [15] applicable in the description of both the liquid and the vapor phase and even supercritical fluids, without conceptual difficulties [39], over a wide pressure range. One of the great advantages of EoS in engineering applications is the possibility to describe the thermodynamic behavior of mixtures starting from the pure-component parameters. Different approaches have been proposed to obtain pure-component parameters, starting from physical properties of the pure-components such as vapor pressure, density or the critical pressure, and temperature. On the other hand, describing multicomponent systems requires an appropriate formulation of the mixture properties of the system as a function of the pure-component parameters (which are universal for each component) through so-called mixing and combining rules [39], and binary interaction parameters; the latter are usually fitted to binary properties in order to improve agreement with experimental data. Unfortunately, the calculation of mixture properties heavily relies on the chosen mixing rule, although some of them are better established for a particular class of EoS (which will be described for each presented EoS).

Molar volume and fugacity coefficients from an EoS In general, EoS are provided as pressure-explicit expressions or as compressibility factor, z, as a function of temperature, T, molar volume, v, and composition, x: p = pðT, v, xÞ z=

pv = zðT, v, xÞ RT

(3:153) (3:154)

Both eqs. (3.153) and (3.154) are perfectly equivalent. When performing phase-equilibrium calculations, the pressure and the temperature are usually provided, with the composition (molar fractions) and the molar volume (or, equivalently, the density) treated as iterating variables to match the isofugacity criterion (eq. (3.50)). For a fixed composition and temperature, eqs. (3.153) and (3.154) may have one or multiple solutions, that is, they are fulfilled by more than one value of the molar volume

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or density, depending on the value of the temperature. This is physically correct, since at a given temperature and composition, both a liquid and a vapor phase can, in principle, exist, both described by the same EoS. Figure 3.8 shows the p-v diagram of pure propane (xi = 1) with three different isotherms, one subcritical, one critical, and one supercritical, calculated with the EoS SRK.

Fig. 3.8: Representation of three different isotherms (supercritical, critical, and subcritical) of npropane using the SRK EoS. At constant temperature, the SRK has only one root for T ≥ Tcr and three different roots for T < Tcr.

The SRK EoS (and all the other cubic EoS) has only one root for a given pressure at the critical temperature or at higher temperatures. However, at a subcritical temperature and in a certain pressure range, there are three different molar volumes that fulfill eqs. (3.153) and (3.154): the lowest corresponds to the liquid phase, the higher to the vapor phase, and the value in between is physically meaningless. In advanced EoS, the liquid and the vapor volume are iterated until the calculated pressure matches the target pressure (i.e., the pressure at which the phase equilibrium is calculated). Once the molar volume-satisfying eqs. (3.153) and (3.154) are found, the fugacity coefficient (and the fugacity) of each component in each phase can be calculated, at the given pressure, temperature and composition, φi = φi ðT, p, xÞ. An expression for the fugacity coefficient φi of a generic component, i, can be obtained starting from the pressure dependence of the residual partial molar Gibbs energy, gires = gi − giid of a generic component, i. The partial molar Gibbs energy gi is related to the pressure and temperature by eq. (3.155), whereas the pressure dependence of the residual Gibbs energy and of the fugacity coefficient are related to the vi − vid residual partial molar volume vres i = i of the same component by

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dgi = − si dT + vi dp
!   ∂ gi − giid ∂ ln φi = RT = vi − vid i ∂p ∂p T

(3:155) (3:156)

T

The partial molar volume of component, i, as an ideal gas is simply the molar volume according to the ideal gas law RT=p, and the (real) partial molar volume vi is given as the partial derivative of the extensive volume, V, over the mole number of the component i, vi = ð∂V=∂ni ÞT, p, n . Thus, by integrating eq. (3.156) from zero pressure (idealj≠i gas conditions) to the actual pressure, p, an explicit expression for the fugacity coefficient of component, i, in a mixture (eq. (3.157)) and as pure component (eq. (3.158)) can be obtained: ln φi ðT, p, xÞ =

1 RT

ðp RT vi − dp p

(3:157)

0

ln φðT, pÞ =

1 RT

ðp v−

RT dp p

(3:158)

0

Equations (3.157) and (3.158) require, however, a volume-explicit EoS, which can be used to calculate either the partial molar volume vi (eq. (3.157)) or the molar volume v (eq. (3.158)) as function of temperature, pressure, and composition. However, most of the EoS are pressure-explicit. That is, the previous equations for the fugacity coefficient (eqs. (3.157) and (3.158)) must be reformulated, so that they need an explicit expression for the pressure as a function of volume, temperature, and composition. This can be accomplished by replacing the pressure as variable of the integral to the volume, as follows:   ∂p dv (3:159) dp = ∂v T    

  ∂p ∂ zRT RT ∂z zRT = = − 2 (3:160) ∂v T ∂v v v ∂v v T T By inserting eq. (3.160) into (3.157) and (3.158), an expression for the fugacity coefficient φi can derive (eqs. (3.161) and (3.162)), which can be directly used with a pressure-explicit EoS: #   ðV " 1 RT ∂p  dV − ln z (3:161) − ln φi ðT, v, xÞ = RT V ∂ni T, V, n ∞

j≠i

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ln φðT, vÞ =

1 RT

ðv ∞

RT − p dv + z − 1 − ln z v

(3:162)

It should be mentioned that the variable of the integral in eq. (3.161) is the extensive volume, V, whereas the variable of the integral in eq. (3.162) is the molar volume, v. One further useful expression for the fugacity coefficient can be derived, if the EoS is given as a Helmholtz energy aðT, v, xÞ or residual Helmholtz energy ares ðT, v, xÞ. In this case, eq. (3.163) can be used directly to calculate the fugacity coefficients: "  res  1 ∂a ln φi ðT, v, xÞ = ares + ðz − 1Þ + ∂xi T, v, x RT

− j≠i

N X k=1

 xk

∂ares ∂xk

#



− ln z T, v, xj ≠ k

(3:163) The mathematical background of eq. (3.163) will not be provided here. Equation (3.163) provides the fugacity coefficient at given temperature, pressure, and composition, and only requires an expression of ares and ð∂ares =∂xi ÞT, v, x . j≠i The usefulness of the introduced concepts will be illustrated for calculating the vapor pressure, pLV, of a pure component, using a pressure-explicit EoS (eqs. (3.161) or (3.162)). In this specific case, only the temperature, TLV, can be provided, since the system has only one degree of freedom (according to the Gibbs Phase-Rule). According to the phase-equilibrium conditions, temperature, pressure, and fugacity must be equal in both phases, at equilibrium. For the specific case of a pure-component system, the isofugacity criterion reduces to the equality of the fugacity coefficient, in both phases: φL = φV

(3:164)

Thus, the phase-equilibrium problem reduces to find the pressure that satisfies eq. (3.164). The algorithmic procedure is illustrated in Fig. 3.9. According to the illustrated procedures, after providing an initial estimate of the vapor pressure, pLV, at the given temperature, TLV, the first step is to calculate the molar volumes of the vapor and liquid phases at the given pressure and temperature. As already explained, this is performed iteratively for the vapor and liquid phases, by adjusting the molar volume until the calculated pressure, pcalc, matches the vapor pressure, pLV. Convergence to the liquid or vapor phase is ensured by an appropriate choice of the initial estimate (a small initial value for vL and a big value for vV ). In a second step, the calculated molar volumes are used to calculate the fugacity coefficients of both phases, according to eq. (3.162) (or with (3.162), for a pure component). If the absolute difference between both fugacity coefficients reaches a given tolerance, the procedure is terminated, and the vapor pressure is taken as the used pLV. Otherwise, a new update of the current pLV is generated

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Fig. 3.9: Algorithmic procedure to determine the vapor pressure of a pure component using a pressure-explicit EoS.

(according to the employed numerical method), and the procedure is repeated until the fugacity coefficients differ by a value smaller than the chosen tolerance.

Cubic EoS Cubic EoS represents a category of models based on the Van der Waals EoS, first proposed in 1873, which was the first EoS capable of representing the vapor-liquid coexistence. The compressibility factor, z, (z = pv/RT) is given, according to the Van der Waals EoS, by z=

v a − v − b RTv

(3:165)

In eq. (3.165), a and b are the only adjustable model parameters, which, for instance can be evaluated using critical data. Both parameters can be traced back to certain

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molecular features: b represents the co-volume occupied by the molecules, and a is a measure of the attractive forces between the molecules. Correspondingly, the first term on the right-hand side of eq. (3.165) is called repulsive term and is a measure of the repulsive intermolecular forces, whereas the second term is called attractive term and is a measure of attractive intermolecular forces. The name cubic originates from the fact that eq. (3.165) can be rewritten as a third-order polynomial, with respect to the volume:   RT − va + ab (3:166) 0 = v3 − v2 b + p Although simple and, to a certain extent, physically based, the Van der Waals EoS gives only a qualitative description of the pvT-behavior of even simple substances; thus, it is not suitable to perform rigorous phase-equilibrium calculations or for design purposes (Soave, 1984). Therefore, several EoS were developed starting from the Van der Waals EoS (eq. (3.165)) by introducing more involved mathematical correlations in either the attractive or the repulsive term and by developing expressions for describing mixtures using the parameters of the single components [41]. This improved the modeling capabilities of such EoS, although the physical significance of the parameters becomes unclear and the EoS have substantially semiempirical character. However, cubic EoS became very popular for describing the thermodynamic behavior of simple compounds and mixtures up to very high pressures. The two most popular Cubic EoS – the Redlich–Kwong and the Peng–Robinson EoS – will be introduced in this section.

Redlich–Kwong (RK) EoS and Soave–Redlich–Kwong (SRK) EoS The first successful modification of the Van der Waals EoS is the Redlich–Kwong (RK) EoS [42]. It retains the repulsive term of the Van der Waals EoS and uses an empirical modification of the attractive term, while retaining only two model parameters, a and b. The final expression for the compressibility factor is given by z=

v a − 1.5 v − b RT vðv + bÞ

(3:167)

The RK EoS shows a significant improvement over the Van der Waals EoS for calculating pressure and density of pure components and mixing enthalpies [43], while retaining two pure-component parameters. The calculated second virial coefficient and isotherms of noble gases showed excellent agreement to experimental data [44]. However, the RK EoS shows decreased accuracy in describing the thermodynamic behavior of complex fluids with increasing deviation from the spherical shape of noble gases [44]. In order to compensate for this deficiency of the RK EoS and to extend its validity to hydrocarbon mixtures with different chain lengths, Soave [45] proposed a further modification of the temperature dependency of the

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energy parameter a and the introduction of the acentric factor ω to account for deviations of real molecules from the spherical shape. The acentric factor is defined T with the critical temperature as a function of the reduced temperature, Tr (Tr = Tc LV at temperature T diTc ), and the reduced vapor pressure, pLV r (vapor pressure p vided by the critical pressure pc ), at Tr = 0.7 by [46]
 ω = − log pLV −1 (3:168) r Tr = 0.7
 The logarithm of the reduced vapor pressure log pLV is approximately linear to the r inverse reduced temperature, ðTr Þ − 1 . Spherical molecules (such as helium, argon, or
 vs. ðTr Þ − 1 diagram, whereas asymmetrikrypton) lie on the same line in the log pLV r cal molecules show a steeper slope, which is more pronounced with increasing deviation from the spherical shape; this slope defines the acentric factor, ω (see Fig. 3.10).


 Fig. 3.10: Definition of the acentric factor as the distance from the actual log pLV line to the r
LV 
LV  reference log pr line (that of the noble gases) at Tr = 0.7 on the log pr vs. ðTr Þ − 1 diagram.

The acentric factor is tabulated for the most common fluids or can be estimated using correlations [46]. The final expression for the compressibility factor z and the cohesive energy a containing the acentric factor ω is given by z=

v að T Þ − v − b RT ðv + bÞ


 2 aðT Þ = ac 1 + m 1 − Tr0.5

(3:169)

(3:170)

3 Thermodynamics for reactive separations

m = 0.48 + 1.5746ω − 0.176ω2

177

(3:171)

The parameters ac and b are functions of the critical properties of the pure component by ac = 0.42748

ðRTc Þ2 pc

(3:172)

RTc pc

(3:173)

b = 0.08664

The SRK is now one of the most popular EoS in the chemical industry, whereas the PR EoS is mostly of historical value [15]. Both the RK EoS and SRK EoS can be used to describe the thermodynamic behavior of a fluid mixture, given that the purecomponent parameters are available. As mentioned in the introduction of this section, this is one of the great advantages of EoS and one of their clear superiority over gE-models, which, per definition, require a minimal experimental data basis of the properties of the mixture (at least, of each binary subsystem). One widely employed way of extending the pure-component parameters of the RK and SRK EoS to N-component mixtures is through the classical Van der Waals one-fluid mixing rule (VdW 1 f, eqs. (3.174) and (3.175)), and the classical combining rules (eqs. (3.176) and (3.177)) for calculating the energy and co-volume parameters a and b of the mixture from those of each component, ai and bi [15]: a=

N X N X

xi xj aij

(3:174)

xi xj bij

(3:175)

i=1 j=1

b=

N X N X i=1 j=1


0.5
 1 − kij aij = ai aj bij =

 bi + bj
1 − lij 2

(3:176) (3:177)

Through the Van der Waals one-fluid mixing rule and the classical combining rules, two further binary interaction parameters, namely, kij and lij , are required. They are fitted to mixture properties in order to improve the model accuracy. However, comparing the two binary interaction parameters, the kij is, by far, the more important one, whereas the lij parameter is often omitted [15] and becomes important when treating asymmetric mixtures with hydrocarbons [47]. When the lij parameter is set to zero, the mixing rule for the parameter b reduces to b=

N X i=1

xi bi

(3:178)

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Peng–Robinson EoS Together with the SRK EoS, the Peng–Robinson (PR) EoS [48] is the most successful modification of the Van der Waals EoS and, today, is one of the most popular EoS. The PR EoS retains the simplicity of a cubic EoS and the predictive capability of the SRK for calculating VLE in natural gas systems. However, compared to the SRK EoS, the PR EoS shows better predictions of liquid densities [49] and other thermodynamic properties near the critical point [50]. In addition to predicting well, the bubble points and dew points close to (and also far away from) the critical point, PR EoS allows predicting the retrograde behavior of near-critical gas-condensate fluids [50, 51]. The PR EoS retains the repulsive term of the Van der Waals and SRK EoS, while the attractive term is further developed. The final expression for the compressibility factor is given by v aðT Þv − v − b RT ½vðv + bÞ + bðv − bÞ

(3:179)


 2 aðT Þ = ac 1 + m 1 − Tr0.5

(3:180)

m = 0.37464 + 1.54226ω − 0.26992ω2

(3:181)

z=

The parameters ac and b are related to critical properties by ac = 0.45724

ðRTc Þ2 pc

(3:182)

RTc pc

(3:183)

b = 0.0778

In contrast to the SRK EoS, the PR EoS predicts a constant value of the critical compressibility factor zc of 0.307 [15] for all substances, which is a more realistic value for zc than that predicted by the SRK EoS [50]. The pure-component parameters of the PR EoS can also be extended to N-component mixtures, as done with the SRK EoS, using the classical Van der Waals mixing rule and the classical combining rules (eqs. (3.174)–(3.177)). Besides the superiority of the PR over the SRK EoS mentioned at the beginning of this section, both models perform comparably well in predicting the VLE of hydrocarbon systems. even without binary interaction parameters, given that the pure-component vapor pressure of each component is reproduced well [49]. However, binary interaction parameters are necessary for an accurate description [15] in mixtures containing hydrocarbons and light gases (N2, CO2, and H2) or mixtures of polar components. One drawback of all the cubic EoS is their poor performance when correlating VLE of complex polar or/and associating mixtures; further, cubic EoS cannot describe highly complex systems like electrolytes or biomolecules [15], and LLE is generally not very well correlated using cubic EoS [52]. Despite these deficiencies, cubic EoS are simple and computationally efficient for

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phase-equilibrium calculations, especially compared to noncubic EoS (see Section 3.2.3). For this reason and for their reliability in describing the VLE of noncomplex mixtures, they have found widespread acceptance in the petroleum industry [49], and they are the first choice in modeling VLE for gas processing and air separation operations [53].

3.2.3 Advanced EoS As explained in the previous section, cubic EoS have found large acceptance as engineering-like models for phase-equilibrium calculations (alone, or in combination with a gE-model); however, they suffer from several issues, which prevent them from being used for complex modeling tasks. The two most popular EoS, the PR and the SRK EoS, were derived by introducing semiempirical expressions in the attractive term of the Van der Waals EoS. The shortcoming of such an approach is the lack of a rigorous framework for developing a useful model and the possible nonreliabilities in model extrapolations. The main contribution to the development of more advanced EoS originates from statistical thermodynamics. This is an active field of research, and for an introduction into the topic, the reader is referred to specialized literature [54]. The basic idea of statistical thermodynamics is that the macroscopic properties of a system, which are described by the laws of classic thermodynamics (Section 3.1), are averaged values of the microscopic properties of the molecules (i.e., their intermolecular interaction potential). By considering a closed isochoric isothermal system (T, v, x), the Helmholtz energy, A (a macroscopic property), of the system is related to the microscopic properties of that system through the canonical partition function, QN : A = − kB T ln QN

(3:184)

The canonical partition, QN function, can, at least, in principle, be obtained once the intermolecular interaction potential of the molecules is known. However, two main problems arise with this approach: – The canonical partition function is an involved multidimensional integral over all the degrees of freedom of the considered system of molecules. There is no analytical solution even for the simplest real molecular model (except for the ideal gas). – The interaction potential of real molecules can be very complicated and, for most of the molecules, is unknown. Regarding the first point, approximated solutions of eq. (3.184) for several model fluids, such as integral or perturbation theories became increasingly available. At the same time the increasing computational power and the widespread use of Monte Carlo or Molecular Dynamic simulations to obtain numerical solutions of eq. (3.184)

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allowed comparison of approximated theories with rigorous data and provided the frame to improve existing theories. Regarding the second point, improved theories allowed developing EoS for model fluids, which showed similar features of real molecules (such as hard core, nonspherical shape, association sites). The main advantage of this approach is that an EoS can be made arbitrarily accurate (at least, in principle) by either improving the representation of the underlying model, or by choosing a more realistic model and interaction potential. One of the most important milestones of this approach, the Statistical Associating Fluid Theory (SAFT), will be introduced in the following.

SAFT-based EoS SAFT is a theoretical model developed, in its actual form, by Chapman et al. [55, 56], based on the pioneering work of Wertheim on statistical mechanics of associating fluids [57–60]. The fluid model, which is described by the SAFT EoS, is essentially a hard-chain fluid consisting of joint hard spheres, each of which can interact through short-range dispersion and highly directional hydrogen bonding, denoting “association” forces (see Fig. 3.11). According to the SAFT EoS (and, essentially, to almost all SAFT developments, which followed since then), the residual Helmholtz energy is given as the sum of four contributions according to ares = ahs + achain + adisp + aassoc

(3:185)

The four contributions are, in turn: – Hard sphere ahs : calculated through the Carnahan-Starling EoS for mixtures of hard spheres, this contribution accounts for repulsion forces arising from the fact that real molecules occupy a defined space region and can hardly penetrate each other. – Chain formation achain : calculated through the Wertheim’s perturbation theory by assuming an infinitely strong physical bound, this contribution accounts for the formation of the hard chain and, together with the hard-sphere term, builds the EoS for hard-chain mixtures. The hard chain accounts for the deviation of the shape of real molecules from the symmetric shape of a perfect sphere. – Dispersion adisp : calculated as a perturbation of the hard-sphere term, this contribution accounts for intermolecular interactions of real molecules through Van der Waals forces. – Association aassoc : calculated through the Wertheim’s perturbation theory, this contribution accounts for strong, short-ranged, and highly directional attractive forces, such as hydrogen bonding.

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The model fluid described by the SAFT EoS is assigned with up to five model parameters for each component, i, each of them with a well-defined physical significance. Those are the segment diameter, σi , the segment number, mi , the dispersion energy, ui =kB , the association energy εAi Bi and the association volume, κAi Bi (see Fig. 3.11).

Fig. 3.11: The model fluid (right) described by SAFT-based EoS and the corresponding physical meaning of the model parameters used to model real molecules such as sucrose (left).

Although the model fluid described by the SAFT EoS is still an oversimplification of the real structure and interaction potential of complex molecules, it accounts explicitly for several of their real features. Furthermore, because of the intrinsic physical meaning of the SAFT parameters, the underlying theory can be improved by choosing more appropriate interaction potential and testing the theory against numerical calculations or properties of real fluids. Thus, several theories followed from the original SAFT publication, among which are the following: – SAFT-LJ [61, 62]: The SAFT-LJ EoS uses the Lennard-Jones potential as the interaction potential to describe the dispersion term. The EoS performs better than the original SAFT in describing pure components and mixtures of n-alkanes, 1alkanoles and water. – SAFT-VR [63]: The dispersion term in SAFT-VR is the square-well potential. This EoS contains, however, the potential width as further model parameter, which gives the model greater flexibility and explains certain anomalous behaviors in aqueous systems [15]. – PC-SAFT perturbed-chain SAFT [64]: The greatest leap of PC-SAFT is to develop the dispersion term as perturbation of the hard chain as reference fluid instead of the hard sphere (as done in the SAFT-based EoS mentioned above). Thus, the dispersion term of component, i, is not simply given by mi -times the dispersion

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of the single segment, but it accounts implicitly for the asymmetric shape of the chain. The PC-SAFT EoS is, therefore, particularly suitable for polymer mixtures. SAFT-based EoS (especially PC-SAFT and SAFT-VR) have been applied to correlate phase- equilibria and physico-chemical properties to a large variety of compounds [64], and have been successfully extended to model electrolyte systems [65–68]. The modeled substances range from low- and high-pressure polymers and polymer–monomer mixtures [64, 69, 70] to alkanes with light gases [71, 72], pharmaceuticals [73, 74], gas solubilities [75], ionic liquids [76, 77], aqueous amino-acid solutions [78, 79], and electrolyte systems [80–87].

3.2.4 Electrolyte models Modeling the thermodynamic behavior of systems containing electrolytes is an own field of research due to specific peculiarities of those systems. Therefore, this paragraph is meant to be a very brief introduction to the subject, and the interested reader is forwarded to the specific literature [88–90]. Particularly, two aspects need to be considered when one or more dissociating salts are present in the system: – The presence of components carrying a net charge and the resulting electrostatic contribution to the chemical potential – The long-range nature of electrostatic forces Regarding the first point, it was stated at the beginning of Section 3.1.1 that the thermodynamic framework is usually derived, neglecting the effect of external force fields. All the subsequent phase-equilibrium formulations are based on this assumption. However, even in the absence of external fields, the presence of charged components causes an electrostatic field, which must be considered in the Gibbs fundamental equations (eqs. (3.8), (3.16), (3.23), and (3.25)). However, it can be shown that under the assumption of electroneutrality in each phase, the explicit consideration of the electrostatic field in the chemical potential can be avoided [91]. For a salt, CA, dissociating in jνC j cations and jνA j anions, according to the following equation: CA ! jνC jC + jνA jA

(3:186)

This leads to the formulation, for the whole salt CA, of a Mean Ionic Activity Coefficient (MIAC), γ ± [91], which should be used for phase-equilibrium calculations, instead of the single-component activity coefficient defined in eq. (3.62). The MIAC is defined by 

 1 jνC j jνA j jνC j + jνA j γ ± = γC γ A

(3:187)

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Regarding the second point, the presence of long-range (LR) interionic electrostatic interactions demands an ad hoc treatment of those forces. When two uncharged molecules are five diameters apart, they barely interact each other, whereas, if two ions are five diameters apart, there is still a strong interaction among them. Two successful theories for describing interionic electrostatic forces are the Debye-Hückel [92] and the MSA (Mean Spherical Approximation) [93] theory. They are formulated as a contribution to the overall Gibbs or Helmholtz energy added as a further term, together with a classical gE-model or an EoS to account for the short range (SR) nonelectrostatic part of the interactions: g = gSR + gLR

(3:188)

a = aSR + aLR

(3:189)

This approach led to several successful electrolyte models developed from established gE-models or EoS. Popular electrolyte (e)-gE-models are eNRTL [94], eUNIQUAC [95], and Pitzer [96, 97]. Popular EoS-based electrolyte models are, among others, eCPA [98], ePC-SAFT [99], and eSAFT-VR [100]. Understanding and modeling the thermodynamic behavior of electrolyte solutions is of vital importance in several applications of reactive absorption (see Chapter 6), for example in sour-gas absorption with chemical solvents [101] (see Example 3.3.3). Due to the electroneutrality condition which must be satisfied in each phase 1,. . .,π at equilibrium, the number of degrees of freedom of an electrolyte system is reduced by π-1 (compared to the corresponding reactive or non-reactive non-electrolyte system).

3.3 Application examples This section presents some concrete examples in which the thermodynamic framework presented in Section 3.1, coupled with an advanced thermodynamic model (PC-SAFT or ePC-SAFT), is used to solve the chemical equilibrium in an homogeneous liquid phase (Sections 3.3.1 and 3.3.2) or in a two-phase vapor-liquid system (Section 3.3.3) with the goal of finding the best solvent, among different candidates, for a specific task.

3.3.1 Solvent selection and design for chemical reactions The maximum yield of reactions is usually governed by thermodynamic equilibrium. Each reaction is an equilibrium reaction, while thermodynamics determines how far the equilibrium is on the right-hand side of a reaction. The solvent is an influencing factor in determining the possible yield (and thus maximum yield, or in

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other words, the equilibrium yield) of the reaction. In this example, the effect of solvents on the maximum yield of an enzyme-catalyzed model reaction is presented. The enzyme is present at ultra-low concentrations in the reaction solvent and, thus, is reasonably assumed to not affect the reaction equilibrium. The example shown here is the alcohol dehydrogenase (ADH) catalyzed reaction in Scheme 3.1. acetophenone + 2-propanol Ð 1 phenylethanol + acetone O

OH

+

OH ADH NADH+H•

O

+

Scheme 3.1: The ADH catalyzed reaction scheme; conditions: pH7, 303.15 K, 1 bar, 0.2 mmol · kg−1of the cofactor NADH + H+, 0.015 w% of the ADH, 10 (or 20) mmol·kg−1 acetophenone, and 200 mmol·kg−1 2-propanol, see [102].

The experimental results show that the equilibrium position and the equilibrium product yield in the considered aqueous single-phase systems strongly depend on the type and the concentration of the added solvent in the reaction mixture. As shown in Fig. 3.12, the product yield can be increased to almost 100%, by adding the solvent Ammoeng 100 to the aqueous reaction mixture. That is, Ammoeng 100 shifts the reaction equilibrium far on the right-hand side of the ADH reaction. This allows optimizing the yield by proper solvent selection. Thermodynamic modeling by means of ePC-SAFT was used to predict the equilibrium product yield, upon addition of the solvents under study.

Fig. 3.12: Example for the solvent influence on the 1-phenylethanol synthesis from acetophenone, expressed as yield of 1-phenylethanol at pH = 7, T = 303.15 K, p = 1 bar [102].

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The following steps are required for modeling such processes: – Access the Ka value of the reaction in Scheme 3.1, as a function of temperature. This requires measuring one experimental equilibrium concentration at any arbitrarily chosen condition and knowing the starting concentrations at t = 0. Calculate the extent of the reaction and the Kx value of the reaction according to eq. (3.117). Use a thermodynamic model to access Kγ according to eq. (3.120), and Ka according to eq. (3.119). – Use an initial guess for the reaction coordinate in the presence of solvent and calculate the Kx value of the reaction according to eq. (3.117). Use a thermodynamic model to access Kγ according to eq. (3.120), and Ka according to eq. (3.119). – Iterate step 2 as long as the Ka from step 2 is in agreement within a defined uncertainty with Ka from step 1. Usually, the defined uncertainty could be defined in the order of magnitude of the experimental uncertainty of Kx in step 1.

3.3.2 Solvent selection and design for separations Besides finding a suitable catalyst or solvent for a chemical conversion as shown in Section 3.3.1, finding the best extraction solvent for a separation task is an expensive proposition, as experiments are designed by experience and by trial-and-error principles (see Chapter 2 for a discussion about systematic methods to choose the best solvent). Unfortunately, the number of possible extraction solvents is very huge and a solvent selection guideline is often missing for the given separation task. Hansen solubility parameters are among the thermodynamic tools that are usually applied to predefine possible extraction solvents. Besides ab-initio methods based on quantochemical calculations (like COSMO-RS [103]) or GC-methods [104], thermodynamic models are much more meaningful and powerful for the solvent selection than empirical methods like the Hansen solubility parameters. UNIFAC, UNIQUAC, NRTL, and PC-SAFT have already been applied to model LLE of ternary systems FA/ water/extraction solvent. Approaches as simple as possible and as complex as necessary (i.e., number of parameters) were achieved for selecting the best extraction solvent; Fig. 3.13 shows that increasing C-chain length of the extraction alcohol causes decreased distribution coefficients of formic acid between the organic and the aqueous phase. Such a decrease with increasing C-chain length is known also for the extraction of acetic acid with 1-alkanols. Obviously, 1-butanol caused the highest distribution coefficients. In the final process, 1-hexanol was identified as the most promising solvent as the selectivities (not shown here) are highest with 1-hexanol being the extraction solvent, while still allowing high distribution factors. In order to solve the liquid-liquid equilibria upon addition of extraction solvent, the Gibbs plot is useful, which, for ternary systems, does not use a double-tangent line but the respective tangential area using eq. (3.72) for ternary systems, or by using the isofugacity, or isoactivity criteria in eqs. (3.76) and (3.77).

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Fig. 3.13: Example of the solvent influence on the distribution of formic acid (FA) between an organic phase and an aqueous phase, expressed as distribution coefficient of FA at T = 298.15 K, p = 1 bar. Feed composition (FA/water/solvent in w.%) was 10/45/45. Orange represents experimental data; green is the PCSAFT prediction [105].

3.3.3 Solvent selection and design for reactive separation processes Several processes require a solvent suitable for chemical reactions as well as for separation processes. Aqueous amine solutions are usually applied to purify raw gas streams or to separate CO2 from power plant exhaust gas streams. Aqueous amine solutions are useful for reducing the total CO2 content of gas streams down to a few ppms. Besides the physical solubility of CO2 in the solvent system, the chemical reactions that take place in the liquid phase take place according to Scheme 3.2. ðIÞ H2 O Ð H + + OH − ðIIÞ CO2 + H2 O Ð HCO3 − + H + ðIIIÞ HCO3 − Ð CO3 2 − + H + ðIVÞ MDEAH + Ð MDEA + H + Scheme 3.2: Overview of the reactions of the liquid water–MDEA–CO2 system that need to be accounted for.

The physical solubility of CO2 in the aqueous amine solution is very low, as represented by the dashed line representatively shown in Fig. 3.14. Please note that the example given in Fig. 3.14 is of qualitative level only, to demonstrate the qualitative influence of the formation of chemical species according to Scheme 3.2 on the phase-equilibrium calculations. Further, it is obvious that experimental data exist on measured pressures upon loading the absorption solvent with a certain amount of CO2. Accurately modeling the gas solubility in the aqueous amine solution is only possible (full line in Fig. 3.14) by accounting for the species formation according to Scheme 3.1 and choosing an appropriate electrolyte model for the charged components (Section 3.2.4). That is, reaction equilibria and phase equilibria have to be solved successively for a successful description of the reactive system.

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Fig. 3.14: Example for the loading influence (moles CO2 per mol MDEA) on the equilibrium pressure of an aqueous solution containing 30 wt.% MDEA at 373 K. ePC-SAFT modeling (solid line) possible by treatments presented by [106]. The dashed line represents physical absorption (without chemical reaction).

In order to solve the chemical absorption problem, the following steps are required: – Access the pKa values (acid dissociation constants) describing the underlying reactions according to Scheme 3.2 as a function of temperature; these pKa values are related to infinite dilution in water for reactions (II–IV). – Use an initial guess, based on the pKa values and solve eqs. (3.110) and (3.111). Often, the Henry constants are used and extended Henry’s law (eq. (3.94) is applied using an EoS-type model to calculate the activity coefficients and fugacity coefficients. – Iterate the species distribution and the phase-equilibrium condition, until reaction equilibrium and phase equilibrium are reached and eqs. (3.110) and (3.111) are fulfilled.

3.4 Quizzes – What do the first and second laws of thermodynamics say? – What are equilibrium conditions of the following systems: adiabatic isochoric, adiabatic isobaric, isothermal isochoric, and isothermal isobaric? – What are the phase-equilibrium conditions of a general multicomponent multiphase system?

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– How do you formulate the total Gibbs energy of a multiphase multicomponent system? – What are global and local methods for phase-equilibrium calculations? – What does the Gibbs phase rule for a nonreactive system say? – What are reference states? Name and explain two reference states used in phase-equilibrium thermodynamics. – What are the fugacity and the fugacity coefficients, and what do they depend on? – What is the expression of the chemical potential of a component, i, in a mixture of ideal gases? – How can you reformulate the phase-equilibrium conditions using the fugacity? – What is the advantage of using the fugacity instead of the chemical potential in phase-equilibrium calculations? – On what bases do condensed phases strongly differ from gaseous phases? – What is the expression of the chemical potential of a component, i, in a ideal mixture of real fluids? – Under which conditions does a mixture of real gases behave like a mixture of ideal gases? – Under which conditions does a real mixture of real fluids behave like an ideal mixture of real fluids? – What does the excess Gibbs energy of a mixture say? – How are activity and activity coefficient defined? On what do they depend? – Under which conditions does the activity coefficient approach the value of one? – What do you understand by φ–φ, γ–γ, and γ–φ concepts? – What is the thermodynamic explanation on partial mixing of two or more liquid phases? – What is the thermodynamic condition of phase instability? – Which concepts and models are usually employed to solve a LLE problem? – Which concepts and models are usually employed to solve a VLE problem? – Derive the general formulation of the VLE problem for a generic component, i, using the γ–φ concept and the pure-component reference state. – Derive the general formulation of the VLE problem for a generic component, i, using the γ–φ concept and the reference state of infinite-dilution at unit molar fraction. – Under which conditions do the Raoult’s and Henry’s law hold? – Which conservation law holds in any chemical reaction? – What are stoichiometric coefficients and what do they reveal in a chemical reaction? – What is the reaction coordinate and what does it characterize? – Write the general expression of the number of moles of a generic component, i, as a function of the reaction coordinate, for the cases of single and multiple reactions.

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– What is the purpose of determining a set of key reactions for a reactive system? – Describe the methodology to determine a set of key reactions in a reactive system of N components. – Formulate the chemical equilibrium as an optimization problem and derive a necessary condition of chemical equilibrium. – Recall the general conditions of chemical and physical equilibrium in a multicomponent multiphase system with multiple (key) reactions. – How are the fugacity- and activity-based equilibrium constants defined? On what do they depend? – What do you understand under Standard Gibbs free energy of reaction? – What does the Gibbs Phase-Rule for reacting systems say? – What are the two categories of models used to model phase equilibria? – What are the differences, advantages, and disadvantages of both model categories for a given modeling task? – How can you calculate the activity coefficient of a generic component, i, from an expression of the excess Gibbs energy? – What is the meaning of the enthalpic hE and entropic TsE contributions to the excess Gibbs energy? – Explain the concept of local composition. – What do you understand by “athermal” mixtures? Name a model which is particularly suitable to describe the thermodynamic behavior of athermal mixtures. – What are strengths and weaknesses of the Wilson model? – What is the biggest advantage of the NRTL model over the Wilson model? – Why is NRTL also called a pure excess enthalpy model? – How does UNIQUAC describe the excess Gibbs energy? Which features of real molecules are described by UNIQUAC? – What do you understand by “group contribution methods?” – Explain the concept of solution of groups. – In which stage of process design does UNIFAC offer great advantages and why? – Explain what you understand by an EoS. What is the simplest EoS that you know and under which condition does it remain accurate? – What are advantages of Equations of State over classical gE-models? – How do you can calculate the fugacity coefficient of a generic component, i, from a pressure-explicit EoS? – How do you can calculate the fugacity coefficient of a generic component, i, from an expression of the residual Helmholtz energy, ares ? – How can you calculate the density of a pure substance at a given temperature from an EoS? How can you choose between the density of the vapor and the density of the liquid? – How can you calculate the vapor pressure of a pure substance at a given temperature from an EoS? – What are cubic EoS? What is the simplest cubic EoS?

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– What are, nowadays, the most popular cubic EoS for phase-equilibrium calculation and under which aspects do they differ? – How can you extend the pure-component parameters of an EoS to handle mixtures? – What are the main advantages and disadvantages of cubic EoS? – In which applications have cubic EoS found widespread acceptance? – What is the main idea behind SAFT-based EoS? Why do they offer flexibility to model complex molecules and to further improve existing SAFT-versions? – What are the model parameters employed by SAFT-based EoS?

3.5 Exercises In this Section, practical examples can be used to test the knowledge presented in Section 3.1 Exercise 1: Provide the number of degrees of freedom, F, of the following systems: pure liquid water, two-phase liquid water and ice, three-phase liquid with vapor and ice, and the two-phase system water with CO2. Solution: According to the Gibbs phase rule (eq. (3.39)), pure liquid water has two degrees of freedom (π = 1, N = 1). This means that two state variables, for instance, the pressure and the temperature, can be fixed independently. The two-phase system of liquid and ice water has only one degree of freedom (π = 2, N = 1), which means that only one state variable can be chosen (for instance, either the temperature or the pressure) and all the others will result from this value. In the threephase system of liquid, vapor and ice water (π = 3, N = 1), no state variable can be chosen, since the number of degrees of freedom is zero. This means that pure water (as well as every pure substance) can show three phases at equilibrium only at given values of temperature and pressure, which cannot be freely chosen and are component- dependent. In the two-phase water-CO2 system (π = 2, N = 2), the number of degrees of freedom is two, that is, two state variables can be chosen independently. Exercise 2: Given the binary mixture benzene(1)–toluene(2) (which behaves nearly ideal), and three different temperatures at constant pressure, calculate the composition of the vapor and liquid phases using Raoult’s law and compare the results to experimental data. The experimental data are given by [107] and are reported at 1.013 bar in Tab. 3.1.

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Tab. 3.1: Concentration of benzene (1) in the liquid and vapor phase in equilibrium at given temperatures and at p = 1.013 bar. T (K)

x (–)

y (–)

. . .

. . .

. . .

Solution: The vapor pressure of benzene and toluene is calculated from the Antoine equation, using parameters from [108, 109], which are reported in Tab. 3.2. log10 pLV 0i = Ai −

Bi T + Ci

pLV i = bar and T = K

Tab. 3.2: Parameters of the Antoine equation used to calculate the vapor pressure of the pure components (1) and (2), at a given temperature. Component

Trange (K)

A

B (K)

C (K)

() ()

.–. .–.

. .

,. ,.

−. −.

To calculate the composition of both phases, Raoult’s law X (eq. (3.86)) and the Anxi = 1 for both phases are toine equation for both components with the condition i used to set up the following system of equations: log10 pLV 01 = A1 −

B1 T + C1

log10 pLV 02 = A2 −

B2 T + C2

x1 pLV 01 ðT Þ = y1 p .

x2 pLV 02 ðT Þ = y2 p x 1 + x2 = 1 y1 + y2 = 1

LV Thus, six independent equations result with eight variables (y1 , y2 , x1 , x2 , pLV 01 , p02 , p, T). However, the total pressure, p, and the temperature, T, in the system are provided. Therefore, the remaining six unknowns can be uniquely calculated from the six independent equations. The calculated values of the mole fraction of benzene in the vapor phase y1 and in the liquid phase x1 are compared with experimental values given as follows:

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x,exp (–) . . .

Moreno Ascani, Christoph Held

x,calc (–)

y,exp (–)

y,calc (–)

. . .

. . .

. . .

Figure 3.15 shows a graphical comparison of the calculated vapor-phase and liquidphase composition, as a function of the temperature and over the whole composition range, with experimental compositions.

Fig. 3.15: VLE of the binary mixture benzene (1)-toluene (2), predicted by the Raoult’s law (dotdashed line) and comparison with experimental data (triangles).

The results show that Raoult’s law gives an excellent prediction of the VLE of chemically similar components. Unfortunately, this is only one exception in which phase equilibrium can be directly calculated from a pure-component property (in this case, the vapor pressure of the pure components at the system temperature). In systems containing components that are largely different in size and/or in intermolecular interactions, such as the binary system ethanol-water, Raoult’s law predicts large deviations from the experimental data (cf. Fig. 3.16). In this case, a thermodynamic model must be used to estimate the activity coefficients of both components in the mixture, accounting for the nonideality of the real-fluid mixture. Exercise 3: Given the binary mixture CO2 (1) – water (2) at the two temperatures (323.15 K and 423.15 K), calculate the concentration of CO2 in both the liquid and vapor phases at different pressures, using the Henry’s and the Raoult’s laws, and compare the results to experimental data. The experimental data are taken from

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p = 1.013 bar

Fig. 3.16: VLE of the binary mixture ethanol (1)-water (2), predicted by the Raoult’s law (dot-dashed line) and comparison with experimental data (triangles) from [110]. Visible in the experimental data is the temperature-minimum azeotrope close to pure ethanol.

[111]. Six data points are reported at the two temperatures, 323.15 K and 423.15 K (see Tab. 3.3). Tab. 3.3: Concentration of CO2 in the vapor and liquid phase in the system CO2 (1)–water (2) as a function of pressure and temperature. T (K)

p (bar)

x (–)

y (–)

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

Solution: The partial pressure of CO2 is estimated through the Henry’s law, and the partial pressure of water is calculated using the Raoult’s law. The Henry’s constant of CO2 in water is calculated at different temperatures using the correlation proposed by [112] and given as follows:

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ln HCO2 − water = C1 + C2 ·

   2  3 T0 T0 T0 + C3 · + C4 · T T T

with H = bar and T = K

The parameters of the correlation are reported in Tab. 3.4. Tab. 3.4: Parameters of the correlation used to calculate the Henry’s constant of CO2 in water as a function of the temperature. Component

C1

C2

C3

C4

T0

()

−.

.

−.

.

.

The vapor pressure of pure water is calculated using a correlation taken by [113] and given as follows: ln pLV 0, water = C1 +

C2 + C3 ln T + C4 · T C5 T

with p = bar and T = K

The parameters of the correlation are reported in Tab. 3.5. Tab. 3.5: Parameters of the correlation used to calculate the vapor pressure of pure water at given temperature. Component

C1

C2

C3

C4

C5

()

.

−.

−.

.E-

.

To calculate the composition of both phases, the Raoult’s law (eq. (3.86)) for water (2) and the Henry’s law for CO2 (1) (eq. (3.95)) are used, together with both correlationsX for the Henry’s constant and the vapor pressure of pure water and the condixi = 1 for both phases. The following system of equations is then set up: tion i

ln HCO2 − water = C1 + C2 · ln pLV 02 = C1 +

   2  3 T0 T0 T0 + C3 · + C4 · T T T

with H = bar and T = K

C2 + C3 ln T + C4 · T C5 with p ðbarÞ and T ðKÞ T x1 H1, 2 ðT Þ = y1 p x2 pLV 02 ðT Þ = y2 p x1 + x2 = 1 y1 + y2 = 1

Again, a system of six independent equations and six unknowns (y1 , y2 , x1 , x2 , H1, 2 , pLV 02 ) results. The calculated values of the mole fraction of CO2 in the vapor y1 and liquid phase x1 are compared with experimental values as follows:

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195

T (K)

p (bar)

x,exp (–)

x,calc (–)

y,exp (–)

y,calc (–)

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

Figure 3.17 shows a graphical comparison of the calculated vapor-phase and liquid-phase composition at the two given temperatures as a function of the pressure. The Henry’s law gives excellent prediction of the solubility of CO2 in water in the low-pressure region. However, the prediction becomes worse as the concentration of CO2 increases with increasing pressure. At high CO2 concentration (i.e., far away from the reference state infinite dilution), the value of the activity coefficient γ*CO2 deviates strongly from unity and, thus, a thermodynamic model is necessary to perform accurate phase-equilibrium calculation. Exercise 4: Given is an equimolar mixture of methane (CH4) and ethane (C2H6) with initial mole number nCH4, 0 = nC2 H6, 0 = 1 mol with the following cracking reactions occurring in the system: R1 : CH4 ! C + 2H2 R1 : C2 H6 ! 2C + 3H2 Calculate the number of moles of all components when the reaction coordinates reach the values, λR1 = 0,4 and λR2 = 0,6, respectively. Solution: From the reactions R1 and R2 the following matrix of stoichiometric coefficients can be written: ν i, j

R1

R2

C H2 CH4 C2 H 6

  − 

   −

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Moreno Ascani, Christoph Held

Fig. 3.17: Comparison between calculated (red line) and experimental (gray symbols, from [111]) solubility data of CO2 in water, at two different temperatures (323.15 K and 423.15 K).

Using the given values of the reaction coordinates and the stoichiometric coefficients, eq. (3.100) can be directly used to calculate the number of moles of all components. The calculation is shown as follows: nCH4 = nCH4.0 + ðν CH4 , R1 · λR1 + ν CH4 , R2 · λR2 Þ = 1 mol + ð − 1 · 0.4 + 0 · 0.6Þmol = 0.6 mol nC2 H6 = nC2 H6.0 + ðν C2 H6 , R1 · λR1 + ν C2 H6 , R2 · λR2 Þ = 1 mol + ð − 1 · 0.6 + 0 · 0.4Þmol = 0.4 mol


 nH2 = nH2.0 + ν H2 , R1 · λR1 + ν H2 , R2 · λR2 = 0 mol + ð2 · 0.4 + 3 · 0.6Þmol = 2.6 mol nC = nC.0 + ðν C, R1 · λR1 + ν C, R2 · λR2 Þ = 0 mol + ð1 · 0.4 + 2 · 0.6Þmol = 1.6 mol

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Exercise 5: In the pyrolysis of ethane, the reaction mixture can be considered, in a first approximation, as being composed of the following components: ethane (C2H6), methane (CH4), ethylene (C2H4), hydrogen (H2), and carbon (C). Determine a minimal number of key reactions using the methodology described in this section. Solution: The first step to determine a set of key reactions is to set up the component-element matrix ε and determine its rank. The component-element matrix ε is given as follows: εj, i C H2 C2 H 4 CH4 C2 H 6

C     

H     

The resulting rank of the component-element matrix is 2. Therefore, the number of independent key reactions, NR , calculated with eq. (3.105), is equal to 4. The second step is to write a system of NR = 4 key reactions and test their linear independence. The following reaction system is proposed as a set of independent key reactions: R1 : C2 H6 ! C2 H4 + H2 R2 : CH4 ! C + H2 R3 : C2 H6 + H2 ! 2CH4 R4 : C2 H4 ! CH4 + C The linear independence of the proposed set of reactions is proved if the rank of the stoichiometric matrix v is equal to NR = 4. The stoichiometric matrix v is given as follows: εj, i

C

H2

C2 H4

CH4

C2 H6

R1 R2 R3 R4

   

  − 

   −

 −  

−  − 

The result is rank = 4. Thus, the proposed set of reactions is linearly independent and, therefore, is a set of key reactions for the given system. Exercise 6: Ammonia (NH3) is, today, one of the most important bulk chemicals and is produced worldwide from gaseous nitrogen (N2) and hydrogen (H2) through the Haber-Bosch process [114]. The chemical reaction on which the Haber-Bosch process is based is given as:

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N2 + 3H2 ! 2NH3 No further key reaction is required to describe this system. Due to the negative change of mole numbers from reactants to the product (and also in order to increase the catalyst efficiency), the reaction is processed at high pressure. Calculate the equilibrium composition in a mixture containing initially only reactants in stoichiometric ratio (N2 :H2 = 1:3) at a pressure of 200 bar and a temperature of 573.15 K. The gaseous mixture can be described by the ideal gas law. Solution: The fugacity-based equilibrium constant Kf is taken from [115] and is equal to 4.469·10−3 at T = 573.15 K. Since only one key reaction is required, only one reaction coordinate λ is required to balance the system. By using eq. (3.99) and considering a hypothetical mixture containing an initial number of moles, nN2.0 = 1 and nH2.0 = 3, the number of moles of each component can be written as a function of λ by the following equations: nNH3 = nNH3.0 + 2 · λ = 2 · λ mol nN2 = nN2.0 − λ = 1 − λ mol nH2 = nH2.0 − 3 · λ = 3 · ð1 − λÞ mol The total number of moles is ntot = nH2.0 + nN2.0 + nH2.0 − 2 · λ = 4 − 2 · λ mol With KX φ = 1 and expressing the mole fractions from the mole numbers, nj , for the considered system, eq. (3.117) can be rewritten as: yi = ni = j



p Kf ð T Þ = Kx ð T Þ · p+

ΔR ν

 2 nNH3 · ðntot Þ2  p  − 2 ð2 · λÞ2 · ð4 − 2 · λÞ2  p − 2 =
· = · 3 p+ ð1 − λÞ3 · ð3 · ð1 − λÞÞ p + nN2 · nH2

with p + = 1 atm (1.01325 bar). The next step is to calculate the reaction coordinate at equilibrium λ* and use this value to calculate the equilibrium composition. There are four solutions of the previous equation. However, only one solution given by λ* = 0.617 is real and has a physical meaning. This value can be used to calculate the number of moles and mole fractions at equilibrium, which are given as:

ni yi

N2

H2

NH

. .

. .

. .

Exercise 7: Calculate the equilibrium composition in the previous example for a pressure of 100 bar. Solution: Since the reaction proceeds from the reactants to ammonia with a reduction of the overall number of moles, a reduction of the pressure will cause a lower yield of

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ammonia and a reduction of its concentration at equilibrium; please note that this is valid for an ideal-gas behavior. The calculation proceeds by first recalculating the reaction coordinate at equilibrium λ* and then the equilibrium composition. At p = 100 bar, the physically meaningful solution of eq. (3.118) is given by λ* = 0.495. The corresponding numbers of moles and mole fractions at equilibrium are obtained as follows:

ni yi

N2

H2

NH

. .

. .

. .

As expected, by reducing the pressure from 200 to 100 bar, the yield of ammonia decreases by 20%. Exercise 8: Provide the number of degrees of freedom, F, of the vapor-liquid twophase reactive mixture containing ethanol (CH3CH2OH), acetic acid (CH3COOH), water (H2O), and ethyl acetate (CH3COOCH2CH3). The reactive system can be described by only one key reaction (esterification of acetic acid and ethanol to ethyl acetate and water), which is given as follows: CH3 CH2 OH + CH3 COOH , CH3 COOCH2 CH3 + H2 O Solution: According to the Gibbs phase rule for reactive systems (eq. (3.125)), the number of degrees of freedom given by eq. (3.39) will be reduced by the number of further mathematical relationships that must be considered in the system, which, in this example, is given by the esterification reaction (the only key reaction which must be considered). The number of degrees of freedom is given by, F = 2 + N − π − NR = 2 + 4 − 2 − 1 = 3. That is, for instance, the pressure, the temperature, and the concentration of one component in one phase, or three concentrations in one or both phases, can be freely chosen in this system.

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Eugeny Y. Kenig

4 Modeling concepts for reactive separations 4.1 Introduction Modeling is a fundamental intellectual instrument to obtain knowledge and comprehension. It is certainly central in engineering. Modeling of technical units and processes represents a widely used theoretical way to understand the existing objects and suggest their improvement. A model represents an abstracted image of a real system to be studied, and thus, modeling is always based on some simplification, while their range and rigor can differ significantly. The modeling rigor is usually chosen in accordance with practical criteria. Often, rigorous models cannot be developed just due to the complexity of the object under study. In some other cases, the necessary data are difficult to obtain. Additionally, model realization can pose further limitations, for instance, regarding simulation time and computer memory capacity. This leads to a combination of modeling and experimental work, and most often, these two fundamental approaches are interrelated. This chapter focuses on modeling methods used in the theoretical treatment of fluid-phase reactive separations (RS), a large class of advanced integrated process engineering operations (cf. Chapter 1). Examples of such integrated operations are reactive distillation (cf. Chapter 5), chemical absorption (cf. Chapter 6), reactive stripping, reactive extraction (cf. Chapter 7), and some other operations. A reasonable combination of chemical reaction and separation has a synergistic effect and offers several economic and ecological benefits. In this chapter, a broad spectrum of different modeling concepts is considered. The modeling principles are explained qualitatively, highlighting the physical basics, without giving the corresponding mathematical framework. This method is chosen because the model equations are largely well-known; thus, the focus is on the modeling background, while duplications within the book are avoided. The modeling approaches are supplemented with corresponding illustrative case studies for individual methods. Finally, the concept of complementary modeling is presented and exemplified.

4.2 General modeling framework Modeling of an industrial process can be represented as a loop shown in Fig. 4.1. It comprises different steps, namely, a thorough process analysis in order to obtain sufficient physical understanding, building of a physical model, its translation into a mathematical model, and its subsequent solution, yielding numerical data for further https://doi.org/10.1515/9783110720464-004

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Process under study

Process analysis Simulations & analysis of results Physical model

Solution strategy Mathematical model Implementation Fig. 4.1: General scheme of theoretical modeling.

investigation. This modeling loop reflects a general procedure valid for nearly all processes. However, its particular steps depend on the specifics of the object being studied. We will consider these steps as applied to fluid-phase RS operations.

4.2.1 Process analysis and physical model First of all, processes must be subjected to a thorough analysis with respect to their physicochemical background and specifics. Such an analysis ends up with the physical model of the process, capable of capturing its major properties. RS have several common features, which helps to develop general concepts for their modeling. These features are as follows: – Processes take place in moving systems; thus, fluid dynamics plays an important part. – At least two phases are involved; therefore, interfacial region and interfacial transport phenomena have to be considered. – Process media represent multicomponent mixtures; consequently, diffusional interactions can become important.

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– Interplay of mass transport and chemical reactions; this results in the need to develop special coupled models. – Nonlinear chemistry and thermodynamics (cf. Chapter 3); the process description is strongly nonlinear. The general modeling concepts can be elaborated to match the desired criteria (e.g., required accuracy, predictivity) and available possibilities (e.g., known data, computer facilities). A model is basically simpler than a real process under study, and a reasonable simplification has always been a welcome approach in engineering. However, the essence of the process behavior must not be lost, and thus, a kind of a balance has to be found between the modeling rigor and simplicity. Along with the general features, peculiarities of the system under study determine the choice of such a balance. They can be subdivided onto – physicochemical properties of the system – flow conditions – system geometry – number of contacting phases – initial and boundary conditions An RS process can be represented as an interrelated combination of several phenomena (fluid flow, mass transfer, heat transfer, interfacial phenomena, chemical reactions, etc.). Accordingly, an overall physical process model is a complex system that can be built up from different submodels describing individual phenomena and connected to each other [1]. The submodels can often be selected independently of the other submodels. For instance, various descriptions of turbulence are possible, beginning with direct numerical simulation and ending with effective turbulent viscosity and diffusivity. Another example is given by the description of multicomponent diffusion, which can either be based on the Maxwell–Stefan approach or, again, on some effective diffusivity method [2]. There are numerous approaches to describe thermodynamic and reaction equilibrium. Depending on the desired/ possible level of understanding, physical models with different rigor and functionality can be developed. We will return to this issue in Section 4.3.

Geometry Fluid-phase RS take place in column units with more sophisticated design than that of traditional operations. Above all, the influence of column internals increases significantly. These internals have to enhance both separation and reaction and to maintain a sound balance between them. This represents a challenging task, since efficient separation requires a large contact area, whereas an efficient reaction strives for a significant holdup and, sometimes, a sufficient amount of catalyst.

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Even if the column internals for homogeneously catalyzed and auto-catalyzed RS processes (e.g., reactive absorption, homogeneously catalyzed reactive distillation, reactive extraction) are very similar to noncatalytic column internals, modifications are often necessary to meet optimum design demands [3]. This is valid both for tray and for packed columns. If the use of solid catalysts is necessary, specific bifunctional internal structures that are capable of combining the separation and catalytic functions – the so-called catalytic internals – are needed. Catalytic internals are commonly manufactured either using immobilization of commercial catalyst pellets or by catalytic activation of conventional internals for fluid separation columns [3, 4]. Among others, various catalytic tray designs have been proposed (see [5–8]), but most often, corrugated packings of the regular type – also referred as structured packings – are applied. These packings provide an enhanced mass transfer performance with a relatively low pressure drop and, consequently, have gained wide acceptance. Since the early 1980s, when corrugated sheet metal structured packings appeared in the market, great advances toward process intensification have been made. Initially developed for the separation of thermally unstable components in vacuum distillation, structured packings have been constantly gaining popularity and cover a large field of applications in chemical, petrochemical, and refining industries due to their more effective performance characteristics [9]. Some typical examples of structured packings are shown in Fig. 4.2. They can be used for homogeneously catalyzed and auto-catalyzed processes, while the packing function is to provide both sufficient residence time and mass transfer area.

Fig. 4.2: Examples of structured packings: metal Mellapak by Sulzer Chemtech Ltd (left), Montz-Pak A3-500 by Julius Montz GmbH (middle) and plastic Mellapak by Sulzer Chemtech Ltd (right).

For heterogeneously catalyzed processes containing solid catalyst phase (e.g., in catalytic distillation and catalytic stripping), structured packings represent complex geometric structures made from gauze wire or metal sheets containing catalyst pellets (see Section 4.5.2). In this case, both mass transfer area and catalyst volume/surface become important parameters influencing the process performance. In

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some RS processes, reactive and nonreactive structured packings are combined within the same column [3, 10]. As we will see in Section 4.5, the design and function of column internals may directly influence the RS models.

4.2.2 Mathematical model Once the physical model is fully established, the object description can be developed as a mathematical model allowing its qualitative and quantitative evaluation. The equations describing the fluid flow and transport phenomena are basically well known. They express the fundamental conservation laws formulated for overall and species mass, momentum, and energy (see [11]). These fundamental laws contain some physical quantities characterizing the process kinetics, e.g., viscosities, diffusion coefficients, heat conductivities, turbulence parameters and – for reacting systems – reaction rates. For such quantities, the corresponding relationships (e.g., dependence on temperature and pressure or mixing rules) must be known. While the transport equations are quite general, they are seldom used in their original form. Very often, particular features of the problem to be solved allow a certain model reduction, for instance, by linearizing nonlinear dependencies, reducing the problem dimensionality (e.g., from three-dimensional to two-dimensional or even to one-dimensional), using constant properties instead of variables, etc. In this regard, a mathematical model is, of course, closely related to its physical basis. The governing equations are valid within the considered computational domain. Most often, the role of the solid phase is to build a framework for the fluid phases, i.e., the geometry, as considered in the previous section. For instance, the packing structure encloses the flow in the RS column. However, sometimes the bulk solid phase must also be included in the mathematical description when heat transfer in the solid walls is important. The geometric boundaries of the computational domain are the boundary conditions set at its solid boundaries – this is what makes a considered problem specific. It is thus very important that the formulation of the boundary conditions is reasonable and unambiguous. In todays practice, model development and structure are closely related to commercial software tools employed for the problem solution. It is especially true when computational fluid dynamics (CFD) methods are used (see Section 4.5.4). In such cases, boundary conditions are simply selected from the portfolio of the tool, while they are often not disclosed to the user, who is thus only partially aware of the mathematical formulation in use. This can lead to errors, both in model formulation and in interpretation of results. An inherent difficulty arises when the boundary conditions must be set at the outlet of the computational domain, where they are basically unknown. This is often encountered in column units, and especially, when they are operated in a two-phase

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countercurrent flow mode. In such situations, additional assumptions are required, which should be made after a careful analysis and, if possible, after a comparative study. Two-phase flows are typical for (reactive) separations, and thus, setting up boundary conditions at the fluid phase interface is indispensable. Here, the conjugation of the quantities of the contacting phases is applied (e.g., continuity of stresses, mass and heat fluxes, and thermodynamic equilibrium relationships). If the interface is spatially fixed, such boundary conditions are formulated without difficulties; when the interface moves, a method to determine its position represents a part of the overall mathematical formulation. An important practical property of the final mathematical model is that it should be solvable within a reasonable computation time and with available computer memory.

4.2.3 Solution strategies and implementation The solution strategies can be subdivided into analytical, semianalytical, and numerical. While analytical methods represent the most exact and straightforward way to the solution, they can be applied only to a very limited subclass of RS problems. Among the reasons are the inherent two-phase nature of the separation operations and the complex flow pattern. In contrast, numerical solution methods can be applied to complex systems, thus avoiding severe simplifications. However, the method must converge, which can seldom be guaranteed, and thus, sophisticated procedures for the generation of suitable starting values for the process variables have to be involved. This can be realized with either formalized or “hand-made” homotopy methods, which allow one to start with a related simplified and easy-to -solve problem and to arrive, step by step, at the original complex problem. This is achieved by using the corresponding output values of a simpler problem as input values for the more complex one (cf., e.g., [12]). Furthermore, relaxation algorithms can be applied that employ better convergence properties of a transient problem, compared to the original steady-state problem [13, 14]. In this case, the simulation starts with an arbitrary initial condition and attains the sought steadystate solution. Most analytical solutions cannot be used directly in calculations without the aid of numerical methods because they contain complex transcendental functions, series, and improper integrals, whose estimation need numerical techniques. Nevertheless, analytical methods represent an important means for solving numerous engineering problems [15]. Besides, they can provide a very good way to check the accuracy of numerical methods by comparison with an exact analytical solution [16]. Sometimes, it is possible to apply a kind of mixed approach combining analytical and numerical techniques. In contrast to purely numerical methods, such semianalytical methods are based on a semidiscretization rather than complete discretization of

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the governing partial differential equations. Consequently, discretization error is reduced. Semianalytical methods show specific advantages when applied to coupled RS problems (see [1, 17]). In the implementation stage, the mathematical model must be linked to some software tool. Here, proper discretization must be performed and a solution tool for the discretized equations must be selected or created. An appropriate solution can only be found if numerical parameters, such as grid dimensions and stability criteria, are properly chosen. A transformation of the mathematical model to a dimensionless form is recommended. This is especially relevant for RS models, with their strongly coupled equations and large difference between the values of the physical parameters (e.g., densities and diffusion coefficients of liquid and gas mixtures). Nowadays, RS problems are mostly solved with the aid of software packages, either commercial or free. Therefore, the choice of the solution strategy is often dictated by the options available within the selected software tool.

4.2.4 Simulations and analysis of results Once the mathematical model is implemented and all the necessary parameters and conditions are set, data generation by simulations can start. In order to obtain a reliable convergence, appropriate termination criteria have to be used. They must be applied to sensitive process variables, above all to the values related to the phase interface, where most intensive changes are usually encountered. It is worth noting that a difficult or a missing convergence does not necessary mean a purely numerical phenomenon caused by, e.g., strong system nonlinearity or poor initial values. Experience shows that this situation can sometimes be attributed to physical reasons, e.g., column flooding (load/heat duty above the maximum value) or application of decanters where no miscibility gap is given. The data obtained by the converged simulations should first be used for model validation. Even when the model equations are sufficiently rigorous, there exist various potential error sources in the model implementation and solution. For simplified modeling methods, errors can also be caused by model assumptions and parameters. Some qualitative conclusions on the model validity can be derived based on its response to parameter variation. However, a solid validation procedure usually involves experimental data obtained under conditions similar to those of the simulations. If such data are not available, simplified analytical or numerical solutions can at least give an evidence of the proper asymptotic behavior of the solution. Obviously, any analysis of the obtained results from the physical point of view only makes sense if the model can be judged as validated. As already mentioned above, a growing part of modeling activities is carried out with software tools, which do not provide sufficient detail on the model formulation, implementation, and solution. The confidence (“digital trust”) in the results created in such a

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manner is often too high. It should also be borne in mind that these tools, no matter how advanced they may appear, cannot be considered completely error-free, and, therefore, the results must be carefully studied with respect to their reasonability before starting to analyze them with respect to process physics. A validated process model can be used to generate various data sets that allow the evaluation of actual process performance (e.g., reasons for certain behavior, estimation of nonmeasurable values), prediction of the process behavior under varied conditions, and identification of sensible process parameters. Along with the possibilities to examine real conditions, model-based simulations can be used for an investigation of ideal process conditions and, thus, provide incentives for process optimization.

4.3 Classification of modeling methods RS processes can be considered as certain extensions of the underlying separation operations. For this reason, RS modeling approaches are often based on the corresponding concepts established for nonreactive operations. This is best matched for processes carried out either with a liquid catalyst or without a catalyst. In such cases, column internals of both nonreactive and reactive process versions are similar, which is typical for chemical absorption when a nearly same flow pattern is encountered. But this is true even for processes that include a solid catalyst, albeit with considerable changes. In this case, specially designed column internals containing a catalyst have to be used, and the modeling becomes more complex (see Section 4.5.2). Great achievements in the description of physical backgrounds, fluid dynamics, heat and mass transfer, and thermodynamics have opened up new modeling opportunities. This has been supported by the revolutionary progress in computer technology, allowing both advanced experimental and numerical process analysis. Nevertheless, the overall complexity of RS processes mentioned above still remains very high, thus requiring significant simplifications in process description. The level and degree of specific simplifications depend on several factors; among others, on the complexity of the system to be separated, the flow pattern, column design, as well as on the particular goals of modeling and the availability of physicochemical data. All these factors result in high model diversity. In Fig. 4.3, a classification of RS models is given, most of which are considered in detail in this chapter. Two large groups can be recognized – equilibrium-based and non-equilibriumbased methods. In contrast to the latter group, the first one does not include mass and heat transfer kinetics directly into the modeling framework, taking advantage of the fact that the underlying separation operation is often dominated by the thermodynamic equilibrium of the contacting phases. This is particularly true for distillation operations [18]. Moreover, many important questions regarding the process feasibility

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Reactive separation modeling

Equilibrium-based modeling

Short-cut methods for conceptual design

Equilibrium stage model

Non-equilibrium-based modeling

Rate-based approach

Hydrodynamic analogy approach

Computational fluid dynamics

Film model Residue curve maps

Penetration model

∞/∞-analysis

Surface renewal model

HTU/NTU concept

Fig. 4.3: Classification of modeling methods for reactive separations.

and design can indeed be answered with the aid of just equilibrium information. A good example is the so-called thermodynamico-topological analysis (TTA), in which both thermodynamic and reaction equilibrium conditions are simultaneously applied in order to examine the very possibility of obtaining the desired process results and avoiding limitations (see Section 4.4.2). The treatment of an RS column as a cascade of similar segments (the so-called stages) is a common feature of its modeling, as it helps to reduce the description of a typically very large object (column) to a sequence of repeating smaller objects (stages). The stages are identified with real trays or segments of a packed column (see Fig. 4.4). This concept has resulted in several different theoretical models for conventional separation processes. These models apply mass and heat balances in combination with thermodynamic equilibrium information, with a wide range of physicochemical assumptions and accuracy. For instance, in the equilibrium stage concept, it is assumed that the liquid and vapor phases can exchange species and energy fast enough to attain thermodynamic equilibrium within the stage, so that the leaving streams are at thermodynamic equilibrium. This method is largely used for many practical tasks [18, 19]. The underlying concept of the equilibrium stage modeling has been extended to consider reactive systems (see Section 4.4.3). The main disadvantage of the equilibrium-based methods is their insufficient link to actual column design. For instance, it is difficult to predict the column performance accurately without involving mass transfer kinetics and fluid dynamics. This information is particularly important when column internals should be optimized. Equilibrium-based methods usually employ lumped coefficients, which roughly estimate the deviation between real (non-equilibrium) and ideal process behavior, for instance, stage efficiencies. However, this method is not always sufficient, especially in the case of complex systems with several components.

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gas stream

liquid stream

Fig. 4.4: A simplified representation of a reactive separation column as a stage cascade with liquid and gas streams.

Non-equilibrium-based models directly include process kinetics description and thus avoid the problem described above. They can also be employed within the stage concept; in this case, the streams leaving a stage are not assumed to reach thermodynamic equilibrium. Such an approach is also known as the rate-based approach (RBA [20]). Moreover, non-equilibrium modeling can also be applied outside the stage concept, either by considering the whole column unit or by using periodic representative elements, other than stages. Such methods may have a very rigorous background, as, for instance, partial differential equations of fluid mechanics and advanced numerical methods in the computational fluid dynamics (CFD). Alternatively, a simplified flow pattern can be used within the hydrodynamic analogy (HA) approach [21]. Yet, at the moment, the application of such methods to large-scale separation columns cannot be considered realistic, thus the idea of complementary modeling, using a combination of different non-equilibrium methods, appears more promising [22]. In the subsequent sections, these different modeling methods are discussed in detail.

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4.4 Equilibrium-based modeling 4.4.1 Short-cut methods Short-cut methods have long been an important modeling tool to understand the basics of the separation process, and they are especially well-elaborated for distillation (see [23]). They are often based on a deep theoretical analysis of process behavior, and, hence, they can still serve useful purposes, for instance, when accurate phase equilibrium and enthalpy data are missing, or when ideal or nearly ideal solutions are considered. Besides, these methods often represent excellent tools for various theoretical studies of separation processes. Short-cut methods are not aimed at obtaining complete process information, e.g., temperature and composition profiles along the column, as more rigorous methods do. Instead, they provide a quick calculation of several specific process characteristics. These characteristics mainly represent the special constraints with respect to separation limit (e.g., feasibility of a selected desired separation), investment costs limit (e.g., minimal number of stages required for a specified separation), and operating costs limit (e.g., minimum reflux ratio). Unfortunately, it is rather difficult to extend the application of the short-cut methods to the RS operations because their underlying concepts are too idealized to cover further complexity. However, for instantaneous chemical reactions, it is always possible to transform the original concentration space using the approach suggested in [24], so that most short-cut methods available for nonreactive distillation operations can be used. Among others, this technique was further elaborated in [25] using the so-called boundary value method to handle the reactive distillation processes. In practice, applications of short-cut methods are limited by RS processes with instantaneous reactions. For kinetically controlled reactions, their results would mostly be ambiguous, even for systems with a single reaction.

4.4.2 Thermodynamico-topological analysis (TTA) This method takes its name from the fact that only (phase and chemical) equilibrium data is required for its application, while conclusions are drawn based on the topological analysis of the resulting process trajectories. TTA is especially widespread in the conceptual design of reactive distillation columns based on the following assumptions [18]: – All reactions occur in the presence of a catalyst, either homogenous or heterogeneous. – All reactions are reversible. – Reactions take place in liquid phase.

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– Reactions are instantaneous in the presence of a catalyst. – The RD column operates under infinite reflux ratio. Within the concentration space, the project trajectories are obtained based on the data on vapor-liquid equilibrium, reaction stoichiometry, and reaction equilibrium (cf. Chapter 3), while the process follows the chemical equilibrium lines. This helps to identify process singularities, e.g., the so-called reactive azeotropes arising when the actions of reaction and distillation cancel each other. Furthermore, reactive and nonreactive zones within the RD column can be determined and feed positions estimated. As the result, a basic design of an idealized RD column can be found. This methodology is presented in detail and its applications are extensively illustrated in the textbook [18]. It is, of course, tempting to design RS units using just this limited data. However, the information on fluid flow and process kinetics is not included, and, therefore, a link to real design must be found beyond the TTA.

4.4.3 Extended equilibrium stage To be able to apply the equilibrium stage modeling to RSs, chemical reactions have to be included in the classical separation description. A homogeneous chemical reaction acts as a source or a sink for all components taking part in it; for multiple reactions, this is true for the production or consumption of the resulting species. Such a source/sink is basically a part of any species balance equation, either differential or algebraic. In the context of the equilibrium stage model, the source term is included in the algebraic species balance equations written for individual equilibrium stages. However, when the considered reaction is instantaneous, its rate cannot be directly accounted for, and its action must be taken into account via the reaction equilibrium relationships. It often makes sense to compare the rate of a kinetically controlled reaction with that of species transport, as this relation may be important for a possible model reduction, especially for models with simplified treatment of fluid dynamics and mass transfer kinetics. For instance, reactive absorption operations are commonly characterized by relatively fast reactions. This means that the interfacial species transport becomes the limiting (slower) step of this combined process, while its kinetics must be considered explicitly. On the contrary, in reactive distillation processes, reaction, even catalyzed, represents a limiting step, while there are always enough molecules in the reaction zone that are delivered by mass transport mechanisms. In such cases, mass transport is fast enough and hence, its rigorous kinetic account is not necessary, and equilibrium-based modeling becomes sufficient. The equilibrium model is thus extended, being equilibrium-based with respect to mass transfer, yet with due consideration of the reaction kinetics.

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As described above, the latter is accounted for by the corresponding source term in the balance equations. Such a model, even when not fully consistent, can show reasonable results [3]. This is illustrated in Fig. 4.5 for the case of methanol esterification in a heterogeneously catalyzed distillation column. The graph shows column profiles of the reacting species, obtained with and without consideration of mass transfer kinetics. In other words, solid lines show results obtained with a non-equilibrium approach, while the dashed lines are obtained with the extended equilibrium model. It is clearly seen that in the reaction zone, where reaction and separation take place simultaneously, solid and dashed lines are close for all components. In contrast, above and below the feed points, i.e., outside the reaction zone, the differences between both models become quite significant. 45 1 comp. - with mass transfer 1 comp. - without mass transfer 2 comp. - with mass transfer 2 comp. - without mass transfer 3 comp. - with mass transfer 3 comp. - without mass transfer

41 37 33

Stage number

29 25 21 17 13 9 5 1 0

0,2

0,4

0,6

0,8

1

Concentration, mole fraction Fig. 4.5: Concentration profiles obtained with a rate-based model and with an extended equilibrium model.

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Unfortunately, it is not easy to find a comparison criterion capable of estimating the reaction rate in reference to the mass transfer rate. The so-called Hatta-number represents an attempt to find such a criterion. It is introduced as the ratio of the maximum possible reaction rate and mass transfer rate, and helps to discriminate between very fast, fast, average, and slow chemical reactions [26, 27]. However, the Hatta-number can only be reasonably determined for very simple single reactions, and it cannot be generalized for complex multiple reaction systems.

4.5 Non-equilibrium-based modeling The name of this modeling speaks for itself. It significantly loosens the dependence on equilibrium data by including process rates directly into the modeling concept. In this regard, it may even appear as a method fully opposed to the equilibriumbased modeling. However, this is not true, since the equilibrium data continues to be an important factor within the non-equilibrium modeling methods. Rather, nonequilibrium-based modeling should be thought of as an extension of the process consideration toward a more rigorous and physically consistent treatment of the complex phenomena in (reactive) separation units. This is especially important, when a process is far from an equilibrium state and its driving forces are substantial. Above all, the rates of mass and heat transfer are essential. They depend on many factors, e.g., column internals, fluid-dynamic regime, and physicochemical system properties. Very often, these factors cannot be explicitly captured due to their complexity, and some assistance is required from experimental measurements, for instance, in the form of correlations for mass and heat transfer coefficients and specific interfacial contact area obtained for similar process conditions [28–30]. Another important kinetic factor in the modeling is certainly the rates of the running chemical reactions. Depending on the nature of the reacting system, these rates can vary tremendously, from instantaneous to very slow. They can be very complex, combing multiple steps, while their behavior (reversible, irreversible, exothermic, endothermic, catalytic, etc.) can be very different. In the last few decades, some kinetics-based methods have been developed that do not require mass and heat transfer coefficient correlations (cf. [21,22,31]). Such methods (computational fluid dynamics, hydrodynamic analogy approach) go beyond the stage concept, considering, where possible, either an entire separation unit or its representative elements. In literature, the notion of non-equilibrium modeling is usually applied to the stage-based consideration of a separation column. In this chapter, however, we follow the terminology suggested in [23] and use the term non-equilibrium modeling in a different, broader manner, covering all modeling methods that include mass and heat transfer kinetics

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in an explicit way. To refer to the truly stage-based non-equilibrium modeling, another widely used notion, the rate-based approach, is applied.

4.5.1 HTU/NTU concept and enhancement factors The simplest approach to account for the mass transfer kinetics was suggested by Chilton and Colburn [32] for physical absorption of one component. This approach is called HTU/NTU method, as it allows determining the column height as a product of two values, HTU (height of a transfer unit) and NTU (number of transfer units). The NTU value can be determined graphically or numerically by integrating an inverse of the mass transfer driving force over the column height. It does not depend on the unit itself and reflects mixture separation difficulty. The HTU value depends on the column load, internals-related geometrical parameters, and empirical mass transfer correlations. To simplify the calculations, the total mass transfer resistance is often referred to one of the contacting phases [33]. The acceleration of mass transfer due to the chemical reactions in the interfacial region is often accounted for via the so-called enhancement factors [27, 34, 35]. These parameters are defined as a relation between the mass transfer rates with and without reaction, assuming the same mass transfer driving force. The enhancement factors are either obtained by fitting the experimental results or derived theoretically based on simplified model assumptions. They depend on the reaction character (reversible or irreversible) and order as well as on the assumptions of the specific mass transfer model chosen [27, 34]. For very simple cases, analytical solutions are obtained, e.g., for a reaction of the first or pseudo-first order or for an instantaneous reaction of the first and second orders. Frequently, the enhancement factors are expressed via Hatta numbers [34]. They can be used in combination with the HTU/NTU method or with a more advanced mass transfer description method. However, it is generally not possible to derive the enhancement factors properly from binary experiments, and a theoretical description of reversible, parallel, or consecutive reactions is based on rough simplifications. Thus, for many RS processes, this approach appears questionable.

4.5.2 Rate-based approach (RBA) RBA is another modeling method using stage discretization of a separation column. It represents a well-known way to design large-scale column units [20]. This approach implies a direct consideration of actual rates of multicomponent mass and heat transfer and chemical reactions within a column stage. Compared to the equilibrium-based stage description, RBA represents a more physically consistent modeling way and provides a direct link to the column and internals design [2, 22]. This is

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possible due to the inclusion of mass and heat transfer equations directly into the modeling framework and due to the usage of process and model parameters governing the process fluid dynamics. Mass transfer at the interface between the contacting phases can be described using different theoretical concepts [1, 2]. Most often, the film model or the penetration/surface renewal model is used, while the model parameters are estimated via empirical correlations. In the film model (Fig. 4.6), it is assumed that the resistance to mass transfer is concentrated entirely in thin films adjacent to the phase interface and that mass transfer occurs within these films by steady-state molecular diffusion alone. Outside the films, in the fluid bulk phases, the level of mixing is assumed so high that there is no change in composition at all. This means that in the film region, one-dimensional diffusional transport takes place, normally to the interface.

component flux

concentration profile heat flux temperature profile

liquid bulk

liquid film δx

gas film δy

gas bulk

interface Fig. 4.6: A column stage represented by the film model. For the sake of clarity, only one exemplifying concentration profile is shown.

The film model has some similarity with phenomena taking place at many real fluid elements in two-phase systems, e.g., fast change of the main process variables (composition, temperature) close to the interface and their significantly slower change far from the interface. However, the flow pattern in the film model is strongly simplified, and no reasonable momentum equation can be used here. The films represent model elements rather than any kind of real film flow. Their thicknesses cannot be measured; instead, they are estimated using mass transfer coefficient correlations (or Sherwood correlations) [33, 36].

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Another simplified representation is given by the penetration model [37]. It is assumed that the contact times of the two phases at the interface are fairly short. Thus, this contact can be modeled by a series of fluid elements each approaching the interface. The elements remain for a short fixed time there and, afterwards, return back to the bulk phase, and are then replaced by another similar element. During the exposure time, mass transfer takes place. This process can be described by a one-dimensional diffusion equation with the corresponding initial and boundary conditions. The solution of this system provides the concentration profiles and, consequently, the corresponding mass flux expression [37]. In contrast to the film model, the penetration model predicts the square root dependence of the mass transfer coefficient on the diffusion coefficient. The surface renewal model [38] can be considered as a further development of the penetration model. The main difference here is in the other distribution of the residence time of the fluid elements at the interface, based on the assumption that the probability of an element being replaced by a new one is independent of the actual time for which it has been exposed. This results in a slightly different expression for the fluxes and the mass transfer coefficient. In both the penetration and the surface renewal model, mass transfer is described using a combination of deterministic (non-steady-state diffusion) and stochastic (residence time distribution of fluid element) principles. An attempt to combine the film and the penetration model was undertaken by Toor and Marchello [39]. They developed the so-called film-penetration model, in which elements of a film adjacent to the interface are continuously replaced by elements having bulk fluid composition. The model gives a more general expression for the mass transfer coefficient and reproduces either the penetration-based or the surface renewal-based expressions, depending on the characteristic dimensionless ratio [40]. Further modifications of the models described above are reviewed in [33]. Basic equations describing the film, penetration, surface renewal, and filmpenetration models are usually given for binary systems. Accordingly, these equations have a scalar form, i.e., they are written for the concentration of one component of a binary mixture. However, they can be extended to multicomponent systems using vector-type composition description and matrix algebra operations (see [1, 2]). The dimension of the corresponding vector-type equations is either equal to the number of mixture components or this number reduced by one. All presented models have much in common; they try to replace real phenomena at the interface by a one-dimensional simplified picture and they exclude real flow and hence exclude the momentum transport equations from the consideration. Therefore, they are not able to estimate their main parameters (e.g., the film thickness or average residence time) without additional information and thus are forced to use experimental correlations for the mass transfer coefficients. In this respect, all four models have the same weak point and can be considered as equivalent with respect to mass transfer prediction. However, the film model appears advantageous,

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since there is a broad spectrum of correlations available in literature, for all types of internals and systems, whereas for the penetration/surface renewal model, the choice is limited. Moreover, many researchers have used the film model as the basis for the evaluation of mass transfer coefficients. For these reasons, in this chapter we focus on the film model.

Film model This model serves as a basis for numerous RBA applications. For nonreactive systems, the main equations comprise [3, 14]: – mass and heat balances for the bulk phases (dynamic or steady-state), including source terms in case of reaction – mass and heat transfer laws (Maxwell–Stefan, Nernst–Planck, or Fick for diffusion and Fourier for heat conduction) – thermodynamic equilibrium relations for the interfacial concentrations and temperature – continuity equations for the mass and energy fluxes at the phase interface – correlations for process fluid dynamics (holdup, pressure drop) and for mass and heat transfer coefficients and specific contact area. The film model can be extended to describe homogeneous reactive systems (Fig. 4.7). In this case, equations for reaction description are required. For instantaneous reactions, kinetic expressions cannot be applied; they are replaced by chemical equilibrium relationships. When reactions are kinetically controlled, the reaction mechanism can be considered either in the bulk phases (slow reaction), or in the film region (fast reaction), or even in both regions [3]. Reaction in the film region results in a curvilinear form of concentration profiles, which is in contrast to their classical linear form for pure mass transfer (cf. Fig. 4.6). The case when the reaction mechanism should be taken into account in the film region is especially complex, since the component balance equations, including simultaneous mass transfer and reaction in the film, become nonlinear (ordinary) differential equations of the second order, which have to be solved in conjunction with all other model equations. This can be done either analytically, provided that some further assumptions with respect to the linearization of the diffusion and reaction terms are made [1, 40], or numerically [3, 14]. Modern computer facilities allow very complex problems to be solved with the RBA. An example of such a problem is a closed reactive absorption/desorption loop presented in [41]. In this work, an industrial process was considered in which aqueous methyl diethanolamine solution was used for selective removal of H2S in the presence of CO2 (reactive absorption), with a subsequent solvent regeneration (reactive desorption). This is a highly integrated process characterized by significant

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reaction in the film

concentration profile

liquid bulk

liquid film δx

gas film δy

gas bulk

interface Fig. 4.7: The film model comprising a chemical reaction in the liquid phase.

nonlinearity due to thermodynamic, kinetic, and fluid-dynamic relationships as well as due to reaction/diffusion coupling in the film region. Regarding the large computational effort and convergence problems typical for such tasks, successful simulation is often difficult. Nevertheless, in [41], both absorber and desorber performance could be validated (see Fig. 4.8). This work has been a basis for the subsequent successful modeling of lumped absorption/desorption loops, even including process dynamics [42] (see also the discussion at the end of this section). It should be noted that some adjustments might be necessary if, for example, tray columns or venturi scrubbers are described by the film model. Tray columns are subdivided into two different model elements, one of which is governed, as before, by the film model (e.g., Fig. 4.7). The second element is introduced in order to capture the free space above the tray where no gas-liquid contact exists. This space can yet be important when gas-phase reactions take place, as, for instance, in some NOx absorption processes. It can be reasonably well described using the ideal flow reactor model [43]. Venturi scrubbers can also be captured by the film model using a combination of three sections – an upper convergent one, a middle one with a constant diameter, and a lower divergent section [43].

Nonideal flow behavior Most often, the mass balances in the film model are used in the form assuming plug flow behavior for both the vapor and the liquid phase. However, real flow behavior in RS units can be much more complex, and, in some cases, it may degrade the

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yCO [-]

y

S

[-]

xCO [10-5]

x

S

[10-5]

Fig. 4.8: Axial concentration profiles of H2S and CO2, and experimental data in the gas phase of the absorber (above) and in the liquid phase of the desorber (below) [41]. The typical zigzag concentration profile in the upper part of the desorber results from the interplay of the loaded solvent feed (maximum concentration value) and the backwash tray at the desorber top.

column performance, for instance, through back-mixing of liquid and vapor phases or through the formation of stagnant zones. In the radial direction on the vapor side, it may be assumed that either the vapor is totally mixed before it enters the stage, or that, after being separated from the liquid on the stage below, the vapor does not mix at all. The real situation obviously lies between these two limiting cases. Radial liquid flow patterns can be very complicated, for instance, because of the interaction with the vapor phase and dispersion. A rigorous modeling of this flow pattern is very difficult, and usually, the situation is simplified by assuming that the liquid flow is unidirectional and the major deviation from plug flow is the turbulent mixing or eddy diffusion. For packed columns, a promising approach is represented by differential models, like the axial dispersion model [44] or the piston flow model with axial dispersion and mass exchange [45]. When applying the axial dispersion model to cover this nonideality,

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correlations for axial dispersion coefficient must also be available [3]. The overall flow pattern becomes even more complex when the liquid falls into a miscibility gap (this phenomenon can be encountered both within column units and in collectors/ distributors). While within the equilibrium-based modeling, only additional thermodynamic complexity arises, the rate-based modeling requires development of special techniques, as two-phase models, e.g., the film model, are no longer applicable. These issues are considered in detail, e.g., in [46].

Catalyst treatment The film model framework allows homogeneous reactions to be governed. However, some RS operations are realized in the presence of homogeneous or heterogeneous catalyst, for instance, reactive distillation or catalytic stripping [10]. In case the liquid catalyst (e.g., sulfuric acid) is applied in reactive distillation, the film model considered in the previous section can still be used without substantial adjustment. The application of solid catalyst changes the situation. First of all, this catalyst represents an additional (solid) phase, which must be included in the model, while this may even require some changes in the model structure. Moreover, the catalyst is a fixed part of the column internals (for instance, reactive structured packings or monolithic supports), and hence, its placement influences the flow pattern in the column. As mentioned in Section 4.2.1, the catalyst can be placed within the RS unit by different methods, using either coated catalytic supports [47], or random packing elements completely made of the catalyst [48], or complex reactive trays combining catalytic and separating parts [6, 8, 49], or specially developed catalytic packings like those shown in Fig. 4.9. The latter variant represents the most common way to fix the catalyst. Compared to conventional column internals that must provide sufficient phase-contact area and throughput, reactive internals have to additionally ensure an efficient contact between the catalyst and the reacting fluid phase as well as a residence time sufficient for the reaction. This is achieved in catalytic packings by using gauze wire structures and alternating reaction and separation subsections. The reaction subsections (“bags”) are filled with catalyst pellets (see Fig. 4.9). In this case, both mass transfer area and catalyst volume/surface become important parameters influencing the process performance. For the rate-based modeling of reactive distillation columns with solid catalyst (catalytic distillation), two different methods were suggested. The first one describes the catalyst as a third, separate phase, as shown in Fig. 4.10. For coated supports, this third phase can be considered as a homogeneous solid bulk, while the overall reaction acts at the solid-liquid interface (Fig. 4.10a). For a porous catalyst, reactions take place within the pores. In both cases, the film model is extended to have three bulk and three film phases.

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catalyst bag 1 corrugated sheet

2 corrugated sheets

Katapak-SP11

Katapak-SP12

Fig. 4.9: Catalytic structured packing KATAPAK®-SP-11 by Sulzer Chemtech Ltd. (above) and schematic representations of two KATAPAK®-SP modifications (below).

Different simplifying assumptions regarding the porous catalyst phase have to be made, for instance, that the catalyst is totally wetted internally and on its external surface and that temperature gradients inside the catalytic packing elements are negligible [50]. Such a liquid-filled catalyst is depicted as the third phase in Fig. 4.10b. The reactants penetrate the liquid phase and reach the catalytic phase in which the reaction takes place; the products leaving the catalyst phase diffuse in the opposite direction. To apply the three-film model, the following information must be known: – wetting degree of the catalyst – intrinsic reaction kinetics – tortuosity of the catalyst – free specific pore surface – mass and heat transfer coefficients describing both vapor-liquid and solid-liquid interfaces – catalyst lifetime. This information is difficult to obtain, and therefore, the three-phase model can seldom be applied [14, 50]. More often, the second method is used, which makes a further simplification and considers the catalyst as evenly distributed throughout

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reaction at the interface

liquid film δx,c

liquid bulk

liquid film δx

gas film δy

gas bulk

interface

interface non-porous catalyst (a) reaction within the catalyst layer

liquid film δx,c interface

liquid bulk

liquid film δx

gas film δy

gas bulk

interface

porous catalyst (b)

Fig. 4.10: Three-film model for a column segment with heterogeneous catalyst: void-free solid catalyst (a) and porous catalyst (b).

the liquid phase, thus arriving at the so-called quasi-homogeneous model (Fig. 4.11). Here, no mass-transfer resistance between the liquid phase and the catalyst is considered explicitly. The application of this model, however, requires the knowledge of overall reaction kinetics determined in geometrical arrangements similar to those being modeled. This macroscopic kinetics includes the influence of the liquid distribution and mass transfer resistances at the liquid/solid interface as well as diffusional

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transport phenomena inside the porous catalyst [3]. The reaction kinetics is then integrated into the mass balances as if it were a homogeneous reaction.

concentration profile

liquid bulk

liquid film δx

gas film δy

gas bulk

interface Fig. 4.11: Quasi-homogeneous film model for a column segment with heterogeneous catalyst.

It is worth noting that in some RS processes, reactive and nonreactive internals are combined within the same column [3], and hence, different models are used for their description. Reactive dividing wall column Another interesting process with a possible application of a catalyst is reactive distillation in a dividing wall column (DWC). The DWC concept is based on an integration of two fully thermally coupled distillation columns within a single shell [51]. It is a modern trend in the process industry, allowing great energy saving in the distillation sector [52]. If a reactive section is implemented into a DWC, this results in a highly integrated unit called the reactive dividing wall column (RDWC). This integration is illustrated in Fig. 4.12; it provides further synergistic effects, e.g., overcoming chemical and thermodynamic equilibrium limitations, ability to separate close boiling components, and reduced number of equipment units. Due to the very high degree of process and equipment integration, the rate-based modeling of RDWC needs a further extension. Because, in reality, the RDWC combines two (reactive) distillation columns, each described by the two-film model, the overall modeling needs two such models used in a coupled way. Even if this coupling could be avoided for mass transfer modeling, it is mandatory considering the phenomenon of heat transfer, including both the transfer within the stage and the heat conduction across the dividing wall, which represents a peculiar feature of this column configuration. The heat transfer

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Reactive distillation

Reactive dividing wall column

Dividing wall column Fig. 4.12: Reactive dividing wall column as an integration of reactive distillation and dividing wall column.

across the wall can be a significant factor that influences the separation efficiency. In reality, the dividing wall is covered by a liquid-vapor mixture and, generally, it is difficult to make an exact estimation of a near-wall phase state. Therefore, some assumption must be made for this issue. In [53], two different cases were considered. The first case is when the dividing wall is covered by the vapor phase from both sides; the second case is when both sides are covered with liquid. To model the heat transfer phenomena, a complete cross-section of the dividing-wall column must be considered because the left-side (prefractionator) and right-side (main column) stages are linked by the heat flux between them (Fig. 4.13). Even if the simplest treatment of the catalyst within the two-film model is used, the overall description comprises at least four film regions. Only if the influence of the heat flux through the dividing wall can be neglected, the two two-film models can probably be used in a sequential manner. The effect of heat transfer across the dividing wall on the column energy demand was studied in [54] for nonreactive DWC, and it was shown that this effect can be kept low if the column is operated close to the point of minimum energy consumption.

liquid film δx, p

interface

gas film δy, p liquid bulk

heat flux

heat flux

Fig. 4.13: A film model-based representation of a dividing wall column segment.

gas bulk

wall with films

prefractionator

liquid bulk

gas film δy, m interface

liquid film δx, m

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main column

gas bulk

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In [55], the transesterification of carbonates was identified as an interesting system for the RDWC, as this reaction is equilibrium-limited and characterized by high conversion yet low selectivity. In a further study, it was found that the selectivity and separation of the products and the nonconverted reactants could be significantly increased by means of the RDWC column [53]. Another reactive system that fits the RDWC concept is given by the hydrolysis of methyl acetate to methanol and acetic acid. Figure 4.14 demonstrates the first successful validation of the rate-based model with the data obtained at BASF SE [56].

Fig. 4.14: Simulated (lines) and experimentally measured (points) temperature profiles (left), and concentration profiles (right) for the hydrolysis of methyl acetate (MeOH, methanol; MeAc, methyl acetate; HAc, acetic acid) [56].

Model parameters Along with the equations, the RBA modeling requires some parameters, which must be known a priori. Examples of such parameters are pressure drop, liquid holdup, specific interfacial area, mass and heat transfer coefficients, and, in some cases, residence time distribution. Commonly, these parameters are represented as functions (correlations) of physicochemical properties, operational conditions, and column geometry. They usually result from comprehensive and expensive experimental studies. The correlations for different columns and internals have been published in numerous papers and are collected in several reviews and textbooks (see, e.g., [28–30, 57]).

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Film thickness is a model parameter, which can be estimated via the mass transfer coefficient correlations that govern the mass transport dependence on system geometry, physical properties, and process fluid dynamics. A number of mass transfer coefficient correlations for various column internals are available in literature (see [28, 57–61]) and a recent comprehensive review in [62]). Similarly, individual heat transfer coefficient correlations can also be found, e.g., in [63–65]. However, in practice, the heat transfer coefficients are usually evaluated using the Chilton–Colburn analogy [66]. A very important and sensitive parameter is the specific gas/vapor-liquid interfacial area. Correlations for this parameter can be found, e.g., in [30, 60, 61, 67]. As long as the relevant process and model parameter correlations for the studied unit are found and a reliable description of the kinetics and equilibrium is available, the film model basically yields reasonably accurate results [2, 17, 68]. The role of the model parameters is substantial, as the accuracy and reliability of the model predictions strongly depend on their quality. In literature, one can find numerous correlations presented in different forms; however, their application to specific problems often results in significant discrepancies, so the choice of a suitable correlation is quite tricky and there is no straightforward way to make a correct choice. Thus, the strong dependence of the RBA performance on the model parameters represents its weak point [9]. In the nature of things, experiments are performed in existing equipment units filled with specific column internals. This represents the main source of information, which otherwise cannot be captured within the RBA. In the last few decades, some attempts have been made to estimate the process parameters by simulations based on more rigorous fluid-dynamic descriptions, above all using CFD. Such simulations can be considered as certain “virtual experiments,” replacing the corresponding real experiments for parameter estimation. These virtual experiments can open the way toward virtual prototyping and manufacturing of column internals and enable computer-aided optimization of both internals and overall processes. We return to this issue later in Section 4.6.1.

Dynamic processes by RBA Steady-state modeling cannot be used for the description of transient processes, e.g., batch or semibatch operations. Furthermore, it is not a proper way to describe the process behavior after disturbances (e.g., flow rate or composition variations), or during either a start-up or a shutdown phase. In this case, an understanding of the process dynamics is necessary. Further areas where the dynamic information is crucial are process control, safety issues, and training. Dynamic modeling can also be considered as the next step toward deep process analysis, which follows the steady-state modeling and is based on its results.

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In the dynamic rate-based stage model, molar holdup terms have to be considered in the mass balance equations, while the change of both the specific molar component holdup and the total molar holdup is taken into account [3]. The gas holdup can often be neglected due to the low gas-phase density, and the component balances are reduced to their steady-state forms (see also [69]). However, this should be avoided if the columns are operated at high pressures [70]. Furthermore, the corresponding holdup terms in the film regions can be neglected due to their much smaller holdups compared to the bulk phases [69]. The dynamic formulation of the model equations requires a careful analysis of the whole system in order to prevent high-index problems during the numerical solution [71]. As a consequence, a consistent set of initial conditions for the dynamic simulations and a suitable description of the fluid dynamics have to be introduced. For instance, pressure drop and liquid holdup must be correlated with the vapor and liquid flows [3]. The dynamic behavior of the coke gas purification process was systematically investigated in [69, 72]. In Fig. 4.15, a system’s response to a sudden increase of the H2S load by 100% is demonstrated. As expected, additional H2S is absorbed, but the parallel reactions of CO2 lead to an increasing amount of carbon dioxide in the purified gas. The new steady state is achieved after about 1 min, which confirms the small time constants of the simulated pilot plant absorber. Further details on the complex process behavior can be found in [69].

Fig. 4.15: Dynamic changes of the top gas-phase concentrations normalized with the steady-state composition just before the disturbance.

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It is worth noting that liquid distributors installed between the packing elements have a significant influence on the dynamic process behavior due to their large holdup. The liquid distributors were modeled in [69] as continuous stirred tank reactors (CSTR). To determine the holdup of the solvent, the knowledge is necessary of the geometry and the filling level of the distributor. The dynamics of a pilot plant for chemical absorption of CO2 with monoethanolamine solution (MEA) in Esbjerg, Denmark [73] has recently been studied in [74]. Here, an extended reactive absorption configuration was modeled, while the periphery was considered using dynamic models of the liquid distributors, liquid holdup in the bottom of the columns as well as of the relevant heat exchangers and pipelines. Based on the simulations, the influence of different closed-loop process elements on the dynamic behavior of the overall configuration can be evaluated, enabling a cause-effect analysis of hazardous situations.

4.5.3 Hydrodynamic analogy approach The simplified fluid-dynamic pattern in the context of the film model may be considered as an advantage that permits avoiding the consideration of real complex flows on, and in, the column internals. On the other hand, as mentioned above, it makes this modeling approach highly dependent on the quality of the experimental parameters, like the specific interfacial area and mass transfer coefficients. Discrepancies between the correlations of the different authors available in literature are quite significant, and, considering that these correlations are usually determined experimentally for a certain internal type, chemical system, and within a definite range of operating conditions, their extrapolation to other conditions is not a trivial task (cf. [9]). Further difficulties arise when the film model is applied to RSs. Being initially developed for binary mass transfer [75], this method directly relates the film thickness with the binary diffusivity. However, reactions usually take place in multicomponent mixtures, and hence, different diffusivities related to different component binary pairs are encountered, which formally results in several thicknesses. To obtain the unique film thickness for each phase, this model parameter has to be estimated as an averaged value. This is not the only inconsistency (see [31]) that has to be borne in mind when applying the film theory to reactive systems. An attempt to avoid using rough fluid-dynamic simplifications brought about a method called the hydrodynamic analogy (HA) approach [1, 21]. This approach is an alternate way to describe the fluid dynamics and transport phenomena in processes in which the exact location of the phase boundaries is not possible, yet the fluid pattern possess some regularity or structure that can be mirrored by an analogy with more simple flow elements. The basic idea of the approach is a reasonable replacement of the actual complex fluid dynamics in a column by a combination of

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geometrically simpler flow patterns. Such a geometrical simplification has to be done in agreement with experimental observations of fluid flow, which play a crucial part for the successful application of this approach. Once the observed complex flow is reproduced by a sequence of simplified flow patterns, the partial differential equations of momentum, energy, and mass transfer can be applied to govern the transport phenomena in an entire separation column. The idea of the HA method was put forward in [21]. It has been successfully applied for different separation operations (e.g., [31, 76, 77]), among others, for distillation processes in columns equipped with corrugated sheet structured packings. The corrugated sheets are installed counter-course in such a way that they form channels, each formed by the two wall sides and one open side shared between two neighboring channels. In line with the HA concept, the basis for the physical model is provided by the observations of the fluid flow, together with the geometrical characteristics of the structured packing. According to experimental studies (e.g., [60, 78–81]), these observations can be summarized as follows: – Gas flow takes place in channels built up by the counter-course arrangement of the corrugated sheets. – There is a strong interaction between the gas flows in adjacent channels through the open channel side responsible for small-scale mixing (that is, via turbulence) of the gas phase. – Liquid generally tends to flow in the form of films over the packing surface, whereas the wave formation is largely suppressed because of corrugations. – Liquid flows at the minimal angle built by the packing surface and the vertical axis (the so-called gravity-flow angle). – Abrupt flow redirection at the corrugation ridges, together with the influence of intersection points with the adjacent corrugated sheets, cause mixing and lateral spreading of the liquid phase. – Side-effects (abrupt flow redirection at the column wall and at transitions between the packing layers) result in large-scale mixing of the gas phase. The physical model represented in Fig. 4.16 comprises all these effects. The pronounced channel flow of the gas phase makes it possible to consider the packing as a bundle of parallel inclined channels with identical cross-sections. For simplicity, a circular channel shape is adopted. The number of the channels as well as their diameter are determined from the packing geometric specific area and corrugation geometry, respectively. The gas-flow behavior depends on the operating conditions and varies from laminar to turbulent flow. The liquid flows counter-currently to the gas flow in the form of laminar nonwavy films over the inner surface of the channels. In addition, a uniform distribution of both phases in the radial direction is assumed, i.e., no maldistribution is taken into account in the model. The ratio of wetted to total number of channels is the same as the ratio of the effective interfacial specific area to the geometric specific area of the packing. The periodic ideal mixing

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id

liqu

α gas

Fig. 4.16: HA-based physical model of structured packing.

approximation is necessary to account for real mixing caused by the abrupt change in the flow direction. The length of the laminar flow interval for the liquid phase corresponds to the distance between the two neighboring corrugation ridges, whereas for the gas phase, it is set to be equal to the average channel length [31]. The system of equations describing this arrangement comprises partial differential equations, written for the gas and the liquid phases, coupled through the boundary conditions at the phase interface [22]. The numerical solution of this system yields the local temperature and composition fields. The computed averaged compositions over the packing height were first compared with measured data for distillation at total reflux for different structured packings under a variety of operating conditions, and an excellent agreement was established (see [9, 31]). In the following studies, the HA method was applied to several RS units [82–85] and proved its potential. For instance, different reactive absorption systems were modeled, among others, sulfur dioxide and carbon dioxide in aqueous solutions of sodium hydroxide [83]. In this way, reactions occurring both within the liquid phase and solely at the gas-liquid interface, and with both infinite and finite reaction rates, could be considered. Furthermore, the HA model was extended to govern a reactive stripping process with heterogeneously catalyzed liquid-phase reactions [85]. The stripping column was packed either with a structured corrugated sheet packing, SulzerTM DX, or with one of the three different types of film-flow monoliths (square channels, internally finned channels, and round channels). These internals shown in Fig. 4.17 acted as supports for the thin catalyst layers. To properly account for a porous catalyst sublayer on the catalytic internals, the liquid film flow was subdivided into a part flowing through the layer and a

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(c)

(a)

(b)

(d)

Fig. 4.17: Different catalyst supports; SulzerTM DX corrugated sheet packing (a), film-flow monoliths with square channels (SQ, b), with internally finned channels (IFM, c) and with rounded channels (MRC, d).

XOctanol, simulation [mol/mol]

part flowing along it. The liquid-phase reactions were modeled using a quasihomogeneous approach. To apply the model for monolithic internals with noncylindrical channels, a model extension was suggested based on an equivalent transformation of the monolith geometries to cylindrical channels. The simulation results were compared with experimental data for all four column internals, and a good agreement was found for all studied cases (see Fig. 4.18).

9.0E-02

+ 10 % – 10 %

6.0E-02

3.0E-02

MRC Sulzer DX IFM SQ

0.0E+00 0.0E+00 3.0E-02 6.0E-02 9.0E-02 XOctanol, experiment [mol/mol] Fig. 4.18: Parity plot of octanol outlet concentration for different monoliths and SulzerTM DX packing.

Recently, a new HA model has been developed to describe (reactive) separation units filled with random packings [86]. In this case, the liquid flow in the real packing is captured by a combination of film, jet, and droplet flow, which are assumed

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to be the dominating flow patterns in the bed. Each of the flow patterns is modeled independent of one another, in a separate channel type with counter-current gas flow (Fig. 4.19). After certain packing specific lengths of undisturbed flow, each phase is mixed to govern the redirection of the flow and the transition from the film to jet and droplet flow and vice versa, as well as of the mixing of gas flows from neighboring packing elements. The overall model becomes more complex than for structured column internals. Nevertheless, it has been successfully validated for the reactive CO2 absorption into aqueous sodium hydroxide solution, carried out in an industrial-scale column filled with two different random packings. This shows that the HA modeling concept can be applied even beyond the range of structured packed columns.

(a)

(b)

(c)

Fig. 4.19: Schematic of main liquid flow patterns (films, jets, and droplets) and mixing in random packings (Pall Ring and ENVIPAC), together with the corresponding liquid and gas velocity profiles in the hydrodynamic analogy model.

In the last few years, valuable insights of the fluid flow in the packing have been gained from the results of tomographic measurements [87, 88]. Analysis of the tomographic images provides quantitative characteristics of the gas-liquid interfacial

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area, mixing points of liquid flow, and fluid patterns other than liquid films. By taking this information into account, the HA model can be refined accordingly. The HA method can not only be used as an alternative design and modeling technique for packed columns, but also be applied to theoretical optimization of packing geometry, because it does not depend on experimentally determined mass transfer coefficients (see Section 4.6.2). Furthermore, this method has a good potential for applications in which mass transfer coefficients are difficult to determine experimentally.

4.5.4 Direct fluid-dynamic modeling In the direct fluid-dynamic modeling, velocity, pressure, temperature, and concentration fields are determined explicitly by using partial differential equations for momentum, mass, and heat transport. In principle, this is the most rigorous approach to the description of a process or a phenomenon, in which local process data can be determined and build the basis for process evaluation and optimization. However, the transport equations have to be supplied by the corresponding initial and boundary conditions, and this means that the phase boundaries must be spatially localized. For (reactive) separation operations, with its inherent multiphase nature, such localization is often difficult.

Analytical methods A few applications can be found in the area of RSs, in which the phase boundaries can be considered as spatially fixed. Such flow patterns can be encountered in simple geometrical arrangements, e.g., in tubes, monolithic structures, and microchannels [1, 17, 89–93]. In this respect, above all, various film-like flows come to mind. For such systems, analytical or semianalytical methods can be applied. Several problems concerning coupled mass and heat transport phenomena in reacting mixtures were solved analytically, both for one-phase and two-phase systems. The velocity profiles were obtained by solving a reduced form of the Navier–Stokes equations in accordance with the simple flat or cylindrical (nonwavy) film-flow conditions. Along with the fixed phase boundaries, this possibility represents a key point allowing analytical treatment. In addition, the governing mass and heat transfer equations take a simple form and can be solved even for multicomponent systems. In such cases, the Maxwell–Stefan equations for the description of multicomponent diffusion [2] are involved, and the governing mass-transfer equations acquire a compact matrix-type form [1]. The solution of such highly coupled systems can be realized using analytical matrix-based solution methods, while, under certain conditions,

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even a direct matrix generalization of the corresponding scalar binary problems is sometimes possible [94, 95]. To obtain an analytical solution of such problems, some special techniques are applied. Above all, a diagonalization of the diffusion matrix can be accomplished in order to reduce a coupled mass transport equation system to a set of scalar decoupled pseudo-binary equations [96]. The conjugate interfacial boundary conditions can be simplified, assuming constant concentration values at the interface [1]. Further on, a matrix governing the reaction kinetics can be implemented and linearized, as suggested in [95, 97, 98]. Finally, a semianalytical approach for the solution of reactive mass and heat transport can be applied, according to [99, 100]. The latter approach combines analytical and simple numerical methods, and such a combination results in more stable solutions and lower computational expense than purely numerical techniques (cf. Section 4.2.3). Comprehensive reviews of the analytically solved problems of this type can be found in [1, 17]. A more recent application is exemplified by the modeling and simulation of reactive stripping in monoliths with rounded channel cross-sections [101].

Application of computational fluid dynamics (CFD) In most RS units, fluid flow is, however, much more complex, both because of the column internals geometry and the tricky phase interactions. Analytical and simple numerical solutions can hardly be applied here. Instead, two-dimensional and three-dimensional numerical simulations of coupled flow and transport phenomena have to be performed, which are usually done with the aid of modern numerical facilities and CFD tools. CFD simulation today represents a powerful approach to many physicochemical problems, and the availability of advanced commercial tools facilitates its application. In the area of single-phase flow, significant progress can be recognized. However, multiphase flow simulations, especially in combination with mass transfer phenomena, are still under development. When the phase contact is very intensive, the fluid phases can be considered as if they were interpenetrating continua, and the so-called Euler-Euler flow modeling can be applied [102–104]. The fluid phases and their interfaces are then modeled as media continuously distributed over the computational domain, while phase interactions are covered by source terms in the transport equations. With this way, some groups attempted direct Euler-Euler modeling of separation units (see, e.g., [105]). However, there is no physically grounded method to determine source terms appearing in the species-transfer equations (the rate of mass transfer per unit volume). On the other hand, such source terms are necessary because they describe the interfacial mass transfer. It is suggested to determine them using macroscopic models

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(e.g., based on the film model) along with correlations for mass transfer coefficients, obtained experimentally. Such an approach is certainly inconsistent [106]. When the fluid phases in a separation column are not fully mixed, a free moving interface between them should be localized. Different strategies to handle the moving interfaces are classified into moving mesh methods, fixed mesh methods, and a combination of both. In the first method, a moving mesh is used to track the interface. As the form of the interface changes, the mesh is adjusted in accordance with the change. Methods falling under this strategy are called front tracking methods [107]. The second approach uses a fixed (Eulerian) mesh, while the interface is tracked using different procedures, e.g., special markers or indicator functions. Such methods are called front capturing methods; they include marker-and-cell, surface capturing, and volume capturing approaches [107]. Today, front capturing methods are widely used for various applications. This trend can be attributed to their availability within commercial and noncommercial software tools. Above all, two methods based on the use of an indicator function are popular, the volume of fluid (VOF) method [108] and the level set (LS) method [109]. The VOF function is defined as a cell-based volume fraction. Cells containing the first fluid phase are assigned the value one, whereas cells containing the second fluid phase are assigned the value zero. Cells that are crossed by the interface are assigned a value between one and zero, according to the phase-fraction distribution. The LS function is a signed distance to the interface that takes negative values in one phase and positive values in the other phase. Both methods are capable of handling significant interface movements stably and with relatively low computational effort. In the last few decades, several CFD studies of two-phase systems with free moving interface have been carried out to investigate the wetting properties of structured packings [110]. This reflects the growing interest in detailed understanding of the flow in structured packings. Figure 4.20 shows the flow patterns for the three linked crossover elements made up from two corrugated sheets and representing conventional structured packing geometry [111]. To facilitate understanding of the wetting results, different colors are used for the rear and front packing layers. The flow along the elements shows recurring flow motives; it tends to follow the packing channels and remixes at contact points. The results of such simulations, identifying the wetting problems for different packings and systems, are largely in line with the corresponding tomographic measurements [88, 112]. The development of such CFD-based methods represents an ongoing research area. However, the simulation of large-scale (reactive) separation columns appears to be too difficult, mostly because of the numerical difficulties and conflict of different scales in the unit model. In most cases, the position of the phase interface is difficult to capture and, thus, the boundary conditions cannot be determined properly [22]. Thus, the direct application of fluid-dynamic equations to the modeling of conventional separation units remains unfeasible.

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Fig. 4.20: Wetting profile as well as local and averaged holdup along three elements of two adjacent packing layers, obtained with static contact angle of 25°. Blue color indicates the liquid on the rear packing layer and red color indicates the liquid on the front packing layer [111].

In contrast, CFD can be very useful for the processes at micro-scale [113–115]. For instance, Chasanis et al. [114] numerically investigated carbon dioxide absorption into a sodium hydroxide solution in a micro-structured falling-film contactor (see Fig. 4.21). A rigorous 2D model was developed and validated against experimental data from literature. The modeling approach comprised two different steps, namely, a transient model in combination with the LS method to capture the interface (Fig. 4.22a) and a steady-state model to describe the whole absorption process (Fig. 4.22b). A good agreement between the simulated and experimental data of Zanfir et al. [116] was found (Fig. 4.23). The validated model was used to perform sensitivity studies and to investigate the impact of different process parameters on absorption performance. The high model accuracy can, above all, be attributed to the proper description of fluid dynamics. It is especially important for the gas phase where the resistance to mass transfer is concentrated. Figure 4.24 shows gas velocity arrow plots for two

4 Modeling concepts for reactive separations

66,4 mm

gas

liquid

2 mm

gas

liquid

Fig. 4.21: A photo of an IMM falling film micro-contactor (left) and a schematic of its inner configuration (right).

5,5 mm 100 μm channel

0,3 mm (a)

gas phase

(b)

Fig. 4.22: Domain used to determine interface position (left) and schematic of liquid and gas domains in the micro-contactor (right).

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Fig. 4.23: Model validation with experimental data from [116] for different process conditions.

a)

b)

c)

d)

Fig. 4.24: Gas velocity arrow plots (a, b) and CO2 molar fractions in the gas phase (c, d). Liquidphase volumetric flow rate is 50 mL h–1, NaOH inlet concentration in the liquid phase is 0.1 mol L–1, CO2 inlet molar fraction in the gas phase is 0.001 and the gas-phase volumetric flow rate is 11.4 L h–1 (a, c) and 0.23 L h–1 (b, d). The dashed line indicates the gas-liquid interface [114].

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different gas-phase volumetric flow rates. While a clear downward-directed parabolic velocity profile can be observed for the high gas flow (Fig. 4.24a), a substantial circulation is visible for the low gas-phase flow rate (Fig. 4.24b). This backmixing phenomenon appears whenever the gas-phase inlet velocity is distinctly smaller than the liquid-phase inlet velocity, and it has a substantial impact on CO2 mass transfer (Fig. 4.24c, d). While CO2 concentration significantly decreases toward the interface for the high gas-phase flow rate (Fig. 4.24c), the CO2 concentration gradient is directed oppositely for low gas-phase flow rates due to the backmixing (Fig. 4.24d). Such local information is very important for the overall process evaluation and micro-separation unit optimization.

Parameter estimation Another important area in which CFD can be successfully applied is the determination of the process and model parameters in the context of the complementary modeling concept that has recently been suggested in [22]. For instance, CFD simulations of small periodic elements in packed columns provide valuable information about the turbulent flow there and can further be used within the HA modeling. Moreover, pressure drop characteristics can be determined by direct numerical simulation, thus providing parameter correlations for the RBA modeling [117, 118]. For example, dry pressure drop of corrugated sheet packing, Sulzer-BX, could be estimated with a reasonable accuracy using CFD simulations of a representative small periodic packing element shown in Fig. 4.25 [117]. The influence of the apparatus wall was not considered and the flow was treated as established, with the periodic boundary conditions satisfied at the open boundaries.

½ b0

(a)

b0 (b)

½ b0

Fig. 4.25: Schematic representation of a periodic element of the corrugated sheet packing (a) and computational domain (b).

Numerical experiments performed with commercial tool CFX 4 by ANSYS® revealed strong pressure-drop sensitivity to the corrugation angle value. The complex flow structure necessitated a high resolution of the vortex scales responsible for the turbulence generation. Correlations between the pressure drop and the gas load determined here with a grid of 96,000 control volumes inside a crossover were compared

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with the corresponding experimental data available from Sulzer Chemtech [117]. This comparison is presented in Fig. 4.26 and a good agreement can be recognized.

Fig. 4.26: Simulated (line) and experimentally measured (points) dry pressure drop.

4.6 Complementary modeling concept As indicated above, most of the RS operations show a very high complexity. They comprise multiphase flows (with two, three, or even four phases), multicomponent systems, complex thermodynamics (often, electrolyte systems) as well as a sophisticated column unit design and geometry. An additional difficulty is brought by a large-scale difference between the characteristic dimensions of the phenomena involved. This complexity is the main reason why it is usually very difficult to describe RS units based on rigorous theoretical concepts. Different fluid separations have much in common (e.g., they occur in moving multicomponent systems and involve at least one liquid phase). On the other hand, the diversity of operating, scale, and boundary conditions of these processes is very high, and thus, it is hardly possible to develop a unified modeling approach applicable to all conditions. Instead, an appropriate approach should be carefully chosen on the basis of different criteria, e.g., possibility to solve the governing mathematical model, availability of process data and model parameters, suitable software and computer facilities, experience of the user, and expectations with respect to accuracy and predictivity.

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The choice of an appropriate method is often dictated by the complexity of the actual multiphase flow in (reactive) separation units. This dependence is reflected by the graphical representation shown in Fig. 4.27 [22]. For the most complex flow pattern and large-scale units, rigorous methods cannot be used, and significant simplifications have to be made, above all with respect to the fluid-dynamic description. In contrast, rigorous models (e.g., CFD-based methods) can be applied to less complex systems (cf. Section 4.5.4), while the HA modeling finds itself between the rigorous and simplified methods. Virtual experiments

Modeling rigor

Fluid-dynamic approach

Hydrodynamic anologies

Rate-based approach

Fluid dynamics complexity within the process Fig. 4.27: A view on the complementary modeling.

Different (reactive) separations problems can thus be solved using the different approaches classified in Fig. 4.27. These modeling approaches complement each other and, together, they cover the whole spectrum of fluid-dynamic complexity of the (reactive) separation processes. In this way, they can be considered complementary. However, a truly complementary effect is achieved due to the established links between the different modeling approaches that reflect possible information transfer. For instance, the data necessary for the realization of the RBA (e.g., fluid-dynamic quantities, mass transfer coefficients) can be obtained using CFD simulations, yielding numerically determined parameter correlations, as mentioned in Section 4.5.4 and illustrated in more detailed in the following section. Such CFD simulations are often carried out with properly chosen representative (mostly, periodic) elements of the real internals, allowing a very fine grid and sufficient resolution of the flow patterns. The subsequent post-processing provides the required functional dependencies of fluid-dynamic and mass transfer parameters, which are transferred to the RBA models. Such a link is also conceivable between the direct fluid-dynamic modeling and the HA methods (cf. Fig. 4.27). In this way, not only can the number of necessary

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real fluid-dynamic and mass transfer experiments be reduced, but column internals can also be optimized directly “on screen,” without the need to manufacture them for the model validation. Moreover, since the HA modeling does not require knowledge on mass and heat transfer coefficients, it can also be used for their experiment-free determination and delivered to the RBA in the form of correlations. This link, shown in Fig. 4.27 by a dashed line, is a topic of an ongoing research. It should be borne in mind that a unified modeling approach is particularly difficult to formulate when a direct account of the process rates (transport and reaction kinetics) is essential, which is typical for RS problems. A combination of the different kineticsbased approaches in a complementary way suggests an alternative recently proposed in [22]. This concept is further illustrated in Section 4.6.2.

4.6.1 Virtual experiments As mentioned in Section 4.5.2, virtual experiments represent a perspective way toward largely experiment-free process design and optimization. Of course, at the moment, this can rather be considered as a vision because the present capability of rigorous multiphase models is not sufficient. However, there exist some examples that bring optimism. Above all, this is related to the impressive progress in the development of multiphase CFD-based models and computer facilities. This allows simulation-based analysis that covers a broad spectrum of process variables and yields parameter correlations capable of competing with the corresponding experimental correlations. In the discussion on the parameter estimation in Section 4.5.4, an example of such virtual experiments is given for the determination of the dry pressure drop in structured packings. Another example is discussed here, in which the characterization of the phenomena in catalytic packings used in heterogeneously catalyzed reactive distillation columns is considered. In particular, liquid flow along an arrangement of catalyst pellets accompanied by mass transfer and chemical reaction was examined. Such arrangements are also typical for packed bed reactors. The random geometry of the bed must be reproduced in a realistic way. In [119], two different configuration types in a tube filled with spherical particles were investigated – a regular type and an irregular one. The regular configurations followed the atomic body-centered cubic and face-centered cubic structure in ideal crystals. For the generation of the irregular packing configuration of nonoverlapping spherical particles, a ballistic deposition method is employed, in combination with the Monte Carlo approach. This combined method results in representative irregular particle configurations. In the CFD simulations of the flow within the particle configurations, inlet effects were neglected and periodic boundary conditions in the main flow direction

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were applied. In a strict sense, the use of periodic boundary conditions introduces some discrepancy; however, it helps to reduce computational power and time. In Fig. 4.28 [119], the typical velocity distributions are shown for two close crosssections of the random bed, and strong changes caused by the irregular bed structure are seen.

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To validate the simulation results, four experimentally determined pressure drop correlations were used. Numerical results for the irregular configuration agree well with the correlations by Zhavoronkov et al. [120] and Reichelt [121], in which the wall effect on pressure drop is taken into account (see Fig. 4.29). Two other older correlations by Carman [122] and Ergun [123] do not consider the wall effects and show larger deviations. This, again, demonstrates that reasonably and carefully performed CFD simulations can be used as virtual experiments, providing parameter correlations to be transferred to less rigorous modeling methods, such as the RBA. 10000 Ergun Carman Zhavoronkov Reichelt CFD

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In [124, 125], the capabilities of virtual experiments are further illustrated, based on the CFD analysis of mass transfer and residence time distribution in random configurations. The residence time distribution was studied with two different methods.

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The tracer method imitates the experimental procedure using a nondiffusive tracer, whereas the post-processing method directly calculates the residence time distribution from the local velocity field. Both methods gave similar results. However, the post-processing method is preferable, as it requires less computational power and time, compared to the tracer method. The simulation results for the mass transfer and residence time evaluations were validated against experimental data from literature.

4.6.2 Development of a new packing with the complementary modeling approach A methodology for the development of optimal internals based on a combination of CFD and process simulation in a special optimization algorithm was suggested in [126]. Sensitivity studies performed with a rate-based process simulator are a part of this procedure. The internals can then be modified in accordance with the results of these studies, and the modified internals can be further investigated theoretically by means of CFD to derive relevant correlations to be used in the process simulator. After several iterations, internals perfectly fitting the process criteria can be created “on screen” and manufactured. In the long-term perspective, this method can be regarded as a way toward virtual prototyping of new, process-specific internals for (reactive) separations, provided that chemical companies and manufactures of internals are interested to collaborate. Another successful demonstration of the benefits of the complementary modeling concept was presented in [127]. Here, all three approaches shown in Fig. 4.27 were employed to develop a new structured packing, best suited for the postcombustion CO2 absorption. The details of this impressive application example are given hereinafter.

Validation of individual approaches First, the approaches presented in Fig. 4.27 were tested with respect to their accuracy and reliability. CFD simulations were performed using commercial software tool STAR CCM + developed by CD-adapco and now owned by Siemens AG. Rigorous simulations could be performed for one-phase gas-phase flow, while neglecting the influence of the thin films at the packing surface. Furthermore, the inherent periodicity of structured packings was used in the fluid-dynamic studies. Figure 4.30 illustrates the choice of the representative periodic element and shows the corresponding velocity field in it. Based on the post-processing of this local data, the specific pressure drop in the packing was evaluated; this procedure is similar to that shown in Section 4.6.1. This allows a reasonable validation of the method by

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streamlines (a)

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Fig. 4.31: Specific pressure drop values for two different packing types, determined by CFD simulations and by measurements (UPB denotes the abbreviation of Paderborn University).

comparing with the experimental pressure drop data of Julius Montz (Fig. 4.31), showing a good agreement for two different packing geometries. Next, testing was performed for the HA method, while the experimental data obtained for CO2 absorption into aqueous monoethanolamine (MEA) in a unit filled with Sulzer Mellapack 250.Y packing [128] was used. Parameters describing turbulence in the two-phase flow were determined – in a complementary way – with the CFD simulations (see [129]), while the correlation for the specific interfacial area was taken from [130]. Good agreement of the simulated and experimental data is clearly visible in Fig. 4.32. Finally, a validation of the RBA tool available at Paderborn University was carried out using, again, the extensive data pool from [128]. Parameter correlations, such

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Fig. 4.32: CO2 mass fractions in the liquid phase, determined by HA simulations and measured by Notz [128].

as pressure drop, holdup, transfer coefficients, and specific interfacial area were taken from [130, 131]. Figure 4.33 shows the examples of concentration and temperature column profiles and demonstrates a very good agreement between the simulated and experimental values, which was also confirmed for all investigated experiments.

Development of a novel structured packing The three approaches thus validated were used to develop a new structured packing for the CO2 absorption with improved properties. Most often, two criteria are used to evaluate the packing appropriateness – separation efficiency and pressure drop, both depending on the packing geometry. CFD-based modeling was used first, while the packing inclination angle was varied and the results were analyzed. As can be clearly seen in Fig. 4.34, the inclination angle indeed strongly influences the pressure drop, but only up to the value close to 75°. For inclination angles above 75°, only marginal reduction of pressure drop can be encountered. Thus, by making the packing “more vertical,” a significant pressure drop reduction can be achieved. Of course, this must not be accompanied by a similarly significant separation efficiency drop, and the latter has to be proven.

Fig. 4.33: Concentration and temperature profiles in the liquid phase obtained by RBA simulations and measured by Notz [128] for two different experiments.

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Fig. 4.34: Pressure drop dependence on packing inclination angle and gas-phase load (represented by the gas capacity factor F) obtained by CFD-based simulations.

As discussed above, such an investigation is hardly possible with CFD methods. Instead, in the second step, the HA modeling approach was used in order to evaluate the separation efficiency. Inclination angles of 45° (standard for many commercial packings), 20°, and 70° were studied. Absorption efficiency for higher angles decreased, which was expected. However, this reduction was rather insignificant (e.g., from 75% to 66% for the experiment A1 by [128]). Such a reduction can be overcome by using higher columns. Based on these results, a new structured packing

Fig. 4.35: Fabricating of the B1-250.75 packing at Julius Montz GmbH.

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with the inclination angle of 75° was considered to be an interesting option. Consequently, Julius Montz fabricated a certain amount of this packing to be tested experimentally (cf. Fig. 4.35).

Experimental testing and large-scale studies The new packing behavior was experimentally studied in the pilot plant at Paderborn University (cf. [132]) using CO2 absorption by aqueous MEA solution as a test system. The new packing showed a dramatic reduction (over 90%!) in pressure drop as compared to conventional packing with 45° inclination angle (cf. Fig. 4.36), thus fully confirming the expectations based on the modeling. In contrast, the corresponding loss in separation efficiency was found to be rather limited [133].

Fig. 4.36: Pressure drop of irrigated packing with 20 m3 m–2 h–1 liquid load. Experiments in Paderborn are validated against the measurements at Julius Months with conventional packing (45°); besides, a comparison with the new packing (75°) is shown.

Further tests of the new packing were performed with the RBA modeling, this time for the CO2 capture system at industrial scale. Large-scale industrial data were used to investigate bituminous coal fired power plant (power output of 650 MWe) and natural gas-fired combined cycle (power output of 420 MWe) (see [133]). For the new packing, parameter correlations from literature were adjusted based on the experimental data available at Paderborn University, and it was found that the efficiency drop did not exceed 5% [133]. Thus, both pilot plant experiments and large-scale simulations prove that the new 75° packing represents a good alternative to standard packings for the amine-based CO2 capture.

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4.7 Take-home messages – Fluid-phase RSs have several common features, which can be used to develop general concepts for their modeling, namely, moving systems, two-phase flows, multicomponent mixtures, interplay of mass transport and chemical reactions, and largely nonlinear process behavior. – RS processes can be considered as certain extensions of the underlying separation operations, and hence, their modeling is often based on the corresponding concepts established for nonreactive operations. – Column internals for RSs have to enhance both separation (a large contact area required) and reaction (a significant holdup and, sometimes, sufficient amount of catalyst) and maintain a sound balance between them. – Film model provides the main background for the rate-based modeling of RSs. – Conventional film model can be extended to consider reactions in film region (fast reactions, mostly in reactive absorption). – Conventional film model can further be extended to consider solid catalyst phase, while either three-phase or a quasi-homogeneous models result. – Finally, conventional film model can be applied as a four-phase arrangement to describe (reactive) dividing columns. – The hydrodynamic analogy approach is an alternative to the rate-based approach and can evaluate (reactive) separation performance without using mass transfer coefficient correlations. – CFD-based simulations can be successfully applied to model (reactive) separation processes at micro-scale. – Another perspective of the CFD application is running virtual experiments to estimate the aggregate process parameters, like pressure drop and mass transfer coefficients. – However, CFD modeling of large-scale (reactive) separation columns is hardly possible, mostly because of numerical difficulties and conflict of different scales in the unit model. – The complementary modeling concept, based on a combination of different kinetics-based approaches, suggests a promising alternative for the simulation of RS equipment.

4.8 Quiz: true or false? – The equilibrium-stage model cannot be applied for the description of RSs, even if it considers reaction kinetics. – Thermodynamic equilibrium relationships are used both in the equilibriumstage model and in the rate-based approach.

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– Reactive azeotrope is a kinetics-based phenomenon. – Reaction kinetics is a particularly important factor in the modeling of RS processes with slow reactions. – When a quasi-homogeneous model for catalytic distillation is applied, intrinsic reaction kinetics must be known. – The hydrodynamic analogy approach helps to evaluate the process fluid dynamics. – CFD simulation of large-scale RS units is currently not feasible.

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[88] Bolenz L, Fischer F, Toye D, Kenig EY. Determination of local fluid dynamic parameters in structured packings through X-ray tomography: Overcoming image resolution restrictions. Chem. Eng. Sci. 2021;229:115997. [89] Grossman G. Heat and mass transport in film absorption. In: Cheremisinoff NP, ed. Handbook of Heat and Mass Transfer. Houston: Gulf Publ. Comp. Book Division; 1986, 211–222. [90] Yih SM. Modeling heat and mass transfer in wavy and turbulent falling liquid films. In: Cheremisinoff NP, ed. Handbook of Heat and Mass Transfer. Houston: Gulf Publ. Comp. Book Division; 1986, 111–122. [91] Boyadjiev C, Babak VN. Non-linear Mass Transfer and Hydrodynamic Stability. 1st edn. Amsterdam u.a: Elsevier; 2000. [92] Heibel AK, Heiszwolf JJ, Kapteijn F, Moulijn JA. Influence of channel geometry on hydrodynamics and mass transfer in the monolith film flow reactor. Catal. Today 2001;69(1–4):153–163. [93] Killion JD, Garimella S. A critical review of models of coupled heat and mass transfer in falling-film absorption. Int. J. Refrig. 2001;24(8):755–797. [94] Toor HL. Dual diffusion – reaction coupling in first order multicomponent systems. Chem. Eng. Sci. 1965;20(11):941–951. [95] Kenig EY, Schneider R, Górak A. Multicomponent unsteady-state film model: A general analytical solution to the linearized diffusion–reaction problem. Chem. Eng. J. 2001;83(2): 85–94. [96] Toor HL. Solution of the linearized equations of multicomponent mass transfer: II. Matrix methods. AIChE J. 1964;10(4):460–465. [97] Delancey GB. Multicomponent film-penetration theory with linearized kinetics – I. Linearization theory and flux expressions. Chem. Eng. Sci. 1974;29(12):2315–2323. [98] Wei J, Prater CD. The Structure and Analysis of Complex Reaction Systems. Elsevier; 1962, 203–392. [99] Kenig EY, Kholpanov LP. Simultaneous mass and heat transfer with reactions in a multicomponent, laminar, falling liquid film. Chem. Eng. J. 1992;49(2):119–126. [100] Kenig EY. Mass transfer-reaction coupling in two-phase multicomponent fluid systems. Chem. Eng. J. 1995;57(2):189–204. [101] Mueller I, Schildhauer TJ, Madrane A, Kapteijn F, Moulijn JA, Kenig EY. Experimental and theoretical study of reactive stripping in monolith reactors. Ind. Eng. Chem. Res. 2007;46(12):4149–4157. [102] Zhang D, Deen NG, Kuipers J. Numerical simulation of the dynamic flow behavior in a bubble column: A study of closures for turbulence and interface forces. Chem. Eng. Sci. 2006;61(23): 7593–7608. [103] Joshi JB. Computational flow modelling and design of bubble column reactors. Chem. Eng. Sci. 2001;56(21–22):5893–5933. [104] Pan Y, Dudukovic MP, Chang M. Dynamic simulation of bubbly flow in bubble columns. Chem. Eng. Sci. 1999;54(13–14):2481–2489. [105] Liu GB, Yu KT, Yuan XG, Liu CJ. A numerical method for predicting the performance of a randomly packed distillation column. Int. J. Heat Mass Transf. 2009;52(23–24):5330–5338. [106] Kenig EY, Shilkin A, Atmakidis T. Comments on “Simulations of chemical absorption in pilotscale and industrial-scale packed columns by computational mass transfer” by Liu et al. Chem. Eng. Sci. 2008;63(16):4239–4240. [107] Ferziger JH, Perić M. Computational Methods for Fluid Dynamics. 3rd edn. Berlin, Heidelberg, u.a.: Springer; 2002.

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Anton A. Kiss

5 Reactive distillation 5.1 Fundamentals In the chemical industry, most processes involve reaction and separation operations that are carried out, typically, in different sections of a plant, and use different equipment types operated under a wide variety of conditions [1]. Recycle streams are often used between these operating units in order to improve the conversion and selectivity, to minimize the production of undesired by-products, to reduce the energy requirements, and to enhance process controllability. The recent economic and environmental considerations have encouraged the industry to focus on novel technologies based on process intensification [2, 3, 4]. RD integrates the reaction and separation steps into a single unit, allowing the simultaneous production and removal of products; hence improving the productivity and selectivity, reducing the energy use, eliminating the need for solvents, and leading to intensified, high-efficiency systems with green engineering attributes [5, 6]. Some of these benefits are realized by using a reaction to improve separation (e.g., overcoming azeotropes, reacting away contaminants, avoiding or eliminating difficult separations), while others are realized by using the separation to improve reactions (e.g., enhancing overall rates, overcoming reaction equilibrium limitations, improving selectivity, and removing catalyst poisons). The best synergistic effect is achieved when both aspects are considered [7, 8, 5]. But the application of RD is somewhat limited by constraints: common operation range for distillation and reaction (similar temperature and pressure), proper boiling point sequence (product should be the lightest or heaviest component, while side or by-products, the mid boiling ones), and difficulties in providing proper residence time characteristics [9, 10]. Although a number of industrial RD applications have been around for many decades [1], even today the RD crown is carried by the Eastman process that reportedly replaced a methyl acetate production plant with a single RD column using 80% less energy at only 20% of the investment costs [11, 12]. Nowadays, the application with the largest number of installations is methyl tertiary butyl ether (MTBE), which is used in gasoline blending. Other esters, such as ethyl tertiary butyl ether (ETBE), tert-amyl methyl ether (TAME), or fatty acid methyl esters (FAME), are nowadays also produced by RD [7, 8]. Considering the large extent of the RD topic, this chapter provides only a brief overview of what process intensification means for RD. For more detailed information, there are several books and reviews published in the past decade, covering a large range of subjects about RD: fundamentals [13], process synthesis [14], conceptual design [5], process design and control [1, 15], optimization [16], practical https://doi.org/10.1515/9783110720464-005

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operation [17, 18], industrial perspective and applications [7, 8, 19, 20, 21], and status and future directions [22]. RD is attractive in systems where specific chemical and phase equilibrium conditions co-exist. Reaction and distillation take place in the same zone of a column, and the reactants are converted with the simultaneous separation of the products and recycle of the unused reactants. Since the products must be separated by distillation, this means that the products should be lighter and/or heavier than the reactants. The ideal case is when one product is the lightest and the other product is the heaviest, with the reactants being the intermediate boiling components [1]. Moreover, as both operations occur simultaneously in the same unit, there must be a good match between the temperatures and pressures required for reaction and separation [10, 23] – as clearly illustrated by Fig. 5.1 [24]. The operating window is typically limited by the thermodynamic properties (e.g., boiling points) of the components involved. But, the window in which the (catalytic) reaction delivers acceptable yields and selectivity also has usually a limited overlap with the separation window. Moreover, this overlap may be reduced further by the feasibility window concerning the equipment design. This usually leads to a very restricted area in which a reactive separation is technically and economically feasible [13]. The combination of reaction and distillation is clearly not possible if there is no significant overlapping of the operating conditions of reaction and separation (e.g., a high-pressure reaction cannot be combined with a vacuum distillation). One must also consider that working in the limited overlapping window of operating conditions is not always the optimal solution, but is merely a trade-off [23]. On the contrary, in a conventional multiunit flowsheet, the reactors can be operated at their optimum parameters, which are most favorable for chemical kinetics, while the distillation columns can be operated at their optimal pressures and temperatures, which are most favorable for the vapor-liquid equilibrium (VLE) properties [1].

Fig. 5.1: Overlapping of operating windows for reaction, separation, and equipment.

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The pressure and temperature effects are much more pronounced in RD than in conventional distillation, as these parameters affect both the phase equilibrium and chemical kinetics [25, 1, 26, 27]. A low temperature that gives high relative volatilities may provide small reaction rates that require large amounts of catalyst or liquid holdups to achieve the required conversion. In contrast, a high temperature may promote undesirable side reactions or give a low equilibrium constant that makes it difficult to drive the reaction to completion [1, 23]. RD is typically applied to equilibrium reactions, such as esterification, etherification, hydrolysis, and alkylation. Luyben and Yu [1] reported that over 1,100 articles and 800 US patents RD were published on during the past 40 years, covering in total over 235 reaction systems. Most of the reaction types belong to the stoichiometry: aA + bB ⇌ cC + dD (over 38%), or aA + bB ⇌ cC (over 25%), aA ⇌ bB + cC (about 9%), or aA ⇌ bB class (nearly 8%), with the rest of them falling into other categories of two- or three-stage reactions [1]. RD has attracted considerable attention, especially for chemical equilibriumlimited, liquid-phase reactions, which conventionally require a large excess of one of the reactants. To aid the decision on considering RD as an option for a new process, Shah et al. [28] proposed a systematic framework for the feasibility and technical evaluation of the RD processes, based on fundamental explanations as well as industrial applications of RD reported in the scientific literature. In order to perform a feasibility evaluation, some basic information on the chemical process is required, such as VLE, stoichiometry of reactions, kinetics, and enthalpy of reactions [2]. But, in the process of deciding whether RD is the right choice, one must keep in mind both the benefits (+) and limitations (–) of reactive distillation [13]: + Process simplification: Complex conventional processes can be reduced to an RD column, which is typically much easier and cheaper to operate and maintain. + Capital savings. Reducing the equipment units used leads to a considerable reduction of Capex. + Increased conversion: The removal of products from the reactive liquid phase causes chemical equilibrium to be re-established at a higher conversion rate, and full conversion is attainable. + Increased selectivity: Undesired side reactions can be suppressed by removing the target product from the reactive section of the RD column. This also means less waste and fewer by-products. + Reduced energy usage: The heat of the exothermic reaction can be used in situ for the vaporization of the liquid, thus reducing the reboiler duty and, consequently, the heat transfer area of the reboiler. + Reduced degradation of chemicals: Due to the lower residence time (as compared to a classic reactor), the chemicals are exposed to high temperatures for shorter periods.

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+ Intrinsic safety: By nature, RD is a boiling system, in which hot-spots and runaways are avoided. Also, due to the relatively low liquid holdup, it can be effectively used for hazardous chemicals. + Overcoming of azeotropes: Under carefully selected conditions, azeotropes can be reacted away, being consumed by the reaction occurring in the liquid phase. + Separation of close-boiling components: A reactive entrainer reacts with one component to form another product (with a larger difference in boiling points) that can be easily separated. The reverse reaction to recover the original component is then performed in a subsequent RD column. – Reduced flexibility: This comes due to higher degree of integration, as compared to classic units. – Volatility constraints: An appropriate order of volatilities is required to ensure high concentrations of reactants and low concentrations of products in the reactive zone. RD should be applied only if the difference in boiling points between the reactants and products is larger than 20 K. – Operating-window constraints: Both reaction and separation processes take place at the same conditions (pressure and temperature); hence, reasonable conversion levels must be attainable at operating conditions that are suitable for distillation (Fig. 5.1, left). – Occurrence of reactive azeotropes: A reactive azeotrope is actually formed when the change in concentration caused by distillation is fully compensated by the reaction. Reactive azeotropes can sometimes create distillation boundaries that make separation difficult or, even, infeasible. – Occurrence of multiple steady states: The complex interplay between reaction and separation, as well as other phenomena, leads to a strongly nonlinear process behavior with possible multiple steady states. For this reason, the same RD column configuration, operated under same conditions, can exhibit different steady-state column profiles and, thus, different conversions.

5.2 Applications The reasons for the many benefits of RD are the synergistic effects of the simultaneous chemical reaction and distillation. However, these synergies make RD so extraordinarily complex [13]. Conceptually, RD belongs to the category of multifunctional reactors, and can be considered as a very complex system due to the simultaneous interactions among the vapor and liquid phases, as well as the solid phase (in the case of using solid catalysts). Owing to its complexity, there are several constraints and difficulties (discussed earlier) that still limit the widespread application of reactive distillation. Nonetheless, it is worth noting that reactive distillation has made already a significant impact at industrial scale with many large-scale applications.

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Table 5.1 [29, 2] lists the most important applications of RD: (trans-)esterification, etherification, hydrolysis, (de-)hydration, alkylation, isomerization, (de-)hydrogenation, amination, condensation, nitration, chlorination, and so on [10, 22]. Currently, the application with the largest number of installations is methyl tertiary butyl ether (MTBE), used as a gasoline additive. CDTECH (a partnership between ABB Lummus Global and Chemical Research & Licensing Company) has licensed over 200 commercial processes operated worldwide at capacities of 100–3,000 ktpy for the production of ethers (MTBE, TAME, and ETBE), hydrogenation of aromatics, and hydro-desulfurization (HDS), ethyl benzene, and isobutylene production [7]. Sulzer ChemTech also reports several industrial-scale applications, such as synthesis of ethyl, butyl and methyl acetates, hydrolysis of methyl acetate, synthesis of methylal, methanol removal from formaldehyde, and fatty acid esters production [7]. Tab. 5.1: Main industrial applications of reactive distillation. Reaction type Alkylation Alkyl benzene from ethylene/propylene and benzene Amination Amines from ammonia and alcohols Carbonylation Acetic acid from CO and methanol/dimethyl ether Condensation Diacetone alcohol from acetone Bisphenol-A from phenol and acetone Trioxane from formaldehyde Esterification Methyl acetate from methanol and acetic acid Ethyl acetate from ethanol and acetic acid -Methyl propyl acetate from -methyl propanol and acid Butyl acetate from butanol and acetic acid Fatty acid methyl esters from fatty acids and methanol Fatty acid alkyl esters from fatty acids and alkyl alcohols Cyclohexyl carboxylate from cyclohexene and acids Etherification MTBE from isobutene and methanol ETBE from isobutene and ethanol TAME from isoamylene and methanol DIPE from isopropanol and propylene Hydration/dehydration Mono ethylene glycol from ethylene oxide and water Hydrogenation/dehydrogenation Cyclohexane from benzene MIBK from benzene

Catalyst/internals Zeolite beta, molecular sieves H and hydrogenation catalyst Homogeneous Heterogeneous N/A Strong acid catalyst, zeolite ZSM- HSO, Dowex , Amberlyst- N/A Katapak-S Cation exchange resin HSO, Amberlyst-, metal oxides HSO, Amberlyst-, metal oxides Ion exchange resin bags

Amberlyst- Amberlyst-/pellets, structured Ion exchange resin ZSM , Amberlyst-, zeolite Homogeneous Alumina supported Ni catalyst Cation exchange resin with Pd/Ni

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Tab. 5.1 (continued) Reaction type Hydrolysis Acetic acid and methanol from methyl acetate and water Acrylamide from acrylonitrile Isomerization Iso-parafins from n-parafins Nitration -Nitrochlorobenzene from chlorobenzene and nitric acid Transesterification Ethyl acetate from ethanol and butyl acetate Diethyl carbonate from ethanol and dimethyl carbonate Vinyl acetate from vinyl stearate and acetic acid Unclassified reactions Monosilane from trichlorsilane Methanol from syngas DEA from monoethanolamine and ethylene oxide Polyesterification

Catalyst/internals

Ion exchange resin bags Cation exchanger, copper oxide Chlorinated alumina and H Azeotropic removal of water Homogeneous Heterogeneous N/A Heterogeneous Cu/Zn/AlO and inert solvent N/A Autocatalytic

More recently, the use of biomass as a feedstock for the production of fuels and chemicals has become attractive in view of the sustainability and circular economy, and it is expected that they will play an important role in the next decades. As a result of the transition from an oil-based to a biomass-based chemical industry, tools and processes must be developed for the conversion of renewable resources into valuable chemical products. Several bio-based platform chemicals were identified, which can be produced by biorefineries. About half of these components have been studied with respect to the use of reactive distillation technology. Table 5.2 provides an overview of selected RD studies related to bio-based platform chemicals, including the catalyst used, and the internals. For the other components (platform chemicals), RD processes have not been studied for various reasons, such as unfavorable property data or thermal decomposition [30]. Tab. 5.2: Reactive distillation technology applications for bio-based platform chemicals. Platform component Succinic, fumaric, and malic acids Diethyl succinate (from succinic acid) Levulinic acid Ethyl levulinate from levulinic acid Ethyl and butyl levulinate from levulinic acid

Catalyst/internals Amberlyst /Katapak SP- Amberlyst  Amberlyst /Katapak-S

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Tab. 5.2 (continued) Platform component Biodiesel Fatty acid methyl ester from fatty acids and methanol Methyl esters from triolein and methanol Methyl esters from Canola oil and methanol Fatty acid ethyl ester from soybean oil and ethanol Fatty acid methyl ester from waste cooking oil Glycerol Triacetin from glycerol and acetic acid Glycerol acetals from glycerol and methylal Dichloropropanol from monochlorohydrin and HCl Dichloropropanol from glycerol Acetol from glycerol -Hydroxypropionic acid, ,-propanediol, lactic acid Ethyl lactate from lactic acid Ethyl lactate from lactic acid Butyl lactate from lactic acid Lactic acid from methyl lactate Acrylic acid from -HPA Acrylic acid/ester from lactic acid Recovery of ,-propanediol, ,-butanediol, glyerol and glycerol acetals from fermentation broth ,-Furan dicarboxylic acid (FDCA) FDCA ester production Tri-ethylcitrate from citric acid and ethanol

Catalyst/internals

Metal oxides of Zr, Ti, Sn, Nb Alkaline catalyst Potassium hydroxide Sodium hydroxide Heteropolyacid Amberlyst /Katapak-S Amberlyst  Acetic acid Acetic acid or heteropolyacid Heterogeneous metallic catalysts SO−/ZrOFeO Amberlyst /Katapak-S Amberlyst  Amberlyst CSP/Katapak n/a Amberlyst  or similar D cation-exchange resin

Heterogeneous acid catalyst Amberlyst /Katapak-S

5.3 Modeling and design RD is a process of multicomponent nature; hence it is qualitatively more complex than similar binary processes. Thermodynamic and diffusional coupling in the phases and at the interface are accompanied by complex chemical reactions [10]. Consequently, RD models must take into consideration the column hydrodynamics, mass transfer resistances, and reaction kinetics. The reader is referred to Chapter 3 for a detailed description of the thermodynamic modeling of reactive separations, and to Chapter 4 for a detailed description of equilibrium (EQ) and nonequilibrium (NEQ) models for reactive separations in general. The complexity of an RD model depends on its application and the problem to be solved – plant design, modelbased control, or real time optimization. A process model consists of sub-models for mass transfer, reaction, and hydrodynamics of various complexities. The mass transfer between the vapor and the liquid phase can be described by the rigorous rate-based approach (Maxwell–Stefan diffusion equations) or it can be accounted

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for by the simple EQ-stage model, assuming thermodynamic equilibrium between the vapor and liquid phases [10]. Detailed modeling of RD was covered by several studies: [31, 32, 33, 34, 35, 36, 37, 38, 39, 10, 40, 41]. Figure 5.2 summarizes the models that are commonly used for representing mass transfer, chemical reaction, and hydrodynamics in reactive distillation processes [30, 10]. Those models differ in rigor and, consequently, in their modeling and calculation complexity. Among the modeling approaches, mass transfer is described using NEQ-stage models and EQ-stage models; chemical reaction is described using film and bulk reaction or chemical equilibria; and hydrodynamics are described using nonideal flow behavior or ideal plug flow. If a NEQ-stage model is used, mass transfer can be described using the Maxwell–Stefan equations of effective diffusion coefficients.

Fig. 5.2: Reactive distillation modeling approaches for representing mass transfer, chemical reaction, and hydrodynamics.

Figure 5.3 illustrates both the EQ- and NEQ-stage models [2, 41]. The EQ-stage model assumes that each vapor stream leaving a tray or a packing segment is in thermodynamic equilibrium with the corresponding liquid stream leaving the same tray or segment. In the case of RD, chemical reaction is additionally considered via reaction equilibrium equations or via rate expressions integrated into the mass and energy balances [10, 41]. The use of the Hatta number, representing the reaction rate in reference to that of mass transfer, helps to discriminate between very fast, fast, average, and slow chemical reactions. If a (very) fast reaction system is considered, then RD can be satisfactorily described by just assuming reaction equilibrium. A more physically consistent way to describe a column stage is the rate-based approach that directly takes into account the actual rates of multi-component mass and heat transfer, and chemical reactions [35, 38, 39, 10, 40, 41]. Both approaches can be conveniently simulated in commercial process simulators, such as Aspen

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Fig. 5.3: Modeling reactive distillation: equilibrium (left) and nonequilibrium stage (right).

Plus (e.g., RADFRAC distillation unit with the RateSep model), Aspen Custom Modeler [42], ChemCAD, Pro II, or gPROMS. It is also important to note that the introduction of an in situ separation function within the reaction zone leads to complex interactions between the VLE and mass transfer, catalyst diffusion, and chemical kinetics. Such interactions were shown to lead to the phenomenon of multiple steady states and complex dynamics, which have been verified in experimental laboratory and pilot plant units [43, 41, 44]. Summarizing, the simulation of RD processes can consider two types of fundamental models: EQ-stage models and NEQ-stage models. The benefits and drawbacks of each approach as well a direct comparison are discussed in the paper of [41], and in the general context of reactive separations in Chapter 4. The EQ modeling can be formulated at two levels: simultaneous phase and chemical equilibrium, and phase equilibrium with chemical kinetics. The full equilibrium model requires only a thermodynamic knowledge. Residue curve maps (RCM) can help to highlight the range of feasible design in terms of pressure, temperature, and separation of products. The simulation is rather easy, but care should be paid to the accuracy of the thermodynamic properties, phase equilibrium, and chemical equilibrium (cf. Chapter 3). Such a model based on phase and chemical equilibrium allows for a rapid assessment of the feasibility of an RD process [10]. The simulation becomes more realistic when knowledge of the chemical kinetics is added. The progression of the reaction in each stage can be followed, and thus the number of theoretical stages for achieving a target conversion can be obtained. A key parameter in the kinetic approach is the reaction holdup. Accordingly, the selection of internals and hydraulic pre-design are necessary. An accurate knowledge of the reaction-rate expression is necessary, which can be extrapolated over the interval of composition and temperature. This is a crucial point in RD, and a major source of failure. The reaction rate must be expressed adequately, either on pseudo-homogeneous basis (volume), or per mass of (solid) catalyst. As outlined in Chapter 3, calculating the reaction rates on the basis of concentrations,

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instead of activities, can also introduce large errors when highly nonideal mixtures are handled (e.g., when containing water). In NEQ modeling, the intensity of the interfacial mass transfer in the liquid and vapor phases are counted for, by using the Maxwell-Stefan equations. The availability of specific correlations for calculating the mass transfer coefficients is necessary, which in turn depend on the selected internals. The potential accuracy of this approach is paid by a much more elaborated procedure that needs customized programming. A comparison with experiments showed that the NEQ modeling gives good results if accurate model parameters are employed [45]. The model of an RD process must account for the phase equilibrium, the rate of reaction, and mass transfer in the bulk as well as in the film. The equilibrium behavior of most RD systems varies between two boundaries, corresponding to the phase equilibrium and the chemical equilibrium control. An RCM derived from the chemical and phase equilibrium for a reactive and nonreactive section of the RD column represents variations of the stationary points – corresponding to the pure components and azeotropes – between equilibrium boundaries for a given temperature and pressure. Variations in these singular points can be represented by the Damkohler number (Da): Da =

H0 kf V

(5:1)

where H0 is the liquid holdup (mol), kf is a pseudo-first-order rate constant (s–1), and V is the vapor rate (mol s–1). The Damkohler number is the ratio of the characteristic residence time (H0/V) to the characteristic reaction time (1/kf). For low values of the Da number (Da ≤ 0.1), the reaction rate in each stage is relatively slow as compared to the residence time available, and the system is dominated by phase equilibrium. For large values of Da (Da > 10), the reaction rate is fast and chemical equilibrium is approached in the reactive stages. If the Damkohler number does not lie between these values, then neither the phase equilibrium nor the chemical equilibrium is controlling; hence the process is, in fact, kinetically controlled. Moreover, the combinations of the Damkohler number and the chemical equilibrium constant can be used to perform a preliminary screening of the suitability of the process for an RD application. Reactive distillation is expected to be significantly beneficial compared to a sequential combination of a reactor and a distillation process, when the process demonstrates a combination of low Da (Da ≤ 0.1) and high KEQ (KEQ > 1) or high Da (Da > 0.1) and low KEQ (KEQ ≤ 1). The combination of low Da and high KEQ represents a slow forward reaction, but a slower reverse reaction leads to a high product formation. RD offers benefits as long as the required holdup is not too large. The combination of high Da and low KEQ represents a fast product formation, but a fast reverse reaction also leads to little product formation. RD is beneficial because the product can be removed quickly from the reactive zone and allows equilibrium shifts to the product side. Since the product

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removal rate solely depends on the rate of mass transfer between the phases, the process must not be mass-transfer-controlled. The combination of high Da and high KEQ represents a fast forward reaction, and a slower reverse reaction leads to a situation of an instantaneous irreversible reaction. Therefore, a simple reactor is sufficient to carry out the process. For this class of processes, reactive distillation can only be useful compared to a simple reactor, when the higher selectivity of the main reaction over a side reaction is noticed. The reactive stage can be assumed to be at chemical equilibrium, and such a reactive stage can be modeled as a vapor-liquid equilibrium stirred tank reactor. Reactive distillation is not beneficial when the process demonstrates a combination of low Da and low KEQ. The combination of a low Da and a low KEQ represents a slow forward reaction and a fast reverse reaction, which essentially leads to zero product formation. This class of processes requires an optimally designed reactor with a large holdup. This technical feasibility analysis of the RD process and the process limitations based on the Da and chemical equilibrium is summarized in Fig. 5.4 [28]. The working regime of the process must be identified to confirm whether the process is mass transfer or kinetically controlled, and whether the reaction takes place only in the bulk or also in the film. This allows one to establish the requirements of internals for the RD column and the modeling approach that needs to be applied to design the RD process. The working regime can be identified based on the Hatta number (Ha), pseudo-first-order rate constant (kf), and the volumetric mass transfer coefficient (kLa). The Hatta number is the ratio of the maximum possible conversion in the film to the maximum diffusion transport through the film. For higher order reactions of the two components, the Hatta number is defined as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 kf CAn − 1 CB DA (5:2) Ha = n + 1 kL2 where n is the order of the reaction (–), kf is the forward reaction rate constant (s–1), C is the concentration (mol m–3), D is the diffusivity (m2 s–1), and kL is the mass transfer coefficient (m s–1). A Hatta number kLa), or a slow mixed regime (kf = kLa). Depending on the working regime, the proper internals can be conveniently selected. Figure 5.4 also summarizes the internal and model requirements for different working regimes. As clearly shown here, the technical evaluation of any RD process can be quickly but systematically performed based only on the Damkohler number, the chemical equilibrium constant,

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Fig. 5.4: Systematic framework for the technical evaluation of the reactive distillation processes.

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the Hatta number, the pseudo-first-order rate constant, and the volumetric mass transfer coefficient. Additionally, a systematic framework for assessing the applicability of RD for quaternary mixtures using a mapping method was recently proposed by [46]. RCM is an invaluable tool for the initial screening and flowsheet development of the reactive distillation processes [45]. RD is characterized by the simultaneous occurrence of chemical and phase equilibrium. This should be the starting point of a feasibility analysis. Useful insights of chemical and phase equilibrium can be found by graphical representations, such as RCM. Only the general frame is presented here; so for more theory, the reader is referred to the books of [25, 27] as well as [47]. Let us consider the general equilibrium reaction: νA A + νB B +    $ νP P + νR R +    or

c X

νi Ai = 0 νt =

i=1

c X

νi with νt =

i=1

c X

νi

(5:3)

i=1

The chemical equilibrium constant formulated by means of activities is given by the expression: Keq =

v v v v v v aPP aRR .... xPP xRR .... γPP γRR .... Y = = ðxi γi Þvi = Kx Kγ v v v v v v aAA aBB .... xAA xBB .... γAA γBB .... i

(5:4)

The composition can be expressed with respect to a reference species k as follows: xi =

xi0 ðvk − vt xk Þ + vi ðxk − xk0 Þ vk − vt xk0

(5:5)

This relation describes the so-called stoichiometric lines [27], which help in the graphical representation and in the introduction of the transformed variables. These lines converge to a pole π, whose location is: vi vi xπ, i = P = vi vt

(5:6)

i

Note that when the total number of moles does not change by reaction (νt = 0), the stoichiometric lines are parallel. A residue curve characterizes the evolution of the liquid composition in a vessel during a batch-wise reactive distillation experiment. The RCM is obtained by considering the different initial mixture compositions. For nonreactive mixtures, the RCM is obtained by solving the following differential equation [48]: dxi = xi − yi dξ

(5:7)

where ξ = H=V is a “warped time” defined as the ratio of molar liquid holdup H to the molar vapor rate V, while xi and yi are the vapor and liquid compositions, respectively. A similar representation based on distillation lines describes the composition on successive trays of a distillation column with an infinite number of stages

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at infinite reflux. In contrast with the relation describing the stoichiometric lines, the distillation lines may be obtained by algebraic computations involving series of bubble and dew points as follows: xi, 1 ! y*i, 1 = xi, 2 ! y*i, 2 = xi, 3 ! yi, 3 =   

(5:8)

Figure 5.5 (left) shows the construction of a distillation line for an ideal ternary mixture in which A and C are the light (stable node) and heavy (unstable node) boilers, respectively, while B is an intermediate boiler (saddle) [47, 45]. The initial point, xi, 1 , produces the vapor, y*i, 1 , which by condensation gives a liquid with the same composition, such that the next point is xi, 2 = y*i, 1 , etc. Accordingly, the distillation line describes the evolution of the composition in the stages of a distillation column at equilibrium and the total reflux from the bottom to the top. The slope of a distillation line is a measure of the relative volatility of the components. An analysis by RCM or distillation curve map (DCM) leads to similar results. When a chemical reaction takes place, the residue curves can be found by the following equation:

Fig. 5.5: Construction of the distillation lines for nonreactive (left) and reactive mixtures (right).

dxi = xi − yi + Daðvi − vt xi ÞR dξ

(5:9)

where Da is the Damköhler number, given by the ratio of the characteristic process time, H/V, to the characteristic reaction time, 1/ro. The reaction rate, ro, is the reference value at the system’s pressure and at an arbitrary reference temperature, usually the lowest or the highest boiling point. For catalytic reactions, ro includes a

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reference value of the catalyst amount. R is the dimensionless reaction rate, R =r/r0. The kinetics of a liquid-phase reaction is described as a function of activities: Y 

Y  vi vj (5:10) − aj =Keq r=k ai pr

eq

Thus, the parameter, Da, is a measure of the reaction rate, but its absolute value cannot be taken as the basis for comparing different systems. Analogous to the procedure presented before, reactive distillation lines can be computed by a series of dew and bubble points incorporating the chemical equilibrium as follows: eq * * xi, 1 ! y*i, 1 $ xeq i, 2 ! yi, 2 $ xi, 3 ! yi, 3   

(5:11)

A graphical construction of the reactive distillation lines at equilibrium is shown in Fig. 5.5 (right) for the reversible reaction A + B ⇌ C [47, 45]. The initial point, xi, 1 , produces a vapor, y*i, 1 , at chemical equilibrium, which, by condensation and equilibrium reaction, gives a liquid with the composition, xi, 2 . This is found by crossing the stoichiometric line passing through y*i, 1 with the chemical equilibrium curve. Then, the liquid, xi, 2 , produces the vapor, y*i, 2 , and so on. Similarly, the points 11, 12, 13,. . ., N show the situation in which the mixture becomes richer in B, and poorer in A and C. Figure 5.5 (right) emphasizes a particular position where phase the equilibrium and the stoichiometric lines are colinear. The liquid composition remains unchanged because the resulting vapor, after condensation, is converted into the original composition. This point is a potential reactive azeotrope, but when the composition also satisfies chemical equilibrium, it becomes a true reactive azeotrope. Figure 5.6 illustrates the construction of an RCM for the reversible reaction A + B ⇌ C, for which the relative volatilities are in the order 3/2/1, and the equilibrium constant Kx = 6.75 [47, 45]. The physical and reactive distillation lines can be obtained using the above equations (e.g., by a simple computation in Microsoft Excel). In this case, the starting point – liquid with composition (0.1, 0.l, 0.8) – is not at chemical equilibrium. The coordinates of the triangle are in normal mole fractions. After a short straight path, the reactive distillation line superposes the chemical equilibrium curve. The same trend is also observed when starting from other points. Figure 5.6 also illustrates graphically the formation of a reactive azeotrope as the point where a particular stoichiometric line becomes tangential to the nonreactive residue curve and simultaneously intersects the chemical equilibrium curve. For more than three species, a change of variables appears useful in order to reduce the dimensionality of a graphical representation. More generally, the composition of a reacting system, characterized by c molar fractions can be reduced to (c–1) new composition variables by the following transformation:

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Fig. 5.6: Residue curves for a ternary mixture involving the equilibrium reaction A + B ⇌ C.

Xi =

νk xi − νi xk νk − νt xk

(5:12)

The reference, k component, should preferably be a product. The kinetics of a reaction rate has a substantial influence on the RCMs. Venimadhavan et al. [49] provides more information about the effect of kinetics on the RCMs for reactive distillation. Distillation boundaries and physical azeotropes can vanish, while other singular points might appear due to kinetic effects. An RCM derived from the chemical and phase equilibrium for a reactive and nonreactive section of the RD column represents variations of the stationary points (corresponding to the pure components and azeotropes] between the equilibrium boundaries for a given temperature and pressure. The variations in these singular points can be represented by the Damkohler number [50, 49]. Hence, the influence of kinetics on RCM can be studied by integrating the equation for finite Da numbers. In addition, the singular points satisfy the relation: DaR =

xi − yi xi − νt xi

(5:13)

Note that the influence of chemical reaction kinetics on the VLE is very complex. As a consequence, evaluating the kinetic effects on RCMs is of great importance for the conceptual design of reactive distillation systems. However, it can be appreciated that, in practice, the reaction rate is fast enough such that the chemical equilibrium

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is reached quickly. The RCM considerably simplifies, but even in this case, the analysis may be complicated by the occurrence of reactive azeotropes [45]. As compared to conventional distillation, RD sets specifications on both product compositions and reaction conversion. Accordingly, the degrees of freedom (DoF) in an RD column must be adjusted to accomplish these specifications while optimizing an objective function, such as the total annual cost (TAC). Several specifications are typically required [45, 2, 1, 51, 22]: – Column pressure and pressure drop on column or stage: Setting the pressure is constrained by the temperature of the top and bottom; more specifically, by the availability of on-site cold and hot utilities. If the bottom temperature is excessive, the solution may be a dilution with the reactant, which will be recovered separately. In general, working at the highest acceptable temperature is recommended because of its accelerating effect on the reaction rate. – Number of stages, feed locations of reactants, and exit points of the product streams: the RD configuration is set up in this way in terms of rectification, reaction, and stripping sections. – Top distillate (liquid, vapor, mixed) or bottom product, and absolute or ratio values. – Condenser and reboiler types. – Reflux ratio or boil up ratio. – Holdup distribution on the reactive stages. Note that in conventional distillation, the typical design specifications are the concentrations of the heavy key component in the distillate and the light key component in the bottom product. The holdup has no effects whatsoever on the steady-state design of a distillation column; only on the dynamic behavior. The column diameter is easily determined from the maximum vapor-loading correlations, after calculating the vapor rates required to achieve the desired separation. However, the holdup is very important in RD as the reaction rates directly depend on the liquid holdup and the amount of catalyst in each tray. Accordingly, RD requires an iterative design procedure, since the liquid holdup must be known before the column can be designed [45]. This means that a tray holdup is assumed and the column is designed to achieve the desired conversion and product purities. Then, the column diameter as well as the required height of liquid in the reactive trays are calculated, corresponding to the assumed holdup. Liquid heights of over 10–15 cm are not recommended due to the limitations of the hydraulic pressure drop. If the calculated liquid height is too large, a smaller holdup is assumed and the calculations are repeated [1]. A shortcut method for the hydraulic design of an RD column can be used [45] as follows: 1. Estimate a mean volumetric liquid flow rate for the operation. 2. Assume an initial value for the superficial liquid velocity at the “load point” (ULP): The recommended value is 10 m3 per m2 h–1.

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3. Assume an initial value for the number of stages per meter (NSTM). 4. Determine the column diameter. Knowing the packing specifications, estimate the volume of packing and the catalyst holdup per reaction stage. 5. Introduce the above values in simulation in which the reaction rate is expressed in units compatible with the holdup (mass, molar, or volumetric). 6. Determine the total number of reactive stages needed to achieve the target conversion. Pay attention to the profiles of temperatures, concentrations, and reaction rate. Extract liquid and gas flows, as well as fluid properties. 7. Recalculate the load point velocity, the liquid holdup from the above information by using specific correlations and diagrams. Check the hydraulic design by selecting a packaging with similar characteristics. 8. Verify if the gas load and the pressure drop are in the optimal region. Afterward, check all values and repeat the points 4 to 8 till acceptable values are achieved. A number of other design and feasibility check methods for RD systems are also available. They can be classified into three main groups: 1) graphical and topological considerations, 2) optimization techniques, and 3) heuristic and evolutionary approaches. Table 5.3 conveniently summarizes these methods, including their principle, assumptions, and a brief pro/con analysis. Tab. 5.3: Main design and feasibility check methods for reactive distillation.

Residue curves map (RCM)

Description and assumptions

Pro/con (+/–) analysis

References

Phase equilibrium representations for a ternary or quaternary system. RCMs can be constructed analytically, based on physical properties of the system, and for cases with reaction, this is expressed by the Damköhler number. The residue curve will always end at a stable node. For Da = , the RC will end at a pure component or nonreactive azeotrope. For high Da numbers, the RC will end at a pure component, chemical equilibrium point, or reactive azeotrope. In this way, the feasibility of RD can be analyzed.

+ +

[, , , , ]

+

– – –

Couples the reaction and VLE. Reliable tool for feasibility analysis in RD. Requires little data (feed composition, phase equilibrium model parameters, chemical equilibrium, and reaction stoichiometry). Cannot analyze the feasibility of hybrid processes. Limited to four components due to graphical nature. Accurate thermodynamic data is required to correctly describe the reactive distillation process.

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Tab. 5.3 (continued)

Static analysis

Description and assumptions

Pro/con (+/–) analysis

Considers the composition in each stage to be constant, with the total column being a succession of reaction and distillation operations. The assumptions allow one to estimate the liquid composition in a stage and the vapor composition below. The composition profiles are estimated by distillation lines, while the number of theoretical stages is determined from the intersection of the distillation line with the chemical equilibrium manifold (CEM]. This CEM line represents the boundary of the forward and backward reaction. – V-L flow rates in RD are infinitely large. – Reactive zone is large enough to achieve a set conversion. – RD column is assumed to be in steady state and theoretical stages are chosen. – Uses only one reversible reaction.

+ + +

+

+

+

+

+

– –

References

Straightforward solution for [, ] whether RD is feasible. Allows a first estimation of the flowsheet. Requires little data (feed composition, phase eq. model parameters, and reaction stoichiometry). An effective tool for studying nonideal mixtures with multiple chemical reactions and components. Allows the selection of appropriate steady states from their complete set. Simplifies troublesome calculations, reducing computational time. Does not require fixed variables as: column structure, number of stages, extent of reaction, and product compositions. The RCM technique allows one to determine the stability of the products, the product compositions, and the column structure for the entire feed region. This method assumes infinite separation efficiency. Matching the operating lines with the assumed product composition can be troublesome.

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Tab. 5.3 (continued) Description and assumptions

Pro/con (+/–) analysis

References

Attainable regions

The processes of reaction, + mixing, and separation are taken into account. For a given + system, the attainable region is the region/portion of the + concentration space that can be achieved from a given – composition by any – combination of reaction and stripping. This technique aims to identify the attainable region by describing them with feasible reactor networks of the model reactors (CISTR and PFR]. For assumptions, c and c are two attainable products compositions. – Vector c1c2 belongs to the attainable region. – In the attainable region, the reaction vector points inward; is tangential or is zero. – No reaction vector intersects the attainable region.

Takes into account the mixing effect. It can be used to point out promising flow sheets. Includes the theory derived for model reactors. Complicated graphical analysis. Economics is not taken into account.

[, , , ]

Thermobased approach

Based on the existence of RD lines and potential reactive azeotropes, first, the potential products are determined from the knowledge of distillation lines. Then, the column mass balance is checked and the possible separation borders are identified. In this way, the feasibility of RD is checked.

Can be applied to fast and slow eq. reactions. Feasible products can be determined within RD. Finding reactive azeotropes might be difficult. Detailed knowledge of phase equilibrium, reaction kinetics, and residence time within the column is needed.

[]

+ + – –

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Tab. 5.3 (continued)

Fixed point algorithm

Graphical techniques

Description and assumptions

Pro/con (+/–) analysis

References

Based upon changes in the location of fixed points that occur at pure component and azeotrope compositions, they move to new positions as the reflux ratio, the boil up ratio, or the Damköhler number is changed. These fixed points represent the chemical and physical eq. conditions, and their location is dependent on process parameters. By analyzing the change of fixed points, the feasibility can be checked. – Ideal vapor-liquid equilibrium – Negligible heat of mixing – Equal latent heats – Constant liq. holdup in reactive stages

+

[, ]

+

–

Based on the conventional + McCabe–Thiele or Ponchon– Savarit methods, the – difference between the traditional methods is the reaction in stages. For the – reaction, the conversion is regulated by adjusting the liquid holdup in each stage. – Binary system with a single reaction. – Constant molar overflow. – Vapor-liquid equilibrium is reached.

Highly flexible in generating alternative designs at various design parameters. Mass and energy balance can be decoupled, allowing the determination of column profile only by means of mass balance and equilibrium equations. Limited; implicitly by its graphical nature.

Gives a visualization of what [, ] happens per stage. Are exclusively applied to binary systems, which are usually isomerization reactions. Limited by their graphical nature.

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Tab. 5.3 (continued)

Reactive cascades

Description and assumptions

Pro/con (+/–) analysis

Each section of the reactive distillation column is represented by a cascade of flashes, either in cocurrent or counter current. In this way, the product compositions can be estimated. – Each flash stage has the same residence time. – The same fraction of feed is vaporized in each stage.

+

+

+ – –

– Phenomenabased approach

Scalar/ vectorial difference points

References

Global feasibility analysis can be [, ] performed as a function of the production rate, catalyst concentration, and liquid holdup. The method does not have any restriction in the number of components or reactions. The method is deemed to be easily implementable. Damköhler number is assumed to be constant. Effect of different operating conditions or designs is not taken into account. Energy balances are not taken into account.

All three phenomena (mixing, separation, and reaction) are written in vectors. When there is no change in composition, the sum of these vectors is  and, as a result of that, a kinetic fixed point occurs. Fixed points are not desired in RD since they represent flat concentration profiles. Therefore, several methods were developed to move away from this fixed point.

+

An approach that combines the phenomena-based approach with the reactive cascade methodology, the assumptions include: – Known top and bottom compositions. – Known reflux ratio. – Constant molar overflow. – Chemical reaction of the type: 2A ⇌ C + D

Combination of pros/cons of phenomena-based approach and the reactive cascades.

+

Only physical and chemical data is required. Can be used independent of the methodology that incorporates the composition change.

–

Its feasibility is not fully proven.

[, ]

[]

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Tab. 5.3 (continued) Description and assumptions

Pro/con (+/–) analysis

References

Memetic algorithms

This algorithm combines a problem-specific evolutionary algorithm with a mathematical programming method. The advantage of this system is the ability to compute and identify multiple optima.

+ +

Can solve complex RD designs. Possible to compute and identify local optimum.

[, ]

Mixedinteger nonlinear programming (MINLP)

A design approach based on rigorous calculations: The objective function tries to minimize the equipment costs and operating costs. However, the function is constrained by the MESH equations on each stage, material balances, kinetic and thermodynamic relationships, and other relationships between the process variables and the number of stages. The function consists of a master and a sub-problem. A master program selects the integer variables, and in the primal problem, the optimal column design is obtained. – V-L phases are in equilibrium. – No reaction takes place in the vapor phase. – The liquid phase is homogeneous. – Enthalpy of the liquid streams is negligible. – The heat of evaporation is constant. – Temperature dependence of the reaction rates can be expressed by the power law form. – The cost of separating the products downstream is given by an analytical function.

+

Wide application field (e.g., [, , multiple reactions, reactive , , ] equilibrium, or thermal neutrality cannot be assured) It allows calculations that are based on economics and controllability. Need for complicated numerical tools. Difficult initialization. Computational time. Multiple (local) optimum points.

+

– – – –

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Tab. 5.3 (continued) Description and assumptions

Pro/con (+/–) analysis

Orthogonal collocation on finite elements (OCFE)

MINLP sometimes has + difficulties in solving the equations for a high number of – stages and for a simultaneous design of more than one distillation unit. The OCFE approach transforms the number of stages from a discrete number in the MINLP approach to a continuous variable, and treats temperature as functions of the position. – Complete mixing of each phase. – Constant liquid holdup and no vapor hold up at each stage. – No liquid entrainment on stages. – Adiabatic stages. – Thermal equilibrium between L-V.

Converts complex problems to simpler formulations.

Mixedinteger dynamic optimization (MIDO)

A method that combines the design with control tasks. This simultaneous approach takes advantage of the interaction between design and control.

+

Simultaneous design and control

–

No general procedure that guarantees convergence to a global solution.

References [, , ]

Not always applicable.

[, ]

For a long time, it was assumed that reaction and distillation can be favorably combined in a column enhanced with special internals or additional exterior volume. However, distillation columns are an appropriate solution only for reactions that are sufficiently fast in order to reach high conversions within the residence time range of such columns. Schoenmakers and Bessling [17] showed that two operating conditions can be distinguished: 1) distillation-controlled range, where conversion is influenced by the concentration of the components to be separated, and 2) kineticscontrolled range, in which the conversion is influenced mainly by the residence time and the reaction constant. The industrial design of an RD should aim at operating conditions within these two ranges, just the sufficient residence time and only the necessary expenditure for the distillation. Figure 5.7 presents the resulting principles for the choice of equipment for homo- and heterogeneous catalysis [2, 17].

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Fig. 5.7: Equipment selection in the case of homogeneous (left) and heterogeneous (right) catalysis.

In the case of heterogeneous catalysis, additional separate reaction volumes are necessary to retain the catalyst inside the column. These volumes can be arranged, either within the equipment or in a side reactor unit, coupled by recycle streams. As catalysis plays an important role in RD processes, several situations are possible in practice [68]. RD processes can be divided into homogeneous (auto-catalyzed or homogeneously catalyzed) and heterogeneous processes, catalyzed by a solid catalyst (catalytic distillation): – Noncatalyzed reaction: The reaction takes place almost anywhere in the RD column (where reactants are present), and no catalyst separation or recovery is required. – Homogeneous catalyst: The reaction takes place almost anywhere in the RD column. The catalyst may be left in one of the product streams (if acceptable, according to the specifications), or it can be neutralized and separated as salt waste stream (cheap acid/base catalysts), or it has to be recovered and recycled (expensive catalysts). – Heterogeneous catalyst: The reaction zone is well-defined (i.e., where the solid catalyst is present); the catalyst does not leave the RD column and hence no recovery is needed. This particular case is also called catalytic distillation. For the most frequently encountered type of reaction (A + B ⇌ C + D), there are several groups of RD configurations possible, as illustrated in Fig. 5.8. For this type, [1] provided a theoretical case study under the following assumptions: equimolar reactant feed, equilibrium constant Keq = 2 (at 366 K), kinetic constants, kF = 8 mol s–1 and kB = 4 mol s–1, liquid holdup defined from tray sizing, kinetic holdup of maximum 20 times the tray holdup, and relative volatility of LLK/LK/HK/HHK fixed at a value of 2. The results based on the TAC (Ip < IIIp < IIp < IIIr < IIr < Ir) indicated that group Ip is the most favorable, while Ir is the most unfavorable.

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Fig. 5.8: Reactive distillation groups for quaternary reversible reactions (A + B ⇌ C + D), based on various orders of relative volatility between the components.

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Additionally, Fig. 5.9 [2] shows the most common RD configuration alternatives, ranging from the conventional RD column and the heterogeneous azeotropic RD column [65, 69, 70, 71, 23, 21], to the reactive dividing wall column [72, 73, 39] and the RD column, combined with pre-reactor and/or side reactors [74, 75, 76].

Fig. 5.9: Conventional reactive distillation (top-left), heterogeneous azeotropic RD (top-right), reactive DWC (bottom-left) and RD column with pre-reactor and/or side reactors (bottom-right).

RD provides an excellent example of the ever-present interaction between design and control. Both steady-state and dynamic aspects of a chemical process must be considered at all stages of the development and commercialization of a chemical process: laboratory, pilot plant, and production [1, 77, 78]. The controllability of an RD column is usually improved by adding more reactive trays while considering the conflict between the steady-state design and dynamic controllability [1]. In neat operation mode, the reactants are fed according to the stoichiometric ratio. Consequently, the

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control system must be able to detect any imbalance that would inevitably result in a gradual accumulation of one of the reactants and a loss of conversion and product purities. An alternative is the operation with an excess of one reactant. This makes the control of the RD column easier, but it requires the recovery and recycle of the reactant that is in excess [1]. Control of an RD distillation column is a challenging task due to process nonlinearity and complex interactions between VLE and the chemical reactions. Different types of control methodologies can be used for RD processes, ranging from simple proportional–integral–derivative controllers to advanced model-predictive controllers (MPC), such as dynamic matrix control (DMC), quadratic DMC, robust multivariable predictive control technology, generalized predictive control, and other advanced controllers [78]. Note that the rate of the autocatalytic reactions can only be influenced by the temperature or pressure of the RD equipment. Homogeneous catalysis allows the influence of the reaction rate too by changing the concentration of the catalyst; thus the reaction rate can be adapted over a wide range to the needs of the RD equipment. While homogeneous catalysis is more flexible, it requires expensive separation steps for catalyst recovery. Solid catalysts require a special construction – e.g., catalyst packed in “tea bags” in trays, or sandwiched in a structured packing, such as Sulzer Katapak – to fix the catalytic particles in the reactive zone, thus limiting the catalyst concentration that can be achieved. The reaction rate can be enhanced only to the limit set by the attainable concentration range. Heterogeneous catalysis is simpler in principle, but it needs more equipment volume and it suffers from increased operating temperature and limited catalyst life time [9, 17]. Unlike conventional distillation, the choice of internals for reactive distillation is much more limited [9]. Figure 5.10 provides an overview of the different internals

Fig. 5.10: Overview of the reaction and separation performances of column internals for homogeneously (left) and heterogeneously (right) catalyzed reactive distillation processes.

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used in homogeneously catalyzed reactive distillation processes, and their performance in terms of separation and reaction. For noncatalyzed or homogeneously catalyzed reactive distillation processes, the development of new internals is not needed, as conventional internals can be used. The catalyst in homogeneous catalysis is generally fed together with the liquid feed streams and the liquid holdup of the internals must be maximized to achieve high conversions. The reaction rate must be considered for the choice of the appropriate internals. High liquid residence times and large liquid holdups are required to perform slow reactions in an RD column. For such cases, tray columns are usually applied, operated in the bubbly flow regime, to ensure a greater liquid holdup and a longer residence time of the liquid. For fast reactions, the selection criterion for internals is not the liquid holdup, but the separation efficiency. As chemical equilibrium can be achieved within short residence times, random or structured packings can be used to ensure a high specific surface area and good separation efficiency [17]. To combine a high capacity (typically offered by trays) with a high mass transfer (usually provided by packing), a new type of internal has been developed, called “flooding packing” or “sandwich packing.” This packing consists of two packing elements with different specific surface areas stacked one on each other; the one with the larger surface area operated close to its flooding point to increase the mass transfer and the residence time, while the one with lower specific surface area (operated below the flooding point) is used as demisters for the stabilization of the operating point. Using this design, the liquid holdup can be easily adjusted over a broad range by changing the heat duty of the reboiler [30]. For heterogeneously catalyzed RD processes, specific internals are needed to immobilize the solid catalyst. The challenge in the development of these packings is ensuring an adequate reaction rate by providing sufficient contact between the liquid phase in the column and the active sites of the catalyst. The catalysts that are used in most catalytic distillation processes are acidic ion-exchange resins (such as the Amberlyst or the Lewatit). Several technologies for the immobilization of heterogeneous catalysts have been developed. Figure 5.11 presents some examples of catalytic packing [2, 9, 41]. The most important are the following [79, 30]: – Tea-bag configurations that immobilize catalyst pellets: In the development of catalyst envelopes, many different structures are possible. The basic structures that have been patented include porous spheres, cylindrical envelopes, wire gauze envelopes of different shapes (e.g., spheres, tablets and doughnuts), horizontally adjusted wire mesh tubes that are filled with catalyst, cloth bags that are twisted in a helical form, and wire gauze boxes. – Catalyst bales, formed by wrapped wire sheets filled with a catalyst: These were patented by CDTECH. The catalytic bales consist of pockets in a cloth belt that are supported using knitted open-mesh stainless steel wire, which results in a cylinder-shaped structure. The voids created by the steel mesh ensure good

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liquid-vapor contact and vapor traffic. Yet, a drawback of the catalyst-bale technology is the poor radial distribution of the liquid. – Catalytic-structured packing (known as “sandwich” or “wafer” packing): The elements have the shape of sandwiches manufactured from corrugated wire gauze sheets, hosting catalyst bags, assembled as cylinders or rectangular boxes. The packing structure consists of alternating catalyst bags and open channel spaces. The structure results in a crisscross flow path of the liquid, which significantly improves the radial distribution. To ensure higher efficiency of the combined reaction and diffusion the catalyst, the particle should have a diameter of about 0.8–1 mm. The advantages of structured packing are: uniform flow conditions with minimum backmixing and maldistribution; good radial dispersion, an order of magnitude better than in conventional packed beds, ensuring a longer residence time; and efficient maintenance and replacement of the catalyst. Moreover, the hydrodynamic behavior is similar to traditional structured packings; hence they can be applied over a wide operating range with good flow conditions, maintaining a small pressure drop. Among the commercial offers available, one could mention KATAPAK-S® (manufactured by Sulzer ChemTech [80]), MultiPak® (supplied by Julius Montz [81]), as well as KATAMAX® (from Koch-Glitsch). – Multichannel packings, developed and patented by BASF: The layers of multichannel packings consist of alternating layers with high and low specific surface areas. The catalysts are transported into cavities in the packings in a loose form. The catalyst particles are immobilized by size exclusion in the packings with low specific surface areas (so-called catalyst barrier layers). The advantage of multichannel packings is the easy replacement of the catalyst particles, but a drawback is the need for a uniform size distribution of the catalyst particles to prevent them from slipping through the barrier layers. – Catalytically active structures that are conventional packings, turned catalytically active by coating them with a catalytically active material or by manufacturing them using this active material: A catalytically active structure, based on Raschig rings or Berl saddles, was developed by VEBA Oel. On the inner and outer surface of these random packings, ion-exchange resins are physically or chemically bonded to the packing (applied to etherification reactions). Another type is the directly coated structured packing, such as stainless steel wire mesh structured packing, coated with zeolites (for the synthesis of ETBE). Sulzer also developed a coated structured packing (KATAPAK-M). Other types include monolithic structures made of catalytic material and coated with catalytic material, as well the use of foams or sponges instead of random or structured packings. The advantages of foams are a good mass transfer between the liquid and vapor phases due to a large interfacial area, low pressure drop, and good corrosion resistance. Foams and sponges can also be coated with a catalytic layer. Another development involves using internals coated with enzymes.

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– Catalytic trays that are available in different configurations (e.g., alternating reaction and distillation trays, tray configurations placing the catalyst along the tray, or the downcomer): BASF developed the so-called D+R tray, which has key advantages, such as flexibility in the catalyst amount and easy catalyst replacement.

Fig. 5.11: Examples of internals for catalytic distillation: various “tea-bag” configurations for trays, gutters (top), and structured catalyst sandwiches for packed columns (bottom).

5.4 Detailed examples 5.4.1 Di-n-pentyl ether production by reactive distillation Improving the quality of diesel fuels in a cost-effective manner is an important issue for the industry. Literature reports that linear ethers, with over nine carbon atoms, showed the best balance between the cetane blending number and the cold flow properties. Among them, di-n-pentyl ether (DNPE) is an excellent candidate for diesel fuel formulations due to its high cetane blending number, good cold flow properties, and effectiveness in reducing diesel exhaust emissions, particulates, and smokes. Moreover, 1-butene is an appropriate feedstock for DNPE production, as it can be selectively hydroformylated and hydrogenated to 1-pentanol, which can then be dehydrated to DNPE.

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Physical properties (such as, boiling points, enthalpy of formation, ideal gas heat capacity, Antoine parameters, and molar density) of all components are available in the pure component database of Aspen Plus v8.4 [82]. As the process takes place at a moderate pressure and involves polar chemical species, only the nonideality of the liquid phase has to be taken into account. Accordingly, UNIQUAC was used as a suitable property model for this system. The Aspen Plus database contains UNIQUAC binary interaction parameters for the water–1-pentanol pair, while the binary interaction parameters for water – DNPE and 1-pentanol–DNPE pairs were estimated by the UNIFAC group contribution method. DNPE is the high-boiling component; hence it can be easily separated. Water is involved in several heterogeneous azeotropes, which suggests the use of a liquid-liquid split in order to cross the distillation boundary. The RCM and the ternary diagram of this system are available in literature [83]. Apart from the presence of azeotropes, the system also exhibits a liquid-liquid miscibility gap, which must be accounted for in the design of the separation sequence – two liquid phases should be avoided inside distillation columns, but a separate decanter could be used for phase splitting. The dehydration of 1-pentanol to yield DNPE is an equilibrium-limited reaction: 2 C5 H9 − OH ! C5 H9 − O − C5 H9 + H2 O ðPÞ

ðDÞ

ðWÞ

(5:14)

The etherification of 1-pentanol was reported to be catalyzed by NaA, H-Beta and ZSM-5 zeolites, eta-alumina, Amberlyst 70 (and other types), Dowex 50Wx4-50, and Nafion NR50. When Amberlyst 70 is used as catalyst, the reaction kinetics is described by the following expression, derived from an Eley–Rideal mechanism [84]:   2 1 aW aD kaP 1 − Keq a2 P  (5:15) r= 1=2Þ aP 1 + KW aW where:    1 1 kmol ðkgcat · sÞ − 1 k = 4.6 × 10 exp − 11, 595 − T 438   778.69 Keq = 8.9229 · exp T    1 1 KW = 4.306 · exp − 6616 − T 438 −6

(5:16) (5:17) (5:18)

with temperature (T) expressed in K. Note that the kinetic experiments performed at temperatures below 150 °C and involving catalyst particles of different sizes proved that mass transfer does not affect the reaction rate. Moreover, the Arrhenius plots of initial reaction rates are

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straight lines for temperatures up to 180 °C. Thus, it can be concluded that diffusion does not influence the process kinetics over the entire temperature range of interest. This can be explained by the fact that the resin beads swell sufficiently in aqueous medium, allowing good accessibility to the inner active centers [83]. According to the feasibility framework, RD is a good candidate for DNPE synthesis, as the reactant is the middle boiling component in the water/1-pentanol/DNPE mixture. The RD process for DNPE production considers a plant capacity of 26.5 ktpy. Rigorous steady-state process simulations and optimization were performed in Aspen Plus. The process flowsheet is schematically shown in Fig. 5.12 [83].

Fig. 5.12: Flowsheet and control of a catalytic distillation process for DNPE production.

The reactant is fed at the top of the reactive section as saturated liquid stream. High-purity (over 99.9%) DNPE is obtained as the bottom product, while the vapor distillate is condensed and sent to liquid-liquid separation, which gives the water product and the organic reflux. MellaPak structured packing is used to enclose the solid catalyst in between the sandwiched sheets of packing – similar to the KataPak-SP structured packing specially developed by Sulzer for reactive distillation systems. After developing the base case design using heuristic methods, the RD column was further optimized using the minimizing the total annual cost as the objective function. The investment cost (CAPEX) included the cost of the column shell, reboiler and condenser, the structured packing (MellaPak cost $10,000 m–3), and the solid catalyst [83]. The operating cost (OPEX) included the cost of high-pressure steam and cooling water. The decision variables considered for the optimization

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procedure are: total column stages (NT), feed stage (NF), first reactive stage (NR1), last reactive stage (NR2), vapor distillate rate (10 < D < 100 kmol h–1), operating pressure (1 < P < 5 bar), and amount of catalyst on each reactive stage (20 < mcat < 200 kg). The problem constraints are related to the minimum product purity (xDNPE > 0.999), the maximum temperature of the reactive stages (Tk < 180 °C, k = NR1, . . . NR2), and the volume fraction of the catalyst per stage (ω < 0.2). An inner loop used the Optimization tool of AspenTech Aspen Plus to find the real-valued decision variables (D, P, mcat), while ensuring that the constraints are satisfied. The integer-valued variables (NT, NF, NR1, NR2) were found in an outer loop, where a direct search algorithm was implemented in MathWorks Matlab [83]. To be fair, optimizing a chemical process is typically a mixed-integer nonlinear problem that is nonconvex and likely to have multiple locally optimal solutions. Such problems are intrinsically very difficult to solve, and the solution time increases rapidly with the number of variables and constraints. A theoretical guarantee of convergence to the globally optimal solution is not possible for nonconvex problems. Figure 5.12 presents the process flowsheet, mass balance, as well as the process control structure, while Tab. 5.4 provides the key parameters of the optimized RD design [83]. The catalytic distillation column has an investment cost of $816k, and operating costs of $251k year–1, leading to a total annual cost of $523k year–1. Tab. 5.4: Design parameters of the DNPE process using catalytic distillation. Parameter (unit) -Pentanol temperature (°C) Condenser pressure (bar) Bottoms pressure (bar) Number of trays Feed tray number First reactive tray Last reactive tray Diameter (m) Amount of catalyst (kg stage–) Reboiler duty (kW) Condenser duty (kW) Installed cost (k$) Utilities (k$ year–)

RDC*  . .     . . . . . .

*The optimal values of the decision variables used in optimization are presented in bold.

In addition, Fig. 5.13 shows the composition as well as temperature and reaction rate profiles along the catalytic distillation column – for the optimal design case [83]. It can be observed that high purity DNPE is obtained as the bottom product, while a mixture of 1-pentanol and water is removed as the top product of the column.

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According to the VLE, the range of temperature values in the reactive stages is 140–180 °C. The reaction rate is quite low on the top 10 reactive stages, but increases toward the bottom of the column. In the reactive stages, the liquid phase mole fraction of 1-pentanol is quite high, exceeding 0.6.

Fig. 5.13: Profiles along the catalytic distillation column: molar composition (left); temperature and reaction rate (right).

It is worth noting that working in the limited overlapping window of operating conditions (reaction and separation) is not always the optimal solution, but merely a trade-off. On the contrary, in a conventional multiunit flowsheet (such as a reactionseparation-recycle process), the reactors can be operated at their optimum parameters that are most favorable for chemical kinetics, while the distillation columns can be operated at their optimal pressures and temperatures where the VLE properties are most favorable for separation. In the case of the DNPE process, the operating window for reaction is limited to the temperature range of 120–180 °C due to the minimum acceptable reaction rate and the maximum temperature at which the solid catalyst is active and stable, while the pressure must have values that allow a liquid or vapor-liquid operation. These limits are shown in Fig. 5.14 by the REACTION area [83]. The optimal reaction conditions are at 180 °C and min. 2.1 bar, where the reaction rate is highest and maximum conversion is possible. Similarly, the separation by distillation is limited by the temperature range of 45–245 °C, which allows condensation with cooling water and heating with high-pressure steam. The corresponding pressure range is, therefore, 0.1–3.6 bar – according to the VLE, such that vapor-liquid phases exist. The temperature limits are shown in Fig. 5.14 by the DISTILLATION area. As vacuum distillation incurs additional costs, optimal separation should be performed at atmospheric pressure, when the range of boiling points is 100–187 °C. As the reaction is only slightly exothermic in a reaction-separation-recycle process, the reactor feed can be at a rather high temperature (160 °C) without violating

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the maximum temperature constraint (180 °C). Therefore, the reaction takes place in the range 160–180 °C, which ensures a reaction rate close to the maximum achievable one. On the other hand, separation is performed at atmospheric pressure; therefore at optimal conditions. In the RD process, operation at a higher pressure is necessary in order to have a temperature range for which the reaction rate is high. However, the higher pressure has a detrimental effect of relative volatilities and, therefore, on the separation efficiency. Moreover, as water mole fraction increases toward the top of the column, the temperature range in the reactive stages is 140–180 °C, with the result of a rather low reaction rate in the first 10 reactive stages (Fig. 5.13). In conclusion, there is no clear overlap of the optimal conditions for both reaction and distillation. As a visual aid, Fig. 5.14 illustrates the overlapping window of the operating parameters (temperature and pressure) for both reaction and distillation operations – the optimal operating range is the area marked, REACTIVE DISTILLATION. Therefore, a reaction-separation-recycle process can be slightly more attractive than the catalytic distillation process, which operates in the overlapping window of process conditions for reaction and distillation; thus suffering from this inherent trade-off.

Fig. 5.14: Overlapping window of operating conditions (pressure and temperature) for reaction and distillation, for the DNPE system.

5.4.2 Fatty ester synthesis by dual reactive distillation Fatty esters are key products of the chemical process industry, being incorporated in a wide variety of high value-added products, from cosmetics to plasticizers and bio-detergents. Among them, the fatty acid methyl esters (FAME) are the main constituents

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of biodiesel fuel, which can be produced by esterification or trans-esterification in reactive separation processes [85]. A key problem in the synthesis of fatty esters by RD is the effective water removal in view of protecting the solid catalyst and avoiding costly recovery of the alcohol excess. This case study presents a novel approach, based on dual esterification of lauric acid with light and heavy alcohols, namely methanol and 2-ethylhexanol. These two complementary reactants have an equivalent reactive function, but synergistic thermodynamic features as one alcohol is light and the other is heavy. The setup behaves rather as a reactive absorption, combined with reactive azeotropic distillation, with the heavy alcohol as a co-reactant and water-separation agent. Super acid solid catalyst, based on sulfated zirconia, whose activity is comparable to both alcohols, can be used at temperatures of 130–200 °C and moderate pressure. Inventory control of alcohols is realized by fixing the reflux of heavy alcohol and the light alcohol column inflow. This strategy allows achieving both stoichiometric reactants feed rate and large flexibility in ester production. The distillation column for recovering light alcohol from water is no longer necessary. The result is a compact, efficient, and easy-to-control multi-product reactive setup, as illustrated by Fig. 5.15 [86]. Other important design details of the RD column are conveniently provided in Tab. 5.5 [85]. In this control structure, the reactants are fed into the process in a ratio that satisfies the overall mass balance imposed by the reaction stoichiometry and the phase equilibrium at the top and the bottom of the RD column. In contrast, control structures fixing the feed rates of all reactants (acid, light and heavy alcohol) will not work in the presence of small control implementation errors, the failure manifesting by the accumulation or depletion of one reactant [87]. Figure 5.16 (top) compares the temperature profiles for the base case and for a 10% increase of the lauric-acid flow rate, with and without temperature control [85]. Accurate control of the lauric acid concentration in the bottom stream is achieved by using a concentration controller that prescribes the setpoint of the temperature controller in a cascade structure. For this control configuration, the change of the lauric acid feed flow rate leads to a change in the methyl-ester production rate. In contrast, when both flowrate ratios (i.e. lauric acid feed/methanol entering the column, and lauric acid feed/heavy alcohol reflux) are constant, the change of lauric acid feed flow rate leads to changes in both the methyl-ester and ethyl-hexyl ester production rates. Figure 5.16 (mid) presents the performance of the control system for the following scenario: the simulation starts from the steady state (feed rate of lauric acid: 100 kmol h–1), which is maintained for 0.5 h [85]. Then, the feed rate of lauric acid is increased from 100 to 110 kmol h–1, and after 1 h, it is decreased to 90 kmol h–1. Finally, the initial flow rate of 100 kmol h–1 is restored. The change in the acid feed flow rate leads to a change in the light ester production rate, having the same magnitude of change, while the production rate of the heavy ester is constant. The dynamics is fast; only 20 min being necessary to achieve the new production rate. The

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Fig. 5.15: Flowsheet configuration of the dual reactive distillation setup.

Tab. 5.5: Design parameters for simulating the dual reactive distillation column. Parameter

Value

Units/remarks

Number of theoretical stages Lauric acid feed (on stage , at . bar,  C) Methanol feed (directly in reboiler, at  bar,  C) -Ethyl hexanol (fed in decanter, at . bar,  C) Catalyst bulk density Volume holdup per stage Mass catalyst per stage Reflux flow rate Column diameter

   . , .  , .

Reactive from  to  kmol h– kmol h– kmol h– kg m– m Kg kg h– m

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Tab. 5.5 (continued) Parameter

Value

Units/remarks

HETP Fatty acid conversion Reboiler duty Condenser duty Production rate Productivity of RD column Bottom product composition(mass fraction]

. >. , −, , .  ppb acid  ppm water . methanol . methyl ester . EH ester .

m % kW kW kg ester h– kg ester kg– cat h– kg kg– kg kg– kg kg– kg kg– kg kg– kWh ton– ester

Specific energy requirements

amount of water obtained at the top of the column reflects the amount of ester formed. During the entire transient period, the concentration of water on the reactive trays remains below the 2 wt.% limit. Figure 5.16 (btm) presents the temperature and concentration of lauric acid in the bottom stream for the same scenario. Both variables remain very close to the nominal values. Notably, the tuning of the controllers is not critical with respect to the performance of the control system. In this case study, the parameters of the controllers were set as follows. The range of the controlled variable was set to the nominal value of ±10 °C for the temperature control loops, and the nominal value of ±50% of it for the level control loops. For all loops, the range for the manipulated variable was set to twice the nominal value. The gain of the feedback controllers was set to 1%/%. An integration time of 20 min was selected for the temperature controllers. In conclusion, the control structure presented here achieves stable operation and is able to modify the throughput while keeping the characteristics of the products at their design values [85]. At optimal operation, the highest yield and purity can be achieved by using stoichiometric feeds in the desired ratio of fatty esters. At this point, the amount of methanol lost in the top is practically negligible. The heavy ester plays the role of a solvent and prevents methanol escape in the top product. In the top stages, the heavy alcohol enhances water concentration in the vapor phase, from which it is separated by condensation and decanting, while heavy ester is produced in an amount proportional to the reflux flow rate. The optimal operation is based on controlling the inventory of reactants by using the principle of fixed recycle flows of coreactants; in this case, the reflux of the organic phase and the methanol inflow to the RDC. This strategy allows large changes in the production rate. The control strategy is generic and can be employed for esterifications involving the formation of azeotropes, as for ethanol and

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Fig. 5.16: Temperature profiles along the reactive distillation column (top). Dynamic simulation results showing the increase and decrease of the production rate (middle). Temperature and concentration of lauric acid in the bottom stream during the production rate changes (bottom).

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(iso-)propanol. The overall result of integrating design and process control is a compact, efficient, and easy-to-control multi-product RD setup.

5.4.3 Industrial RD process for methyl acetate production Methyl acetate is a high volume commodity chemical with applications as an intermediate in the manufacture of a variety of polyesters, such as photographic film base, cellulose acetate, Tenite cellulosic plastics, and Estron acetate [88]. The industrial process for methyl acetate (MeOAc) synthesis is based on the equilibrium-limited esterification reaction of methanol (MeOH) with acetic acid (AcOH). The reaction takes place in liquid phase in the presence of an acid catalyst, such as sulfuric acid or a sulfonic acid ion exchange resin [89]: MeOH + AcOH Ð MeOAc + H2 O

(5:19)

The rate expression, in the form of activities, is strongly preferred since water and methanol have higher polarity than methyl acetate; thus leading to a strongly nonideal solution behavior. An activity-based rate model for the reaction chemistry is given by the relation [90]:   aMeOAc aH2 O (5:20) r = kf aAcOH aMeOH − Keq where the reaction equilibrium constant (Keq) and the forward rate constant (kf) are given by Keq = 2.32 × expð782.98=T Þ; with T expressed in K

(5:21)

kf = 9.732 × 108 × expð − 6, 287.7=T Þ;h − 1

(5:22)

Figure 5.17 illustrates the conventional and the RD process for methyl acetate production [29]. Due to the commercial success of the RD process, replacing the conventional process and the potential of the ion exchange resins as solid acid catalysts, a rate expression for an ion exchange resin-catalyzed reaction was proposed [88]. The expression for the reaction rate (r) is based on kinetic data generated over a range of molar feed ratios, more typical of reactive distillation conditions:

 k aAcOH aMeOH − aMeOAc aH2 O =Keq
 (5:23) r= 1 + KAcOH aAcOH + KMeOH aMeOH + KMeOAc aMeOAc + KH2 O aH2 O where k is the rate constant, Keq is the equilibrium constant [equal to 5.2 according to 1], and Ki values (i being the component: AcOH, MeOH, MeOAc, and H2O) are the adsorption coefficients of the Langmuir-Hinshelwood-Hougen-Watson (LHHW) model. The expression has been successfully used to verify the experimentally

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Fig. 5.17: Methyl acetate production: conventional process (left) versus reactive distillation (right).

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observed RCMs of this system. The heat of the reaction is low (ΔH = −3.0165 kJ mol–1), indicating a slightly exothermic reaction that is typical for acetate esterifications. The liquid-phase activity coefficients are well represented by the Wilson model [90]. The reaction can be carried out at 310–393 K and at atmospheric pressure. The only main side reaction is the formation of dimethyl ether (DME) by the etherification of methanol, which is predominant at high temperatures [88]. Conventional processes use reactors with a large excess of a reactant to achieve high conversion, followed by an energy-intensive downstream separation due to the formation of MeOAc/MeOH and MeOAc/H2O azeotropes. A typical process employs one to two reactors, eight distillation columns, and one liquid extraction column; thus making it rather complex and capital intensive. Eastman Kodak has developed an RD process that delivers a high-purity product using a near-stoichiometric ratio of MeOH to AcOH [11]. Figure 5.18 shows the fundamental tasks (functions) involved in the process and the new way of combining all these tasks into an extractive reactive distillation column. The RD column for methyl acetate production (shown in Fig. 5.17) has four key sections: – Methyl acetate enrichment section (which performs task 7), where acetic acid and methyl acetate are separated above the acetic acid feed, allowing pure methyl acetate to be recovered as overhead product. – Water extraction section (which performs task 4), where acetic acid acts as a mass separating agent (extractant) and extracts water (thus breaking the methyl acetate/water azeotrope) and some methanol. – Reaction section (performing tasks 1, 2, and 3), where the reaction occurs in a series of counter-current flashing stages with sulfuric acid as homogeneous catalyst. – Methanol stripping section (for tasks 5 and 6), where methanol is stripped from water, as the bottom product. Figure 5.19 shows the composition and temperature profiles along the reactive distillation column [11, 89]. High-purity methyl acetate is obtained as distillate, while water byproduct is removed as the bottom product. Some mid-boiling components are formed due to the impurities present in the feed. For this reason, a small sidestream is withdrawn above the catalyst feed point and treated separately in an impurity-removal system, where the impurities are stripped and concentrated, while a methanol and methyl acetate stream are recycled to the reaction zone of the RD column. Notably, the RD column is operated at a near-stoichiometric molar ratio of acetic acid and methanol, but it is capable of yielding methyl acetate of high purity as the product. The whole process is practically integrated in a single column; thus eliminating the need for a complex distillation column system and recycle of the methanol/methyl acetate azeotrope. Remarkably, a single RD column, built at Eastman Kodak’s Tennessee plant, produces 180 ktpy of high-purity methyl acetate [88].

Fig. 5.18: Methyl acetate production: task based design leading to reactive distillation.

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Fig. 5.19: Composition and temperature profiles in the RD column for methyl acetate production.

5.5 Take-home message Reactive distillation is a process intensification method that has attracted considerable attention over the past decades as a promising alternative to conventional reaction-separation sequences. RD technology has already been successfully applied in the process industry, especially to overcome the conversion of chemical-equilibrium-limited reactions [13]. However, the potential of RD technology has not been fully tapped and there is research in progress to improve RD processes by various means: ultrasound assisted RD [91], use of high-gravity fields [92], or coupling RD with other operations, such as membrane separations [13]. The main drivers for RD applications are economical (over 20% reduction of variable cost, capital expenditure, and energy use), environmental (lower CO2 emissions, no or reduced salt waste), and social (improved safety and health due to reduced footprint, lower reactive content, and run away sensitivity). It is thus clear that RD contributes to all three pillars of sustainability in the chemical industry. The industrial implementation of RD by the collaboration of various partners in research, scale-up, design, and operation can be considered as a model for the rapid implementation of other PI techniques in the chemical process industry [7]. Taking into account the remarkable progress in hardware development, modeling for design and simulation, control strategies, real time optimization, and also considering the pace at which new applications are being explored, RD remains one of the most important tools for process intensification using green chemistry and engineering [7, 8, 2, 22]. Despite the more complex design, control and equipment, RD remains a PI technology that fulfills the principles of green engineering (e.g., prevention, instead of treatment, design for separation, maximize efficiency, output-pulled vs inputpushed, meet need and minimize excess, integrate local material and energy flows, design for a commercial afterlife, and renewable vs depleting). RD offers unique features such as: reduced number of processing units, enhanced overall rates, overcome

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unfavorable equilibrium, avoid difficult separations, improved selectivity, reduced energy requirements, and low or no solvent use [6, 22]. RD is currently an established unit operation in the chemical process technology, also being the front-runner in the field of process intensification [7, 8]. Nowadays, there are a variety of models for screening, analysis, design, and optimization of RD columns. Moreover, RCM are an invaluable tool for the initial process screening and flowsheet development. EQ models have their place in preliminary designs, while the NEQ models are used for the final RD design, development of control strategies, and commercial RD plant design, and simulation [7, 86, 17, 41]. Future research and development should focus on the quick evaluation of RD applicability, an easy methodology to choose the most suitable equipment, and the scale-up of equipment, since this is where great deficiencies still lie. Moreover, considering the green opportunities created by the use of reactive separations, future prospects aim to spread the use of RD technologies in the production of bulk or specialty chemicals (such as ethers, esters, polyesters, and biofuels) as well as biobased chemicals (using biocatalytic reactive distillation).

5.6 Quiz Question 1. True or false: Residue curve maps are used in the conceptual design of reactive distillation. Question 2. True or false: Reactive distillation is always the optimal choice as compared to stand-alone units (reactor and distillation columns). Question 3. True or false: Reactive distillation should be used for low relative volatilities and slow reactions. Question 4. True or false: Structured packings exhibit a low reaction performance but very good separation efficiency. Question 5. True or false: In RD processes, the reaction rates directly depend on the liquid holdup and the amount of catalyst in each stage. Question 6. True or false: RD columns always use solid catalyst and special internals. Question 7. True or false: Reactive distillation pulls the chemical equilibrium by continuously removing the products. Question 8. True or false: RD can use a homogeneous catalyst or solid catalyst, or no catalyst at all. Question 9. True or false: RD using a solid catalyst is also known as catalytic distillation.

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Question 10. What properties and data must be known to identify the potential feasibility of a reactive distillation process for a new chemical system? Question 11. Which of the following reactions are suitable for reactive distillation? □ Esterification of methanol and acetic acid: CHCOOH + CHOH ⇌ CH-COOCH + HO □ Etherification of methanol:  CHOH ⇌ CH-OCH + HO □ Methanol synthesis from CO: CO + H ⇌ CHOH + HO

□ Hydrolysis of an ester: CHCH-COOCH + HO ⇌ CHCH-COOH + CHOH □ Combustion of hydrogen: H + O ⇌ HO □ CO absorption in amines: MEA + CO + HO ⇌MEAH+ + HCO–

Question 12. Should reactive distillation be applied to endothermic reactions? □ No, only to exothermic reactions. □ Yes, but not for strong endothermic reactions.

□ Yes, it can be used for both endothermic and exothermic reactions. □ Yes, it can be used only for endothermic reactions.

Question 13. What is the main purpose of trays, random packings, and structured packings? □ These internals are used to separate particles from the final product, □ These internals are used to achieve a good mixing of the liquid phases at the feed stage to increase the reaction rate,

□ These internals try to avoid contact between the vapor and liquid phases to reduce side reactions, □ These internals are used to increase the mass transfer by achieving a high interfacial area,

Question 14. Which of the following are advantages of reactive distillation? □ Reactive distillation can reduce investment and operating costs due to a reduced number of necessary apparatus □ Reactive distillation can decrease the required catalyst amount. □ Reactive distillation is very effective because the optimal conditions for the reaction are always identical to the optimal conditions for the distillation. □ Selectivity and conversion can be increased in a reactive distillation column due to the removal of products from the reactive section.

□ Reactive distillation is very effective for the separation of solid and liquid components. □ For exothermic reactions, the required heat is reduced because the heat of reaction is directly used for the evaporation of products. □ Reactive distillation is advantageous for catalysts with a short catalyst lifetime because it is easy to replace the catalyst in reactive distillation columns. □ By “reacting away” participating components, azeotropes can be avoided in reactive distillation columns.

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Question 15. What models can be used to simulate reactive distillation? □ Equilibrium model for both phase and chemical reaction. □ Hybrid model for phase equilibrium and (rate-based) reaction rate. □ Computational fluid dynamic models with molecular simulations.

□ Nonequilibrium (rate-based) model for VLLE and chemical reaction. □ Electrolyte models with solid state chemistry. □ Compartmental model with ideally mixed or plug-flow reactors.

Question 16. Which modeling approach is typically more accurate? □

□

Equilibrium-stage approach

Nonequilibrium-stage approach

Question 17. RD is an example of process intensification in the: □ □

□ □

Spatial domain (structure) Thermodynamic domain (energy)

Functional domain (synergy) Temporal domain (time)

Question 18. Which of the following are drawbacks of reactive distillation? □ □ □ □

□ □ □ □

Trade-off operation Occurrence of multiple steady states Less equipment and lower CAPEX Increased conversion and selectivity

Reduced process flexibility Operating-window constraints Reduced energy usage Reduced degradation of chemicals

5.7 Exercises A new reactive distillation process must be developed for the production of component D. The synthesis of D is performed in a catalyzed and equilibrium-limited reaction of components A and B. The side product of this reaction is C. The reaction is performed at a pressure of 300 mbar. The reaction, the boiling points, and the molecular weights of the components are given below: cat.

A + B!C+D S

Component A B C D

Boiling point (K)

Molecular weight (g mol–)

   

   

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Exercise 1. Draw a conventional reactor and distillation column, schematic for the synthesis and purification of component D. Assume ideal behavior of the components. Indicate all components in every stream. How many columns are necessary; which streams can be recycled? Next, draw a reactive distillation process for the same synthesis and purification task and compare it with the conventional process. Exercise 2. In an industrial process that is in operation for 8,000 h per year, 950 tons of D must be produced per year. What total molar feed stream is necessary for this production, assuming a conversion of 100% of reactant A and a reactant ratio of 1.5 kgB/kgA in the feed? Exercise 3. By calculating the mass and component balance for the column, determine the amount of side product C that is produced in this process. Unfortunately, you determined that your system does not exhibit an ideal behavior and that a heavy boiling azeotrope is formed by components A and D, with a boiling point of 395 K. Exercise 4. Discuss two options to obtain pure product D after the purification steps in a conventional process. Exercise 5. How is the production of pure component D in the reactive distillation process possible without adding additional unit operations? Exercise 6. Which operating parameters of the reactive distillation column would you monitor in a simulation study? Why?

5.8 Solutions Question 1. True Question 2. False Question 3. False Question 4. True Question 5. True Question 6. False Question 7. True Question 8. True Question 9. True

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Question 10. Reaction and distillation conditions; ranking of the boiling points; equilibrium constant; reaction rate (kinetics) Question 11. Which of the following reactions are suitable for reactive distillation? ■ Esterification of methanol and acetic acid: CHCOOH + CHOH ⇌ CH-COOCH + HO ■ Etherification of methanol:  CHOH ⇌ CH-OCH + HO □ Methanol synthesis from CO: CO + H ⇌ CHOH + HO

■ Hydrolysis of an ester: CHCH-COOCH + HO ⇌ CHCH-COOH + CHOH □ Combustion of hydrogen: H + O ⇌ HO □ CO absorption in amines: MEA + CO + HO ⇌ MEAH+ + HCO–

Question 12. Should reactive distillation be applied to endothermic reactions? □ No, only to exothermic reactions. □ Yes, but not for strong endothermic reactions.

■ Yes, it can be used for both endothermic and exothermic reactions. □ Yes, it can be used only for endothermic reactions.

Question 13. What is the main purpose of trays, random packings, and structured packings? □ These internals are used to separate particles from the final product. □ These internals are used to achieve a good mixing of the liquid phases at the feed stage to increase the reaction rate.

□ These internals try to avoid contact between the vapor and liquid phases to reduce side reactions. ■ These internals are used to increase the mass transfer by achieving a high interfacial area.

Question 14. Which of the following are advantages of reactive distillation? ■ Reactive distillation can reduce investment and operating costs due to a reduced number of necessary apparatus. □ Reactive distillation can decrease the required catalyst amount. □ Reactive distillation is very effective because the optimal conditions for the reaction are always identical to the optimal conditions for distillation. ■ Selectivity and conversion can be increased in a reactive distillation column due to the removal of products from the reactive section.

□ Reactive distillation is very effective for the separation of solid and liquid components. ■ For exothermic reactions, the required heat is reduced because the heat of reaction is directly used for the evaporation of products. □ Reactive distillation is advantageous for catalysts with a short catalyst lifetime because it is easy to replace the catalyst in reactive distillation columns. ■ By “reacting away” participating components, azeotropes can be avoided in reactive distillation columns.

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Question 15. What models can be used to simulate reactive distillation? ■ Equilibrium model for both phase and chemical reaction ■ Hybrid model for phase equilibrium and (rate-based) reaction rate □ Computational fluid dynamic models with molecular simulations

■ Nonequilibrium (rate-based) model for VLLE and chemical reaction □ Electrolyte models with solid state chemistry □ Compartmental model with ideally mixed or plug-flow reactors

Question 16. Which modeling approach is typically more accurate? □

Equilibrium-stage approach

■

Nonequilibrium-stage approach

Question 17. RD is an example of process intensification in the: □ □

■ □

Spatial domain (structure) Thermodynamic domain (energy)

Functional domain (synergy) Temporal domain (time)

Question 18. Which of the following are drawbacks of reactive distillation? ■ ■ □ □

Trade-off operation Occurrence of multiple steady states Less equipment and lower CAPEX Increased conversion & selectivity

■ ■ □ □

Reduced process flexibility Operating-window constraints Reduced energy usage Reduced degradation of chemicals

Equilibrium reaction Solution (Exercise 1). For the conventional process and ideal separations, three distillation columns are necessary. Recycling is possible for components B (bottom product of column 2) and A (top product of column 3). The ideal RD process for the same synthesis is shown in Fig. 5.20 [30]. Solution (Exercise 2). ṅD = 950 × 103/8,000 = 118.75 kg h−1 = 118.75/128 = 0.92773 kmol h−1 ṅA = ṅD = 0.92 kmol h−1 (full conversion of A; 1 mol of A leads to 1 mol of D by reaction) ṅB = 1.5×( ṅA×Mw,A)/Mw,B = 1.5×(0.92×72)/74 = 1.354 kmol h−1 ṅFeed,total = ṅA + ṅB = 2.28 kmol h−1 Solution (Exercise 3). ṅC,total = ṅA = 0.92773 kmol h−1 = 7,421.88 kmol a−1 ṁC,total = ṅC,total×Mw,C = 133.59 t a−1

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Fig. 5.20: Conventional process for the synthesis and purification of component D (left). Ideal reactive distillation process for the synthesis and purification of component D (right).

Solution (Exercise 4). 1. Complete conversion of A in the reactor to avoid separation problems in the purification steps. 2. Use of additional purification steps that can separate A and D, such as a membrane process. Solution (Exercise 5). Because component D is obtained at the bottom of the column, a complete conversion of the acrylic acid at the bottom of the reactive distillation column is required. Solution (Exercise 6). The operating parameters that are typically monitored in an RD process are the reflux ratio, the distillate-to-feed ratio, the pressure and the reactant ratio/total feed flow. For RD columns, a higher pressure leads to a higher reaction rate and smaller required residence time or smaller reactive sections. An increase in pressure results in higher temperatures in the column and higher operating costs for the reboiler. If no restrictions are imposed, such as upper temperature limits for the catalyst, determining the appropriate pressure is often a cost-optimization problem. The total feed flow and the feed ratio of the two reactants are often chosen based on the reaction that is performed in the column. For reactions with an equimolar consumption of both reactants, a molar feed ratio of 1 should be used for almost complete conversions of the reactants. If a reactant ratio significantly larger or smaller than 1 is chosen, recycling of unused reactants is necessary. The total feed flow is often chosen based on the required final product amount. The reflux ratio and distillate-to-feed ratio are two parameters that are usually monitored in simulation studies of reactive distillation columns. By varying the reflux ratio, the residence

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time in the column can be controlled, which can increase the separation of the components, and the conversion of the components can be varied. The distillate-to-feed ratio determines the flow of the components that are removed at the top of the column. This parameter is chosen based on the required purity and the product location (distillate or bottom product) of the desired component. If the desired component is removed at the top of the column, heavy boiling impurities can be removed from the distillate by decreasing the distillate-to-feed ratio, which also increases the product purity [30].

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[16]

Luyben WL, Yu CC. Reactive Distillation Design and Control. Hoboken, New-Jersey, US: WileyAIChE; 2008. Kiss AA. Advanced Distillation Technologies – Design, Control and Applications. Chichester, UK: Wiley; 2013. Patrut C, Bildea CS, Kiss AA. Catalytic cyclic distillation – A novel process intensification approach in reactive separations. Chem. Eng. Process.: Process Intensif. 2014;81:1–12. Reay D, Ramshaw C, Harvey A. Process Intensification – Engineering for Efficiency, Sustainability and Flexibility. Second edn. UK: Butterworth-Heinemann; 2013. Malone MF, Doherty MF. Reactive distillation. Ind. Eng. Chem. Res. 2000;39:3953–3957. Malone MF, Huss RS, Doherty MF. Green chemical engineering aspects of reactive distillation. Environ. Sci. Technol. 2003;37:5325–5329. Harmsen GJ. Reactive distillation: The front-runner of industrial process intensification: A full review of commercial applications, research, scale-up, design and operation. Chem. Eng. Process.: Process Intensif. 2007;46:774–780. Harmsen GJ. Process intensification in the petrochemicals industry: Drivers and hurdles for commercial implementation. Chem. Eng. Process.: Process Intensif. 2010;49:70–73. Krishna R. Reactive separations: More ways to skin a cat. Chem. Eng. Sci. 2002;57:1491– 1504. Noeres C, Kenig EY, Gorak A. Modelling of reactive separation processes: Reactive absorption and reactive distillation. Chem. Eng. Process. 2003;42:157–178. Agreda VH, Partin LR, Heise WH. High-purity methyl acetate via reactive distillation. Chem. Eng. Process.: Process Intensif. 1990;86:40–46. Siirola JJ. Industrial applications of chemical process synthesis. Adv. Chem. Eng. 1996;23:1–62. Keller T. Reactive distillation. In: Gorak A, Olujic Z, eds. Distillation: Equipment and Processes. Elsevier; 2014. Schembecker G, Tlatlik S. Process synthesis for reactive separations. Chem. Eng. Process.: Process Intensif. 2003;42:179–189. Mansouri SS, Sales-Cruz M, Huusom JK, Woodley JM, Gani R. Integrated process design and control of reactive distillation processes, 9th IFAC Symposium on Advanced Control of Chemical Processes ADCHEM 2015, Whistler, Canada, 7–10 June 2015, IFAC-PapersOnLine, 48 2015, 1120–1125. Segovia-Hernández JG, Hernández S, Bonilla Petriciolet A. Reactive distillation: A review of optimal design using deterministic and stochastic techniques. Chem. Eng. Process.: Process Intensif. 2015;97:134–143.

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[17] Schoenmakers HG, Bessling B. Reactive and catalytic distillation from an industrial perspective. Chem. Eng. Process.: Process Intensif. 2003;42:145–155. [18] Sundmacher K, Kienle A, Seidel-Morgenstern A, eds. Integrated Chemical Processes: Synthesis, Operation, Analysis, and Control. Weinheim: Wiley-VCH; 2005. [19] Hiwale RS, Bhate NV, Mahajan YS, Mahajani SM. Industrial applications of reactive distillation: Recent trends. Int. J. Chem. React. 2004;2:R1. [20] Stankiewicz A. Reactive separations for process intensification: An industrial perspective. Chem. Eng. Process.: Process Intensif. 2003;42:137–144. [21] Tuchlenski A, Beckmann A, Reusch D, Dussel R, Weidlich U, Janowsky R. Reactive distillation – industrial applications, process design & scale-up. Chem. Eng. Sci. 2001;56:387–394. [22] Sundmacher K, Kienle A, eds. Reactive Distillation: Status and Future Directions. Weinheim: Wiley-VCH; 2003. [23] Thery R, Meyer XM, Joulia X. Analysis of the feasibility, synthesis and conception of processes of reactive distillation: State of the art and critical analysis. Can. J. Chem. Eng. 2005;83:242–266. [24] Kiss AA, Jobson M, Gao X. Reactive distillation: Stepping up to the next level of process intensification. Ind. Eng. Chem. Res. 2019;58:5909–5918. [25] Doherty MF, Malone MF. Conceptual Design of Distillation Systems. New York: McGraw-Hill; 2001. [26] Schmidt-Traub H, Gorak A. Integrated Reaction and Separation Operations. New York: Springer; 2006. [27] Stichlmair JG, Fair JR. Distillation, Principles and Practice. New York: Wiley-VCH; 1998. [28] Shah M, Kiss AA, Zondervan E, de Haan AB. A systematic framework for the feasibility and technical evaluation of reactive distillation processes. Chem. Eng. Process.: Process Intensif. 2012;60:55–64. [29] Kiss AA. Applying reactive distillation. NPT Procestechnol. 2012;19(1):22–24. [30] Niesbach A. Reactive distillation. In: Lutze P, Górak A, ed. Reactive and Membrane-assisted Separations. De Gruyter; 2016. [31] Baur R, Higler AP, Taylor R, Krishna R. Comparison of equilibrium stage and nonequilibrium stage models for reactive distillation. Chem. Eng. Sci. 2000;76:33–47. [32] Egorov Y, Menter F, Klöker M, Kenig EY. On the combination of CFD and rate-based modelling in the simulation of reactive separation processes. Chem. Eng. Process.: Process Intensif. 2005;44:631–644. [33] Grosser JH, Doherty MF, Malone MF. Modeling of reactive distillation systems. Ind. Eng. Chem. Res. 1987;26:983–989. [34] Lee J-H, Dudukovic MP. A comparison of the equilibrium and nonequilibrium models for a multicomponent reactive distillation column. Comput. Chem. Eng. 1998;23:159–172. [35] Kenig EY, Gorak A, Pyhalahti A, Jakobsson K, Aittamaa J, Sundmacher K. Advanced rate-based simulation tool for reactive distillation. AIChE J. 2004;50:322–342. [36] Klöker M, Kenig EY, Hoffmann A, Kreis P, Górak A. Rate-based modelling and simulation of reactive separations in gas/vapour–liquid systems. Chem. Eng. Process.: Process Intensif. 2005;44:617–629. [37] Kreul LU, Górak A, Barton PI. Modeling of homogeneous reactive separation processes in packed columns. Chem. Eng. Sci. 1999;54:19–34. [38] Mueller I, Pech C, Bhatia D, Kenig EY. Rate-based analysis of reactive distillation sequences with different degrees of integration. Chem. Eng. Sci. 2007;62:7327–7335. [39] Mueller I, Kenig EY. Reactive distillation in a dividing wall column – Rate-based modeling and simulation. Ind. Eng. Chem. Res. 2007;46:3709–3719. [40] Taylor R, Krishna R. Multicomponent Mass Transfer. New York: Wiley; 1993.

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[41] Taylor R, Krishna R. Modelling reactive distillation. Chem. Eng. Sci. 2000;55:5183–5229. [42] Aspen Technology, Aspen Plus: User guide – Volume 1 & 2, 2018. [43] Güttinger TE, Morari M. Predicting multiple steady states in distillation: Singularity analysis and reactive systems. Comput. Chem. Eng. 1997;21:S995–S1000. [44] Venimadhavan G, Malone MF, Doherty MF. Bifurcation study of kinetic effects in reactive distillation. AIChE J. 1999;45:546–556. [45] Dimian AC, Bildea CS, Kiss AA. Integrated Design and Simulation of Chemical Processes. 2nd edn. Elsevier; 2014. [46] Muthia R, Jobson M, Kiss AA. A systematic framework for assessing the applicability of reactive distillation for quaternary mixtures using a mapping method. Comput. Chem. Eng. 2020;136:106804. [47] Dimian AC, Bildea CS. Chemical Process Design – Computer-aided Case Studies. Weinheim: Wiley-VCH; 2008. [48] Doherty MF, Perkins JD. On the dynamics of distillation processes. 1: The simple distillation of multicomponent non-reacting, homogeneous liquid mixtures. Chem. Eng. Sci. 1978;33:281–301. [49] Venimadhavan G, Buzad G, Doherty MF, Malone MF. Effect of kinetics on residue curve maps for reactive distillation. AIChE J. 1994;40:1814–1824. [50] Okasinski MJ, Doherty MF. Design method for kinetically controlled, staged reactive distillation columns. Ind. Eng. Chem. Res. 1998;37:2821–2834. [51] Nagy ZK, Klein R, Kiss AA, Findeisen R. Advanced control of a reactive distillation column. Comput. Aided Chem. Eng. 2007;24:805–810. [52] Almeida-Rivera CP, Swinkels PLJ, Grievink J. Designing reactive distillation processes: Present and future. Comput. Chem. Eng. 2004;28:1997–2020. [53] Espinosa J, Aguirre P, Pérez G. Some aspects in the design of multicomponent reactive distillation columns with a reacting core: Mixtures containing inerts. Ind. Eng. Chem. Res. 1996;35:4537–4549. [54] Fien G-JAF, Liu YA. Heuristic synthesis and shortcut design of separation processes using residue curve maps: A review. Ind. Eng. Chem. Res. 1994;33:2505–2522. [55] Ung S, Doherty MF. Synthesis of reactive distillation systems with multiple equilibrium chemical reactions. Ind. Eng. Chem. Res. 1995;34:2555–2565. [56] Gadewar SB, Chadda N, Malone MF, Doherty MF. Feasibility and process alternatives for reactive distillation. In: Sundmacher K, Kienle A, eds. Reactive Distillation: Status and Future Directions. Wiley; 2003. [57] Glasser D, Crowe C, Hildebrandt D. A geometric approach to steady flow reactors: The attainable region and optimization in concentration space. Ind. Eng. Chem. Res. 1987;26:1803–1810. [58] Frey T, Stichlmair J. Thermodynamic fundamentals of reactive distillation. Chem. Eng. Technol. 1999;22:11–18. [59] Lee JW, Hauan S, Westerberg AW. Graphical methods for reaction distribution in a reactive distillation column. AIChE J. 2000;46:1218–1233. [60] Hauan S, Lien KM. A phenomena based design approach to reactive distillation. Chem. Eng. Res. Des. 1998;76:396–407. [61] Urselmann M, Barkmann S, Sand G, Engell S. Optimization-based design of reactive distillation columns using a memetic algorithm. Comput. Chem. Eng. 2011;35:787–805. [62] Urselmann M, Engell S. Design of memetic algorithms for the efficient optimization of chemical process synthesis problems with structural restrictions. Comput. Chem. Eng. 2015;72:87–108.

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[63] Amte V, Nistala SH, Mahajani SM, Malik RK. Optimization based conceptual design of reactive distillation for selectivity engineering. Comput. Chem. Eng. 2013;48:209–217. [64] Zondervan E, Shah M, de Haan AB. Optimal design of a reactive distillation column. Chem. Eng. Trans. 2011;24:295–300. [65] Damartzis T, Seferlis P. Optimal design of staged three-phase reactive distillation columns using non-equilibrium and orthogonal collocation models. Ind. Eng. Chem. Res. 2010;49:3275–3285. [66] Seferlis P, Damartzis T, Dalaouti N. Efficient reduced order dynamic modeling of complex reactive and multiphase separation processes using orthogonal collocation on finite elements. In: Georgiadis MC, Banga JR, Pistikopoulos EN, eds. Process Systems Engineering: Dynamic Process Modeling, Vols , 7. Wiley; 2011. [67] Paramasivan G, Kienle A. Inferential control of reactive distillation columns – An algorithmic approach. Chem. Eng. Technol. 2011;34:1235–1244. [68] Kiss AA. Novel catalytic reactive distillation processes for a sustainable chemical industry. Top. Catal. 2019;62:1132–1148. [69] Daza OS, Perez-Cisneros ES, Bek-Pedersen E, Gani R. Graphical and stage-to-stage methods for reactive distillation column design. AIChE J. 2003;49:2822–2841. [70] Serafimov LA, Pisarenko YA, Kulov NN. Coupling chemical reaction with distillation: Thermodynamic analysis and practical applications. Chem. Eng. Sci. 1999;54:1383–1388. [71] Subawalla H, Fair JR. Design guidelines for solid-catalyzed reactive distillation systems. Ind. Eng. Chem. Res. 1999;38:3696–3709. [72] Hernandez S, Sandoval-Vergara R, Barroso-Munoz FO, Murrieta-Duenasa R, HernandezEscoto H, Segovia-Hernandez JG, Rico-Ramirez V. Reactive dividing wall distillation columns: Simulation and implementation in a pilot plant. Chem. Eng. Process. 2009;48:250–258. [73] Kiss AA, Pragt H, van Strien C. Reactive dividing-wall columns – How to get more with less resources?. Chem. Eng. Commun. 2009;196:1366–1374. [74] Baur R, Krishna R. Distillation column with reactive pump arounds: An alternative to reactive distillation. Chem. Eng. Process.: Process Intensif. 2004;43:435–445. [75] Kaymak DB, Luyben WL. Effect of the chemical equilibrium constant on the design of reactive distillation columns. Ind. Eng. Chem. Res. 2004;43:3666–3671. [76] Klöker M, Kenig EY, Schmitt M, Althaus K, Schoenmakers H, Markusse AP, Kwant G. Influence of operating conditions and column configuration on the performance of reactive distillation columns with liquid-liquid separators. Can. J. Chem. Eng. 2003;81:725–732. [77] Luyben WL. Distillation Design and Control Using Aspen Simulation. 2nd edn. Hoboken, NewJersey, US: Wiley-AIChE; 2013. [78] Sharma N, Singh K. Control of reactive distillation column – A review. Int. J. Chem. React. 2010;8:R5. [79] Kiss AA. Process intensification for reactive distillation. In: Rong B-G, ed. Process Synthesis and Process Intensification: Methodological Approaches. de Gruyter; 2017. [80] Goetze L, Bailer O, Moritz C, Von Scala C. Reactive distillation with Katapak. Catal. Today 2001;69:201–208. [81] Hoffman A, Noeres C, Gorak A. Scale-up of reactive distillation columns with catalytic packings. Chem. Eng. Process.: Process Intensif. 2004;43:383–395. [82] Aspen Technology, Aspen physical property system – Physical property models, 2018. [83] Bildea CS, Gyorgy R, Sanchez-Ramirez E, Quiroz-Ramirez JJ, Segovia-Hernandez JG, Kiss AA. Optimal design and plant-wide control of novel processes for di-n-pentyl ether production. J. Chem. Technol. Biotechnol. 2015;90:992–1001.

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[84] Bringue R, Iborra M, Tejero J, Izquierdo JF, Cunill F, Fite C, Cruz V. Thermally stable ionexchange resins as catalysts for the liquid-phase dehydration of 1-pentanol to di-n-pentyl ether (DNPE). J. Catal. 2006;244:33–42. [85] Dimian AC, Bildea CS, Omota F, Kiss AA. Innovative process for fatty acid esters by dual reactive distillation. Comput. Chem. Eng. 2009;33:743–750. [86] Kiss AA, Bildea CS. A review on biodiesel production by integrated reactive separation technologies. J. Chem. Technol. Biotechnol. 2012;87:861–879. [87] Kiss AA, Bildea CS, Dimian AC. Design and control of recycle systems by non-linear analysis. Comput. Chem. Eng. 2007;31:601–611. [88] Mahajani SM, Chopade SP. Reactive distillation: Processes of commercial importance. In: Wilson ID, Edlard TR, Poole CA, Cooke M, eds. Encyclopedia of Separation Science. London, UK: Academic Press; 2000, 4075–4082. [89] Kiss AA. Process intensification: Industrial applications. In: Segovia-Hernandez JG, BonillaPetriciolet A, eds. Process Intensification in Chemical Engineering: Design, Optimization and Control. Springer International Publishing; 2016, 221–260. [90] Huss RS, Chen F, Malone MF, Doherty MF. Reactive distillation for methyl acetate production. Comput. Chem. Eng. 2003;27:1855–1866. [91] Wierschem M, Skiborowski M, Gorak A, Schmuhl R, Kiss AA. Techno-economic evaluation of an ultrasound-assisted enzymatic reactive distillation process. Comput. Chem. Eng. 2017;105:123–131. [92] Krishna G, Min TH, Rangaiah GP. Modeling and analysis of novel reactive HiGee distillation. Comput. Aided Chem. Eng. 2012;31:1201–1205.

Anna-Katharina Kunze

6 Reactive absorption 6.1 Fundamentals Absorption is the transfer of gases (absorptive) into a washing liquid (solvent or absorbent) by physical dissolution (physisorption) or by physical dissolution with additional chemical reactions (chemisorption). Hence, absorption is a separation by phase affinity that is initiated by the addition of a mass-separating agent [1, 2]. The solvent entering the absorber is also called the lean solvent, while the solvent that leaves the absorber is often referred to as the loaded or rich solvent Fig. 6.1). The entering gas stream is the crude gas stream, while the gaseous outlet is called purified gas. The gaseous components entering the solvent are called solutes or absorbates. The underlying driving force that evokes the mass transfer of components between the phases is a gradient in chemical potential between the gas and the liquid phases. In diluted systems, this potential gradient can be simplified to a concentration gradient, which is valid for systems under low pressure and with few interactions between components [2].

Fig. 6.1: Process flow diagram of an absorption–desorption closed loop (exemplarily shown for CO2 separation).

Desorption or stripping is the reverse of absorption, in which the absorbate is removed from the rich solvent. Desorption is used for solvent regeneration in continuous absorption–desorption processes, in which the solvent runs in a closed loop. The solvent is loaded in the absorption operation and is regenerated in a subsequent desorption operation (see Fig. 6.1). https://doi.org/10.1515/9783110720464-006

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6.1.1 Separation principle In general, absorption processes are categorized by the physicochemical properties that induce mass transfer. As a result, the two absorption categories, which are, physical and reactive absorption, can be distinguished. In physical absorption, the separation is achieved due to the dissolution of the gaseous component in the solvent. The selectivity of physical absorption is determined by the difference in solubility of the various gaseous components in the solvent. Henry’s law describes the gas-liquid equilibrium, which relates the concentration of the target component in the gas to the corresponding gaseous component dissolved in the solvent. There are several types of Henry coefficients, although the most commonly used coefficients relate the partial pressure of component i in the gas phase with the mole fraction of component i in the liquid phase: pi = Hei · xi

(6:1)

Moreover, the concentration can be expressed by either the molality or molarity [3]. Henry’s law is only valid for low solute partial pressures. In the case of higher concentrations or pressures, the application of Henry’s law is not possible (see Fig. 6.2). Instead, Raoult’s law is used to describe the gas-liquid equilibrium:

Fig. 6.2: Phase equilibrium described by Henry’s law and Raoult’s law [4].

pi = p0, i · xi .

(6:2)

In Raoult’s law, the Henry coefficient, Hei, in eq. (6.1) is substituted by the vapor pressure, p0,i, of the pure component i. The assumption that the Henry coefficient, Hei, is equal to the vapor pressure of the pure component i, p0,i, is valid for ideal solutions.

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For real solutions, an overlap of Henry’s law and Raoult’s law that is dependent on the mole fraction of component i in the liquid can be assumed (see Fig. 6.2). Because the efficiency of physical absorption is dependent on the solubility of the gaseous component in the liquid, high pressures and low temperatures are generally favorable. In the case of reactive absorption, physical absorption is supported by a chemical reaction. This integration of reaction and separation aims to maintain the driving force and intensify the mass transfer because it continuously causes further reaction of the target component and shifts the chemical equilibrium toward the product side [5]. For most reactive absorption processes, the reaction occurs in the liquid phase, although there are some examples in which it occurs in both phases or even as an instantaneous reaction at the interface between the gas and liquid phases. The application of reactive absorption is beneficial for processes in which the concentration of the target component (absorptive) in the gas stream is low. Additionally, reactive absorption can be applied at lower pressures and for limited solubility of the target component in the solvent [5]. The reason is that reactive absorption comprises a combined operating window in terms of the applied temperature and pressure, which is due to the influence of the operating conditions on the solubility and reaction (see Fig. 6.3). Because the reaction rate is temperature dependent, higher temperatures are favorable, whereas the pressure range is dependent on the stoichiometry for reversible reactions. In regard to the solubility of gases in the liquid, high pressures and low temperatures are generally favorable.

Fig. 6.3: Combined operating window for reactive absorption, which is the integration of a reaction in a physical absorption process.

The reaction itself is often reversible to allow for continuous solvent regeneration in the desorption unit (Fig. 6.1), although it can also be selected from the class of irreversible reactions. Table 6.1 summarizes the different categories of absorption discussed thus far in this chapter. In physical absorption, no reaction occurs. One example of

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physical absorption is the absorption of CO2 in water [6]. For reactive absorption, either a reversible or irreversible reaction can be used to increase the absorbed molar flow of a target component from the gas into the liquid phase. Reversible reactions, for example, reactive CO2 absorption using amines, are favored when high-volume gas flows must be treated and no valuable reaction products can be generated based on the gas solvent reaction. As a result, the recycling of the solvent allows more economical and less waste producing processes. Irreversible reactions can be used especially when the solvent is extremely inexpensive and/or a valuable product can be formed by the gas solvent reaction. A well-known example of such an absorption process is the production of sulfuric acid by the reaction of SO3 with water. Tab. 6.1: Summary of the categories of absorption processes based on the reaction type. Absorption

Physical

Reactive

Reaction

None

Reversible–irreversible

Example

CO with HO

CO with amines SO with water

Desorption is the process of mass transfer from a dissolved component in the solvent to the gas stream, which is the reverse of absorption and is used to regenerate the solvent in a continuous absorption–desorption closed-loop process. Compared with physical absorption processes, it is more challenging to regenerate the solvent using continuous reactive absorption processes [5]. Desorption is often the cost-determining step, especially in large-scale CO2 separation processes. In general, four methods to desorb a dissolved component are used [7]: – increase the temperature in the system and reboil the solvent – reduce the pressure in the system (if necessary, reduce to a vacuum) – strip with an inert gas stream or steam – precipitate the reaction products Furthermore, a combination of these four methods is also possible. Regeneration with reduced pressure compared to the absorption operating pressure is favorable if the absorption process is conducted at high pressures [4]. Stripping and pressure reduction are primarily used for temperature-sensitive solvents or for temperaturesensitive components that are dissolved in the solvent, such as (bio-)catalysts. Depending on the desorption process, stripping with an inert gas is often more economical than temperature-based regeneration. This approach is chosen when the solvent has a very low boiling point such that a temperature increase would lead to high solvent losses [8]. Another method is the chemical reaction between the absorbed component and an auxiliary substance, in which the reaction product is precipitated and can be easily removed from the process. However, the handling of solids in the process must be carefully evaluated for this application.

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6.2 Modeling A model-based absorption column design is common in industry. The use of more detailed and reliable models results in reduced experimental effort required to upscale absorption columns and design them for industrial applications. Therefore, an extensive understanding of both mass and heat transfer is necessary. In general, modeling approaches used for reactive distillation (see Chapter 4) have also been proposed and used (see Fig. 6.4) that incorporate equilibrium-stage models (Section 6.2.1), mass transfer efficiencies (see HTU-NTU model in Section 6.2.1), and rate-based models (Section 6.2.1). Rate-based models involve an axial discretization of the absorber. The reaction rate as well as mass transfer and other relevant parameters are calculated for each discretization element. For reactive absorption processes, the reaction can also be integrated using different modeling approaches depending on the available data and the influence of the reaction process on the absorber’s performance. Hence, in addition to axial discretization, the liquid film is also divided into discrete elements to calculate the film reactions in a detailed manner (Section 6.2.2). The current state of absorption process simulations unites models for thermodynamics and reaction kinetics with absorption equipment that is specific to hydrodynamics and the mass and heat transfer between gas and liquid phases.

Fig. 6.4: Model complexity in absorption column design [9].

6.2.1 Mass transfer This section explains how mass transfer without reaction is modeled for absorption processes, which can be applied to physical absorption processes. This is also the basis for describing reactive absorption processes because they are formulated around the physical solubility of the target component in the liquid, which is

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followed by a reaction of this component (see Section 6.2.2). Mass balances are calculated using concentrations, such as mole fractions of the solute, i, in the gas, yi, and in the liquid phase, xi. Assuming that reactive absorption processes are commonly operated at very low concentrations, it is possible to use molar loading in the gas, Yi, and in the liquid phase, Xi, instead: Xi =

moles of component i in the liquid phase ni xi = = nSolvent 1 − xi moles of solvent

(6:3)

Yi =

moles of component i in the gas phase moles of inert gas

(6:4)

=

ni yi = ninert gas 1 − yi

The absorption column can be divided into vertical segments; both mass and heat balances are solved for each segment. Figure 6.5 shows a separation segment within the absorber, where G ̇ and L ̇ are the inert gas and liquid streams entering and leaving the segment, respectively. The assumption made in Fig. 6.5 is that G ̇ and L ̇ do not change significantly because the transferred molar flow, N ̇ i, is small in comparison to the inert fluid streams.

Fig. 6.5: Schematic of a single segment in an absorber.

The component balance for segment n that is shown in Fig. 6.5 can be mathematically described as follows: Yi, n + 1 G_ + Xi, n − 1 L_ = Xi, n L_ + Yi, n G_

(6:5)

Equilibrium-stage models Equilibrium-stage models are based on the assumption of a theoretical plate for these segments (comparable to those described earlier for distillation). The concept of a theoretical stage is used when the three following assumptions are fulfilled: – complete mixing of the liquid in the segment – no entrainment of droplets with the gas stream to the next segment – phase equilibrium of the streams leaving the segment

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For practical applications of absorbers, these assumptions are rarely fulfilled, meaning that the actual mass transfer is lower than that predicted by equilibrium-stage models. However, the application of equilibrium models in absorber design provides a first estimate to determine whether a reasonable amount of solvent is sufficient for a certain separation task. For a more detailed discussion on equilibrium-stage models for reactive separation, refer to Chapter 4. Moreover, the application of an equilibrium model as an initial evaluation of absorption processes is described in Section 6.3.2 based on the McCabe–Thiele plot, which is a graphical method to design absorption processes.

HTU–NTU model The HTU–NTU model was developed to describe the absorption efficiency in an absorption column, which assists in identifying the necessary column height for a separation task, assuming that mass transfer is limited and equilibrium is not reached. The model is based on the assumption that the height of a column H can be expressed as the product of the height of the transfer unit, HTU, and the number of transfer units, NTU [10]: H = HTU · NTU

(6:6)

Furthermore, NTUOG is the integrated driving force of the mole fraction of component i in the entering (1) and leaving (2) gas streams: Zyi, 2 NTUOG, i = yi, 1

dyi yi − y*i

(6:7)

Depending on the absorption processes, the integrated driving force in eq. (6.7) can be reformulated for physical absorption assuming a linear equilibrium and operating line: 0
1 yi, 1 − y*i, 1 yi, 1 − yi, 2    · ln@ A (6:8) NTUOG =  yi, 1 − y*i, 1 − yi, 2 − y*i, 2 yi, 1 − y*i, 2 where yi is the equilibrium mole fraction of component i in the gas phase. If yi is equal to, then the maximum possible amount of component i is absorbed. For reactive absorption processes, the following simplification of eq. (6.7) is reasonable when the concentration of component i in the liquid bulk phase is negligible due to a chemical reaction in the liquid film [11]:

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yi, 1 NTUOG = ln yi, 2

 (6:9)

HTU can be determined based on eq. (6.6).

Rate-based models using film theory The driving force for molecular diffusion is a concentration gradient, which must be balanced. Therefore, diffusion describes the flux of at least one component A along a concentration gradient, and the basic equation for a binary mixture of components A and B can be written following Fick’s first law [12]: JA = − DAB ·

∂c ∂z

(6:10)

Diffusion ceases as soon as the concentration becomes spatially uniform. In reactive absorption, two different mass transfer concepts can be found: convective mass transfer appears in the bulk gas and liquid phases, whereas diffusion controls the mass transfer through the interface between the gas and liquid phases. In general, two basic concepts can be used to describe the mass transfer: – Film theory assumes a stagnant film on the gas-liquid interface, whereas the bulk liquid phase is assumed to be ideally mixed with no variability in the concentration [13]. Thermodynamic equilibrium is reached at the gas-liquid interface. – Surface renewable theory assumes that the elements at the gas-liquid interface are periodically replaced by liquid elements from the bulk phase. While the liquid element is exposed to the gas at the interface, it absorbs the gaseous component. Based on this theory, Danckwerts developed the penetration theory [13]. The focus in the following is on film theory, which was first developed by Lewis and Whitman and describes the existence of a layer at the interphase between the liquid and gas phases, which has a thickness of δ [14]. It is assumed that within the bulk liquid phase, the concentration of component i is constant, whereas within the film, a certain concentration profile is present. The mass transfer coefficient for the liquid side, kL, can be described as the ratio between the diffusion coefficient, Di,B, of a component i in liquid component B and the film thickness on the liquid side of the film [15]. The mass transfer coefficients discussed below always refer to the transferred component i; the index is not included in the notation for clarity: kL

Di, B δ

(6:11)

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Danckwerts enhanced this model by assuming that there is an equivalent film on the gas side of the gas-liquid interphase as shown in Fig. 6.6, which is the basis for two-film theory [12].

Fig. 6.6: Two-film theory concentration profiles for component i [12].

The overall mass transfer resistance between the gas and liquid phase can be defined using the following equations: 1 1 He = + KG aeff KG aeff KL aeff 1 1 1 = + KL aeff KL aeff He · KG aeff

(6:12)

where KGa and KLa are the volumetric mass transfer coefficients on the gas and liquid sides, respectively. Their reciprocal values can be described as the sum of the mass transfer resistances on both sides of the gas-liquid interface. The interface itself is infinitesimally small compared to the films; thus, it can be assumed that the interface does not add mass transfer resistance (see eq. (6.12)) [12]. The mass transfer coefficients can either be determined experimentally or based on correlations. Because correlations are mainly based on experimental data in the literature, an accurate parameter determination is necessary in terms of experimental setup, procedures, and calculation pathways. The VDI guideline 2761 describes how to measure mass transfer in packed columns [16].

6.2.2 Mass transfer and reaction This section describes how the reaction is implemented in the modeling of reactive absorption processes. In general, different reaction regimes can be distinguished, which is shown below for a second-order reaction with reactants A and B, where A is the component transferred from the gas phase to the liquid phase (Fig. 6.7).

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Fig. 6.7: Different reaction regimes for liquid film reactions [17].

Different reaction models with varying modeling depths have been presented in the literature (as shown in Fig. 6.4) and are discussed in the following.

Enhancement factor and Hatta number Enhancement factors describe the ratio between the mass transfer with reaction and without reaction: E=

Flux with reaction Flux without reaction

(6:13)

The application of enhancement factors commonly refers to simplified reaction systems and mainly accounts for one reaction (first or second order). It is assumed that the reaction in the film does not influence the bulk phase composition, where reaction equilibrium is assumed. Furthermore, the Hatta number can be used to classify the absorption. Based on this dimensionless number, the reaction can be characterized as being limited by either the reaction rate or the mass transfer: Ha =

Reaction rate in the film Diffusion through the film

(6:14)

The enhancement factor of the instantaneous reaction, Ei, can be determined as follows for the film model: Ei = 1 +

DB, L cB∞ · DA, L Z.cAI

(6:15)

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Table 6.2 shows the classification of irreversible second-order reactions based on the Hatta number. Tab. 6.2: Classification of irreversible second-order reactions into reaction regimes [17]. Hatta number

Enhancement factor

Reaction regime

. < Ha < .

E=

Slow reaction

. < Ha < ; Ei > 

E = ( + Ha).

Intermediate reaction

 < Ha < .Ei

E = Ha   1 1 − 1=Ei 1 2=3 + 3=2 = 3=2 E Ha E

Fast reaction of pseudo-first order

 < Ha; .Ei < Ha < Ei

Fast reaction

Ha > Ei

E = Ei

Instantaneous reaction

Ha = ∞

E=∞

Marginal case: instantaneous reaction

For an irreversible, fast, pseudo-first-order reaction, the assumption that the enhancement factor is equal to the Hatta number is valid [12]: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DCO2 · kOH − cOH − (6:16) E = Ha = kL One example of such a reaction is the chemical absorption of CO2 in aqueous NaOH, which is used to determine the effective interfacial area, aeff. The enhancement factor can be directly integrated into the film model (eq. (6.12)), leading to the following description of the mass transfer coefficients: 1 1 H = + KG a kG a E · kL a 1 1 1 = + KL a E · kL a He · kG a

(6:17)

Film discretization A solid representation of film concentration profiles permits a more detailed analysis of the mass transfer acceleration due to the chemical reactions in the film, which results in a sufficient accuracy of the model. Hence, it is common to subdivide the liquid film into balance segments for the detailed modeling of reactive absorption. In these segments, simultaneous reactions and mass transfer are considered. As a result, a nonlinear or curvilinear film profile that results from the reaction can be calculated (Fig. 6.8).

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Fig. 6.8: Two-film theory concentration profiles for reactive absorption of component i with film discretization. Profile 1 displays a reaction in the bulk phase, whereas profile 2 shows a reaction in the liquid film [12].

Several studies have put forth different approaches to realize this film discretization. In addition to the equidistant distribution of segments, a weighted segment size distribution is also possible, which is dependent on the reaction rate [18].

6.2.3 Hydrodynamics It is essential that the experimental mass transfer parameters are determined in regions with both gas and liquid flows, in which the mass transfer parameters are independent of the hydrodynamics in the column. To compare the experimental results in different column dimensions, the gas and liquid volume flows are normalized. The liquid volume flow relative to the cross-sectional area of the column is called the specific liquid load [19]: uL =

V_ L . Ac

(6:18)

Due to the high temperature dependency of the gas phase, the gas volume flow is not only normalized by the cross-sectional area of the column but also by the density of the gas, which results in the gas load factor, which is commonly called the F-factor FV [19]: FV =

V_ G pffiffiffiffiffi · ρG Ac

(6:19)

The fluid dynamics of a column can be characterized based on these values. Important parameters include the liquid holdup and the dry and wet pressure drops. These parameters define the loading and flooding range of a column.

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335

Liquid holdup, hL, defines the amount of liquid within the packing during operation, which can be divided into the static holdup that occurs due to the adhesion force of the packing and the dynamic holdup, which is dependent on the liquid volume flow. When a column is operated below the loading point, a constant liquid holdup in the column is present, which is independent of the F-factor, FV, and only depends on the liquid load. Beyond the loading point, the liquid holdup increases with the gas load up to the flooding point, where it reaches its maximum value. The dry pressure drop represents the pressure drop within a packed column when gas is flowing without any liquid contact. The wet pressure drop represents the pressure drop within a packed column in which the gas and liquid phases are in contact. Below the loading point, the slopes of the dry and wet pressure drop are parallel because there is no interference between the liquid and gas streams. Above the loading point, the liquid holdup represents an additional resistance for the gas flow. Therefore, the slope of the wet pressure drop beyond the loading point is larger. The region where the slope is close to vertical is called the flooding range. In this range, the gas flow is sufficiently high such that liquid cannot flow down the column and spills on top of the packing. Mass transfer measurements are often collected below the loading point, that is, at 65% of the F-factor, FV, beyond which flooding occurs [19]. A detailed description of determining the hydrodynamics in packed columns can be found elsewhere [19]. Based on the measured hydrodynamics correlations can be used to model the hydrodynamics in an absorber/desorber. The accuracy of the results depends on the right choice of correlations [20].

6.3 Conceptual process design The design of a reactive absorption process can be classified into four phases: feasibility, conceptual process design, detailed engineering, and construction. Based on the defined separation problem, the specifications of the inlet streams, the desired product purity or recovery rate, the potential operating window, and the list of potential solvents or stripping agents are evaluated and determined. Hence, the 183 feasibility of using absorption/desorption is analyzed using approximate calculations or simulations and experimental tests. Within conceptual process design, the dimensions of the equipment and the configuration, as well as the utilities, are determined based on both the mass and energy balances. In detailed engineering applications, all equipment-related design parameters must be determined, including the actual absorption equipment, liquid distributors, internals, gas distributors, heat exchangers, and pumps, before the absorption and desorption columns and the periphery can be constructed in the final phase. The model complexity and corresponding model accuracy (see Section 6.2) increase

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within the phases. The focus of this subchapter is on determining a set of column design parameters within the conceptual process design phase using simple models.

6.3.1 Design considerations The column height determines the contact length between the gas and liquid phases and is defined by the number of separation stages necessary to meet the separation task. By building taller absorber columns, the gas and liquid streams exhibit more intense contact; thus, more mass transfer can occur, assuming that reaction equilibrium is not reached. The diameter of the absorber column is primarily determined by the amount of crude gas that should be handled and the necessary lean solvent volume flow that is used to fulfill a given separation task. The solvent volume flow is primarily determined by the cyclic capacity of the solvent. The cyclic capacity of the solvent determines the preloading of the lean solvent leaving the desorber and entering the absorber, resulting in a reduced driving force compared to the use of fresh solvent and defining the maximum absorption efficiency of a single stage.

6.3.2 McCabe–Thiele plot For the conceptual design of absorber columns, the application of equilibriumstage models (Section 6.2.1) provides a first impression of the absorber design. The McCabe–Thiele method is a widely applied graphical method to design absorption processes based on thermodynamic equilibrium [21]. The McCabe– Thiele plot represents gas and liquid compositions in a separation process (Fig. 6.9) for a countercurrent absorber. The circles on the equilibrium line represent the equilibrium composition of the gas and liquid streams leaving one stage, whereas the squares on the operating line represent two parallel streams between the stages. A key assumption for this plot is that the leaving streams of each stage have reached thermodynamic equilibrium. The operating line in absorption processes can also be described mathematically by rewriting eq. (6.5) in the following way: Yn = ðXn + 1 − Xn Þ

L_ + Yn − 1 G_

(6:20)

A description of the absorption process in a McCabe–Thiele diagram is represented via the following steps:

6 Reactive absorption

337

Fig. 6.9: McCabe–Thiele plot for reactive absorption.

– Equilibrium data for the chemical system are measured or can be found in the literature and plotted on an X–Y graph. – The gas and liquid streams and three molar loadings are known; the fourth can be calculated using the mass balance in eq. (6.5). Moreover, the operating line can be constructed as follows: – The liquid-to-gas ratio L̇/Ġ is the slope of the operating line. – One point on the operating line is fixed, such as the inlet molar loadings of the gas and liquid streams. – Another molar loading is the target value, for example, the minimum concentration of a gaseous component in the gas outlet Y1. – The number of necessary separation stages can be determined by stage construction, in which the lowest stage number describes the top of the column and the highest describes the bottom of the column. The operating line for absorption processes in a McCabe–Thiele plot is above the equilibrium line because the mass transfer of the target component, i, occurs from the gas phase to the liquid phase. For desorption processes, the mass transfer is in the opposite direction; thus, the operating line is below the equilibrium line (see Fig. 6.10). Based on the McCabe–Thiele plot, the minimum solvent amount can be derived; the incorporation of solvent recycling should be considered at this point in the design process. This aspect is discussed next.

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Fig. 6.10: Operating and equilibrium lines for (a) absorption and (b) desorption processes.

Minimum solvent rate The minimum solvent rate can be determined assuming that the operating line and the equilibrium line intersect at the lowest gas and liquid loadings as shown in Fig. 6.11, which occurs at the bottom of the column. More specifically, the liquid stream leaving the column and the gas stream are in thermodynamic equilibrium; the maximum amount of solute has been absorbed, which is equivalent to assuming an infinitely tall absorber, requiring an infinite number of equilibrium stages.

Fig. 6.11: Maximum absorption efficiency defined by the minimum amount of solvent.

The mass balance described in Section 4.2 results in the following equation for the molar flow:
*  − Xin (6:21) n_ i = G_ · ðYin − Yout Þ = L_ min · Xout which results in the following equation for the minimum solvent rate:

6 Reactive absorption

ðYin − Yout Þ L_ min = G_ · * ðXout − Xout Þ

339

(6:22)

Generally, the actual liquid molar flow should be 30–60% higher than the minimum solvent molar flow: L_ = 1.3 − 1.6 · L_ min

(6:23)

Solvent recycling One option to reduce the amount of energy needed for a continuous absorption process is to split the solvent stream leaving the absorber column. One portion of this stream proceeds to the solvent regeneration process, whereas the other portion is directly recycled as shown in Fig. 6.12, resulting in a higher preloading of the solvent entering the column.

Fig. 6.12: Flow diagram of an absorption process with recycled solvent.

The application of recycled solvent to the absorber column results in an increase in the solvent loading of the ingoing liquid stream, Xin, which means that the operating line is steeper than for absorption processes without recycled solvent (see Fig. 6.13). A higher solvent preloading results in a higher stage number. The maximum solvent loading, Xin,max, is defined by the thermodynamic equilibrium, which means that no additional absorption can occur.

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6.3.3 Side effects In the previous chapters, a simplified reactive absorption process was analyzed for the mass balance of a single component. In reality, several side effects in addition to the absorption of the target component can occur, resulting in a more complex absorption process and reducing the absorption efficiency:

Fig. 6.13: McCabe–Thiele plot for absorption with recycled solvent.

1. 2. 3.

The solvent is volatile and is consequently soluble in the gas phase. The carrier gas components are soluble in the solvent, which means multicomponent mass transfer is encountered. Temperature changes over the absorber length result in a temperature profile.

Volatile solvents Deviations from the simplified absorption characteristics discussed above can occur due to the usage of volatile solvents. When the gas stream is not presaturated with the solvent, mass transfer from the liquid phase to the gas phase occurs. Hence, the operating line in the McCabe–Thiele plot is curved (see Fig. 6.14). The amount of solvent, nsolvent, is not constant in this case; instead, it is a function of the column height (nsolvent = f(z)). The amount of solvent decreases from the solvent inlet to the solvent outlet; thus, the loading Xout increases significantly. Therefore, reaction (6.3) can be rewritten as

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Fig. 6.14: McCabe–Thiele plot for absorption with volatile solvents.

Xi =

ni nsolvent ðzÞ

(6:24)

Carrier gas that is soluble in the solvent Another possible deviation from simplified absorption processes is the solubility of the inert gas stream in the solvent. Hence, the loading of the target component in the outlet gas stream is significantly higher because the amount of carrier gas, which is not inert, decreases over the column height (ncarrier gas = f(z)). Hence, eq. (6.4) can be rewritten as follows: Yi =

ni ncarrier gas ðzÞ

(6:25)

Thus, the selectivity of the solvent toward the target component decreases; that is, the affinity of the solvent towards the target component, i, decreases. Figure 6.15 shows the change in the operating line resulting from an enhanced gas phase loading at the column outlet Yout.

Nonisothermal absorption Due to the enthalpy of condensation for the absorbed component or the enthalpy of the solution and because of exothermal reactions, a temperature gradient within the column is present. Furthermore, a temperature difference

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Fig. 6.15: McCabe–Thiele plot for absorption in which the inert gas stream is soluble in the solvent.

between the gas and liquid streams results in a temperature profile over the column height. Because the phase equilibrium and the Henry coefficient are dependent on temperature (He = f(T)), different equilibrium lines must be considered for different stages. Figure 6.16 shows that the real equilibrium line can be described by varying the temperature over the column height.

Fig. 6.16: McCabe–Thiele plot for nonisothermal absorption.

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6.4 Applications For industrial applications, selecting the appropriate solvent and equipment for a given separation task must be conducted; a short introduction is provided in the following section. Furthermore, an overview of industrial absorption processes is given; a few of these processes are discussed in detail in Section 6.5.

6.4.1 Solvent selection The selection of a suitable solvent for a given separation task is highly relevant to the economic and ecological feasibility of the absorption process. Therefore, performance criteria and economic and ecological properties must be evaluated. Separation performance criteria include the solubility of the solute in the solvent or the selectivity of the solvent. Physical and chemical data for the solvent must be analyzed because they determine the absorption efficiency and the handling of the solvent and column design. A low volatility, low ignition point, and low-to-moderate viscosity are preferred. Economically, the price of the solvent, possible solvent losses, and oxidative or thermal degradation must be considered. Additionally, the absorption enthalpy of the solvent is essential, which is a measure for the energy that is needed to regenerate the solvent. To reasonably handle the solvent in the process, highly corrosive and low-safety solvents should be avoided. The theoretical capacity of a solvent is determined by the molarity of the reactive species and the stoichiometry of the reaction. The cyclic capacity of the solvent is more important for the selection of a solvent in continuous absorption processes because the complete regeneration of the solvent is difficult, as discussed earlier. Figure 6.17 summarizes the most important measures for solvent selection.

Fig. 6.17: Categories of performance criteria for solvents in reactive absorption processes.

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6.4.2 Type of absorbers For the industrial application of absorption processes, the absorption equipment must be selected carefully. Criteria for this selection are: – capacity of the equipment, which is dependent on the gas and liquid volume flows – required operating window (such as the temperature and pressure region) – required gas and liquid holdup and contact time – physical and chemical properties of the system (e.g., viscosity and surface tension) – safety requirements (e.g., corrosive and hazardous materials) Tab. 6.3: Categories of absorbers divided by the characteristics of the gas and liquid phases [8]. Liquid phase Gas phase Scheme

Continuous

Continuous

Disperse

Continuous

Disperse

Continuous

Absorber

Packed column

Plate column Bubble column Packed bubble column

Spray columns

Absorbers can be categorized based on their characteristics in the continuous and disperse phases, as shown in Tab. 6.3 [8]. In industry, the most widely applied absorbers are packed columns due to their high performance and relatively easy handling. The packing in such columns provides a large gas-liquid interface that is dependent on the type of packing. In general, there are two types of packing that are commonly used: structured packing and random packing. Structured packings offer larger interfaces, whereas random packings offer a larger portfolio of materials because they are produced with metal, plastic, ceramic, or graphite. In addition to the packing, the column is also equipped with several nonseparation efficient internals:

6 Reactive absorption

– – – –

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gas and liquid distributors grids to hold the packing wall wipers demisters

Please see the description of column internals in the chapter on reactive distillation (see Chapter 4). The necessary contact area between the gas and liquid phases for a given separation task determines the selected column internals and the designated sizes of the internals. For the choice of column internals, various parameters must be considered: – pressure drop – chemical properties of the gas and liquid streams – impurities of the gas and liquid streams – gas and liquid throughputs – foaming – corrosion In general, trays are advantageous regarding complex column configurations, for example, intercooling, and they exhibit lower maldistribution than packed columns. Moreover, trays exhibit higher pressure drops than packed columns. Structured packing material generally has a lower pressure drop per mass transfer efficiency [22]. Low sensitivity to blockage due to fouling is also important because this is a major cause of malfunction in packed columns [23]. Random packings are significantly cheaper and can be used for foaming systems or components that might cause fouling. Detailed comparisons between packings used for certain applications can be found in the literature [24]. The high energy consumption as well as the often compliance relevant gas purification makes a reliable absorption/desorption process essential. Therefore, basic as well as advanced process control is applied in industrial applications [25]. This supports the operators to make the absorber run stable. To develop an advanced process control, reliable models are essential. This also helps to evaluate the column performance in failure modes. Assuming an absorption column in operation shows malfunction and does not reach the targeted purities anymore there are several questions that should be asked during troubleshooting: – Is there a likelihood of polymerization or any other kind of blockage either in the packing or in the distributors that would reduce the contact are between gas and liquid? – Are the distributors and the packing still in place as planned (e.g., if the liquid distributor is not in balance, there might be a loss of contact area at the top of the column due to a bad distribution)? – Has there been a significant change in temperatures of the inlet stream?

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These are just a few examples on where to start searching for the failure mode, further ideas can be found elsewhere for example [19].

6.4.3 Examples of applications Absorption, on a purely physical basis or as an integration of reaction and physical absorption, is one of the most mature separation processes and has already been applied in the chemical industry for several decades. Reactive absorption processes are integrated into chemical processes for three different reasons: purification, production, or reactant recovery. Table 6.4 provides a brief overview of different applications of reactive absorption in industrial activities. The process of CO2 separation from a process gas stream is discussed in more detail in Section 6.5.1.

Tab. 6.4: Categories of reactive absorbers and desorbers divided according to the characteristics of the gas and liquid phases [26]. Application

Examples

Example solvent

Absorbate

Nitric acid [] Sulfuric acid [] Hydrochloric acid []

HO HSO (+ HO) HO

NO SO HCl CHO

Ethylene oxide

Water

Carbon dioxide Sulfur oxides Nitrous oxides Hydrogen sulfide Hydrochloric acid

Amines Amines Amines Amines Limestone

CO SOx NOx HS HCl

Glycerol

HO

Ethanolamine/cuprous nitrate

Olefin

Production of chemicals Acids

Gas treatment [] Removal of toxic components

Gas drying [] Water Separation of substances Olefin/paraffin []

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Fig. 6.18: Distribution of anthropogenic greenhouse gas emissions in 2007 in carbon dioxide equivalents [30].

6.5 Detailed examples The following section provides more detailed information regarding the use of reactive absorption in specific processes. Therefore, the separation of CO2 from a flue gas stream, the production of nitric acid, and biogas upgradation are discussed.

6.5.1 Example 1: separation of CO2 from a flue gas stream One approach to reduce CO2 emissions from fossil-fueled power plants is postcombustion capture, which means that CO2 is captured before it enters the atmosphere. The standard technology for gas purification in terms of carbon capture is reactive absorption. Within the past few decades, several pilot plants have been installed to scrub CO2 from flue gas streams in power plants to verify the potential of carbon capture and storage. The investigated and applied solvents for the chemical absorption of CO2 can be classified into three classes of aqueous solutions: amines, alkali carbonates, and alkali hydroxides. Although alkali hydroxides have a high reaction rate towards CO2, the reaction is irreversible, forming stable salts. As a result, alkali hydroxides are not applicable for the continuous removal of CO2 from gas streams with high CO2 contents. Additionally, various special solvents, such as ionic liquids, have been investigated for the purpose of CO2 capture [28, 31]. A big challenge in applying reactive absorption for CO2 capture in large scale is the energy intensity of the solvent regeneration. Therefore, in literature, chemical absorption processes connected to other unit operations, so called hybrid processes have been evaluated [32] to increase the economic potential of such processes. Therefore, chemical absorption can be coupled to membranes, cryogenics, or adsorption steps to either reduce the energy intensity in the solvent recovery (desorption) or support the actual separation task by, for example, additional increase of the purity of the flue. The different unit operations can outperform the others in certain operating windows. Therefore, a careful evaluation of a beneficial hybrid system must be conducted. Detailed information can be found in literature [32, 44], but large-scale

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application of these processes is still limited and information is primarily based on lab scale experiments or feasibility studies [32]. Besides hybrid processes, literature shows examples to modify the solvent system so that the desorption process is optimized, like adding a catalyst that favors CO2 desorption [33]. Also, the application of biphasic solvent system has been investigated which allow the separation of a CO2 rich phase, which reduces the volume stream of solvent that needs to be regenerated [34, 35].

Alkanolamines as reactive solvents The capability of alkanolamines for CO2 capture has been verified in several studies. Alkanolamines are ammonia derivatives in which the hydrogen atoms are replaced by an alkanol group (CnH2n–OH). Some commercially relevant amines for CO2 capture include monoethanolamine, diethanolamine (DEA), and methyldiethanolamine [28]. In general, amines can be divided into three classes that depend on the hydrogen atom bonded to the nitrogen atom. The physical and chemical properties vary according to the amine class, as shown in Tab. 6.5. A detailed description of the reaction mechanism for CO2 with the solvent can be found in the literature [28]. However, the general reaction for CO2 absorption with alkanolamine and the reaction of CO2 with water and its ions is the protonation of alkanolamine [28]: R1 R2 R3 NHx + H + > R1 R2 R3 NHx++ 1

(6:26)

For primary and secondary amines, the formation of carbamate also occurs: R1 R2 NHx + CO2 > R1 R2 NHx COO − + H +

(6:27)

Tab. 6.5: Classification of amines for reactive absorption of CO2 and the corresponding influence on the physical and chemical properties (bar color intensity: black = high, grey = low) [28].

Example Number of H atoms Alkalinity Reaction rate Loading capacity

Primary amines MEA 2

Secondary amines DEA 1

Tertiary amines MDEA 0

≈0.5mol CO2/mol amine

≈1.0mol CO2/mol amine

12–32%

30–55%

Energy amount for regeneration Concentration range

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Carbamate is a very stable molecule; the hydrolysis to bicarbonate is very slow, which is the reason for the low capacity of primary amines because it is the predominant reaction for these amines. Ternary amines do not directly react with CO2 [28]. Table 6.6 shows industrially relevant amine-based reactive absorption solvents. Tab. 6.6: Industrially relevant amine-blended reactive absorption solvents [28]. Patented process

Licensor

aMDEA® Flexsorb® Sulfinol® ADIP-X® UCARSOL™ Econamine™

BASF SE Exxon Shell Shell DOW Fluor

Alkali carbonates as reactive solvents Processes based on alkali carbonates have achieved economically beneficial reaction rates due to the introduction of a catalyst in conventional processes. The Activated Benfield Process is one such example, which uses DEA to enhance the reaction rate of aqueous solutions of K2CO3 with CO2 [28]. The Flexsorb HP Process from Exxon uses sterically hindered amines to catalyze the reactive CO2 absorption of a K2CO3based absorption process [28]. Amino acids are also often used to enhance the reaction rate of chemical absorption. Shen et al. showed that the addition of 0–5 wt.% arginine to a K2CO3 solution led to an increase of CO2 uptake by a factor of 2.0–3.0; the added arginine also improved the desorption rate [36]. Table 6.7 shows industrially relevant K2CO3-based solvents for reactive CO2 absorption. Tab. 6.7: K2CO3 reactive absorption solvents [28]. Patented process ®

Flexsorb HP Giammarco–Vetrocoke process Benfield Vacasulf® Catacarb®

Licensor Exxon Giammarco–Vetrocoke UOP Krupp Uhde Eickmeyer and Associates

Typically, the CO2 capture unit is in direct downstream of the CO2 producing process of the flue gas to reduce the emissions. But there are also applications to reduce the already emitted CO2 concentration by direct air capture. In 2021, the

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to date biggest climate positive facility to capture CO2 from is built in Iceland and will capture up to 4,000 tons of CO2 per year [37].

Storage and utilization The separation of CO2 is only one portion of the solution to the increased emissions. Reducing CO2 emissions is strongly connected to the next step, which addresses the following question: what should be done with the separated CO2? Here, two pathways can be distinguished: – storage of the separated CO2 – utilization of the separated CO2 to form valuable products The storage of CO2 comprises geological sequestration, in which CO2 is pressed into sedimentary formations. Potential sinks include – saline aquifers – empty gas and oil fields – coalbeds Furthermore, CO2 can be used for natural gas and oil recovery, in which it is pressed into gas and oil fields. The criteria to evaluate storage sinks include their capacity, requiring storage for several Gt of CO2, and both their lifetime and stability [38]. Utilization is the application of CO2 as a reactant for further processes. Various studies have been conducted to find applications that can consume the separated CO2. Such applications would have to be large-scale activities to utilize the CO2 separated via CO2 capture from fossil-fueled power plants. The potential synthesis routes include [38] – reaction of CO2 and propylene glycol – CO2 reforming of CH4 – reaction of CO2 with ethane and propane – CO2 hydrogenation to methanol – synthesis of dimethyl carbonate from CO2 and methanol – plastics/polyurethane

6.5.2 Example 2: production of nitric acid Nitric acid is well known for its use in the production of fertilizers via reaction with ammonia to yield ammonium nitrate. Furthermore, it is also used as a chemical in metallurgy and as a reagent for explosives [27].

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351

Nitric acid is produced by the so-called Ostwald process, which can be divided into three steps, where the oxygen in the reactions is derived from the atmosphere [27]: 1. Catalytic combustion of ammonia 4NH3 + 5O2 ! 4NO + 6H2 O 2.

Oxidation of nitrogen monoxide 2NO + O2 > N2 O4

3.

(6:28)

(6:29)

Reactive absorption of nitrogen oxide 3NO2 + H2 O ! 2HNO3 + NO

(6:30)

Reactive absorption of NO2 in water is highly exothermic; constant cooling is necessary. Chemical absorption is commonly performed in plate columns [27]. In general, two process variations are used: – mono-pressure process, in which combustion (1.) and absorption (3.) occur at the same pressure – dual-pressure process, in which absorption (3.) occurs at a higher pressure than combustion (1.) The reactive absorption step includes up to 13 primary relevant reactions that occur simultaneously, while as many as 40 reactions have been investigated in previous studies including side and further reactions [39, 40]. For a better understanding, this process was described by Hoftyzer and Kwanten based on two-film theory, which is shown in Fig. 6.19 [41]. The modeling of this process is very complex because there are many chemical compounds being absorbed in addition to NO2, such as NO, N2O3, and N2O4, and multicomponent mass transfer must be considered [14].

Fig. 6.19: Mass transfer in chemical absorption for nitric acid production [39].

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6.5.3 Example 3: biogas upgrading In biogas production, biomass is fermented by anaerobic bacteria to methane and several by-products, such as CO2 and H2S. Based on the biomass type, for example, waste or landfill, the concentrations in the raw biogas can vary. Therefore, biogas upgrading is very important for using methane in the gas grid. Gas permeation and (reactive) absorption are the most applied technologies for biogas upgrading. Absorption processes have been shown to be especially feasible for this process because they exhibit a high selectivity toward different impurities, such as CO2 andH2S. The most well-known applications of absorption in biogas upgradation include high-pressure water scrubbing and the use of different amines. Due to the difference in technologies that are applicable for biogas upgradation, an evaluation of potential process designs is necessary. Figure 6.20 shows one arrangement of technologies for the biogas upgradation process, in which adsorption, absorption and cryogenic distillation are considered. This process is based on the knowledge-based approach outlined by Barnicki et al. [42].

Fig. 6.20: Possible splits using different unit operations for biogas upgradation [42].

Therefore, the composition of landfill-based biogas was used as the basis for this setup, which is shown in Tab. 6.8. Barnicki et al. summarized various heuristics for gas separation processes. The following is a list of those related to absorption processes [42]: – Physical absorption is a reasonable separation method for a selectivity >3 if the goal of the process is product enrichment. For a sharp split, it should be >4. – Chemical absorption is advantageous for low partial pressures, especially when a partial or a high-capacity solvent is necessary.

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– Chemical absorption should also be considered if the target species contains acid-base functional groups. – Glycol absorption should be considered for large-scale desiccation operations. Tab. 6.8: Composition of landfill biogas [42]. Component

xi (mol mol−)

Methane Carbon dioxide Nitrogen Oxygen Hydrogen sulfide Aromatics (benzene) Halohydrocarbons (chloroethane)

. . . . . . .

First, ranked property data were evaluated to define possible separation points. The chemical family, nominal kinetic diameter, equilibrium adsorption loading and relative volatility were evaluated. Based on this first possible process configuration, a detailed economic analysis must be conducted [42]. For this process, the potential of decentralization at different biogas production locations is high, while the dependency on the variability in the raw gas composition makes a highly flexible process beneficial. Hence, modularization of the gas separation process is worth evaluating. A potential technology for this purpose is the so-called membrane contactor, which can be used in membrane absorption. A porous hydrophobic membrane separates the gas and liquid phases and has a defined interfacial area where mass transfer occurs.

6.6 Take-home messages – Absorption processes can be divided into physical and reactive absorption. – Physical absorption is based on the solubility of a gaseous component in a liquid solvent. – An integrated reaction can be used to maintain the concentration difference as a driving force because it consumes the target component in the liquid phase. – A combined operating window of reaction and solubility must be identified for an optimal process. – Standardized mass transfer measurements to determine the mass transfer parameters applied in rigorous models are essential. – In industrial applications, the most used absorbers are packed columns due to their high performance and relatively easy handling and design.

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– Equilibrium-stage models do not necessarily meet the needs for a reasonable conceptual design, although they provide a first estimate of a technology’s potential. – The application of rate-based models for a detailed column design is common. – Side effects, such as the solvent being soluble in the gas phase, the inert gas being soluble in the solvent, and nonisothermal absorption, must be considered. – The selection of a suitable solvent for a given separation task is not only defined by its absorption properties (absorption rate and capacity) but also by its handling characteristics, such as toxicity, degradation of the solvent, and volatility.

6.7 Quiz Question 1. True or false: absorption processes can be divided into physical and reactive absorption. Question 2. Which parameter describes the solubility of the absorptive in the solvent? □

Hatta number

□

Enhancement factor

□

Henry coefficient

□

Separation factor

Question 3. Absorption processes are used for (multiple answers possible)? □

Product recovery

□

Impurity upgradation

□

Product upgradation

□

Separation of impurities

Question 4. Which solvents are used for chemical CO2 separation in a continuous process? □

Sodium hydroxide

□

Aqueous sodium hydroxide solution

□

Water

□

Aqueous amine solution

Question 5. True or false: reactive absorption processes are feasible for high concentrations of the target component in the gas stream? Question 6. Which properties should a reaction that is applied in closed-loop reactive absorption and desorption processes exhibit? □

Equimolar

□

Fast

□

Reversible

□

Endothermic

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6.8 Exercises 6.8.1 Hydrodynamics and mass transfer efficiency The hydrodynamics in a miniplant absorption column with an inner diameter of 110 mm and a packing height of 2 m are investigated using water and air. The following pressure drop curve is plotted in Fig. 6.21.

Fig. 6.21: Specific pressure drop versus time for a liquid volume flow of 5 L min−1.

Exercise 1. What is the maximum F-factor that should be used for measuring the mass transfer? The following information is given by the chemical data sheets: ρG (T = 293 K) = 1.2 kg m−3. Exercise 2. The set operating point is VG = 40 m3 h−1; VL = 5 L min−1. The column is operated at an ambient temperature of 20 °C. Calculate the F-factor FV and specific liquid load uL for this operating point. Exercise 3. The hydrodynamic experiments are followed by the investigation of the mass transfer of a gaseous component, i, into a liquid solvent. Reactive absorption is used, and the concentration of the component, i, in the liquid bulk phase is negligible due to the reaction in the liquid. Define the molar loading of the gas streams entering and leaving the absorber. Calculate the height of the transfer unit, HTU, and the number of transfer units, NTU, required for this process. Table 6.9 provides experimental measurements obtained for this process.

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Tab. 6.9: Experimental values for the mass transfer experiments. yi,in (mol mol−)

yi,out (mol mol−)

T (K)

.



.

6.8.2 CO2 absorption using an aqueous solution of NaOH The reactive absorption of CO2 in an aqueous solution of NaOH is a fast, pseudofirst-order reaction: CO2 + 2NaOH ! Na2 CO3 + H2 O

(6:31)

Mass transfer measurements were collected in an absorber column with a packing height of H = 3 m and a column diameter of dC = 1 m; a random packing was used. An average gas volume flow of 1.38 m3 s−1 and a temperature of 300.15 K can be assumed. The concentrations determined for the gas and liquid phases are shown in Tab. 6.10. Tab. 6.10: Experimental values for the concentrations in the gas and liquid phase. yCO,in (ppm)

yCO,out (ppm)

cNaOH (kmol m)

cNaCO (kmol m)





.

.

The following correlation can be used to describe the kinetic constant for the reaction of CO2 with hydroxyl ions in aqueous electrolyte solutions [11, 43]: log kOH − = 11.916 −

2, 382 · cNaOH − + 0.29 · cNa2 CO3 T

(6:32)

The diffusivity of CO2 in water can be calculated according to the following relation [11]: log DCO2, L = − 8.1764 +

712.5 259, 100 − T T2

(6:33)

Exercise 4. Determine the kinetic constant for the reaction of CO2. Exercise 5. Determine the diffusion coefficient of CO2 in the water and in the NaOH solution assuming a correction factor of 0.74. Exercise 6. The enhancement factor can be assumed to be 30. Determine the partial mass transfer parameter on the liquid side kL.

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6.9 Solutions Solution (Question 1). True Solution (Question 2). Henry coefficient Solution (Question 3). Product recovery, product upgrading, and separating impurities Solution (Question 4). Aqueous amine solution Solution (Question 5). False Solution (Question 6). Reversible

6.9.1 Reactive absorption Solution (Exercise 1). To answer this question, the specific pressure drop is plotted against gas volume flow in a logarithmic diagram, as shown in Fig. 6.22. Gas volume flow where the flooding region begins:

Fig. 6.22: Logarithmic diagram of the specific pressure drop versus the gas volume flow for a liquid volume flow of 5 L min−1.

V_ G ≈ 60 m3 h − 1 which has an F-factor of

.

VG pffiffiffiffiffiffi . pG = 1.92 Pa0.5 FV, F1. = Ac

see eq. (6.2).

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Because mass transfer experiments are supposed to be conducted below 65% of the flooding point to ensure that nearly constant separation efficiencies are achieved in the column, the following holds: FV, load = 1.25 Pa0.5 Solution (Exercise 2). .

VL m3 = 31.57 2 uL = Ac m .h V_ pffiffiffiffiffiffi . pG = 1.28Pa0.5 FV = Ac Solution (Exercise 3). mol · mol mol YCO2 , out = 0.0098 mol

YCO2 , in = 0.0022

  mol − 1 , mol  −1 mol , · mol

see eq. (6.1); see eq. (6.2).

see eq. (6.4); see eq. (6.4);

NTUCO2 , OG = 0.79

see eq. (6.9);

HTUCO2 , OG = 2.54 m

see eq. (6.6).

6.9.2 CO2 absorption using 1 M NaOH Solution (Exercise 4). kOH − = 14, 419 m3 ðkmol sÞ − 1

see eq. (6.32).

Solution (Exercise 5). DL,2CO = 2.1 × 10 − 9 m2 s − 1 H O

2

DNaOH L, CO2

= 1.55 × 10 − 9 m2 s − 1

see eq. (6.33).

Solution (Exercise 6). For fast, pseudo-first-order reactions, the enhancement factor is equal to the Hatta number [11]: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DL, CO2 · kOH − · cOH − , see eq. (6.16). E = Ha = kL Based on this reaction and the assumption: E = Ha = 30 Equation (4.16) can be solved to determine kL:. KL = 1.57 × 10 − 4 m2 s − 1

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List of symbols Latin letters aeff A c D E FV Ġ He H h Ha HTU J K k kOḢ– L NTU n ni p T u V X x Y y Z z

Effective interfacial area Area Concentration Diffusion coefficient Enhancement factor F-factor Inert gas molar flow Henry coefficient Height Holdup Hatta number Height of a transfer unit Molar flux Overall mass transfer coefficient Mass transfer coefficient Reaction rate constant Inert liquid molar flow Number of transfer units Stage number Molar flow of component i Pressure Temperature Velocity Volume flow Molar loading in the liquid phase Mole fraction in the liquid phase Molar loading in the gas phase Mole fraction in the gas phase Stoichiometric factor Length

m m− m mol L− m s− – Pa. mol s− bar m % – m mol m− s− ms− s− m kmol− s− mol s− – – mol s− bar K ms− m s− mol mol− (mol mol−)− mol mol− mol mol− (mol mol−)− mol mol− – m

Film thickness Density

m kg m

Greek letters δ ρ

Subscripts  A B bulk C

Saturation Component A Component B In the bulk Column

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film G i in L max min O out ∞

In the film Gas Component Entering the column Liquid Maximum Minimum Overall Leaving the column At infinity

Superscripts *

equilibrium

List of abbreviations DEA MDEA MEA

Diethanolamine Methyldiethanolamine Monoethanolamine

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[33] Alivand MS, Mazaheri O, Wu Y, Stevens GW, Scholes CA, Mumford KA. Catalytic solvent regeneration for energy-efficient CO2 capture. ACS Sustain. Chem. Eng. 2020;8(51): 18755–18788. 10.1021/acssuschemeng.0c07066. [34] Ye J, Jiang C, Chen H, Shen Y, Zhang S, Wang L, Chen J. Novel biphasic solvent with tunable phase separation for CO2 capture: Role of water content in mechanism, kinetics, and energy penalty. Environ. Sci. Technol. 2019;53(8):4470–4479. 10.1021/acs.est.9b00040. [35] Zhang J, Nwani O, Tan Y, Agar DW. Carbon dioxide absorption into biphasic amine solvent with solvent loss reduction. Chem. Eng. Res. Des. 2011;89(8):1190–1196, ISSN 0263–8762. https://doi.org/10.1016/j.cherd.2011.02.005. [36] Shen S, Feng X, Ren S. Effect of arginine on carbon dioxide capture by potassium carbonate solution. Energy Fuels 2013;27(10):6010–6016. [37] Climateworks Website, https://climeworks.com/orca-4000ton-dac-facility (22.03.2021) [38] Li L, Zhao N, Wei W, Sun Y. A review of research progress on CO2 capture, storage, and utilization in Chinese Academy of Sciences. Fuel 2013;108(0):112–130. [39] Hüpen B, Kenig EY. Rigorous modelling of absorption in tray and packed columns. Chem. Eng. Sci. 2005;60(22):6462–6471. [40] Miller DN. Mass transfer in nitric acid absorption. AIChE J. 1987;33(8):1351–1358. [41] Nonhebel G. Gas Purification Processes for Air Pollution Control. London: NewnesButterworths; 1972. [42] Barnicki SD, Fair JR. Separation system synthesis: A knowledge-based approach. 2. Gas/ vapor mixtures. Ind. Eng. Chem. Res. 1992;31(7):1679–1694. [43] Pohorecki R, Moniuk W. Kinetics of reaction between carbon dioxide and hydroxyl ions in aqueous electrolyte solutions. Chem. Eng. Sci. 1988;43(7):1677–1684. [44] Wang M, Lawal A, Stephenson P, Sidders J, Ramshaw C. Post-combustion CO2 capture with chemical absorption: A state-of-the-art review. Chem. Eng. Res. Des. 2011;89(8):1609–1624, ISSN 0263–8762. https://doi.org/10.1016/j.cherd.2010.01.005

Robin Schulz, Thomas Waluga

7 Reactive extraction 7.1 Fundamentals Reactive extraction is the integration of reaction and extraction into one apparatus. There can be different approaches and motivations why this integration is performed. For example, an in situ product removal from a reaction mixture may be desired to increase the conversion of the reaction. Using reactive extraction is particularly useful when the product is poorly soluble in the reaction phase. A prominent example is the Shell higher olefin process (SHOP), in which long-chain α-olefins (insoluble in the solvent) are formed by polymerizing ethylene (soluble in the solvent). In this chapter, a distinction is made between physical extraction, which describes only the separation of ternary mixtures either by pure liquid-liquid extraction, or by reactive extraction, which is a combination of physical extraction and reaction. Physical extraction is often used as a separation principle when distillation is not possible or too expensive. Liquid-liquid extraction can be used to purify azeotropic mixtures or nearly boiling mixtures or is applied for thermal-sensitive substances, too. In addition, extraction can be used to separate high-boiling components at low concentrations, without requiring a large amount of energy, which would be needed by thermal separation. To ensure sufficient separation, extraction is often applied as multistage extraction in the chemical industry. The physical and thermodynamic principles of physical extraction, as well as the extraction equipment and processes, were reviewed by Rydberg [1]. The combination of reaction and extraction offers five basic advantages: 1. Integrated reaction can increase the capacity of the extraction phase, which can lead to higher yields and processes that are more economical. 2. The extraction rate can be increased by the reaction (and vice versa), which usually leads to smaller apparatus. 3. In some cases, the selectivity of a reaction can be increased by choosing an appropriate solvent. An example is the direct separation of products and the associated shift of the reaction equilibrium. 4. Reactive extraction can be used to perform separation procedures or reactions that were not previously realized due to the insolubility of a component. 5. Reactive extraction can also be used for the retention of (expensive) catalysts, since it directly separates the products and the catalyst.

Robin Schulz, Julius Montz GmbH Thomas Waluga, TU Hamburg https://doi.org/10.1515/9783110720464-007

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The principles of reactive extraction were briefly presented in [2] for metal extractions.

7.1.1 Separation principle Physical extraction is a separation process based on two immiscible or partially immiscible liquid phases, exploiting the limited miscibility of two liquid phases. Here, a third component, e.g. the product is distributed in these two phases. The desired product is enriched in one of the two phases. In this case, the desired product is labeled as solute X. The phase in which the solute is dissolved at the beginning is the carrier phase C, while the phase that is added is called solvent S. After the separation process has occurred, the phase with the enriched solute X is called the extract E. The phase which is thinned out of the solute is referred to as the raffinate R (Fig. 7.1). Mixing

Separation

S

E

F

R

C

X

S

C=Carrier S=Solvent X=Solute Fig. 7.1: Liquid-liquid extraction scheme with feed (F), solvent (S), extract (E), raffinate (R), carrier (C), and solute (X) components.

To illustrate physical extraction, a ternary triangular diagram can be used (Fig. 7.2). A detailed description was given by Rydberg [1] and Treybal [2]. The corners of the triangular diagram always characterize the pure components, whereas the edges belong to two-component mixtures. The miscibility gap is between the extract phase and the raffinate phase. It describes the concentration range in which the mixture is divided into two liquid phases. The boundary between the homogenous mixture and the two liquid phases is the binodal curve. The phase decomposition of a mixture point in the two-phase region proceeds alongside a tie line to the binodal curve. There are an infinite number of tie lines; however, each is a straight line, all approaching the critical point, which describes the transition from the two-phase into the single-phase region, where the extract phase and raffinate phase have equal compositions. The two-phase region is dependent on

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X

Critical point

Raffinate

Binodal curve

Extract

Miscibility gap

C

S Tie line

Fig. 7.2: Ternary triangular diagram with miscibility gap, binodal curve, and tie lines.

temperature and primarily increases with decreasing temperature, although the opposite is possible. For example, there are mixtures that exhibit larger miscibility gaps at higher temperatures. Extraction is primarily used as a separation step in the downstream process for purifying a product. The product is the dissolved substance in the extract stream after extraction. The extract phase must be purified in a further step, for example, by distillation to obtain the pure product. Another application of extraction is the separation of impurities. Because very small impurities can be separated via extraction, it is often used as the final purification step in a whole process. When extraction is identified as a feasible candidate to perform the desired separation, the following general tasks must be addressed: – Identify a suitable solvent to perform the task (Section 7.1.4). – Determine the operational mode (e.g., batch, semibatch, or continuous) (Section 7.1.5). – Determine the connection (single stage vs. multistage; a countercurrent, cocurrent, or cross-flow mode) (Section 7.1.5). – Select suitable equipment (Section 7.1.6). Details regarding the conceptual process design of reactive extraction are provided in Section 7.4. If no reaction is involved, the process is named “physical extraction;” however, if a reaction occurs either in the carrier or in the solvent phase, the process is called “reactive extraction.”

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7.1.2 Reactive extraction Compared to physical extraction, reactive extraction operates in a similar manner. The only difference is the integrated reaction in a liquid-liquid system. With the simultaneous application of extraction with a reaction, the mass transport limitations in extraction as well as the reaction limitations can be overcome, moved, or set. Reactive extraction applications can be divided into four different approaches I–IV. Industrial applications for approaches I–III are discussed in Section 7.2. The classification is not strict; a combination of approaches is possible. Approach I overcomes or moves the mass transport limitations by shifting the thermodynamic equilibrium. It is possible to increase the capacity of the solvent via a solute reaction in the solvent phase. During this reaction, less solute is present in the solvent phase; the thermodynamic equilibrium is reconfigured by extracting more solute. An example is shown in Fig. 7.3. Solute A distributes in the organic phase until the thermodynamic equilibrium is reached. With a reaction of A to B in the organic phase, the amount of the separated A increases. As soon as A reacts to B again, the thermodynamic equilibrium must be reached, which results in additional extraction of A.

Reaction: A → B Org. B

B A A

A

A A A

A Aqu. Fig. 7.3: Reactive extraction example for approach I.

Approach II sets the mass transport limitations. For example, a homogeneous catalyst can be held back by a liquid-liquid system. The catalyst and the products can be distributed in different phases (Fig. 7.4). Phase separation can easily minimize catalyst losses. In comparison to a homogeneous reaction in one phase, the costs of a liquid-liquid system are much lower due to a high retention of the catalyst based on easy phase separation. Approach III overcomes or moves the reaction limitations. If the reaction equilibrium limits a reaction, the reaction equilibrium can be shifted to the products side via the selective extraction of the products in another phase, which is particularly useful

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Reaction: A + B → C Org.

Org.

B

B

C C

B

B

B

B

C

C

A A A Cat. A A Cat. Cat. A

Aqu.

Before reaction

Cat. A Cat.

A Cat. Aqu.

After reaction

Fig. 7.4: Reactive extraction example for approach II.

when there are side reactions or subsequent reactions. Then, the removal of the products from the reaction mixture increases the selectivity and the yield. Figure 7.5 shows an example for a reaction of A and B to C and a side reaction to D. Via the selective separation of the product C, the yield and selectivity can be increased. Reaction: A + B → C + D Org. C

C C

C C C

A D

A B

C

A A

D B Aqu. Fig. 7.5: Reactive extraction example for approach III.

For approaches I–III, a detailed example of an industrial application is highlighted in Section 7.2. Approach IV sets the reaction limitations, which is often applied in biotechnology. For example, a reactant can inhibit the enzymes (substrate inhibition). If the reactant is soluble in the second (usually the organic) phase, this phase can act as a “donator phase.” By continuous extraction into the (aqueous) reaction phase, the concentration of the reactant is set low and no inhibition of the enzymes occurs in the reaction phase (Fig. 7.6). The same applies to chemical reactions, when large concentrations of one reactant lead to unwanted incidental or subsequent reactions.

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Enzyme reaction: A → B

B Enz. A

Aqu. Enz. B

B A A

A

A A A

A Org. Fig. 7.6: Reactive extraction example for approach IV.

An example of the superposition of approaches I and II is the separation of two solutes that are present in the carrier phase and cannot be separated by purely separation processes. By the reaction of one solute and selective separation of the other, separation of the two solutes can be achieved. Approach I overcomes the mass transport limitation of the second solute, whereas approach II sets the mass transport limitation of the reaction product of the first solute. Therefore, with approach I it is possible to separate both solutes, while with approach II it is possible to separate selectively two solutes.

7.1.3 Equilibrium conditions The reactive extraction process is fundamentally based on hydrodynamics, thermodynamics, and mass transfer. Therefore, it is particularly important to understand the distribution of the solute between the two phases, referred to as the liquid-liquid equilibrium, and the ongoing reaction, described as the reaction equilibrium. A detailed description of the liquid-liquid equilibrium has been provided in Chapter 2 as well as in several textbooks [3]. A heterogeneous system with two phases, that is, I and II, has four equilibrium conditions: – mechanical equilibrium with equal pressures p: pI = pII

(7:1)

– thermal equilibrium with equal temperatures T: T I = T II

(7:2)

– physical equilibrium with equal chemical potentials µi: μIi = μIIi

(7:3)

7 Reactive extraction

– reaction equilibrium with a minimum of the Gibbs free energy G: Y  n vi 0 ai = 0 ΔG = ΔG + RT · ln

369

(7:4)

i=1

Liquid-liquid equilibrium The chemical potential of each component i in the two phases, I and II, must be identical at the physical equilibrium (eq. (7.3)) and can be replaced by fugacities [4]. They can be calculated from the activity coefficients γ and mole x fractions and the Nernst’s distribution coefficient D can be calculated from the following equation: Di =

cIi cIIi

(7:5)

The activity coefficients can be determined by thermodynamic models, for example, group contribution methods such as UNIversal QUAsiChemical (UNIQUAC) [5, 6], or an equation of state, for example, perturbed-chain statistical associating fluid theory (PC-SAFT) [7]. Chapter 2 provides a detailed description of the thermodynamic modeling of liquid-liquid equilibria.

Reaction equilibrium The reaction equilibrium can be calculated using eq. (7.4). This kind of limitation can occur in several reaction systems: A ⇆ B or A + B ⇆ C or A + B ⇆ C + D or other systems. Reactive separation is often used for the latter one. Therefore, it will be discussed in the following, but the other systems can be described analogously. A reaction of components A and B to the components C and D having stoichiometric coefficients a, b, c, and d can be represented as follows: a·A+b·B⇆c·C+d·D

(7:6)

The reaction rate v of the forward and backward reactions is proportional to the activity of the reactants a. Therefore, for an equilibrium reaction, the reaction rates of the forward and backward reaction can be defined using a reaction rate constant k as follows: β

v1 = k1 · aαA · aB

(7:7)

v − 1 = k − 1 · axC · aδD

(7:8)

If the reaction is at equilibrium, the forward reaction is as fast as the backward reaction, which results in the reaction equilibrium constant K:

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Ka =

ax · aδ k1 = C Dβ k − 1 aα · a B A

(7:9)

Ka =

γxC · γδD xxC · xDδ · β β γαA · γB xAα · xB

(7:10)

or

If the activity coefficients have value 1, eq. (7.10) can be simplified. Subsequently, the equation for the reaction equilibrium based on the concentration then becomes Kx =

xCx · xδD β

xAα · xB

(7:11)

A combined approach using the liquid-liquid equilibrium and reaction equilibrium is necessary for a theoretical description of reactive extraction. This is also described in more detail in Chapter 2 of this book. Process simulation tools such as ASPEN Plus® provide a variety of thermodynamic and unit operation models and property databases, which significantly ease the modeling of these integrated phenomena and the solution of the complex nonlinear models.

7.1.4 Solvent systems The requirements for a physical solvent, reviewed by Henley et al. [8] and Bart [9], can be summarized as follows: 1. With a high selectivity, fewer separation stages are required, and further purification is facilitated. 2. A high capacity has positive effects on the amount of solvent required, which decreases with increasing capacity. 3. No or low cross-mixing between the carrier phase and solvent reduces the separation costs after extraction and the effort required for the separation of impurities in the product. 4. A simple recovery is important to easily separate the product from the extract. Examples include flash and distillation processes. 5. The desired material properties include a high-density difference for easy phase separation and small viscosities to increase mass transport and to enable easy pumping and dispersion; a moderate interfacial tension allows for coalescence, capacity, and phase dispersion to be balanced. 6. To minimize the apparatus costs and safety requirements, it is important that the solvent is noncorrosive, nontoxic, and nonflammable. Moreover, the solvent should also not be hazardous to the environment in case the solvent is discharged via waste or wastewater or due to a fault in the apparatus.

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For a long persistence, the solvent should be chemically and thermally stable and available at an affordable price.

A general statement regarding the requirements for the reactive solvent cannot be provided because the requirements of the process must always be considered. However, the selectivity, conversion, and yield are crucial because higher selectivity results in fewer purification steps after the reactive extraction process. In addition, a high conversion is helpful to reduce the number of stages and the effort required for purification. If these two aspects can be combined with the requirements for physical solvents, a narrow range of solvents can be established in the first step.

7.1.5 Operation modes Reactive extractions can be performed in continuous or batch-wise manners. For continuous operation, extraction can be operated in a cross-flow, countercurrent, or cocurrent mode (Fig. 7.7). In the cocurrent operating mode, the raffinate and extract phases are operated in parallel. However, this mode is only used if equilibrium in a single-stage process is not desired. For example, this may be the case if the residence time is very long or the temperature increases in several steps. In a cross-flow process, fresh solvent can be added at any stage. In this case, the term “fresh” means that the solvent may already have an initial loading, which is the case when the solvent is used in a continuous process and is regenerated between processes. Because the full regeneration is never possible, an initial loading in each stage still exists. In the counter-current process, the flow direction of the extract and raffinate are in opposite directions, which means that the extract stream leaving stage n is fed into stage n + 1; moreover, the raffinate stream resulting from stage n is passed to stage n − 1. The amount of solvent required can be minimized using the counter-current process.

7.1.6 Type of apparatus There are four different types of extraction equipment commonly used in industrial applications: – mixer-settlers – columns: – static columns – stirred and pulsed columns – centrifugal extractors – membrane extractors

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Fig. 7.7: Cross-flow and countercurrent operation modes for a liquid-liquid extraction process.

Membrane extractors will not be discussed here because they are used only in special cases and under certain conditions.

Mixer-settler In a mixer-settler, the mixture is first stirred to ensure the necessary mass transfer and subsequently settled to perform the phase separation process. The two zones are delimited by either different vessels or a dividing wall (Fig. 7.8).

(a)

(b)

Fig. 7.8: Mixer-settler with (a) different vessels compared to (b) a dividing wall.

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Static columns: spray, packed, and plate columns When operating a mixer-settler, emulsion formation is possible. Therefore, simple columns, which are often used for continuous distillation, are utilized (Fig. 7.9). The heavy phase (i.e., higher density) is fed at the top of the column, whereas the light phase is fed at the bottom. Due to the density difference, the phases move counter-currently through the column. To ensure sufficient mass transfer, the effective mass transfer area, which is the interface between the two phases, is increased by very often by adding one of the phases through nozzles, rising in the form of bubbles through the other phase. However, the risk of back-mixing is relatively high; therefore, internals, such as packing or trays, are used. The most used static columns in chemical industry are packed columns.

Spray column

Packed column

Sieve tray tower

Fig. 7.9: Static columns.

Stirred and pulsed columns The most commonly used stirred and pulsed extraction columns in chemical industry are the Karr [10, 11] column and the Kühni column [12] (Fig. 7.10). To increase the mass transfer area, stirred or pulsed columns can be used. A well-known type of these columns is the Kühni column. The Kühni column is a stirred column with perforated disks and a centrifugal mixer. The free cross section determines both the throughput and the residence time of the dispersed phase and can be customized to

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Karr column

Kühni column

Fig. 7.10: Karr column and Kühni column (equal to stirred cell extractor).

the separation problem by choosing different perforated disks. Thus, the Kühni column is also very well suited for reactive extractions with an integrated chemical reaction because the residence time is an important process parameter. The Karr column is a pulsed column. However, the fluid is not pulsed; instead, the column internals are pulsed. These columns typically contain sieve trays attached to a shaft, resulting in a highly targeted dispersion of one liquid phase. Furthermore, the upscaling and the change in the column internals are very simple because only the shaft must be removed from the column, making it possible to save time. In chemical industry, liquid-liquid extraction is primarily applied for the separation of aromatic hydrocarbons, such as benzene, toluene, and xylenes, which are known as BTX components [13]. They are typically produced in a steam cracker. The range of applications of liquid-liquid extraction has continuously expanded and includes, for example, the separation of the rare earths from mixtures with small concentrations [14, 15]. The rare earths are important raw materials for the high-tech industry (electrical and computer industry). Moreover, because resources are limited (which increases global market prices), it is profitable to remove even the smallest quantities. However, continuous distillation for a separation task with

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small concentrations is far too costly and energy intensive, which makes extraction an economical alternative.

Centrifugal extractors Centrifugal extractors consist of a double-walled cylinder, where the outer cylinder is a static housing and the inner cylinder is the rotating rotor, as shown in Fig. 7.11. Compared to conventional systems, centrifugal extractors offer accelerated settling, which is beneficial if the phases to be mixed tend to form emulsions or have only a slight difference in density. They are advantageous for short residence times as well as low hold-up volumes, and they also offer flexible phase ratios. In the gap between the two cylinders, the light and heavy phases are introduced and mixed, so the actual extraction takes place here (mixing zone; mixer). At the bottom of the inner cylinder is the rotor inlet so that the mixture can enter the inner cylinder. There, the two phases are separated (separation zone; settler), with the heavy phase running along the outer end of the inner cylinder and being drawn off at the outer end of the inner cylinder. The light phase runs along onto the heavy phase, close to the axis of the cylinder, and drawn off at the top corresponding to the inner end of the cylinder.

Fig. 7.11: Scheme of a centrifugal extractor.

The reaction can be implemented both internally and externally. If the reaction takes place, for example, without a catalyst at the interphase, the reaction takes place internally in the mixing zone [16]. For internal heterogeneous catalysis, the catalyst can be added to the mixing zone. Therefore, the inlet of the two phases as

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well as the rotor inlet have to be covered via a sieve so that the catalyst is immobilized [17]. If necessary, a mixing chamber can be added to increase the volume of the mixing zone. For an external reaction, the centrifugal extractor is connected to the reactor via the loop principle. This is particularly suitable for comparatively slow reaction rates, as is often the case in biotechnological processes [18, 19]. The external setup allows for individual process parameters, for example, temperatures of reaction and extraction, if contradictory requirements have to be accommodated.

Comparison of different technologies For the selection of the correct apparatus, Henley et al. [8] and Frank et al. [20] gave a comprehensive overview of liquid-liquid extraction. The same aspects are also applied to reactive extraction and can be extended to the reaction process based on the particular requirements. In most cases, temperature management and control are crucial for the reaction. Therefore, the favored apparatuses for reactive extractions are mixer-settler units. In this case, a simple heating or cooling of the reaction mixture is possible using a double jacket. Moreover, mixer-settler units also provide simple mechanisms, such as stirred tanks, to ensure the safety requirements. Their design is much simpler than that of columns because the mixer can simply be designed as a stirred tank and the settler can be based on the thermodynamic properties of the phases. Thus, the design of the apparatus, the reaction, and the separation can be considered separately. This is not the case in the design of columns. Therefore, columns are more likely to be used when many stages or an exact retention time are required, whereas mixer-settlers are used at high flow rates and temperature inputs. Otherwise, columns are used to minimize operating and capital costs when only a small amount of space is available.

7.2 Applications The main disadvantage in the field of reactive extraction is the lack of available reactive extraction systems. In addition, the industrial (large-scale) application of reactive extractions involves complex measurement and control technology, since not only the extraction system must be set up but the reaction must also proceed simultaneously. In the chemical industry, metal extractions dominate the applications of reactive extraction because of a lack of solvents and complexing agents for organic chemistry (e.g., enantioselective separation of chiral compounds). However, reactive extraction becomes established also in industrial organic chemistry. This chapter presents four large-scale processes that involve reactive extraction: the SHOP [21], the Ruhrchemie–Rhône–Poulenc process [22, 23], Merox [24, 25], and

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the plutonium uranium redox extraction (PUREX) process [26]. The SHOP and Ruhrchemie–Rhône–Poulenc processes are reactive extraction processes according to approach III. To increase the conversion and the selectivity, the product is selectively separated. The PUREX process is used for the separation of impurities according to approach I because no solvent is available to separate the impurities via conventional extraction. The Merox process is a reactive extraction process based on approach II, in which the mass transport limitations for the retention of the catalyst are set.

7.2.1 Approach I: shifting the thermodynamic equilibrium The PUREX process [26] (plutonium and uranium recovery by extraction) is used for the recovery of uranium and plutonium from nuclear waste in nitric acid solutions. Therefore, tri-n-butyl phosphate (TBP), which is dissolved in kerosene, is used as the extractant. Uranium and plutonium form nitrate complexes and distribute in the organic phase. The nuclear waste remains in the aqueous phase. The purification of the nuclear waste by separating the uranium and plutonium can be achieved via phase separation (Fig. 7.12). Newer applications, which are not used industrially, use renewable raw materials, although they also use reactive extractions for the separation of acids. In this case, an amine is used as the second reactant. The amine and the acid form a complex or salt, which is water soluble. After phase separation, the aqueous phase can be easily purified by continuous distillation.

Fig. 7.12: Simplified PUREX process: I. Pu, U extraction; II. Pu back extraction; III. U back extraction; IV. solvent (tri-n-butyl phosphate) scrubbing.

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7.2.2 Approach II: retention of homogenous catalysts The Merox process [24, 25] (mercaptan oxidation) is used for desulfurization of natural gas by accelerating the oxidation of thiols to disulfides. Here, a catalyst, for example, cobalt, which is dissolved in a basic solution, is used as the solvent. Thiols are subsequently converted from the gas or liquid phase with the aid of the catalyst from the solvent to disulfides, which are not soluble in water. Air is used as an oxidizing agent. The solvent can be recycled after regeneration. More than 700 Merox plants exist worldwide and approximately 800,000 Nm3 of natural gas are treated in these plants every day. Figure 7.13 shows the process flow diagram with the extractor and the oxidation reactor. Another possible application is the use of a thermomorphic multicomponent system [27, 28]. This system contains a temperature-dependent miscibility gap of two solvents with different polarities. The substrates are primarily in the nonpolar phase, while the catalyst remains in the polar phase. Chemical reactions occur in a homogeneous solution at the reaction temperature. The reaction mixture is cooled after the reaction forms a two-phase system. The catalyst and product phases can easily be separated via phase separation (Fig. 7.14). Thus, high catalyst retention can be achieved in addition to high conversions. Excess air Disulfide

Extracted product

H2S free feed

Air

Rich merox caustic

Merox-caustic solution

Catalyst injection Fig. 7.13: Merox process (according to Matar and Hatch [25]).

According to Monflier et al. [29] and Cornils and Wolfgang [30], another possibility for achieving high withholdings of catalysts is a liquid-liquid system. Using this technique, the catalyst and the products are located in different phases after the reaction, which requires a minimal transversal solubility that can be achieved by a targeted selection of the catalyst and a reaction site at the interface of the two

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Product

TSeparation TReaction Carrier

Solvent

Fig. 7.14: Temperature dependence of liquid-liquid equilibrium.

phases. The catalysts can be tailored according to this criterion. In organometallic catalysis, the homogenous catalysts often consist of a transition metal with a complex-forming ligand. This ligand can influence not only the performance of the catalyst, for example, the yield and selectivity, but also the solubility of the catalyst system in both phases. Therefore, the catalyst tie lines have slopes opposite to the slopes of the product tie lines (Fig. 7.15). Thus, the catalyst is concentrated in a different phase than the products. Product/catalyst

Carrier

Solvent

Fig. 7.15: Different tie line slopes for product and catalyst.

An example of this can be found with triphenylphosphine(mono-)/(di-)/trisulfonate (TPPTS) [31]. Use of a catalyst system that consists of TPPTS in combination with a transition metal is a state-of-the-art addition to the Ruhrchemie–Rhône–Poulenc process, which performs the hydroformylation of propylene.

7.2.3 Approach III: shift in the reaction equilibrium The SHOP [21] is used for the production of linear α-olefins and consists of a combination of oligomerization, isomerization, and olefin metathesis. The oligomerization of ethylene uses nickel catalysts in a polar liquid phase like butane-1,4-diol. Because the produced α-olefins are not miscible with polar solvents, a simple separation is possible. In Fig. 7.16, the reactor is shown for a feed stream of ethylene,

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Unpolar phase Polar phase solvent 1,4 butanediol + Ni-catalyst

α-Olefins

Ethylene

Fig. 7.16: Shell higher olefin process (SHOP).

which flows through the polar phase and contains a nickel catalyst. The produced α-olefins can be easily removed from the top of the reactor. A complete conversion of ethylene with a high selectivity can be attained via the selective separation of the produced α-olefins. The worldwide capacity for the production of α-olefins via SHOP is approximately 1.2 Mio t/a. In the Ruhrchemie–Rhône–Poulenc process [22, 23], the hydroformylation of propene to n- and iso-butanal is conducted in an aqueous catalyst system consisting of rhodium and TPPTS. Here, butanal and the heavy by-products are not soluble in the aqueous phase; thus, they can be easily separated by the liquid-liquid extraction of the rhodium catalyst. Using a surplus of the ligand TPPTS, a loss in the rhodium catalyst in the organic phase is achieved in the ppb range. Another advantage of using TPPTS is the high regioselectivity toward the produced alkanes. Figure 7.17 shows the Ruhrchemie–Rhône–Poulenc process, including the purification stage. A decanter is connected to the reactor in order to separate and recycle the aqueous phase after the reaction. A complete conversion of propylene with a high selectivity can be achieved via the selective separation of the product butanal. Furthermore, the catalyst loss is limited to 0 results in a decrease in the concentration of component i. Although rejection is usually used for the solute, it can also be calculated for any other component of the mixture. Furthermore, the following simple expression relates rejection and separation factor [9]: βi, j =

1 − Rj 1 − Ri

(8:7)

Other measures for selectivity have also been proposed, such as the selectivity figure of merit that also incorporates the molecular weight of the separated components [9]. Additionally, the molecular weight cut-off (MWCO), which is the molecular weight of a solute rejected by 90% is used to differentiate between OSN membranes [5]. For further details on determining the MWCO, see Section 8.1.2. For the enrichment of a minor component in the retentate, the concentration or enrichment factor, EFi, can be used. The enrichment factor relates the concentration of component i in the retentate to its concentration in the feed [5]:

8 OSN-assisted reaction and separation processes

EFi =

ci, ret ci, feed

401

(8:8)

According to Melin and Rautenbach [7] and apparent from the literature, the separation factor, βi,j, the solute rejection, Ri, and the enrichment factor, EFi, are also commonly expressed in terms of mole fractions or weight fractions.

8.1.2 OSN membrane materials and membrane fabrication In OSN, solid synthetic organic or inorganic membranes are applied. As organic building blocks, polymers, such as polyimides (PI) and polydimethylsiloxanes (PDMS) are often used, whereas inorganic OSN membranes are based on ceramic materials, such as amorphous silicon oxide (SiO2), zirconia oxide (ZrO2), titanium oxide (TiO2), and their composites. Challenges for the development of OSN membranes include efficient and economic fabrication of membranes, chemical and thermal membrane stability in organic solvents and mechanical stability under high pressure. Moreover, an understanding of the relationship between membrane performance in different organic solvents and both membrane formation parameters and the molecular (nano-)structure is desirable [1]. In addition to membranes specifically produced for applications in organic solvents, solvent-stable NF or UF membranes originally developed for aqueous applications can also be applied in OSN [1]. Polymeric OSN membranes are sensitive to high temperatures because polymers tend to lose mechanical stability when exposed to temperatures exceeding 40–70 °C. Moreover, polymers exhibit an increased tendency to swell in organic solvents and compact under high pressure [7]. Both effects can lead to a change in the membrane separation efficiency, such as decreased rejection and/ or flux over time, and solvent dependent separation behavior [1]. In OSN, two types of polymeric membranes are primarily used: phase-inversion membranes, which are produced from one polymer (Fig. 8.4 (a)), and thin-film composite (TFC) membranes, which are fabricated using two different polymers (Fig. 8.4 (b)). Most polymeric OSN membranes are integrally skinned asymmetric membranes due to their lower production costs and the possibility of manufacturing a very thin active layer [1]. The structure of a three-layered ceramic OSN membrane is shown in Fig. 8.4 (c). In contrast to polymeric membranes, ceramic membranes exhibit better thermal, chemical, and mechanical resistance and do not swell in organic solvents or compact under high pressures [1]. Therefore, the lifetime of ceramic OSN membranes is longer. However, their large-scale synthesis is more expensive. Compared to polymeric membranes, ceramic membranes are considered less versatile due to the limitation in available materials. Also, there are only very few ceramic membranes with MWCO values of less than 400. However, surface modifications of

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ceramic membranes such as functionalization with organic compounds can lead to significant performance increases regarding selectivity and flux making them competitive with polymeric membranes [10]. A recent overview about these techniques can be found in the literature [11]. A general overview of suitable materials for polymeric and ceramic OSN membranes and information regarding preparation techniques is also available in the literature [1, 8].

Fig. 8.4: Schematic representations of different types of OSN membranes: (a) phase inversion membrane, (b) thin-film composite membrane, (c) three-layered ceramic membrane. Adapted from [1].

Although more than 70% of research articles on OSN focus on the development of new membrane materials with improved separation performance [12], there is only a relatively small number of OSN membranes commercially available which are produced by only a handful of manufacturers. An overview of some available membranes is given in Tab. 8.1. Although many different publications, mostly from the years 2000 to 2015, report performance data for other commercial membranes such as the Starmem membranes or MPF membranes, their production has been discontinued or the membranes have been replaced by newer products and therefore they are not listed here. Two exceptions are the DuraMem membranes and some PuraMem membranes, which are no longer available since mid-2021. However, since they were used in many OSN-focused publications in the last 10 years they are still included in the list.

Alcohols, aliphatic hydrocarbons, aromatic hydrocarbons, BuAc, EtAc, MEK, MTBE

Polyimide (P) Silicone-coated polyimide (P) Silicone-coated polyacrylonitrile

PuraMem® Performance

PuraMem® Selective

PuraMem® Flux

ACT, THF, MeOH, EtOH, MTBE, MEK, MIBK, BuAc, EtAc, DMF, DMSO, NMP

Modified polyimide (P)

DuraMem®  DuraMem®  DuraMem®  DuraMem®  DuraMem®  PuraMem®  PuraMem® S

Evonik

Stability in solventsa

Materiala

Name

Manufacturer

Tab. 8.1: Non-exhaustive overview of commercially available and frequently used OSN membranes.

Not specified

 Dab  Dab  Dab  Dab  Dab  Dab  Dab

Rejection characteristica

(continued )

. in TOLc . in HEPc . in MEKc . in EtOHc  in TOLc . in HEPc . in MEKc . in EtOHc . in TOLc  in HEPc . in MEKc . in EtOHc

. in TOLc  in TOLc

Not specified

Flux characteristica / L m− h− bar−

8 OSN-assisted reaction and separation processes

403

AMS Technologies Ltd.

MeOH, EtOH, IPA, ACT, ACN, HEX, EtAc, THF, DMF

NanoProTM S-

NanoProTM S-

NanoProTM S-

Polymer not specified

Alkanes, aromatics

NF

NF

NF Aldehydes, ketones, crude alkanes, ACT, MeOH, EtOH, IPA, HEX,, EtAc, TOL, CM Alcohols

Aldehydes, ketones, crude alkanes, ACT, MeOH, EtOH, IPA, HEX, EtAc, TOL, CM, CB, TCE

NF

Polymer not specified

Stability in solventsa

Aldehydes, ketones, crude alkanes, ACT, MeOH, EtOH, IPA, HEX, EtAc, TOL, CM Hydrocarbons, aromatics

NF

SolSep BV

Materiala

NF

Name

Manufacturer

Tab. 8.1 (continued )

 in ACTd

% fatty acid ( Da) in ACT  +% dye ( Da) in EtOH or ACT  +% dye ( Da) in EtOH  +% dye ( Da) in ACT  +% oily molecule ( Da) in HEX  +% dye ( Da) in EtOH or ACT

. in watere

 Da .% MgSO  Da % MgSO  Da % MgSO

. in watere

. in watere

 in HEXd . in HEPd  in TOLd  in HEPd

 +% dye ( Da) in EtOH  +% sterol ( Da) in HEP

 in HEXd 2 is set as the main target for the analysis, whereas the enrichment factor, EFnBut, should be less than 1.5.

OSN membrane and solvent selection The iso-butyl benzene enrichment factor is not a direct property of the OSN membrane, although it is dependent on the permeability of toluene, the applied OSN membrane area and butyl benzene rejections. Therefore, a linkage of the enrichment factors with the required rejections is only possible by assuming certain toluene permeabilities and OSN membrane areas. Therefore, a second analysis based on standard toluene permeabilities of 1 and 0.5 kg h−1 m−2 bar−1 and fixed OSN membrane areas of 250, 500, 750, and 1,000 m2 is conducted to determine the minimum iso-butyl benzene rejection required to reach a minimum enrichment factor of 2 (EFisoBut = 2). The OSN membrane areas are chosen to resemble processes with limited OSN membrane replacement costs (based on 250 € m−2 a−1). The associated costs are less than 250 000 € a−1, which is approximately half of the projected savings in distillation costs according to Fig. 8.17. To determine the minimum required iso-butyl benzene rejections, a process model consisting of a single membrane stage with fixed membrane area and permeability is simulated, and the required iso-butyl benzene rejection is determined based on an annual iso-butyl benzene production of 10 000 t a−1. In Tab. 8.6, the resulting required iso-butyl benzene rejections are summarized for different membrane areas and two different permeabilities. The rejection requirements range from 21% to 84% for iso-butyl benzene; the enrichment factor requirement is not always attainable for low permeabilities. Tab. 8.6: Iso-butyl benzene rejection requirements for a single stage to reach an overall rejection of 99.9% in two- to five-stage enriching cascade setups. Membrane area (m)

   ,

Minimum iso-butyl benzene rejection with toluene permeability of  kg h− m− bar−

Minimum iso-butyl benzene rejection with toluene permeability of . kg h− m− bar−

. . . .

not possible . . .

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433

In summary, the butyl benzene enrichment requirement can be attained either by increasing the permeability and maintaining the same rejection or by increasing the rejection. In general, possible measures to reach the butyl benzene enrichment requirements include changing the process conditions (e.g., increasing the pressure or changing the temperature), modifying the membrane, or altering the solvent. Because butyl benzenes were not applied in the generation of the MRM and MMM, the MRM and MMM of 1-phenyldodecane are analyzed herein because it originates from the same chemical class. In Fig. 8.18, the 80%, 40%, 30%, and 20% rejection isolines, which nearly correspond to the required iso-butyl benzene rejections for singlestage setups with membrane areas of 250, 500, 750, and 1,000 m2 and a permeability of 1 (typical for the Puramem™ 280 membrane), are highlighted in the MRM and MMM of 1-phenyldodecane. According to the MRM in Fig. 8.18 (a), the rejection of 1-phenyldodecane is largest for toluene (which is the standard solvent and reactant during butyl benzene synthesis). Consequently, no change in the solvent mixture is recommended. Moreover, the MMM of 1-phenyldodecane in Fig. 8.18 (b) suggests that a membranefocused measure is promising because in pure toluene, 26% of the 1-phenyldodecane permeation results in a membrane-focused measure. Because butyl benzene molecules are smaller than 1-phenyldodecane molecules (the only difference with 1-phenyldodecane is the shorter C-chain length), it can be assumed that the contribution of individual pore flow is even larger for butyl benzenes. Therefore, a membrane-targeted measure is recommended.

Fig. 8.18: Membrane and solvent preselection for example 1 based on (a) the MRM and (b) the MMM of 1-phenyldodecane, as a substitute for butyl benzene, through the Puramem™ 280 membrane. The 80%, 40%, 30%, and 20% isolines are highlighted because they represent the single-stage rejection requirements for processes with membrane areas of 250–1,000 m2 to reach an iso-butyl benzene enrichment factor of 2 [24].

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Experimental investigation The shortcut economic analysis above revealed that an enrichment in the main product, i.e., iso-butyl benzene, by an OSN membrane is favored, whereas the overall enrichment of n-butyl benzene is limited. Therefore, an OSN membrane with a high rejection with respect to iso-butyl benzene and a good selectivity between isobutyl benzene and n-butyl benzene is necessary. To determine the focus of the experiments, e.g., concerning the experimental investigation using additional OSN membranes, the rejection of n-butyl benzene through Puramem™ 280 and Duramem™ 300 membranes in the reaction solvent toluene is investigated as a first step in a crossflow laboratory apparatus. The toluene permeability and n-butyl benzene rejection results are shown in Tab. 8.7. As expected, the rejection of n-butyl benzene through the Puramem™ 280 membrane (37.4%) is significantly lower compared to the rejection of 1-phenyldodecane (>80%). Moreover, the rejection of n-butyl benzene through the Duramem™300 membrane is very low. In combination with a very low permeability, additional experimental characterization of the Duramem™ 300 membrane is not promising, and the suggested improvements due to changing the OSN membrane cannot be validated. Tab. 8.7: Rejection of n-butyl benzene and permeabilities in toluene using Puramem™ 280 and Duramem™ 300 membranes. Membrane Puramem™  Duramem™ 

n-Butyl benzene rejection / %

Permeability / kg h− m− bar−

. .

. .

Consequently, the following analysis focuses on an experimental characterization with respect to membrane permeability and both n-butyl benzene and iso-butyl benzene rejections through the Puramem™ 280 membrane as a function of different operating conditions, such as temperature and solute concentration. The feed pressure is fixed to a maximum of 50 bar because the membrane characterization showed that a larger feed pressure results in both higher rejections and higher permeabilities for the Puramem™ 280 membrane. In Fig. 8.19, the experimental results for the Puramem™ 280 membrane permeability for different feed temperatures (20–40 °C) and different feed solute concentrations are shown. Both the solute concentration and the feed temperature affect the permeability significantly, which varies between 0.4 and 1.8 kg h−1 m−2 bar−1. A threefold increase in the solute feed concentration results in a decrease in the membrane permeability of 50% due to an increase in osmotic pressure. Moreover, the permeability is linearly to exponentially dependent on the feed temperature,

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435

where an increase of 20 °C results in an increase in the membrane permeability of approximately 100%.

Fig. 8.19: Permeabilities through the Puramem™ 280 membrane at Δp = 50 bar for different temperatures and solute concentrations based on the validation experiments conducted for example 1. Adapted from [24].

The effect of the feed temperature and the solute concentration on the n-butyl benzene and iso-butyl benzene rejections is shown in Fig. 8.20. In general, the n-butyl benzene rejections (12–26%) are lower than the iso-butyl benzene rejections (26–42%). This effect was expected due to the molecular size effect of a branched side chain. This difference is favorable from a process economics perspective because higher iso-butyl benzene rejections are required. Moreover, the absolute values of the rejections indicate that a process having a membrane area of less than 250 m2 is likely not capable of achieving an iso-butyl benzene enrichment factor of 2, although at higher temperatures, processes with membrane areas between 250 and 500 m2 may be realized (Tab. 8.6). Concerning the influence of operational parameters, the same trends can be observed for both solutes. An increase in the feed temperature by 20 °C results in a decrease in the solute rejection by approximately 5–10%, whereas an increase of the feed concentration by a factor of three results in a decrease in the solute rejection by approximately 10% for all temperatures and both solutes. Therefore, the feed temperature determines whether the Puramem™ 280 membrane acts as a high-flux membrane with lower butyl benzene rejections (at 40 °C) or as a low-flux membrane with higher butyl benzene rejections (at 20 °C). Because the decrease in

Rejection iso-butyl benzene [%]

Stefan Schlüter, Patrick Franke

Rejection n-butyl benzene [%]

436

Fig. 8.20: Rejections of (a) n-butyl benzene and (b) iso-butyl benzene through the Puramem™ 280 membrane at Δp = 50 bar for different temperatures and solute concentrations based on the validation experiments in example 1. Adapted from [24].

the solute rejection as a function of temperature is small, higher temperatures may be more suitable for reaching the required enrichment factors with smaller areas.

Process modeling and optimization This section presents the process modeling and optimization step, in which the results of the OSN-assisted distillation process are compared with those of the conventional process without pre-enrichment using OSN. The applied model for OSN membrane separation is based on correlations between the OSN membrane permeability and OSN membrane separation efficiency, which are represented by solute rejections. The correlations for this case study are two-dimensional because both the feed temperature and the solute concentration varied during the experimental validation step. The process model consists of an OSN membrane cascade superstructure for the pre-enrichment of butyl benzenes, a distillation column for toluene recovery and a distillation column for butyl benzene isomer separation (Fig. 8.21). The process is optimized with respect to minimizing the overall production costs of iso-butyl benzene, including the depreciated investment costs of the OSN separation, both distillation columns and the operating costs of all necessary equipment. For this process, a fixed iso-butyl benzene production capacity of 10,000 t a−1 with a product purity of 99 wt.% is assumed. Moreover, the purity constraints for both the side product (n-butyl benzene) in the bottom of the second column and the recycled toluene in the distillate of the first column are set to 99 wt.%. The retentate of the OSN membrane separation is connected to the first distillation column (Fig. 8.21).

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Fig. 8.21: Process flowsheet applied in example 1. Two-product process passing the retentate of the OSN membrane cascade superstructure to the first distillation column for toluene recovery. Adapted from [24].

As an optimization variable, the feed temperature can be varied from 20 to 40 °C in every OSN stage. Moreover, the transmembrane pressure difference is fixed at 50 bar, and spiral-wound membrane modules (2.5′′ × 40′′) having a membrane area of 2.1 m2 each and a fixed feed demand of 500 L h−1 are applied. Furthermore, preheating of the distillation column feed and fixed F-factors of 0.5 in the first stage (below the distillate) of the distillation columns are assumed. The dimensions of the distillation columns are optimized after the optimization of the OSN membrane separation, including the reflux ratios and the heights of the stripping and rectifying sections [24]. Tab. 8.8: Results of the optimization for example 1 using the Puramem™ 280 membrane compared with the conventional distillation-based process for the OSN-assisted distillation process.

−

Cost per ton iso-butyl benzene / € t Membrane cost / M€ a− Column  cost / M€ a− Column  cost / M€ a−

Standalone distillation

OSN-assisted distillation

.  . .

. . . .

In Tab. 8.8, the key results of both setups are shown for the specific production costs of iso-butyl benzene and the annual costs of the OSN membrane separation and both distillation columns. The iso-butyl benzene production costs using the optimized OSN-integrated process are approximately 23% lower than those for the conventional process. This difference is a direct consequence of savings, especially in the reboiler and condenser heat duties of the distillation columns, resulting in a 60% cost reduction for column 1 and a 15% cost reduction for column 2. The savings for column 1 enhance the overall process economics because the absolute costs for toluene recovery are high. The decreased operating costs can be attributed to steam savings in the

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reboiler, in which a decrease in the annual costs from approximately 0.51 Mio € a−1 to 0.18 Mio € a−1 is realized. This decrease is a direct consequence of the pre-enrichment step when using OSN. In the conventional process, a total feed flow of 17 401 kg h−1 must be processed in column 1, whereas the pre-enrichment by OSN (with a pre-enrichment factor of 2.66 for iso-butyl benzene) reduces the feed flow to 6,092 kg h−1. Therefore, the integration of OSN for the pre-enrichment of butyl benzene isomers significantly improves process economics by decreasing the amount of toluene that must be evaporated in the first distillation column. However, an additional toluene/butyl benzene separation in the permeate of the OSN membrane was not considered. Therefore, for a full analysis, a subsequent study with an additional constraint on the maximum butyl benzene concentration in the permeate should be conducted.

8.5.2 Example 2: integration of OSN and reaction for catalyst recycling The hydroformylation of alkenes to produce aldehydes is of considerable commercial interest because aldehydes are intermediates for other compounds, such as amines, alcohols, carboxylic acids, and ethers, which are primarily used in the polymer and detergent industries [80]. In addition to developing stable and active catalysts by applying different transition metal complexes and ligands, the efficient recycling of the catalyst complex is an important challenge for process economics [80]. Because homogeneous catalysts are sensitive to high temperatures, their recycling in continuous processes must be achieved before purification steps that involve high temperature processes, e.g., distillation [81]. Therefore, the recycling of homogeneous catalysts using OSN is a promising technology. The advantages of OSN compared to other separation processes, e.g., those based on biphasic systems, are the smaller reaction volumes due to the direct dissolution in the product phase, the prevention of mass transfer resistances, and the ease of scale-up.

Problem statement In this case study, the hydroformylation of 1-pentene is investigated. A simplified reaction schematic for the formation of n-hexanal and 2-methylpentanal is shown in Fig. 8.22. For the reaction, both isomerization from 1-pentene to 2-pentene and hydrogenation from 1-pentene to pentane are neglected. Because the properties of n-hexanal and 2-methylpentanal are very similar and high regioselectivity, i.e., the ratio of linear to branched aldehydes, can be attained, full reaction conversion and a single reaction product (i.e., n-hexanal) is assumed.

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8 OSN-assisted reaction and separation processes

Fig. 8.22: Homogeneously catalyzed hydroformylation of 1-pentene forming n-hexanal and 2methyl-pentanal.

The properties of the involved chemicals are summarized in Tab. 8.9. In all the experiments, triphenylphosphine (TPP) is used to represent the catalyst complex. This results in a conservative rejection estimate because the molecular weight of the rhodium-TPP complex (365.2 g mol−1) is larger than that of the ligand (262.3 g mol−1). Tab. 8.9: Properties of the main compounds in the chemical reaction in example 2. Chemical -Pentene n-Hexanal -Methyl pentanal Triphenylphosphine

δHildebrand / MPa.

Molecular weight / g mol−

Viscosity η / mPa s

. . . .

. . . .

. . . –

Tboil / °C . . . .

For a shortcut analysis of the required OSN membrane performance, the operating costs are analyzed based on costs for the rhodium-catalyst and OSN membrane replacements. The basic assumptions are summarized in Tab. 8.10 for a small- to medium-scale production capacity of 50 000 t a−1 of n-hexanal. Concerning the cost parameters, a medium-level membrane price/stability factor of 250 € a−1 m−2 (e.g., representing a unit cost of 500 € m−2 and a membrane lifetime of two years) is assumed due to uncertainties in both OSN membrane lifetimes and large-scale fabrication costs. Tab. 8.10: Cost assumptions for the shortcut economic evaluation used in example 2. Criterion

Assumption

Production capacity of n-hexanal Transmembrane pressure difference Rhodium inlet concentration Rhodium price Membrane price factor

  t a−  bar  mg kg−  € g−  € a− m−

The estimated operating costs as a function of OSN membrane permeability and catalyst rejection are shown in Fig. 8.23. The catalyst rejection influence on the overall operating

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costs is very large, and the membrane permeability has only a minor effect. Specifically, a rejection exceeding 99.9% must be reached because 99.9% rejection still leads to a rhodium loss of 2.5 kg a−1 (or 250 000 € a−1, which is equal to 5 € t−1 n-hexanal).

Fig. 8.23: Shortcut economic analysis for example 2. The resulting operating costs as a function of the OSN membrane permeability and catalyst rejection are calculated using the input values listed in Tab. 8.10. Adapted from [24].

Based on the results shown in Fig. 8.23, the subsequent analysis focuses on TPP rejection rather than on OSN membrane permeability. For verification, initial experiments were performed using the standard solvent n-hexanal which is also the reaction product. The experiments are conducted in a dead-end test cell setup using nitrogen as the pressurizing gas. The experimental temperature and feed pressure are set to 30 °C and 30 bar, respectively, while the TPP concentration is 1 wt.%. The results are shown in Tab. 8.11. Tab. 8.11: TPP rejections and permeabilities attained in the reaction product nhexanal using Puramem™ 280 and GMT-oNF-2 membranes. Membrane Puramem™  GMT-oNF-

TPP rejection / %

Permeability / kg h− m− bar−

. .

. .

8 OSN-assisted reaction and separation processes

441

None of the two membranes meets the minimum rejection requirement of 99.9% and both have similar permeabilities. Consequently, 99.9% rejection can only be realized in multistage setups.

OSN membrane and solvent selection Because the shortcut economic analysis in the previous section determined that a very high catalyst rejection is crucial for process economics, the preselection of membranes and solvents is based on the minimum catalyst rejection requirement of 99.9%. In Tab. 8.12, the required single-stage rejections, Rstage, to reach an overall rejection, Rtotal, of 99.9% in two- to five-stage setups are summarized. These results show that the initial experiments did not sufficiently demonstrate large single-stage rejections. Specifically, the application of the Puramem™ 280 membrane demands setups with more than four serial OSN membrane stages, whereas a GMT-oNF-2 membrane is only applicable in setups with more than five stages (Tab. 8.12). Consequently, the individual rejections must be increased for economic OSN membrane setups with fewer stages. Tab. 8.12: Rejection requirements for a single stage to reach an overall rejection of 99.9% in two- to five-stage enriching cascade setups. Number of stages

Required single-stage rejection Rstage / %

   

. . . .

The required single-stage rejections, Rstage, are calculated by multiplying the individual rejections, not accounting for any recycling structures: X

Nstages

Rtotal =


i − 1 Rstage 1 − Rstage

(8:16)

i=1

In general, possible measures to increase the TPP rejection include a change in the process conditions (e.g., increasing the pressure), a change in the membrane or a modification of the solvent. To analyze these measures, the rejection isolines of 90%, 80%, and 70%, which approximately correspond to the required single-stage rejections for three-, four-, and five-stage OSN membrane setups, respectively, are highlighted in the MRM and MMM of TPP in Fig. 8.24, for the quaternary mixture of TPP, 2-propanol, n-hexane and toluene with the Puramem 280 membrane. According to the MRM of TPP in Fig. 8.24 (a), a rejection exceeding 80% (which may result

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in a three-stage serial membrane setup using a Puramem™ 280 membrane) is only feasible for solvent mixtures with large weight fractions of toluene. In this case, a TPP rejection exceeding 90% is also feasible, which may lead to a serial setup with less than three stages. The MMM in Fig. 8.24 (b) indicates that a solvent-focused measure is recommended for all solvent mixtures.

Fig. 8.24: Membrane and solvent preselection for example 2 based on (a) the MRM and (b) the MMM of TPP through a Puramem™ 280 membrane. The 90%, 80%, 75%, and 70% isolines are highlighted because they represent the single-stage rejection requirements for three-, four-, and five-stage OSN membrane setups. Adapted from [24].

In conclusion, the membrane and solvent preselection step results in a selection of Puramem™280 membranes and a solvent-focused measure (most likely to be focused on the selection/ addition of aromatics to increase the rejection of TPP, which is indicated in the corresponding MRM) during the experimental investigation step.

Experimental investigation Because both the MRM and MMM of TPP through a Puramem™ 280 membrane indicate that an increase in rejection is possible by focusing on solvent (mixtures) modifications, the experimental investigation step focuses on targeted solvent variations and additions to the standard solvent n-hexanal. To accomplish this, a targeted rejection screening in different solvents is conducted to preselect the most promising solvents that can be applied to increase TPP rejections. Then, targeted solvent addition experiments are conducted. In the first step, a solvent screening procedure that focuses on the rejection of TPP using different solvents is performed; the objective of this step is to find a suitable solvent and subsequently validate the large influence of the solvent on the rejection process. To demonstrate the same effects for a different polymer, the PDMS-based GMT-oNF-2 membrane is also regarded in the experimental investigation. The screening

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solvents are selected based on large variations in the solvent properties, including the Hildebrand solubility parameter, δHildebrand, the Hansen solubility parameters, δHansen,D, δHansen,P, and δHansen,H, and the solvent viscosity, η. A small difference in the solubility parameters indicates an affinity between a solvent/solute and a membrane material (i.e., “like dissolves like”). For further information, the reader is referred to the textbook by Hansen [82]. Moreover, the boiling temperature, Tboil, of the solvent is important because the added solvent must be recovered via distillation. For this purpose, solvents with a boiling temperature lower than that of n-hexanal are necessary so that the added amount of solvent (which is most likely small) can be recycled in the distillate stream of a distillation column. The solvents include the reaction product n-hexanal, aromatics (toluene and o-xylene), alkanes (n-hexane and n-decane), alcohols (2-propanol and 1-pentanol), and esters/ketones (DMC, PC, and acetone). Both good rejections and permeate fluxes are favored during the process; the results of the solvent screening, concerning TPP rejections and permeate fluxes through the Puramem™ 280 and GMT-oNF-2 membranes, are shown in Fig. 8.25. The results highlight that an increased TPP rejection and solvent permeate flux is possible by changing the solvent, especially for the GMT-oNF-2 membrane, in which the rejection of TPP is significantly improved. For the Puramem™ 280 membrane, a correlation between the permeate fluxes and rejection is found, i.e., larger permeate fluxes correspond to higher rejections of TPP (see Fig. 8.25 (a)). Exceptions include o-xylene and 2-propanol, which lead to high rejections of TPP and low permeate fluxes. The promising chemical classes for high TPP rejections include aromatics, validating the observed effects in the MRM of TPP. Moreover, the rejections in DMC and 2-propanol exceed 80%. However, only the application of toluene and DMC results in permeate fluxes exceeding those of n-hexanal. For the GMT-oNF-2 membrane (see Fig. 8.25 (b)), no clear correlation between the solvent permeate flux and TPP rejection is observed. However, the increase in both the

Fig. 8.25: TPP rejections as a function of the permeate fluxes in solvent screening experiments for example 2 through (a) Puramem™ 280 and (b) GMT-oNF-2 membranes. Adapted from [24].

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TPP rejection and solvent flux is larger than that observed for the Puramem™ 280 membrane, resulting in comparable rejections for aromatics (>90%) and medium rejections for esters/ketones and alcohols. The largest flux increase is observed for n-hexane, which can be attributed to comparable Hildebrand solubility parameters of the membrane material (PDMS) and n-hexane. Hence, the solvent screening step shows that solvents exist that result in both larger permeate fluxes and/or higher TPP rejections through both membranes compared to the standard solvent, i.e., n-hexanal. This finding is especially true for toluene, which results in both larger permeate fluxes and higher TPP rejections for both membranes. For the Puramem™ 280 membrane, a permeate flux of 41.6 L h−1 m−2 and a rejection of 96.7% are obtained, whereas the GMT-oNF-2 membrane shows in a permeate flux of 57.9 L h−1 m−2 and a rejection of 90.5%. In the second step, laboratory-scale targeted solvent addition experiments are conducted to analyze TPP rejection, overall permeability, and separation between n-hexanal and toluene. In these experiments, different toluene weight fractions are added to n-hexanal (from 2.5 wt.% to 50 wt.%). Because the results using the Puramem™ 280 membrane are the most promising (especially concerning TPP rejection), the solvent addition experiments are performed using this membrane. For these experiments, the feed pressure is set to 50 bar because an increased feed pressure results in both larger permeate fluxes and higher rejection due to membrane contraction. All experiments are conducted in a lab-scale crossflow OSN apparatus using 1 wt.% TPP and a temperature of 30 °C. The results of the addition experiments concerning both TPP rejections and the overall and partial permeate fluxes through the Puramem™ 280 membrane are shown in Fig. 8.26. A large TPP rejection increase from 87% for pure n-hexanal to approximately 98% for a solvent mixture with 50 wt.% toluene is observed (Fig. 8.26 (a)). This validates both the expected rejection based on the MRM and the solvent screening experiments. Moreover, only a small addition of toluene results already in a large increase in rejection, which is very favorable from a process perspective because only very small changes in the solvent mixture result in large rejection increases. Concerning the permeate flux (Fig. 8.26 (b)), an increase in the overall permeate flux is also observed. However, the partial flux of n-hexanal decreases, especially for larger toluene weight fractions. Compared to the standard value of 60 L h−1 m−2, the partial flux decreases to approximately 40 L h−1 m−2 for a solvent mixture with 50 wt.% toluene, although this is still comparable to the value for a solvent mixture with 10 wt.% toluene. Compared to the attained experimental permeate flux in the solvent screening step, a larger permeate flux is observed (approximately 55 L h−1 m−2 at 50 bar compared to approximately 18 L h−1 m−2 at 30 bar in the screening experiments).

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Fig. 8.26: Experimental results for toluene additions to n-hexanal using the Puramem™ 280 membrane. (a) TPP rejections and (b) permeate fluxes. Adapted from [24].

In summary, the solvent addition step and the targeted additions of toluene to n-hexanal demonstrate that improvements in both the permeate fluxes and TPP rejections are possible. In particular, the main target of increasing the TPP rejections is fulfilled such that a two-stage process with 97% single-stage rejection is feasible using Puramem™ 280 membranes.

Process modeling and optimization Regarding the optimization of the OSN membrane cascade for recycling the homogeneous catalyst complex, which is represented by TPP, shortcut models based on correlations are applied, as also described in the first example. These correlations are based on the experimental data generated from the experimental validation with the Puramem™ 280 membrane. Because the focus of the validation experiments was on the rejection properties of TPP utilizing targeted additions of toluene, direct correlations of TPP rejection and permeability with the toluene weight fraction are used. The selectivity of toluene/n-hexanal is set to 1.45, favoring the permeation of n-hexanal, which is the average value observed in the experiments. The process flowsheet consists of an OSN membrane cascade superstructure in which the overall permeate is passed to a distillation column to recover the added solvent if solvent additions are conducted (Fig. 8.27). The process is optimized with respect to minimizing the overall production costs of n-hexanal, including the depreciated investment costs of the OSN separation, the distillation column and the operating costs of all necessary equipment. For the process, a fixed n-hexanal production capacity of 50 000 t a−1 with a product purity of 99 wt.% is assumed. Moreover, the recovered toluene in the distillate

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Fig. 8.27: Process flowsheet applied in example 2, i.e., one-product process passing the permeate of the OSN membrane cascade superstructure to one distillation column. Adapted from [24].

stream of the distillation column has a fixed purity of 98 wt.%. Solvent additions are possible in each stage of the OSN membrane cascade superstructure. Moreover, the heights of the stripping and rectifying sections (0–10 m) and the column pressure (0.1–1 bar) in the distillation column are optimized. In Tab. 8.13, the toluene addition results for processes with different numbers of stages are summarized. In these process setups, high overall TPP rejections, Rtotal Triph , ranging from 98.35% to 99.99%, are realized by adding enough toluene, especially for the one- and two-stage processes (approximately 9 wt.%) and the threeto five-stage processes (approximately 5–6 wt.%). The average internal reflux ratios, , are determined according to the demands of the corresponding process RRaverage int setups, which are directed toward high triphenylphosphine rejections for processes , values of 0.02 and 2.20 for the one- and twowith fewer stages (average RRaverage int stage processes, respectively) and toward smaller overall membrane areas for pro, > 10 for the four- and five-stage processes). The cesses with more stages (RRaverage int average , describes the ratio of internally recycled retentate to internal reflux ratio, RRint the retentate that is passed to a different stage. Accordingly, a larger internal reflux ratio leads to increased catalyst concentrations within a single stage and a sufficient feed flow for the modules in that stage, which minimizes the amount required , is large, from the stage below. As a result, the overall areas are smaller if RRaverage int whereas the overall rejections are decreased due to the accumulation. Based on these adjustments, the overall membrane areas, Rtotal memb , are limited to values less , of 99.99%. In contrast to the opthan 1,000 m2 with overall TPP rejections, Rtotal Triph timized processes without toluene additions, the average internal reflux ratios, , are larger. Regarding the total production cost of n-hexanal, CPTn-hexanal, RRaverage int the three-stage process is the most economic one. Because toluene additions result in increased TPP rejections, the internal reflux ratios are large, reducing the required membrane areas, especially in 2nd and 3rd stages. To increase TPP rejections in all the individual stages with as little toluene addition as possible, an amount of 5.62 wt.% is added in front of stage 3. Details of the optimized three-stage OSN membrane cascade with respect to the individual stage membrane areas, TPP rejections, reflux ratios, and added amounts of toluene are shown in Fig. 8.28. The results show that in the optimized processes, both the reflux ratios and the toluene additions vary according to the individual stages,

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Tab. 8.13: Resulting production costs per ton of total n-hexanal, rejection, membrane areas and average internal reflux ratios for different optimizations for example 2 using toluene additions. Setup -stage -stage -stage -stage -stage

CPTn-hexanal / € t−

R total TPP / %

A total memb / m

RR average int / mol mol−

Added toluene / wt.%

. . . . .

. . . >. >.

. . . . .

. . . . .

. . . . .

highlighting the need for applying rigorous optimization algorithms based on superstructures. Similar results are also obtained for the processes with a different number of stages, showing that toluene additions are favorable within the first three membrane stages because they minimize the membrane area required in stages 4 and 5, which are not needed to obtain a sufficient TPP rejection.

Fig. 8.28: Optimized three-stage OSN membrane cascade for example 2 using the Puramem™ 280 membrane. Adapted from [24].

8.5.3 Example 3: integration of OSN, decantation and reaction for co-product separation As discussed in the previous example, OSN is well suited to be combined with homogeneously catalyzed reactions, because the catalyst can be separated from the product and recycled to the reactor in its active form. This case study demonstrates a slightly different application of OSN in a reaction separation process, in which a co-product is

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separated from a catalyst-rich stream by OSN. Detailed descriptions of the experiments and additional information about the case study can be found in the literature [36, 83].

Problem statement In contrast to the previous case study, this case study focuses on the implementation of membranes into reaction processes by experimental membrane screening and process evaluation. The focus will be the membrane selection and the additional challenges that arise if the actual implementation into a continuously operated process is regarded. Especially the prediction of membrane performance in complex mixtures is not necessarily incorporated into model-based design processes, but these effects can have a significant influence on membrane performance and stability which will be demonstrated herein. Furthermore, the implementation in small-scale continuous processes (also called miniplants) is often necessary to investigate the interaction between different process units such as the accumulation of certain components. In this context, the current study investigates the more complex hydroaminomethylation (HAM), which combines the hydroformylation and the reductive amination in a tandem catalytic synthesis [84–86]. In the following example the hydroformylation converts 1-decene to the aldehyde undecanal using synthesis gas (CO/H2), while the reductive amination combines the resulting aldehyde with the secondary amine diethylamine and hydrogen to form the long-chain tertiary amine N,N–diethylundecylamine. Water is produced as a co-product in the enamine condensation step resulting in a high atom economy, as depicted in Fig. 8.29. The main side-reaction that occurs is the aldol condensation of undecanal, promoted by the intermediate enamine.

Fig. 8.29: Reaction scheme of the hydroaminomethylation of 1-decene. Adapted from [36].

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The proposed process concept involves the reactor and a subsequent decanter for phase separation to separate product and catalyst. This is facilitated using a thermomorphic multiphase system [87] that combines two solvents that are homogeneous at reaction temperature but form a two-phase system at a lower separation temperature. After the separation in the decanter the non-polar solvent and the product are further purified, while the polar solvent and the dissolved catalyst are recycled back to the reactor. This approach is a promising alternative to the membrane-assisted process concept that was shown and evaluated for the hydroformylation in the previous example. Due to the polarity of the co-product water, it distributes sharply to the polar catalyst phase, which results in accumulation. The accumulation has been shown in previous works [83]. Therefore, an additional separation is necessary to remove the co-product from the catalyst rich recycle stream (Fig. 8.15 (c)). This separation can be performed using OSN membranes because the high pressure in the process can be exploited as the driving force. Also, due to the presence of reactive chemicals, such as amines, solvent resistant membranes are required. The chemicals that appear throughout this section are listed in Tab. 8.14 with a short description and their molecular weights as a reference. Tab. 8.14: Chemicals relevant for this case study. Chemical

Description

-decene Diethylamine Undecanal Water N,N-diethylundecylamine Aldol condensate Sulfoxantphos Methanol n-Dodecane

Reactant  Reactant  Intermediate aldehyde Co-product Product By-product Ligand Polar TMS solvent Non-polar TMS solvent

Molecular weight / g mol− . . . . . – . . .

Membrane preselection A variety of solvent resistant nanofiltration membranes are commercially available. There are several requirements for these OSN membranes to be applied in the described process. The most important aspects are a high retention of the catalyst and a selective removal of water from the remaining components of the catalyst recycle stream. Especially catalyst retention is crucial, because of the rather high catalyst concentration in the recycle stream and the high cost associated with the precious metal. The selective removal of water can be expressed by a negative rejection of water for the investigated membranes. Besides the desired separation characteristic

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of the membranes the stability in the catalyst phase is another restriction because the substrate diethylamine is a quite reactive and highly corrosive chemical. It is also desirable to retain any mutually dissolved components in the catalyst phase such as the product. Based on these aspects, a membrane with a low MWCO and good chemical stability is required for the separation. Furthermore, hydrophilic membranes are more likely to yield a good water separation than hydrophobic ones. However, hydrophobic membranes could be able to retain the catalyst to a higher degree since the catalyst complex is also polar because of the polar ligand. A preselection of four different membranes is listed in Tab. 8.15. The membranes were selected based on the polarity of the membrane material and with the goal of high catalyst rejection and therefore low MWCOs. The DuraMem 150 and 200 membranes are made of modified polyimide, which can be characterized as semi-hydrophobic. The NanoPro S-3012 is supposedly made from hydrophilic polyamide and the NF030306 is silicone based and therefore hydrophobic. Tab. 8.15: OSN membranes used in this work [36]. Membrane

Material

Supplier

DuraMem 

Modified polyimide

DuraMem 

Modified polyimide

NanoPro S-

Undisclosed, potentially polyamide Silicone based

Evonik Resource Efficiency GmbH Evonik Resource Efficiency GmbH AMS Technologies SolSep BV

NF

pmax / bar

MWCO / g mol−



a



a



b



-c

a

Based on 90% rejection of styrene oligomers in acetone Manufacturer information c 99 +% rejection of a non-specified colorant (500 g mol−1) in ethanol and acetone b

Membrane screening with model solutions To evaluate the performance of the selected membranes, experiments are performed in which the target separation is investigated. Simplified mixtures are first used to reduce the experimental effort. Since high catalyst rejection is crucial for the feasibility of the process, the selected membranes were first tested for an ideal catalyst recycle stream which consists only of the polar solvent methanol with the dissolved ligand Sulfoxantphos being representative of the catalyst. The composition of this simplified test mixture is given in Tab. 8.16. The rejection of the ligand serves as a conservative estimate of the catalyst rejection as described in the previous example.

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Rejection / %

100

90

80

0 DuraMem 150

DuraMem 200 NanoPro S-3012

NF030306

Membrane Fig. 8.30: Rejection of Sulfoxantphos in methanol for different OSN membranes at ambient temperature. Error bars represent standard deviations estimated from three independent experiments. Adapted from [36].

Figure 8.30 depicts the rejection of Sulfoxantphos in pure methanol for each of the investigated membranes. All membranes achieve a rejection of the ligand higher than 90% with the NF030306 displaying the lowest rejection followed by the DuraMem 200. The DuraMem 150 and NanoPro S-3012 significantly outperform the other two membranes with Sulfoxantphos rejections of 99.8%. These values are very promising for single stage membrane operation. The measured fluxes are depicted in Fig. 8.31. The flux through the DuraMem 150 and DuraMem 200 membranes are very similar with average fluxes of 11.7 kg m−2 h−1 and 11.1 kg m−2 h−1. The NanoPro S-3012 exhibits a slightly lower flux of 8.7 kg m−2 h−1 compared to the DuraMem membranes, while the NF030306 membrane has by far the lowest flux. This is expected, because the NF030306 is a hydrophobic membrane and the less hydrophobic polyimide from which the DuraMem 150 and DuraMem 200 are made shows a higher permeability for methanol. Based on this simplified mixture, the DuraMem 150 and NanoPro S-3012 are most promising for high catalyst rejection. Next, to examine the potential of the membranes to selectively remove water from the catalyst phase of the TMS while retaining the catalyst and potentially other key components that are present in the catalyst phase, further experiments are conducted using a model test mixture that approximates the catalyst phase from a reaction experiment. The composition of the test mixture is given in Tab. 8.16. The selected key components water, diethylamine, undecanal, and n-dodecane represent the co-product, reactant, intermediate, and non-polar solvent, respectively.

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Fig. 8.31: Total flux of model solutions for different OSN membranes at ambient temperature. The key components are diethylamine, n-dodecane, undecanal, and water. Error bars represent standard deviations estimated from three independent experiments. Adapted from [36]. Tab. 8.16: Composition of the feed mixtures for membrane experiments with model solutions. Component Methanol Diethylamine n-Dodecane Undecanal Water Sulfoxantphos

Solvent and ligand wFeed / -

Solvent, ligand, and key components wFeed / -

. – – – – .

. . . . . .

The measured rejections of the different components are illustrated in Fig. 8.32. The rejection of Sulfoxantphos is very high for all membranes with rejection in the same range as in the previously described screening experiments. Especially the NanoPro S-3012 achieves a high rejection of 99.4%. The DuraMem 150 is at 98.9%, whereas DuraMem 200 and NF030306 perform slightly worse. Water rejection for the DuraMem membranes and the NanoPro membrane are negative. This means that water is enriched in the permeate. Negative rejection is a phenomenon that can occur in OSN applications and in this case can be explained since water is smaller and even more polar than methanol resulting in better permeation through the DuraMem and NanoPro membranes. The NanoPro S-3012 shows the highest rejection for all additional components while the two DuraMem membranes exhibit similar rejection for these components around 40% to 50%. The NF030306 shows a very

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low rejection for diethylamine and undecanal and even a negative rejection for n-dodecane. This is again attributed to the non-polar membrane material and therefore higher affinity to the non-polar components. The expected high rejection of the catalyst due to the different polarity of the membrane and the ligand was not observed, although the manufacturer information indicated very high rejection (99% +) for a colorant with a molecular weight of 500 g mol−1, which is much lower than the molecular weight of the ligand. This demonstrates that MWCO values and the rejection of reference components cannot easily be extrapolated to different mixtures. Based on these initial investigations, it is concluded that hydrophobic membrane seems to be rather unsuitable for the investigated separation. The total flux is comparable for all membranes with fluxes below 5 kg m−2 h−1 (cf. Fig. 8.31). However, compared to the experiments without the key components the flux drops significantly for the DuraMem and NanoPro membranes. This is most likely closely related to the diethylamine concentration as further mentioned in the following sections. Based on the screening experiments the most promising membranes are the DuraMem 150 and NanoPro S-3012 which are used for further characterization with the actual catalyst solution.

Fig. 8.32: Rejection data of the components in the model catalyst solution at ambient temperature. Rejection data above 75% is displayed on a different scale for higher resolution. Error bars represent standard deviations estimated from three independent experiments. Adapted from [36].

Membrane screening with process solutions The next step to evaluate the membrane performance and to differentiate between the two most promising membranes are experiments in the actual process solution, which is the catalyst phase from a reaction experiment without membrane separation. This

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solution contains several additional components most of them by-products of the reaction. In contrast to the previous experiments the rejection of the catalyst is presented in terms of rhodium and phosphorus rejection. The phosphorus rejection is attributed to the free and the coordinated ligand whereas rhodium rejection represents the catalyst complex assuming that it is only present in the coordinated form in the solution due to an excess of the ligand. The results for the DuraMem 150 (Fig. 8.33) indicate that rhodium rejection is still high (96.6%) and comparable to the Sulfoxantphos rejection in the previous screening experiments, while the phosphorus rejection (83.1%) is considerably lower than in the previous experiments with the model solution. This can be caused by degradation of the catalyst complex or the ligand which can result in smaller phosphorus compounds that can permeate through the membrane. It is possible that the presence of diethylamine leads to a degradation of the DuraMem membrane which results in higher permeation of the ligand while still rejecting the larger catalyst complex. This is supported by the manufacturer information that DuraMem membranes are not recommended in the presence of strongly basic amines. Rejection of diethylamine, undecanal, n-dodecane, and water is similar to those in previous experiments proving that the experiments with test solutions can be used to approximate the rejection in the real catalyst phase quite well. The rejection of the remaining components in the reaction mixture (1-decene, iso-decene, amine, and aldol condensates) increases with increasing molecular weight.

Fig. 8.33: Rejection data for the catalyst solution from a previous reaction experiment using the DuraMem 150 and NanoPro S-3012. Error bars represent standard deviations estimated from three membrane cut-outs in one experiment. Adapted from [36].

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Compared to the DuraMem 150, the Nano-Pro S-3012 performs considerably better in retaining all the components in the catalyst phase. The rejection of rhodium as well as phosphorus is very high (98.4% and 97.4%), while the rejection of undecanal, iso-decene, product amine, and aldol condensate is shown as 100% because the components were detected in the feed solution but not in the permeate. Additionally, diethylamine, 1-decene, and n-dodecane are also retained much better by the NanoPro S-3012. A further benefit of the NanoPro S-3012 is the very low water rejection of − 61.2% which is even lower than in the screening experiments. The only drawback of the NanoPro S-3012 is the lower flux, which is only 0.54 kg m−2 h−1, compared to 2.9 kg m−2 h−1 for the DuraMem 150. The low flux can be caused by increasing concentrations of substrates, by-products, and the co-product in the catalyst phase and therefore a lower driving force for each component. Consequently, there is a trade-off between a higher membrane area required for membranes with low flux but with high catalyst rejection and a smaller membrane area for higher flux membranes with lower catalyst rejection. Since catalyst cost is usually the main contribution for processes using precious metal catalysts, the NanoPro S-3012 was chosen for the following continuous experiment.

Continuous experiment in a miniplant Since the previous membrane screening showed promising results the proof of concept in a continuous process is regarded in this part. The operation in a continuous process with recycle streams is important to observe accumulating components and mutual influences of different process units. This is especially important for the membrane because changes in the feed concentrations can lead to significant changes in the separation behavior. Thus, a long-term experiment was conducted in a continuous miniplant (cf. Fig. 8.15 (c)) using the NanoPro S-3012 due to its better overall performance in the screening experiments. The reaction performance throughout most of the experiment was constant with an average conversion of 80% of 1-decene and 62% average product yield of the amine. Detailed descriptions about the experimental setup, the reaction conditions, and the reaction performance are further discussed in [36]. The water content in the recycle and permeate stream is depicted in Fig. 8.34. It shows that throughout the miniplant experiment the water content in the recycle stream is effectively kept considerably below 5 wt.%. The significant impact of the OSN is highlighted by the comparison with a comparative experiment without the membrane, for which the water content increases to about 15 wt.% in the same time. This proves the feasibility of the described process concept for water removal. Furthermore, as already observed in the screening experiments, water permeates

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the membrane preferentially which is indicated by the higher water content in the permeate compared to the catalyst recycle stream and the respective negative water rejection (Figs. 8.33 and 8.34).

Fig. 8.34: Water content in the catalyst phase (retentate) and in the permeate during the continuous reaction-separation experiment. Data for the catalyst recycle without membrane is taken from [83] in which the same experiment was performed but without membrane separation [36].

The membrane performance is not only determined by water separation but also by catalyst rejection due to the high associated costs with catalyst lost. Figure 8.34 depicts the rejection of water, rhodium, and the product amine during the experiment. Water rejection is negative throughout the experiment as already observed in the screening experiments. However, water rejection increased over time resulting in worse water separation at the end of the experiment which could indicate membrane degradation. Rhodium rejection is determined to be considerably above 99% throughout most of the experiment, while it decreases slightly in the end, with a final value of 97%. Thus, the rhodium rejection is close to the rejection observed in the screening experiments using only the ligand as well as the catalyst complex. This confirms the suitability of the previously applied simplified model systems to predict the catalyst rejection in the real process. Remarkably, the rejection of the linear product amine exceeds 99% throughout the experiment, highlighting that not only the catalyst but also the non-polar components are very well retained by the NanoPro S-3012. The total permeate flux through the membrane is illustrated in Fig. 8.36. While the flux in the beginning of the experiment is comparable to the flux observed in the screening experiments with the model solution with key components, the flux decreases during the experiment to values below 1 kg m2 h−1. A similar flux was

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Fig. 8.35: Rejection of the product, catalyst (rhodium), and water during the continuous reactionseparation experiment [36].

also observed in the experiments for the NanoPro S-3012 using the real catalyst solution. In addition to the membrane flux, the weight fraction of diethylamine in the catalyst recycle stream during the experiment is also shown in Fig. 8.36. It appears that the increasing weight fraction of diethylamine correlates with a decreasing membrane flux. While this is not a proof that diethylamine causes this behavior, it is in line with the previous results that showed lower fluxes when diethylamine was present in the feed mixtures. Despite the decrease in flux, water separation was sufficient to avoid water accumulation. However, longer operation times would require an increased membrane area to reach a steady state water concentration if the membrane flux declined further. Additionally, the accumulation of diethylamine should be avoided by a different dosing strategy, which should result in a higher membrane flux and better water separation. Also, a two-stage membrane separation should be investigated at least on a theoretical basis, to reduce the loss of rhodium even further. Using the described experimental workflow, it is possible to select suitable membranes for complex reaction separation processes. The results also show that simplified model systems can provide reasonable estimates of membrane performance indicators such as flux and rejection and that membrane selection using only an MWCO is not sufficient for process design. This is summarized again in Tab. 8.17 in which the rejection and flux from the different experiments are compared for the DuraMem 150 and NanoPro S-3012 membranes. It should be noted that the flux decreased from the simplified experiments with only solvent and ligand to the model solution and the catalyst solution while the lowest flux values were observed at the end of the continuous miniplant experiment. As previously described, this might be

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Fig. 8.36: Total membrane flux over time during the continuous reaction-separation experiment (left axis). Weight fraction of diethylamine in the catalyst recycle stream over time (right axis) [36].

caused by the presence of diethylamine in the feed solution. In this regard the continuous experiment provides valuable data for this assumption that are not easily available from the previous screening experiments. Although high experimental effort is required for the miniplant experiments, the additional insight into the process and the interconnections of different process parts supports their use in process design workflows. Tab. 8.17: Comparison of membrane performance in the different experiments. DuraMem 

Experiment

Methanol / Ligand Model solution Catalyst solution Continuous Process (t =  h)

NanoPro S-

Rcat / %

Rwater / %

Jtotal / kg m− h−

Rcat / %

Rwater / %

Jtotal / kg m− h−

.* .* .** –

– −. −. –

. . . –

.* .* .** .**

– −. −. −.

. . . .

* Based on the rejection of the ligand ** Based on the rejection of rhodium

A scale-up of the investigated process would require more insights into the membrane separation and the development of a suitable membrane model, which is quite complex due to the large number of different components present in the mixtures. Also, optimized reaction conditions are necessary especially regarding the

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diethylamine feed strategy. This example highlights that process conditions suitable for one process unit, might not necessarily be the optimum for other process units and that a balance should be aimed for when designing complex processes that involve OSN separation. Additionally, the described process highlights the potential of OSN application even in complex reaction-separation processes.

8.6 Take-home messages – OSN is a pressure driven membrane separation that is able to separate liquid organic mixtures on a molecular level. – OSN can be applied as a complement to conventional unit operations, such as distillation. OSN is usually not suitable as a standalone separation technology. – The number of OSN-assisted industrial processes is limited. However, the feasibility of OSN for a variety of separation tasks has been proven in fundamental research studies or at the laboratory scale. – The design of OSN-assisted processes is complex due to interactions between membranes, solvents, and solutes, and these interactions are hard to predict. – Seizing the opportunities of OSN demands an interdisciplinary approach, including improved modeling approaches and methods for efficient process design. – Membrane selection plays an important role in process design because predictive models for membrane performance are not yet available. Experiments are almost always necessary for membrane selection. – Multistage OSN setups can be applied to fulfill desired separation tasks. Therefore, process design based on the optimization of OSN membrane cascades is a promising tool. Nevertheless, costs of such multi-stage processes can be high. – By applying an integrated process design (e.g., using MRMs, MMMs, or data-based models and targeted experiments), optimized process setups with fewer stages or improved process economics can be attained.

8.7 Quiz 8.7.1 OSN fundamentals Question 1. How can the performance of OSN be evaluated? Which measures are applied for evaluating the separation efficiency? How are they defined and what are their advantages/disadvantages?

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Question 2. What is the main difference between OSN and pervaporation/vapor permeation? Question 3. Which types of OSN membranes exist? What are their advantages/ disadvantages? Question 4. Why is a membrane characterization based on MWCO often not sufficient for membrane selection? Question 5. What types of membrane modules are applied in OSN and for which membranes are they suited? What are the challenges associated with the use of organic solvents? Question 6. What is a membrane cascade and how many additional degrees of freedom exist compared to distillation columns? Question 7. What are the main permeation model types applied for OSN? What is the challenge in distinguishing between both model types? Question 8. Which physicochemical parameters are important for the permeation of (a) solvents, (b) solutes through a polymeric OSN membrane? Question 9. Which effects result in decreased net driving forces for OSN permeation and must be accounted for when calculating the required membrane areas? Which parameters/ characteristics are these effects dependent on?

8.7.2 Process design for OSN Question 10. What are the most important challenges for OSN process design during the conceptual process design phases? How can they be addressed? Question 11. What are the most important challenges for OSN process design during the detailed process design phases? How can they be addressed? Question 12. What is an MRM? What is it useful for? What are its limitations? Question 13. What is an MMM? What is it useful for? What are its limitations?

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8.8 Exercises Exercise 1. What is the separation factor between components A and B if the following rejections were measured: RA = 30% and RB = 90%? Exercise 2. A production of 100 000 t a−1 of n-hexanal must be achieved. An OSN membrane test using spiral-wound modules has demonstrated that the catalyst can be efficiently recycled within a single stage. What is the total membrane area if the membrane permeance is 0.5 kg m−2 h−1 bar−1) and the membrane is operated at 50 bar TMP? How many 8′′ spiral-wound modules are required? Exercise 3. What is the total membrane area required to produce 80 000 t a−1 (8 000 h a−1 operating time) of a product based on the following boundary conditions? – A two-stage OSN process setup is used to meet the required permeate specifications. – The membrane permeate flux for both stages is 40 kg m−2 h−1. – The specific feed flow per m2 membrane area is 400 kg h−1. – In both stages, 50% of the retentate is internally recycled. Exercise 4. A homogenous Rh-based catalyst must be rejected using a single-stage OSN process (annual production capacity of 100 000 t a−1 and 8 000 h a−1). The rejection of the catalyst must exceed 99%; the feed concentration is 100 ppm by weight. You are asked to decide between two membranes (see Tab. 8.18). The price of Rh is 100 € kg−1.1 Which membrane would you select based on investment and operating costs? Both membranes can be operated at 50 bar TMP. Tab. 8.18: Assumptions for Exercise 4. Membrane

Polymeric Ceramic

Installed cost

Annual membrane replacements

Rh rejection

Permeance

(€ m−)

(–)

(%)

(kg m h− bar−)

 ,

 .

 .

. 

1 Please note that the rhodium price has increased significantly in recent years.

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8.9 Solutions 8.9.1 OSN fundamentals Solution (Question 1). The main criteria include the specific permeate flux (in kg m−2 h−1) and the separation between different components. In the literature, different measures are available to analyze both properties (Tab. 8.19). Tab. 8.19: Measures for separation efficiency. Measure

Definition

Rejection

Ri = 1 −

Ci, perm Ci, feed

Advantages

Disadvantages

Easy to use; widespread application

Depends on operating conditions

Refers to a direct separation property of the membrane

No indication of purities in permeate because it is only a relative value

Permselectivity Si, j =

Pi Ji with Pi = Pj Δ DFi

Separation factor

Ci, perm Cj, feed 1 − Rj Indicates a property of the = Ci, feed Cj, perm 1 − Ri whole separation process, allowing comparison with other processes (e.g., OSN vs. pervaporation)

βi, j =

Depends on operating conditions

Solution (Question 2). OSN is a pressure driven separation process in which only liquid phases are present. In contrast, vapor permeation includes vapor phases in both the feed and permeate, whereas pervaporation contains liquid in the feed and vapor in the permeate. The chemical potential as the universal driving force can be simplified for the different processes (absolute pressure difference in OSN vs. partial pressure difference in pervaporation or vapor permeation). Consequently, the permeances in OSN are typically much larger than those for pervaporation or vapor permeation. Solution (Question 3). The types of OSN membranes are described in Tab. 8.20. Solution (Question 4). A characterization based on MWCO is not sufficient for membrane selection because the MWCO value varies largely as a function of the applied solvent. Therefore, no transfer to other solvents or real applications is possible. Moreover, different membrane manufacturers use different methods and operating conditions for MWCO determination. Solution (Question 5). The types of OSN membrane modules are described in Tab. 8.21. Solution (Question 6). A membrane cascade is a (mostly counter-current) configuration of membrane modules that is analogous to distillation columns. The permeate of a membrane stage is fed to the next stage as feed, whereas the retentate is

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recycled to a “lower” stage. In contrast to distillation columns, the additional degrees of freedom include the operating conditions in every stage (feed pressure and temperature) and the internal reflux ratios to supply the membrane modules with a sufficient feed flow. Tab. 8.20: Types of OSN membranes. Type

Advantages

Disadvantages

Polymeric (integrally skinned asymmetric)

Very thin active layer possible (lower resistance to mass transfer); cheap fabrication

Complicated relationship between the production process and separation performance

Polymeric (thin-film composite)

Use of different polymers possible (flexibility), very thin active layers are feasible.

Interface between different polymers must be stable

Ceramic

Mechanical and chemical stability; use at high temperatures

Until recently, only larger MWCO values have been available (> Da); less versatile based on the required materials; more expensive

Tab. 8.21: Types of OSN membrane modules. Type

Types of membranes

Challenges

Spiralwound

Polymeric membranes

Stability of glues (membrane bags) in organic solvents; susceptible to plugging in the presence of solid particles

Tubular

Mostly ceramic membranes; polymeric also available

Larger crossflow velocities are necessary (e.g., – m s−)

Solution (Question 7). The main permeation models are solution-diffusion models and pore-flow models. The main challenge for distinguishing them from each other is that both driving forces are similar (i.e., the net pressure difference, including the osmotic pressure of the solutes, in the solution-diffusion model and the transmembrane pressure difference in the pore-flow model). Solution (Question 8). The important physicochemical parameters are as follows: a. Solvents: The solvent solubility parameter compared to that of the membrane polymer, the solvent molar volume and the diffusion coefficient of the solvent in the membrane material. b. Solutes: The solute solubility parameter compared to that of the membrane polymer, the solute size and the pore size of the membrane.

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Solution (Question 9). Osmotic pressure (reduced driving force due to dissolved components) results in decreased net driving forces for OSN permeation. Higher osmotic pressures are due to smaller dissolved components and higher concentrations. Moreover, the net transmembrane pressure difference depends on the pressure loss over the length of a membrane module. The pressure drop is higher for smaller cross-sectional areas and larger crossflow velocities (and viscosities).

8.9.2 Process design for OSN Solution (Question 10). The primary challenge is the selection of a suitable OSN membrane and solvents. Possible solutions include establishing a large experimental database, an improved understanding of permeation in OSN and the development of more stable membranes (reduction of uncertainties using real mixtures). Also, data-driven models can help in the selection of OSN membranes. Solution (Question 11). The primary challenge is the design of the OSN process. Possible solutions include the application of rigorous optimization methods based on OSN membrane cascades and the development of flexible standard process setups. Solution (Question 12). An MRM shows the rejection of solutes in multicomponent solvent mixtures in a ternary diagram, which can be used to determine suitable solvents for fulfilling given separation tasks by relating a given process solute to an already measured/ known solute. An MRM is always limited to a single solute and a single membrane. Transfer may only be possible within the same solvent/solute class and for very similar OSN membranes. MRMs have only been applied for a few solvents/solutes/membranes thus far. Solution (Question 13). An MMM shows recommended measures to improve solute rejections in a ternary diagram. The measures are directed toward changes in the solvent and/ or the OSN membrane. The recommendations are based on the dominant transport mechanisms (solution-diffusion and/ or pore-flow). An MMM is always limited to a single solute and a single membrane. Moreover, in many cases, the permeation mechanisms are not clear (both mechanisms occur at the same time).

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8.9.3 Exercises Solution (Exercise 1). Definition of rejections: RA = 1 −

cA, perm cA, feed − cA, perm = = 0.3 , cA, perm = 0.7cA, feed cA, feed cA, feed

RB = 1 −

cB, perm cB, feed − cB, perm = = 0.9 , cB, perm = 0.1cA, feed cB, feed cB, feed

Calculation of separation factor: βA, B =

cA, perm cB, feed 0.7cA, feed cB, feed 0.7 = = =7 cA, feed cB, perm cA, feed 0.1cB, feed 0.1

Also, a direct calculation is possible: βA, B =

1 − RA 1 − 0.3 0.7 = = =7 1 − RB 1 − 0.9 0.1

Solution (Exercise 2). – Membrane permeate flux per m2: 0.5 kg m−2 h−1 bar−1 ⋅ 50 bar = 25 kg m−2 h−1 – Total permeate flux: 100 000 t a−1 = 12 500 kg h−1 – Membrane area: A = 12 500 kg h−1 / 25 kg m−2 h−1 = 500 m2 An 8′′ spiral-wound OSN module has (depending on the spacer thickness) an area of approximately 30 m2, which results in 17 spiral-wound modules. Solution (Exercise 3). Final process layout is shown in Fig. 8.37 (the numbers in brackets indicate the calculation order):

Fig. 8.37: Resulting two-stage setup for Exercise 3.

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The total area is 1,500 m2 (250 m2 in stage 1 and 1,250 m2 in stage 2). Solution (Exercise 4). Both membranes fulfill the minimum Rh rejection. Therefore, both membranes can be applied within a single-stage process setup. The total permeate flux is 12 500 kg h−1. Based on these results and the given specifications, the membrane areas, the annual membrane replacement costs and the rhodium loss can be calculated. – Polymeric membrane: 1. Membrane area: A = 500 m2 Annual membrane replacement costs: 500 € m−2 a−1 ⋅ 500 m2 = 250 000 € a−1 2. Costs of rhodium loss: 12 500 kg h−1 ⋅ 10−4 kg kg−1 ⋅ 8 000 h a−1 ⋅ 100 € kg−1 = 1 000 000 € a−1 Operating costs of polymeric membrane: 1 250 000 € a−1 – Ceramic membrane: 1. Membrane area: A = 250 m2 Annual membrane replacement costs: 4000 €m−2 a−1 ⋅ 500 m2 = 1 000 000 € a−1 2. Costs of rhodium loss: 12 500 kg h−1 ⋅ 2 ⋅ 10−5 kg kg−1 ⋅ 8 000 h a−1 ⋅ 100 € kg−1 = 200 000 € a−1 Operating costs of ceramic membrane: 1 200 000 € a−1 From an operating cost perspective, the ceramic membrane is slightly better. However, the investment costs of the ceramic membrane plant are 1 000 000 €, whereas the polymeric membrane plant costs only 250 000 €. Both aspects must be considered in the investment decision. Based on a linear depreciation model, the cost for depreciation is 100 000 € a−1 for the ceramic membrane plant and only 25 000 € a−1 for the polymeric membrane plant. Including these values in the operating cost analysis favors the polymeric membrane plant. – Total operating costs of polymeric: 1 250 000 € a−1 + 25 000 € a−1 = 1 275 000 € a−1 – Total operating costs of ceramic: 1 200 000 € a−1 + 100 000 € a−1 = 1 300 000 € a−1

List of symbols A a B0 c D ΔDF EF J M

Membrane area Activity Viscous permeability of the membrane Concentration Diffusion coefficient Driving force for permeation Enrichment factor Permeate flux through the membrane Molecular weight

m – m mol m− m s− – – kg h− m− g mol−

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Mass Permeance Transmembrane pressure difference Ideal gas constant Membrane resistance Rejection Radius Permselectivity Temperature Time interval Molar volume Mass fraction

m P Δp R R R r S T Δt V w

kg kg h− m− bar− Pa s J mol− K− Pa s m− – m – K m mol−

Greek letters δM β δ ε η π τ ’

Thickness of the membrane active layer Separation factor Solubility parameter Membrane porosity Viscosity Osmotic pressure Membrane tortuosity Sorption coefficient of the solvent

List of abbreviations AI API DMC MMM MRM MWCO NF oNF OSN PC PC-SAFT PDMS PEG PI RO SRNF STNF TFC TMP UF

Artificial intelligence Active pharmaceutical ingredient Dimethyl carbonate Membrane modeling map Membrane rejection map Molecular weight cut-off Nanofiltration Organophilic nanofiltration Organic solvent nanofiltration Propylene carbonate Perturbed-chain statistical associating fluid theory Polydimethylsiloxane Polyethylene glycol Polyimide Reverse osmosis Solvent-resistant nanofiltration Solvent tolerant nanofiltration Thin film composite Transmembrane pressure difference Ultrafiltration

m – MPa. – mPa s Pa s – kg kg −

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[57] White LS. Development of large-scale applications in organic solvent nanofiltration and pervaporation for chemical and refining processes. J. Memb. Sci. 2006;286(1–2):26–35. [58] Köseoglu SS, Engelgau DE. Membrane applications and research in the edible oil industry: An assessment. J. Am. Oil Chem. Soc. 1990;67(4):239–249. [59] Buonomenna MG, Bae J. Organic solvent nanofiltration in pharmaceutical industry. Sep. Purif. Rev. 2015;44(2):157–182. [60] Boam A, Nozari A. Fine chemical: OSN – A lower energy alternative. Filtr. Sep. 2006;43(3): 46–48. [61] Scarpello J. The separation of homogeneous organometallic catalysts using solvent resistant nanofiltration. J. Memb. Sci. 2002;203(1–2):71–85. [62] Cseri L, Fodi T, Kupai J, Balogh TG, Garforth A, Szekely G. Membrane-assisted catalysis in organic media. AML 2017;8(12):1094–1124. [63] Dijkstra M, Bach S, Ebert K. A transport model for organophilic nanofiltration. J. Memb. Sci. 2006;286(1–2):60–68. [64] Lonsdale HK, Merten U, Riley RL. Transport properties of cellulose acetate osmotic membranes. J. Appl. Polym. Sci. 1965;9(4):1341–1362. [65] Wijmans JG. The role of permeant molar volume in the solution-diffusion model transport equations. J. Memb. Sci. 2004;237(1–2):39–50. [66] Mason EA, Lonsdale HK. Statistical-mechanical theory of membrane transport. J. Memb. Sci. 1990;51(1–2):1–81. [67] Machado DR, Hasson D, Semiat R. Effect of solvent properties on permeate flow through nanofiltration membranes. Part I: Investigation of parameters affecting solvent flux. J. Memb. Sci. 1999;163(1):93–102. [68] Hesse L, Sadowski G. Modeling liquid–liquid equilibria of polyimide solutions. Ind. Eng. Chem. Res. 2012;51(1):539–546. [69] Marchetti P, Livingston AG. Predictive membrane transport models for Organic Solvent Nanofiltration: How complex do we need to be?. J. Memb. Sci. 2015;476:530–553. [70] Schmidt P, Köse T, Lutze P. Characterisation of organic solvent nanofiltration membranes in multi-component mixtures: Membrane rejection maps and membrane selectivity maps for conceptual process design. J. Memb. Sci. 2013;429:103–120. [71] Goebel R, Glaser T, Skiborowski M. Machine-based learning of predictive models in organic solvent nanofiltration: Solute rejection in pure and mixed solvents. Sep. Purif. Technol. 2020;248:117046. [72] Goebel R, Skiborowski M. Machine-based learning of predictive models in organic solvent nanofiltration: Pure and mixed solvent flux. Sep. Purif. Technol. 2020;237:116363. [73] Hu J, Kim C, Halasz P, Kim JF, Kim J, Szekely G. Artificial intelligence for performance prediction of organic solvent nanofiltration membranes. J. Memb. Sci. 2021;619:118513. [74] Zeidler S, Kätzel U, Kreis P. Systematic investigation on the influence of solutes on the separation behavior of a PDMS membrane in organic solvent nanofiltration. J. Memb. Sci. 2013;429:295–303. [75] Schmidt P, Lutze P. Characterisation of organic solvent nanofiltration membranes in multicomponent mixtures: Phenomena-based modelling and membrane modelling maps. J. Memb. Sci. 2013;445:183–199. [76] Stevens MG, Anderson MR, Foley HC. Side-chain alkylation of toluene with propene on caesium/nanoporous carbon catalysts. Chem. Commun. 1999;5:413–414. [77] Black LE, Boucher HA Process for separating alkylaromatics from aromatic solvents and the separation of the alkylaromatic isomers using membranes. US19840603028; 1984. [78] Pines H. Base-Catalyzed Reactions of Hydrocarbons and Related Compounds. Oxford: Elsevier Science; 1977.

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[79] Stuart NJ, Sanders AS Phenyl propionic acids. Patent. GB19610003999;(US3385886 (A)); 1963. [80] Baerns M. Technische Chemie. 2nd edn. Hoboken: Wiley; 2013. [81] Wiese K-D, Obst D. Hydroformylation. In: Beller M, ed. Catalytic Carbonylation Reactions. Berlin: Springer; 2006, 1–33. [82] Hansen CM. Hansen Solubility Parameters: A User’s Handbook. 2nd edn. Boca Raton: Taylor & Francis; 2007. [83] Bianga J, Künnemann KU, Goclik L, Schurm L, Vogt D, Seidensticker T. Tandem catalytic amine synthesis from alkenes in continuous flow enabled by integrated catalyst recycling. ACS Catal. 2020;10(11):6463–6472. [84] Ahmed M, Seayad AM, Jackstell R, Beller M. Amines made easily: A highly selective hydroaminomethylation of olefins. J. Am. Chem. Soc. 2003;125(34):10311–10318. [85] Chen C, Dong X-Q, Zhang X. Recent progress in rhodium-catalyzed hydroaminomethylation. Org. Chem. Front. 2016;3(10):1359–1370. [86] Kalck P, Urrutigoïty M. Tandem Hydroaminomethylation Reaction to Synthesize Amines from Alkenes. Chem. Rev. 2018;118(7):3833–3861. [87] Bianga J, Künnemann KU, Gaide T, Vorholt AJ, Seidensticker T, Dreimann JM, et al. Thermomorphic multiphase systems: Switchable solvent mixtures for the recovery of homogeneous catalysts in batch and flow processes. Chem. Eur. J. 2019;25(50):11586–11608.

Johannes Holtbrügge, Jerzy R. Pela

9 Pervaporation and vapor permeation– assisted reactive separation processes 9.1 Fundamentals In a conventional reaction-separation sequence, the reaction step is followed by one or multiple separation steps performed within individual apparatuses. This setup can result in a complex configuration of reaction and separation tasks that are necessary to fulfill the design task. However, the efficiency and sustainability of these processes are deemed to be low. Integrating the reaction and separation can result in a significant intensification of the processes by increasing their efficiency. The resulting processes (Fig. 9.1) are reactive separations, hybrid separations, or a combination of both, i.e., an integrated hybrid reactive separation. This chapter will elaborate on reactive and hybrid reactive separations created by combining a reactor, distillation column, and pervaporation or vapor permeation. Emphasis will be placed on utilization of pervaporation or vapor permeation for membraneassisted (reactive) distillation and membrane reactors (MR). A general introduction to hybrid separation processes is provided in Chapter 2, while a detailed discussion of reactive distillation is conducted in Chapter 5.

Fig. 9.1: Principles of integrated reactive, hybrid, and integrated hybrid reactive separation processes (adapted and extended from [1]).

Similar to organophilic nanofiltration discussed in Chapter 8, pervaporation (PV) and vapor permeation (VP) enable selective removal of a specific component from a treated mixture. PV/VP membranes are generally non-porous membranes and therefore rely solely on the solution-diffusion separation mechanism [2]. With a properly selected membrane matrix, the targeted component will preferentially dissolve in https://doi.org/10.1515/9783110720464-009

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and diffuse through the membrane enabling a more selective separation of small or similarly sized molecules such as mixtures of water and methanol. The use of this unique quality finds applications in membrane reactors for selective removal or distribution of the components of the reactive system [3, 4], hence opening new possibilities for controlling the reactions or improving the selectivity and conversion of reactions limited by chemical equilibrium. Similar to other reactive separation processes, such as reactive distillation, the number of components that can be recovered in their pure states is limited. Typically no more than two pure components can be recovered in the product streams, impeding the application to multiproduct reactions, multiple-reaction systems, or systems that require a large excess of one reactant [5]. This is especially true for the separation steps within systems that comprise thermodynamic limitations, e.g., azeotrope formation in distillation, which are energyintensive processes when using conventional separation sequences [6]. Alternatively, hybrid separation processes coupling at least two different operations implemented in separate apparatuses and offering substantial synergistic effects for each operation compared to standalone operations have also been developed [7]. These interactions can overcome the individual limits of standalone operations, leading to increased efficiency and sustainability in multicomponent separations [8]. The combination of membranes and distillation is beneficial due to the high investment costs for membranes and modules, which result in economically inefficient standalone membrane processes when high throughputs must be processed or high purities must be reached [9]. Membrane separation processes are preferably combined with unit operations that can handle high throughputs while not being capable of overcoming thermodynamic limitations, such as azeotropes [10]. In doing so, membrane-assisted (reactive) distillation processes represent promising alternatives to special distillation processes, such as azeotropic, extractive, and pressure swing distillation. Therefore, energy-intensive operations, especially pressure changes or the separation of additional entrainers, can be avoided.

9.1.1 Pervaporation and vapor permeation Drioli et al. [11] discussed several ways to use membrane separation processes. They found three promising application areas of membranes, including desalination, membrane-based reactive separations, and membrane-based hybrid separations. They noted that PV and VP processes are promising for membrane-based reactive and hybrid separations. PV and VP are characterized by the simultaneous occurrence of different mass transfer phenomena (e.g., sorption and diffusion) and the existence of different phases (e.g., solid membrane and vaporous permeate phase). This section presents a brief overview of the state-of-the-art PV and VP processes. For a complete overview of this broad area in chemical engineering, the interested reader is referred to

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the literature that comprises several publications on both processes. Huang [12] published a textbook on PV and VP. General overviews of membrane separation processes, including chapters on PV and VP, are published in the book series by Noble, Melin and Rautenbach, Baker, and Drioli and Giorno, Böddeker [13–17]. Comprehensive reviews of both processes can be found in Dutta et al., Feng and and Huang, Abetz et al., and Shao and Huang [2, 18–20].

Separation principle PV and VP can be used to separate volatile components from a multicomponent mixture via a dense membrane. The separation mechanism is based on the different sorption and diffusion characteristics of the processed components in interaction with the membrane matrix [14]. The feed mixture (F) is separated into the retentate (R), which primarily consists of the retained components, and the vaporous permeate (P), which contains the preferentially permeating components (Fig. 9.2).

Fig. 9.2: Operating modes of PV and VP under (left) vacuum and (right) sweep gas operations (adapted from [19]).

The following equation represents the separation factor, which can be used to describe the separation efficiency of a membrane material for a given separation task: βij =

yP, i =yP, j xF, i =xF, j

(9:1)

Component i is the better permeating component, whereas j is the component that is preferentially retained by the membrane material. A high separation factor indicates a good separation, whereas a separation factor of one indicates that no separation of the feed mixture occurs using the selected membrane material. The main difference between PV and VP is the physical state of the feed, i.e., liquid for PV and vapor for VP. Hence, the principles of vapor and gas permeation are very similar [21]. Despite the difference between the individual processes, the same expression for the mass transfer driving force is used. For membrane separation processes, the mass transfer driving force, DFi, is generally expressed by the chemical potential difference, Δμi, between the feed and permeate side of the membrane [12]. Hence, the

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following approach is used to describe the chemical potential difference between the liquid feed and vaporous permeate in the PV case:   xF, i · yF, i · pLV i , i = 1, ..., nc = R · T · ln (9:2) DFiPV = Δμ PV F i yP, i · pp The contribution of the Poynting correction term is not considered in eq. (9.2) because it is negligible at low pressures [22] (also see Chapter 3). In addition, an ideal vapor phase behavior is assumed for the permeate. The expression for the VP driving force differs slightly from the one for PV to account for the vaporous feed. The following equation represents the VP driving force for ideal vapor phase behavior on both sides of the membrane:   yF, i · pF VP VP , i = 1, ..., nc (9:3) DFi = Δμ i = R · TF · 1n yP, i · pp The driving force is a function of the feed temperature TF, feed concentration xF/yF, permeate pressure pP and, in the case of VP, the feed pressure pF. To establish a high driving force for mass transfer, a low partial pressure of component i on the permeate side is commonly established. Figure 9.2 shows the different operating modes of PV and VP for lowering the partial pressure on the permeate side. The sketch on the left shows the operation with a vacuum on the permeate side, whereas a sweep gas stream lowers the partial pressure in the operation mode presented in the sketch on the right. Tab. 9.1: Benefits and drawbacks of pervaporation and VP (adapted and extended from [14, 23]). Membrane process

Benefits

Drawbacks

Pervaporation High transmembrane flux, only permeate vaporized

Intermediate heating, chemical stability (e.g., acids), mass transfer resistances

Vapor permeation

Feed vaporization, high temperature

High selectivity, isothermal operation, reduced strain on membrane

PV and VP offer distinctive benefits and drawbacks. Because the permeate is removed as vapor, a phase transition occurs during the PV process. The necessary enthalpy of vaporization is taken from the feed mixture, resulting in an axial temperature decrease along the membrane and a decreasing mass transfer driving force (eq. (9.2)). In contrast, VP is isothermally operated, although it requires a vaporous feed. Hence, VP is deemed beneficial when the feed is already in its vapor state. Table 9.1 provides a brief comparison between the different benefits and drawbacks of PV and VP.

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The driving force cannot describe the mass transfer resistance caused by the dense membrane material [24]. According to the solution-diffusion approach for dense membrane separation processes, the membrane permeability Pi, which accounts for the interactions between the used membrane material and the permeating components, is necessary to describe PV and VP [25, 26]: Ji =

Pi · Mi · DFi = Qi · Mi · DFi , δMemb

1, ......, nc

(9:4)

Because the membrane thickness, δMemb, is typically unknown, the membrane permeance, Qi, which combines the membrane permeability and thickness, is introduced [27]. The membrane permeance depends on the operating conditions and represents the sorption of components to the membrane, their diffusion through the membrane material and desorption on the permeate side of the membrane (Section 9.3.1) [23]. Finally, the permeate flux, Ji, can be calculated from the product of the membrane permeance and the mass transfer driving force. Membrane permeances must be determined via permeation experiments with different driving forces, which can be conducted by changing the operating conditions and measuring the corresponding permeate flux. In addition to the membrane permeance, the molar membrane selectivity, αij, is also a crucial parameter that is used to evaluate membrane separation processes [28]. The molar membrane selectivity, or permselectivity, is defined as the ratio of both permeances, with the preferentially permeating component in the numerator: aij =

Qi Qj

(9:5)

Using the membrane selectivity to describe the separation performance of membranes is superior to the use of the separation factor (eq. (9.1)) because the permselectivity represents only the separation ability of the membrane material and is independent of the mass transfer driving force. High membrane permeances and permselectivities are desired when applying membrane separation processes [29]. However, it is not possible to realize both objectives simultaneously, which results in a trade-off scenario [30].

Membrane materials and module types Membranes for PV and VP can be produced from hydrophilic or hydrophobic materials. These materials can be further classified into inorganic and organic (polymeric) materials; polymeric ones are currently preferentially applied in academia and industry [23]. Recently, asymmetric composite membranes have found their way into industrial-scale applications [14]. These membranes consist of a thin active separation and a porous support layer that are made from different polymers. They

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offer a trade-off between high mechanical stability and membrane thickness, resulting in a low mass transfer resistance and high permeate fluxes [31]. In addition to these polymer membranes, inorganic membranes, which have higher mechanical and thermal stabilities, can be used for PV and VP. Zeolite membranes have been successfully tested to dewater alcohols, namely, ethanol and i-propanol, resulting in the first industrial application [32–35]. Other ceramic membranes are still in the developmental phase and have not yet attained properties that permit their largescale industrial implementation [23]. A major drawback of inorganic membranes is their difficult and high-cost production. This drawback can be equalized by better process performance with higher permeate fluxes and constant selectivities in comparison to polymer membranes [23]. To allow an economically meaningful application of PV and VP at the industrial scale, membranes are combined in membrane modules. However, the development of suitable membrane modules is based on several design requirements. The first important aspect is the need for low production costs for modules with high chemical, mechanical, and thermal stabilities [14]. Membrane replacement must be easy, and the modules must have a high packing density [36]. Other requirements include uniform flow across the membrane surface, negligible polarization effects (Section 9.3.1) and very low pressure drops on the permeate side (and, in the case of VP, on the feed side as well) [23]. Because not all design requirements can be fulfilled by one membrane module, various module types exist for different applications. Baker [15] provided a guideline for the proper selection of suitable membrane modules for a given task. In principle, membrane modules can house flat-sheet or tubular membranes [23]. Table 9.2 lists the three most common modules from each group. Modules for flat-sheet membranes have low production costs and a high packing density combined with a low pressure drop and negligible polarization effects [23]. Plate-andframe modules are most commonly used in industry for PV and VP [14]. Brüschke et al. (Sulzer Chemtech Ltd., [37]) developed a plate-and-frame module that has been applied in several industrial-scale processes. These modules have low production costs, although this benefit is counterbalanced by the large number of gaskets necessary to seal the modules, making their operation difficult [38]. Modules for tubular membranes are simple to flush and are usable for tasks with high solid contents. In particular, hollow-fiber modules, which have become a state-of-the-art technology for gas permeation, are typically applied for VP due to their high packing density and the resulting low specific costs for such membrane modules [15]. However, these membrane modules exhibit a high fouling risk and have not yet been applied to PV. Despite the increase in knowledge, membrane separation processes remain underutilized in the chemical and petrochemical industries due to the poorly understood scale-up of membrane modules from the laboratory scale to the industrial scale [39]. Thus, the transfer of knowledge between these scales requires additional

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Tab. 9.2: Different membrane modules (adapted from [14]). Flat-sheet membranes

Tubular membranes

Plate-and-frame module

Tubular module

Cushion module

Capillary module

Spiral-wound module

Hollow-fiber module

research to determine reliable scale-up options. Furthermore, model-based tools that provide precise theoretical descriptions of membrane separation processes with typically changing process variables along the membrane are necessary to promote their industrial application.

9.1.2 Membrane-assisted distillation Membrane-assisted distillation processes are used for the integration of complex separations that exhibit difficult thermodynamic behaviors. Such systems can consist of ideal, but narrow boiling and also nonideal, e.g., azeotropic, mixtures. The use of membrane-assisted distillation can result in the following advantages for the separation of these systems: – Overcoming thermodynamic limitations. Thermodynamic restrictions of at least one of the operations combined in this process type can be overcome by combining different separation mechanisms [7]. – Energy savings. Reduced recycle streams may result in decreased energy costs because heating and cooling operations are minimized [40]. Despite the benefits of membrane-assisted distillation processes, the following drawbacks should be considered when evaluating the reliability of these processes: – Operating-window constraints. The operating window of the combined operations must match to fulfill the requirements due to the strong interdependency of the individual operations [41]. – Complex process design. The additional decision variables that must be considered during the design phase impede a meaningful process design [42]. – Lack of process know-how. Membrane-assisted distillation processes remain sparsely applied in industry. The few data available on these processes are neither able to provide detailed insights into the operation nor eliminate the skepticism toward them [43].

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Process configurations For different potential applications of membrane-assisted distillation processes, different configurations are required. To demonstrate this notion, two different chemical systems are considered. In the first step, the integration of a chemical system comprising two components, namely, A and B, in such a process is presented. Furthermore, the implementation of a chemical system consisting of three components, namely, A, B, and C, is discussed. In both systems, component A has the highest boiling point, and the boiling point order is as follows: TA > TB ( > TC). A large number of decision variables within the design of membrane-assisted distillation processes cause a multitude of possible configurations for the distillation column and the membrane separation process. Figure 9.3 provides three examples for the first (configurations 1–3) and one example for the second (configuration 4) chemical system.

Fig. 9.3: Possible process configurations for the combination of distillation with pervaporation or vapor permeation (adapted and extended from [44]).

In configuration 1, the binary feed mixture is separated until a minimum azeotrope between the two components (A,B) limits the purification of the binary mixture. The membrane is used to overcome this azeotrope. When an azeotrope is in the middle of the concentration range, the use of configuration 2 can be beneficial. The membrane is used to overcome the minimum azeotrope and the permeate is recycled into the distillation column. A second distillation column is fed with the retentate, whose concentration is shifted to the other side of the azeotrope. This distillation column is used to purify component A up to the predefined specification. Configuration 3 shows another example of a membrane-assisted distillation process. Here, membrane separation is used in the side stream of the distillation column to support the separation in the column. This process configuration is especially beneficial for narrow boiling mixtures and can result in smaller columns or lower reflux ratios, which ultimately result in significantly decreased energy demands or a capacity increase for a constant energy demand. Configuration 4 shows the separation of a ternary mixture into its pure components for a membraneassisted distillation process. Here, membrane separation is used in the side stream

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of the distillation column and acts to remove component B. This configuration can be advantageous when the component forms an intermediate azeotrope with either component A or C that can impede additional separation in a subsequent distillation column. There are various additional configurations that can increase the efficiency of conventional separation processes. Membrane separation processes can be used in front of the distillation column, which is especially beneficial when the mass transfer driving force in distillation is low for the given concentration range or when thermodynamic limitations of distillation can be avoided by separating one of the components in advance. Refer to Chapter 2 and Section 9.4 for an overview of conceptual tools that support the development and evaluation of such process configurations.

9.1.3 Membrane-assisted reactive distillation Membrane-assisted reactive distillation processes are preferentially used for the integration of complex chemical systems comprising chemical equilibrium limited reactions with multiple products and/or complex thermodynamic behavior. These systems typically consist of one or more esterifications, etherifications, and transesterifications. In addition to the advantages already presented for membrane-assisted distillation, the application of membrane-assisted reactive distillation processes can result in additional benefits for these systems when using reactive distillation technology (Chapter 2). The most important advantages in terms of membrane-assisted processing are summarized as follows: – Increased reactant conversion. The removal of products from the reactive liquid phase by distillation shifts the equilibrium of chemical equilibrium limited reactions toward the products. Thus, improved conversions approaching 100% are attainable [45]. – Increased product selectivity. Low product concentrations are maintained in the reactive liquid phase. Thereby, the risk of undesirable consecutive reactions is minimized [46]. – Capital and energy savings. Capital costs can be reduced due to the integration of two operations into one apparatus. Energy costs can be reduced by using the heat of exothermic reactions to provide the heat needed for distillation [47]. – Improved separation efficiency. Superimposition of reaction and distillation can improve the separation efficiency in various chemical systems. Thereby, azeotropes can be overcome, and the separation of close boiling mixtures can be facilitated [48]. In addition to the additional benefits of using membrane-assisted reactive distillation processes that primarily result from the use of reactive distillation technology, several technological constraints have also been identified. These constraints result

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from the high system complexity that is induced by the simultaneous occurrence of several phases. The most limiting constraints are summarized as follows: – Operating-window constraints. Reaction and distillation must be feasible at the same pressures and temperatures because both are superimposed in a single apparatus [49]. Additionally, the operating window of the combined operations must match to fulfill the requirements due to the strong dependency of the individual operations on each other [41], which is especially challenging for membrane-assisted reactive distillation processes. The recycled material from the membrane separation process that enters the reactive distillation column has a strong influence on the chemical reaction and on the overall process [50]. – Volatility constraints. A meaningful operation of reactive distillation requires an appropriate volatility difference between the reactants and products to maintain high reactant and low product concentrations in the reactive liquid phase [51]. – Occurrence of reactive azeotropes. In addition to non-reactive azeotropes, reactive azeotropes can also occur when using reactive distillation. A reactive azeotrope is formed when the concentration change caused by the reaction is exactly compensated by distillation. Reactive azeotropes may result in additional distillation boundaries that may make the separation more difficult or infeasible [52]. – Occurrence of multiple steady states. The complex interaction between superimposed reaction and distillation processes causes nonlinear behaviors, which can result in multiple steady states with different steady-state column profiles and reactant conversions for the same column configuration operating under the same conditions [53].

Process configurations For different applications various configurations of membrane-assisted reactive distillation processes are required. To demonstrate this notion, two chemical systems are considered. First, the integration of a chemical system comprising one conventional chemical equilibrium limited reaction (eq. (9.6)) is reviewed. After obtaining insights into this chemical system, the integration of a second system with two consecutive chemical equilibrium limited reactions (eqs. (9.6) and (9.7)) is discussed in detail. For both systems, component A has the highest boiling point, and the boiling point order is as follows: A > B > C > D (> E). The reaction schemes are as follows: A+B ⇆ C+D

(9:6)

D+B ⇆ C+E

(9:7)

Figure 9.4 presents two different examples for each scenario, i.e., the first (configurations 1 and 2) and the second (configurations 3 and 4) chemical systems.

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Fig. 9.4: Possible process configurations for the combination of reactive distillation with pervaporation or vapor permeation.

In both configuration 1 and 2, different minimum azeotropes prevent the production of two pure products in the reactive distillation column. Thus, a membrane is added to overcome the azeotrope in the distillate, to purify the target product D bound in the azeotrope and to recycle the involved reactant A or B to the column. In configuration 1, the heavy boiling reactant A is involved in the azeotrope formation process and recycled as retentate to the top of the reactive section to maintain an excess of component A. In contrast, the low boiling reactant B is part of the minimum azeotrope in configuration 2 and recycled as retentate to the corresponding feed stream to maintain its excess in the reaction section. In configurations 3 and 4, three different products (C,D,E) are obtained from the consecutive reaction. In configuration 3, a high yield of product E is intended and the membrane is used to separate the azeotropic (D,E) mixture recycling the undesired product D to the reaction section to maintain its excess, whereas the target product E is removed from the process. For configuration 4, all products generated during the chemical reaction are target products. Here, a membrane is placed in the side stream to withdraw product D, whereas the other products and the reactants are recycled to the reaction section. Products C and E are recovered as bottoms product and distillate. There are various other possible configurations. The selection of an adequate reactive distillation column configuration and a suitable membrane is a challenging optimization problem that must be solved for each design task.

9.1.4 Membrane reactors The benefits of integrating a membrane and a reactor are associated with the unique ability of the membrane to selectively separate specific components while retaining the others in the feed. In membrane reactors this combination is mostly utilized for (i) extracting components from the reactor while retaining others, or (ii) selective and controlled supply of substrates to the reaction site. An exhaustive overview of membrane reactor functions is given by Sirkar et al. [54], whereas the objectives are:

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– Overcoming thermodynamic limitations. In situ product removal shifts equilibrium composition of reversible reactions toward the product side or prevents inhibitory effects, therefore increasing conversion and yield [3]. Similar to hybrid separations, removal of some components by the membrane directly from the reactor can facilitate or simplify separations limited by vapor-liquid equilibrium. – Improving selectivity. For consecutive or parallel reactions, removing a substrate of a subsequent reaction or the desired intermediate product will increase the selectivity [55]. – Prolonging catalyst usability. By continuous removal of the reaction products and catalyst retention, it can be reused for longer. This finds the greatest use in biocatalysis [56]. Aside from the benefits of applying a membrane reactor, some challenges have to be taken into account in the design process: – Operating-window constraints. Due to integration, the membrane should work under similar or the same conditions as the reaction. When integrated inside the reactor the same conditions will apply for reaction and separation [49]. – Complex design. Compared to conventional reactors, there are additional design degrees of freedom, and some are interrelated with each other, hence posing an additional challenge for finding an optimal design [57]. – Membrane separation costs. The cost of the membrane separation plays a significant role in the process economy. The main factors are price per area, membrane stability, replacement intervals, as well as transmembrane flux [11].

Process configurations A membrane reactor results from an interconnection between a chemical reaction and a membrane separation. This connection can be realized in a few ways depending on the type of reactor and membrane integration method. All implementation methods can be represented by four generalized concepts of a membrane reactor shown in Fig. 9.5. The concepts result from (i) the choice of a continuously stirred tank reactor or a tubular reactor and (ii) internal or external integration of the membrane. The way the membrane is integrated with the reaction influences the final performance of the process. Moreover, all configurations have different technical limitations resulting from integration, e.g., fixed ratio of membrane area to reactive volume in a tubular membrane reactor (Fig. 9.5d). For a case of the tubular membrane reactor with internal integration, these design constraints can be relaxed by substituting it with a cascade of continuously stirred tank membrane reactors (such as in Fig. 9.5a or b) or repeating units of subsequent conventional tubular reactors and membrane modules [58] as shown in Fig. 9.6. Further options for implementation of integration in real equipment are described by Carstensen et al. [3].

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External membrane integration

485

Internal membrane integration (b)

(c)

(d)

Tubular

CSTR

(a)

Fig. 9.5: Possible implementations of a membrane reactor.

(...) Fig. 9.6: External integration of tubular reactors and membrane modules as consecutive reactionseparation units.

Ultimately, internal integration in the sense of (a) is equivalent to the external integration in the sense of (b), when the recycle is infinite [59]. That implies that similar or nearly the same performance is achievable with an external integration of the membrane as with an internal one, which provides additional means of relaxing the aforementioned constraints. However, to achieve that, it is necessary to utilize a high circulation rate, hence also related operating costs will rise. The most common mode of using a membrane reactor for increasing the yield of equilibrium-limited reactions is in situ product recovery or product removal. The term “recovery” usually applies to the separation of the desired product from the reactive mixture, while “removal” refers to the separation of the co-product [3]. Further, the term removal will be used for both cases. Considering a reactive system in equilibrium A + B ⇋ C + D, the yield of the desired product in a conventional reactor is limited by the chemical equilibrium. According to Le Chatelier’s principle, removing one of the products from the system will shift the equilibrium to the product side. If the product or products are removed from the system continuously and if substrates were fed in stoichiometric ratio, a nearly complete conversion will be achieved. Moreover, if one of the products can be removed to a high degree, eventually a highly pure other product can be obtained. This principle can be exploited in membrane reactors. If the main product is removed by the membrane separation, it will be collected directly from the reactor as permeate. If the primarily permeating component is a co-product, the main

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product is concentrated in the reactor. In both cases, a high selectivity of the membrane toward the permeating component is desired to maximize the efficiency of the process. Co-permeation of the other product or substrates will result in losses and require a cascade of membranes or a different subsequent separation method to recover the components. There are also applications of processes with dual membranes that selectively remove both products with high purity and retain the substrates and catalyst in the reactor [60]. Another use of a membrane reactor to increase the yield and selectivity is the controlled distribution of reactants. Typically one of the reactants is fed at the inlet of the reactor, while the other limiting reactant permeates through the membrane to the reactor. Application of the membranes in such a mode enables continuous dosing of the substrates to the reaction site, which allows for more control over the concentration profile in the reactor. With a selective membrane, a substrate can also be separated from a mixture of other components and fed directly to the reactor without preceding purification. This type of membrane reactor is mostly applied to gas phase reactions [4, 61]. Systems containing subsequent or parallel reactions are also a promising application for membrane reactors. In such systems, the function of a membrane is to suppress the reactions that reduce the yield of the desired product and promote the reactions that increase it. In such systems, the application of a membrane reactor depends on the component that is to be separated and the availability of a suitable membrane. Considering a system of two equilibrium reactions: (r1) A + B ⇋ C + D and (r2) A + D ⇋ E, where the desired product is C, while D, E are by-products. Both strategies described above can be applied. A membrane can be used for in situ product removal by either separating the main product C or by-product D. If technically feasible, removal of component D should be favored, as it will both promote reaction r1 and suppress reaction r2, hence further increasing the selectivity toward C. A membrane can also be used for a controlled distribution of the reactant A with an excess of B can be applied to maximize the conversion of reaction r1 [62]. While product removal is more effective for equilibrium-limited systems, controlled distribution proves effective for systems of non-reversible reactions [63], also in a more sophisticated manner with catalytic membranes [55]. Prolongation of the catalyst usability with membrane reactors is realized in two ways, either directly or indirectly influencing the catalyst. A direct influence on the catalyst is its retention in the reactive mixture (homogeneous catalyst), therefore enabling its reusability and creating an alternative to catalyst immobilization. Even though immobilization is probably the most effective way to retain the catalyst and ensure its longevity, its downside is an additional cost of immobilization and reduced catalyst activity due to limited surface area [64]. While most of the known applications focus on membrane-based retention of biocatalysts such as bacteria or enzymes, with the application of PV potentially even smaller catalyst particles can be retained, such as metal complexes. Refer to Chapter 8 for examples on OSN-assisted reaction.

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The membrane can also affect the catalyst usability indirectly, by removing the components that would induce inhibition or inactivation. This is especially important for enhancing the productivity of whole-cell catalysis [65]. Removal of the components that reduce catalytic efficiency creates an elegant synergistic effect with the retention of the catalyst in the reactor. It improves process productivity over a conventional batch or continuous process.

9.2 Applications 9.2.1 Vapor permeation and pervaporation Both VP and PV are primarily applied to remove components from a liquid mixture that (i) have a low concentration in the feed, (ii) are difficult to remove with conventional techniques or require much energy, or (iii) show a significant difference in molecule structure, size, or component behavior in comparison to the other components present in the feed mixture. In this context, PV and VP are often referred to as replacements for azeotropic, extractive, or pressure swing distillation [66]. The three practical application areas of both processes have been the dewatering of organics, the removal of volatile organic compounds from water, and the separation of purely organic mixtures [15]. According to Jonquières [67], GFT (Germany) installed 63 PV plants for the dewatering of organic solvents between 1984 and 1996. This is equivalent to an overall share of 90% of all PV plants installed during this period [68]. The main applications of these plants include the dehydration of alcohols, esters, ethers, solvent mixtures, and triethyl amine with common capacities between 5,000 and 30 000 l d−1. Newer plants are able to process volume flow rates of up to 150 000 l d−1. During the same period of time, only one PV plant for the removal of volatile organic compounds from water was installed [67]. To the best of our knowledge, there are no known industrial applications of PV for the separation of purely organic mixtures. However, Smitha [69] summarized different research interests in this area. Most recent efforts in this area focus on separation of non-aqueous mixtures containing methanol and other organics, e.g., methyl acetate [70, 71], dimethyl carbonate [72], trimethyl borate [73], or toluene [74]. Favre et al. [75] identified 38 VP plants that have been in operation since 1994. Baker et al. [76] estimated the number of industrial-scale VP plants in operation to be approximately 100 just 4 years later. Ohlrogge et al. [77] predicted that there would be 160 industrially operating VP plants in 2002. According to Jonquières [67], Sterling (Germany) and Sulzer Chemtech Ltd. have installed VP systems for the dehydration of organic solvents (i-propanol and n-butanol), gas drying, the extraction of volatile organic compounds from air (acetone, methylene chloride, hexane, and vinyl chloride) and the separation of purely

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organic mixtures (methanol/trimethyl borate) [9, 67]. Membrane Technology and Research (U.S.) has implemented several VP plants for the recovery of monomers and the recycling of inert gases used for polymer devolatilization [67]. In addition, they have applied VP for the elimination of hydrocarbons and acid gases, the drying of gases and the recovery of liquefied petroleum gas (LPG) [67].

9.2.2 Membrane-assisted distillation Until recently, only a few special applications of membrane-assisted distillation processes have been presented in the literature, such as patents or journal articles, and/ or implemented at the industrial scale; some of these applications have been summarized in the review published by [7]. In the recent years, the interest in hybrid PV/VPdistillation separations rises. Several studies have been published, e.g., on separation of methanol-methyl acetate [78], isobutanol-water [79], diisopropyl ether-isopropanol -water [80], ethyl acetate-isopropanol-water [81], tetrahydrofuran-methanol-water [82]. Selected important applications are discussed in the following section. The separation of ethanol from a binary mixture with water can be performed in an azeotropic distillation process with benzene as the mass-separating agent to separate the binary azeotrope with an ethanol mass concentration of 95.5 wt.% (Fig. 9.7). However, despite a substantial understanding of this process, various researchers have studied membrane-assisted distillation processes for this separation task to decrease the investment and operating costs.

Fig. 9.7: Azeotropic distillation for the purification of binary mixtures consisting of ethanol and water using benzene as the mass-separating agent.

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Tusel and Ballweg [83] suggested dehydrating ethanol in a distillation column connected to two subsequent hydrophilic PV units in 1983. The first membrane unit consists of high-flux (low-selectivity) membranes that are used to overcome the binary azeotrope. The second membrane is a high-selectivity (low-flux) membrane used to produce ethanol with the usual specification of 99.8 wt.% (Fig. 9.8, left).

Fig. 9.8: Configurations of membrane-assisted distillation processes for the purification of binary mixtures consisting of ethanol and water.

A further development regarding the membrane-assisted distillation process was presented by Sander and Soukup [84], who suggested removing a side stream from the distillation column and feeding it into a three-stage PV unit to overcome the binary azeotrope and to produce ethanol with a purity of 99.9 vol.%. To demonstrate its operability, a demonstration plant with a capacity of 6,000 l d−1 dehydrated ethanol, which was operated with the fermentation products of a pulp and paper mill, was constructed. Another configuration for ethanol dehydration was suggested by Gooding and Bahouth [85], who placed a single PV unit between two distillation columns to overcome the azeotrope (Fig. 9.8, right). The overall costs of their configuration were estimated twice as high as the costs of the conventional process [86], although Brüschke and Tusel [87] concluded significant saving potential for optimized operating conditions. Refer to Section 2.4.3 for a detailed analysis of several hybrid process configurations for ethanol dehydration. Different process configurations have been investigated for various chemical systems using both experimental and model-based methods. Sommer and Melin [44] summarized the dehydrations of organic compounds that can be integrated into membrane-assisted distillation processes. These applications contain advanced ethanol [88] and i-propanol [44] dehydration in addition to several other dehydrations, including the dehydration of dimethyl acetal [89], methyl i-butyl ketone [90], acetonitrile [91], tetrahydrofuran [92], acetic acid [93], and dimethylformamide [94]. Furthermore, the separation of three-component mixtures was considered, such as the dehydration of methanol and i-propanol [95, 96] and acetone and i-propanol

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[42, 97]. A detailed discussion of a membrane-assisted distillation process for the dehydration of acetone and i-propanol is presented in Section 9.5.1. In addition to the separation of water with hydrophilic membranes, various membrane-assisted distillation processes using hydrophilic membranes to separate polar organic components were proposed, especially for the separation of the alcohols methanol and ethanol. In this respect, membrane-assisted distillation processes for the separation of methanol from methyl tert-butyl ether (MTBE) [98–100], tetrahydrofuran [101] and dimethyl carbonate [99, 102, 103], methyl acetate [104] have been suggested. The economic feasibility requires, however, a detailed process investigation, as demonstrated by the recent study of Scharzec et al. [82], which investigated the separation of tetrahydrofuran from a mixture of methanol and water and showed that the membrane-assisted process cannot compete with a heat-integrated pressure swing distillation process. The application of membrane-assisted distillation processes for the separation of purely organic (nonpolar) mixtures has received attention in the literature, which is largely due to the limited availability of membrane materials that are capable of separating these mixtures in an economical manner (Section 9.2.1). However, some membrane-assisted distillation processes have been identified for the separation of organic mixtures, such as binary mixtures of benzene and cyclohexane [105]. Different industrial applications of membrane-assisted distillation processes have recently been summarized. Kobus et al. [106] reviewed industrial experiences with membrane-assisted distillation processes and focused on the separation of a ternary mixture consisting of an alcohol, an ester and water. Roza and Maus [107] provided insights into the industrial applications of distillation columns combined with PV or VP membranes. They discussed the integration of membrane separation processes into existing plants for the production of methyl ethyl ketone, acetonitrile, and tetrahydrofuran and reported a drastic increase in plant capacities.

9.2.3 Membrane-assisted reactive distillation Membrane-assisted reactive distillation processes remain the focus of basic research, while only a few pilot-scale studies to experimentally investigate reactive distillation columns with attached pervaporation (PV) or vapor permeation (VP) membranes have been attempted. All these studies, which have been conducted and are closely related to this work, are presented in Tab. 9.3. All the chemical reactions are esterifications, etherifications, or transesterifications. Within the investigated esterifications and etherifications, one target product and a co-product (primarily water) is synthesized. The reactive distillation column is then used to overcome the chemical equilibrium, whereas membrane separation is applied to overcome the phase equilibrium by selectively removing the co-product with a hydrophilic membrane. The experimental study performed by Holtbruegge et al. [50] considered a

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transesterification in which two target products, i.e., dimethyl carbonate and propylene glycol, were synthesized. In their work, a hydrophilic membrane was used to separate and recycle unreacted methanol into the reactive distillation column, thus maintaining the reactant excess and guaranteeing high propylene carbonate conversion. They also showed the possibility of simultaneously producing and purifying two target products in a membrane-assisted reactive distillation process. Tab. 9.3: Selected journal articles that encompass the experimental investigations on membraneassisted reactive distillation processes. Column Membrane diameter area . m

PV []

Katapak®-  mm SP

. m

VP []

Ionexchange resin

Katapak®-  mm SP

nda*

PV []

Synthesis of trimethyl borate: boric acid + methanol ⇋ trimethyl borate + water

nda*

nda*

nda*

nda*

VP []

Synthesis of tert-amyl ethyl ether: tert-amyl alcohol + ethanol ⇋ tertamyl ethyl ether + water

Amberlyst® 

“Tea bag” envelopes

 mm

. m

PV []

Synthesis of n-butyl acetate: methyl acetate + n-butanol ⇋ n-butyl acetate + methanol

Amberlyst® 

Katapak®-  mm S

nda*

PV []

Synthesis of dimethyl carbonate and propylene glycol: propylene carbonate + methanol ⇋ dimethyl carbonate + propylene glycol

Sodium methoxide

Sulzer BX™

. m

VP []

Synthesis of ethyl acetate: acetic acid + ethanol ⇋ ethyl acetate + water

Purolite CT

“Tea bag” bales

Synthesis of n-propyl propionate: propionic acid + n-propanol ⇋ n-propyl propionate + water

Amberlyst® 

Synthesis of fatty acid i-propyl ester: myristic acid + i-propanol ⇋ i-propyl myristate + water

 mm

 mm

*nda: no data available.

Most of the presented processes have been operated according to configuration 2 (Fig. 9.4) by separating the low boiling reactant from a minimum azeotrope and recycling it into the reactive distillation column. Interestingly, Lv et al. [108] placed a hydrophilic membrane in the bottom product stream to remove the co-product water and recycle the heavy boiling reactant acetic acid into the reactive section of

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the column. This process design is analogous to configuration 2 with the membrane placed in the bottom product. In contrast to the conventional configurations, Aiouache and Goto [111] mounted a tubular membrane in the center of a reactive distillation column to continuously remove water from all sections of the column during the production of tert-amyl methyl ether. However, this configuration is difficult to implement at an industrial scale. Over the last few years, many studies were published that focused on a modelbased evaluation of PV-assisted reactive distillation (PVRD). Dai et al. [113] conducted a techno-economical evaluation of PVRD application for ethyl lactate production utilizing Aspen Custom Modeler. Schmitz et al. [114] investigated PVRD applicability to the production of oxymethylene ether, an alternative diesel fuel. The applicability of PVRD to biodiesel production from cooking oil was evaluated in a simulation study by Petchsoongsakul et al. [115]. Novita et al. [116] analyzed the influence of applying PV and thermal coupling to reactive distillation-based production of ethyl levulinate. Wang et al. [117] analyzed several various implementations of reactive distillation and reactive dividing wall columns with and without the assistance of PV for the production of isopentyl acetate. The same research group has also applied a modelbased approach for the analysis of propyl acetate production based on PV-assisted pressure swing reactive distillation [118]. Following the research of Steinigeweg and Gmehling, Harvianto et al. [119] published their study on applying reactive distillation for the production of butyl acetate, but utilizing a polyamide-6 membrane and conducting an optimization of the process. Li et al. [120] also investigated butyl acetate production, however utilizing a reactive dividing wall column. Babaie and Nasr [121] evaluated possibilities of reducing energy consumption through PVRD in the production of a promising fuel additive – tert-amyl methyl ether. Li and Kiss [122] elaborated on the previous study of Holtbruegge et al. [50] and analyzed the economics of applying PVRD to the production of DMC. All the studies conducted thus far have demonstrated the general feasibility of operating membrane-assisted reactive distillation processes using a PV or VP membrane to withdraw one of the involved components and recycle a recovered reactant into the reaction section of the column, maintaining the reactant excess. A detailed discussion of the simultaneous production of dimethyl carbonate and propylene glycol is provided in Section 9.5.2.

9.2.4 Membrane reactors Membrane reactors are long recognized as an interesting concept for intensifying reactive processes. The first patent for a membrane reactor was created by Jennings and Binning in 1960 [123]. The reactor was meant for conducting organic reactions where water is formed (such as esterification) to drive them to complete conversion. This concept was developed over the years and resulted in a steeply rising number

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of studies, especially in the last three decades. Utilizing the principles described in the previous section, PV-based membrane reactors found applications in a few types of chemical reactions. The main fields for applying membrane reactors with dense membranes are condensation reactions (especially esterification), bioreactors, and specific petrochemical applications. The most investigated applications for membrane reactors are esterification reactions in the presence of an acidic catalyst, such as sulfuric acid or acidic resins: Alcohol + Acid ⇆ Ester + Water

(9:8)

The reaction is equilibrium-limited [124], resulting in low reaction yield and an increased effort for substrate recycling and product removal. Moreover, downstream processing and substrate recycle are also challenging, as many of the alcohols form azeotropes with the co-produced water. These limitations can be conveniently lifted with a membrane reactor. While some strategies with organophilic membranes were investigated for the removal of ester [125], these have significantly lower selectivity and fluxes than hydrophilic PV membranes for water removal. Hydrophilic membranes are widely commercially available, offering a variety of available modifications of the active layer, making them well suitable for a range of applications, such as dewatering to low water contents (