Lectures on the course: Fundamental processes and devices of chemical technology 9786010443976

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AL-FARABI KAZAKH NATIONAL UNIVERSITY

D.N. Akbayeva, Zh.T. Yeshova

LECTURES ON THE COURSE: FUNDAMENTAL PROCESSES AND DEVICES OF CHEMICAL TECHNOLOGY Stereotypical pyblication

Almaty «Qazaq University» 2020

UDC 665.9(075.8) BBC 24.1я73 А-38 Recommended for publication by the decision of the Academic Council of the Faculty of Chemistry and Chemical Technology, Editiorial and Publishing Council of the Al-Farabi Kazakh National University (Protocol № 4 dated 16.04.2019) and Educational-methodical Association of the Republican Educational-Methodical Council at M. Auezov South-Kazakhstan State University (Protocol № 2 dated 23.11.2018) Reviewers: doctor of chemical sciences, professor G.A. Seilkhanova doctor of chemical sciences, professor B.S. Selenova doctor of chemical sciences, professor R.M. Iskakov

A-38

Akbayeva D.N. Lectures on the course: Fundamental processes and devices of chemical technology / D.N. Akbayeva, Zh.T. Yeshova. – Ster. pub. – Almaty: Qazaq University, 2020. – 398 p. ISBN 978-601-04-4397-6 The manual contains brief lecture notes covering theoretical foundations of hydrodynamic, heat and mass transfer processes of chemical engineering. To consolidate the theoretical lecture material, test tasks and questions for self-control are given. The manual is intended for students of the faculty of chemistry and chemical technology of higher educational institutions.

UDC 665.9(075.8) BBC 24.1я73 ISBN 978-601-04-4397-6

© Akbayeva D.N., Yeshova Zh.T., 2020 © Al-Farabi KazNU, 2020

INTRODUCTION Changes in the condition of substances happening under these or those conditions are called processes. In the environment surrounding us the phenomena called natural processes are observed. For example, evaporation of water from the surface of reservoirs, heating and cooling of the Earth’s surface under the influence of various factors, driving of water in the rivers, ice melting, removal of moisture from various materials or substances and many others. Studying of natural processes is a subject of physics, chemistry, mechanics and other natural sciences. On the basis of the data obtained as a result of studying of natural processes and the analysis of achievements of science and technology scientists develop and realize numerous commercial processes for the purpose of processing of natural products (raw materials) in order to produce products and consumer goods. Such processes are called production, or technological processes. The modern engineering chemistry studies production of various substances: products of petroleum refining, mineral coal and natural gas, organic and mineral substances, polymeric and other materials. However, despite a huge variety of chemicals, their production is connected with carrying out of a number of the same processes – such as movement of liquids and gases, heating and cooling, concentrating of solutions of solid substances, separation of gas or steam and liquid mixtures, drying, chemical interaction, etc. These processes are characterized by the common laws of hydromechanics, physics, physical chemistry, chemical kinetics, mechanics of solid bodies. The devices of various designs used for the same purpose in various branches of engineering chemistry are also characterized by similarity.

3 

1. THEORETICAL BASICS OF PROCESSES OF CHEMICAL TECHNOLOGY Classification of the main processes of chemical technology. Processes of chemical technology can be classified, depending on the regularities characterizing their velocity, into the following groups: 1. Hydromechanical processes, the rate of which is defined by hydrodynamics laws. Hydrodynamics is science about movement of liquids and gases. It studies movement of liquids, compression and movement of gases, separation of liquid and gas of non-uniform systems in the fields of gravity and centrifugal forces, and also under the influence of a pressure difference at movement through a porous layer and hashing of liquids. 2. Thermal processes, the rate of which is defined by heat transfer laws. Such processes are heating, cooling, evaporation, condensation of vapors. Velocity of thermal processes substantially depends on hydrodynamic conditions under which heat transfer between environments exchanging heat is carried out. 3. Mass-exchange (diffusive) processes. The rate of these processes is defined by the velocity of substance transition from one phase to another, i.e. mass transfer laws. Absorption, extraction, rectification, adsorption, drying, etc. belong to diffusive processes. Processes of mass exchange are closely connected with hydrodynamic conditions in phases and on the limit of their section and are close to the processes of heat transfer accompanying mass exchange. 4. Chemical processes connected with transformation of substances and change of their chemical properties. The rate of these processes is defined by regularities of chemical kinetics. 5. Mechanical processes include crushing of solid materials, classification of uniform bulks and their mixing. The processes and devices, common for various branches of chemical technology, were called the main processes and devices. The theoretical base of science about the processes and devices of chemical technology is formed by the following fundamental laws of nature. 4 

1. The laws of conservation of mass, energy and impulse allow only such transformations at which the sums of mass, energy and impulse in the system remain unchanged (i.e. the final sum is equal to the sum in the initial state). The laws of conservation take the form of the equations of balances (for example, material and thermal) which are an important part of the analysis and calculation of chemical and technological processes. 2. The laws of thermodynamic equilibrium determine conditions under which the process of transfer of any substance (mass, energy, impulse) comes to the end. A condition of the system at which irreversible transfer of a substance is absent, is called equilibrium. The equilibrium state is described by such laws as Henry’s law, Raul’s law, etc. The knowledge of conditions of balance allows us to solve problems very important for the analysis and calculation chemical technological processes i.e. determination of the direction of the transfer process (from what phase in what substance it passes) and borders of its current, calculation of the driving force of the process. 3. The laws of mass, energy and impulse transfer define a stream density of any of these substances depending on the gradient of the transfer potential interfaced to it, i.e. the specific gravity, energy or impulse, related to the unit of the stream volume. The potential of transfer in case of mass transfer is density () or concentration (C), energy transfer is enthalpy (cpt), transfer of an angular momentum of the movement of a volume unit of liquid is w. Thus, the laws of transfer define the intensity of chemical and technological processes and productivity of devices used for these processes. The above-listed laws make a theoretical basis of all technological processes – hydromechanical, heat- and mass-exchange. Studying chemical and technological processes it is necessary to add the fourth group to these laws – laws of chemical kinetics. Method is a set of techniques used for practical or theoretical investigation of reality. In relation to the course “Processes and devices of chemical technology” such a method is modeling – physical and mathematical. Modeling is a method of studying objects (in this case the processes proceeding in any device – nature) on 5 

their models. In physical modeling (scaling) an experimentally studied object (model) differs from the natural one by scale, although physical nature of the phenomenon (process) remains the same. In mathematical modeling the process (the influence of various parameters – pressure, temperature, stream speeds, etc.) is studied by solving the equations of systems describing this process, with addition of boundary conditions (i.e., unlike physical modeling, in mathematical modeling theoretical or ideal model is used). In calculations of processes and devices the process engineer is usually faced with the following objectives: 1) at a given flowrate of raw materials to define the quantity of obtained products and the energy necessary for carrying out process; 2) to define conditions of an equilibrium (limit) condition of a system; 3) to define optimum operating modes of devices; 4) to calculate the main sizes of devices working under optimum conditions. The solution of these tasks is based on the conservation laws, thermodynamic balance and transfer of substances [1-9]. 1.1. Laws of conservation We will accept that a substance (mass, energy, impulse) passes through the borders of the considered area of space within which they can change. In this area (it is called a control volume, and a limiting surface is called a control surface) external forces can work. The sizes of the control volume can be either finite, or infinite. For a complete definition of the control volume, it is necessary to set a system of coordinates in relation to which it moves or is at rest. 1.1.1. The law of conservation of mass In the closed system the laws of conservation of mass and energy mean that in the system they can turn into each other, remaining in total invariable. If the system consists of several c components and one P phase, in the absence of chemical interactions by the law of 6 

 

conservation of mass the sum of masses of all components must be equal to the mass of the whole system, i.e.

⋯

or

∑

.

(1.1)

If the system has several (m) P phases and one component, by the law of conservation of mass the sum of masses of all phases must be equal to the total mass of the system, i.e. ⋯

or

∑

.

(1.2)

From the last expression of the law of conservation of mass, it follows that the larger the mass of one phase, the smaller the mass of the other, but the sum of the masses of all phases remains unchanged. By means of the considered two limit cases, it is possible to obtain the balance equations for each component and each phase participating in the process. Usually in chemical and technological processes all substances are in movement or as it is said, in stream. The stream is the movement of any environment in space. Most often the process engineer should deal with convective streams which are characterized by movement of a set of particles under the influence of any force from one place of space to another. If the convective stream is carried to the unit area through which it is transferred, we speak about the density of a convective stream.   If the convective stream is related to the unit area through which it is transferred, then the density of the convective stream is indicated. The density of the stream is a vector whose direction coincides with the direction of movement of the stream; the dimension of density of the stream is [q] = [quantity unit/(m2s)]. For the characteristic of any system there are three streams: mass (or component), warmth (or enthalpy) and impulse. The laws of conservation of mass, energy and impulse are usually considered in common. Therefore the approach to drawing up the balances of these substances has to be identical. Material balance. For substances involved in the chemicaltechnological process, material balances are distinguished in the 7 

 

following way: 1) common for the whole substance (brutto-balance); 2) private – for one component; 3) elemental – for a chemical element or a free radical (for example, the balance of oxygen, carbon, hydrogen, benzene ring, etc.). Usually in engineering calculations, the balances for the first two options are used. An analysis and calculation of any chemicaltechnological process begins with the preparation of a material balance. Note that the material balance must include as many equations as there are components in the processed substance. In the hierarchical structure of production, material balances are divided into the following types: 1) parts of the apparatus (that is, parts of the process element); 2) apparatus (i.e. the entire element of the process); 3) installations (i.e., parts of production); 4) the whole production – from raw materials to the finished product (i.e., a section of the shop, shop or several shops); 5) many industries (i.e., the plant); b) branches of the national economy. The course “Processes and devices of chemical technology” is usually limited to the first three types of balances, the rest are studied in special courses or in engineering practice. On the basis of material balance, the yield of the product is determined in comparison with the theoretically possible yield (in %), as well as the quantity (mass) of products obtained per unit time. According to the law of conservation, the mass (quantity) of substances entering the processing (Gin) should be equal to the mass of substances obtained as a result of the process (Gf), i.e. ∑

∑

.

(1.3)

In practical conditions, when technological process have irreversible losses of substance Gl (for example, to sewage or gas emissions, through defects of equipment, etc.), the material balance in the general case takes the form ∑

∑

.

(1.4)

For nonstationary processes, the material balance has a slightly different form, since the streams directed inside the volume under 8 

 

consideration (coming) and the outward (consumption) flows may not be equal (for example, mass accumulation takes place), i.e. or ∑

С

∑

. (1.5)

For stationary processes the right part of expression (1.5) is equal to zero, and without losses it takes a form of equation (1.3). The material and energy balances in macrovolumes (for example, in the apparatus) when, for example, two phases for heat or mass transfer are interacting, will depend on their relative motion. The most common types of such relative motion of streams (or phases) are shown in Fig. 1.1.

Fig. 1.1. The relative direction of streams driving in devices: a – co-current; b – countercurrent

When considering specific processes of heat and mass transfer, it will be shown that the temperatures (for heat transfer) or concentration (for mass transfer) of the streams at the exit of the apparatus can differ significantly, for example, for the co-current (Fig. 1.1, a) and countercurrent (Fig. 1.1, b) stream motions at the same values (initial temperatures and concentrations) at the entrance to the equipment [1,9]. 1.1.2. The law of conservation of energy From the first law of thermodynamics the law of conservation of energy can be formulated as: the internal energy U of a system isolated from the environment is constant, i.e. V = const. Then . 9 

 

(1.6)

In equation (1.6), the heat values δQ and the produced work δA characterize not the system, but the processes of its interaction with the environment, therefore they are not full differentials. The transition of a system from one energy state to another is characterized by a new value of the internal energy U, since U varies by a certain amount regardless of the transition path. Equation (1.6) can be used as the law of conservation of energy. Energy balance. When analyzing and calculating chemical-technological processes, it is often necessary to determine the energy consumption for their conduct, and in particular, heat. To determine heat consumption, you should make up the heat balance as part of the overall energy balance. The heat balance is calculated for many processes occurring in reactors, heat exchangers, mass exchange apparatus (distillation of liquids, drying, etc.). By analogy with the material balance, the energy balance in the general form is expressed as follows: ∑

..

∑

. .

∑

. .

.

(1.7)

where Qh.in. is the heat introduced into the apparatus with initial materials; Qt.e. is the thermal effect of physical and chemical transformations; Qh.o. is the heat output from the appliance by the products; Ql is loss of heat to the environment.

In addition to heat consumption, the energy balance makes it possible to determine the costs of kinetic and potential energy for the process (liquid transfer, compression and transport of gases, etc.) [1,9]. 1.1.3. The law of conservation of impulse The impulse is by definition equal to the product of the mass of the selected element of the liquid m and the velocity vector of its motion ; hence, the impulse is also a vector. Therefore, the law of conservation of impulse can be represented both in a vector form and in a scalar one in the form of three scalar equations in the directions of the x, y, z coordinate axes. In more detail, balances of substances (mass, energy, impulse) will be considered further in the analysis and calculation of concrete processes of heat and mass transfer. 10   

1.2. Hydromechanical processes 1.2.1. The equation of continuity of a flow Chemical technology processes are usually associated with the movement of liquids, gases or vapors in pipelines and apparatus, the formation or separation of heterogeneous systems (mixing, dispersing, settling, filtering, etc.). Since the speed of all these processes is determined by the laws of hydrodynamics, they are usually called hydromechanical processes. The laws of hydrodynamics have a very simple form for liquids in which the movement of separate parts relative to the others occurs without friction, and the volume or their density doesn’t change. Such liquids are called ideal. Though any real liquid doesn’t meet these requirements, nevertheless, many of them under certain conditions can be considered as ideal. Gases are easily compressed, but at flow velocities of not more than 50 m/s, the pressure change is small, and accordingly, the volume change, so the laws of motion of ideal liquids are applicable to the motion of gases under these conditions. There are two types of fluid motion: steady (stationary) and unsteady. With the steady motion of the liquid at each point of the volume of the fluid, the velocity of motion remains constant in magnitude and direction: w  w ( x , y , z ).

(1.8)

Similarly, the pressure remains constant: p  p ( x , y , z ).

(1.9)

An example of steady motion is the flow of water from a tap at a constant pressure of the water supply line. With unsteady motion, the speed and pressure at each point of the volume of the fluid changes with time, i.e. speed and pressure are functions of not only the position of the point in the volume of the liquid, but also of time: w  w ( x , y , z , ), 11 

 

(1.10)

   ( x , y , z , )

(1.11)

An example of an unsteady motion is the flow of liquid from the opening of the vessel, which occurs with a changing pressure due to a lowering of the liquid level. With steady flow of liquid through a closed pipeline, the same weight quantity of liquid flows through each section of the pipeline per unit time. The moving liquid completely fills the tube, in which, thus, there are no voids or ruptures of the flow. If we denote by G1, G2, G3 the weight quantities of liquid flowing per unit time through the sections of the pipeline, then the equation of continuity of the flow can be written as follows (see Fig. 1.2): G 1  G 2  G 3  const

(1.12)

or

f 1 w 1  1  f 2 w 2  2  f 3 w 3  3  const ,

(1.13)

where w 1 , w 2 , w 3  flow velocity through the pipe sections; f 1 , f 2 , f 3  sections of the pipe;  1 ,  2 ,  3  the density of the liquid in these sections.

Fig. 1.2. To the equation of continuity of a flow

For an incompressible fluid whose density remains unchanged along the entire length of the pipeline, the continuity equation takes the form [1-3,9]: f 1 w 1  f 2 w 2  f 3 w 3  const .

12 

 

(1.14)

1.2.2. Determination of liquid and gas consumption

The movement of liquids through pipelines, ducts, and apparatus is due to the pressure difference created by the difference in liquid levels or by the operation of special machine-pumps. The volume of fluid that flows through any section of the flow per unit time is called the volumetric flow rate of the liquid Q. Due to the influence of friction forces at different points of the cross section of the flow, the velocity of the fluid particles is not the same: along the flow axis it is maximal, and at the pipeline wall it is zero. Since it is often difficult to establish the distribution of speeds over the cross section of the flow, in engineering calculations the socalled average velocity is usually used; while admitting that all particles of the stream move with the same speed. Such a conditional velocity w is determined by the ratio of the volume flow rate of fluid Q to the flow area S: w

Q/S.

(1.15)

Then the volume flow rate Q (V) (m3/s, m3/h) and its mass flow rate M (kg/s, kg/h) are determined by the equations: Q

wS.

(1.16)

М

wSρ.

(1.17)

Equations (1.16) and (1.17) are called flow equations and are widely used in calculations of pipelines and chemical apparatus [3,9]. 1.2.3. Calculation of pipe and apparatus diameters

At a given flow rate V and the known velocity w, the diameter of the round section is determined from the equation for the volumetric flow rate (1.16): ,

13 

 



.

(1.18)

When flowing through channels of a non-circular cross-section, instead of a diameter, an equivalent diameter can be used:

4 / ,

(1.19)

where S – the cross section of the channel, m2; P – the so-called wetted channel perimeter, along which the flow material contacts the internal surface of the channel, m.

The equivalent diameter of the channel of the round section is calculated by the formula:

.

(1.20)

The equivalent diameter of the round pipe, according to the general expression (1.19), is equal to the diameter of the pipe: 4

/

.

(1.21)

Questions for self-control: 1. List the main groups of processes of chemical technology. 2. What basic laws of nature constitute the theoretical basis of all technological processes? 3. What are the main tasks facing the process engineer? 4. Formulate the law of conservation of mass for a system consisting of one component and for a multicomponent system. 5. What are the characteristics of material balances? 6. Give the expression of material balances for stationary and nonstationary processes. 7. Formulate the heat balance in general form by analogy with the material balance. 8. What other parameters besides the consumption of heat does the energy balance allow us to define? 9. Define the impulse. 10. How can we imagine the law of conservation of impulse? 11. What processes are called hydromechanical? 12. What is the difference between the ideal fluids and real ones? 13. Explain the difference between steady and unsteady movement. 14. What is the physical meaning of the equation of continuity of flow?

14 

 

15. 16. 17. 18. 19. 20.

What is the volumetric flow rate? What formula can be used to calculate it? What is the mass flow rate? What formula is used to calculate it? What formula is used to find the diameter of the round pipe? How is the equivalent diameter of the non-circular section calculated? Give the formula of the equivalent diameter of the channel of the ring section. What is the equivalent diameter of a round pipeline?

1.3. The basic equation of hydrostatics

Euler’s differential equations of equilibrium are expressed by a system of equations:

0;

0;



0.

(1.22)

It follows from equation (1.22) that the pressure in the liquid at rest changes only along the vertical (i.e., along the z axis), remaining the same at all points of any horizontal plane, since the pressure changes along the x and y axes are zero. Since the partial derivatives / and / у are equal to zero, the partial derivative / can be replaced by / . Then 0 или –

0.

(1.23) and

Dividing the left and right sides of equation (1.23) by multiplying all its terms by –1, we obtain: 0.

(1.24)

For an incompressible homogeneous fluid, /

0 или

. Then 0.

Hence, after integration, we obtain: . 15 

 

(1.25)

For two arbitrary horizontal planes I – I and II – II (Fig. 1.2), equation (1.25) takes the form: .

(1.26)

Equation (1.25) [or (1.26)] is called the basic equation of hydrostatics. The value of z, which characterizes the distance of a given point from an arbitrarily chosen horizontal reference plane (see Fig. 1.3), is often called the leveling height. It is expressed in units of length: ∙

∙

∙

/

.

Fig. 1.3. To the basic equation of hydrostatics

Thus, in terms of physical meaning, the leveling height is the energy (Hm) per unit weight (H) of the liquid. In other words, the leveling height, also called the geometric head, characterizes the specific potential energy of the position of a given point over an arbitrarily chosen plane of comparison. The quantity / is called hydrostatic or piezometric (piezo (Greek) – press, squeeze) pressure. Like the leveling height, the hydrostatic pressure in terms of physical meaning is the energy per unit weight of the fluid, and characterizes the specific potential energy of the pressure at a given point. According to the basic equation of hydrostatics, the sum of the specific potential energies of position and pressure in a fluid at rest is 16 

 

constant and equal to the total hydrostatic pressure. Consequently, the basic equation of hydrostatics is a particular case of the law of conservation of energy. Rewriting equation (1.26) with respect to , we obtain: .

(1.27)

Equation (1.27) is an expression of Pascal’s law, from which it follows that the pressure created at any point of the stationary incompressible fluid is transmitted in all directions with the same force. Indeed, in accordance with equation (1.27), when the pressure changes at a point of a liquid by some amount, the pressure at any other point of the liquid changes by the same amount. Equations (1.26) and (1.27) are derived for an ideal fluid and therefore do not take into account the effects of compression and tension forces, surface tension. However, for real liquids, which can be considered incompressible at not too high pressures, tensile and surface tension forces are manifested only in the case of very small volumes of liquid, for example, in narrow capillaries. Since usually the volumes of liquids used in the technological processes are large, then equations (1.26) and (1.27) without appreciable error can be applied to real liquids. The basic equation of hydrostatics (or Pascal’s law) is used to calculate pressure on the bottom and walls of vessels, hydrostatic machines (hydrostatic press, hydrostatic accumulator), hydraulic locks, to determine fluid levels in communicating vessels, pressure measurement by differential pressure gauges, and other. The pressure of the resting liquid on the bottom and the walls of the vessel. The pressure of the liquid on the horizontal bottom of the vessel is the same everywhere. The pressure on its side walls increases with increasing depth of immersion. At the same time, the pressure on the bottom of the vessel does not depend on the shape or angle of inclination of the side walls of the vessel, nor on the volume of the liquid in it. For and H (see Fig. 1.2) (where and – the pressure on the liquid surface and the bottom of the vessel, respectively). 17 

 

Thus, at a given fluid density, the pressure force P on the bottom of the vessel depends only on the height of the liquid column H and the area F of the vessel bottom: or

.

(1.28)

Since the hydrostatic pressure of the liquid on the vertical wall of the vessel varies along its height, the total force of pressure on it is distributed unevenly and will be equal to ,

(1.29)

where h is the distance from the upper liquid level to the center of gravity of of the wall. the wetted area

It follows from expression (1.29) that the pressure force on the vertical wall is equal to the product of its wetted area by the hydrostatic pressure at the center of gravity of the wetted area of the wall. The point of application of pressure forces to the wall is called the pressure center. This point is always located below the center of gravity of the wetted area of the wall. For example, for a vertical flat wall, the pressure center is located at a distance of 2/3 H from the upper liquid level [1,2,9]. 1.3.1. The Bernoulli equation

The system of equations:



dw x p  wx , x dx

(1.30)



dw p  wy y , y dy

(1.31)

p  dw    g    wz z . z  dz  18 

 

(1.32)

is the differential equations of motion of an ideal Euler’s fluid for a steady flow. The solution of these equations leads to one of the most important and widely used equations of hydrodynamics – the Bernoulli equation. Multiplying the left and right sides of each of the equations (1.301.32), respectively, by dx, dy, dz and dividing by the density of the liquid, we obtain 1 p

dx dw x d

(1.33)

1 p dy dy  dw y d  y

(1.34)

 1 p  dz dz   dw   gdz   z  d z 

(1.35)





 x

dx 

We add these equations, taking into account that the derivatives dx dy dz express the projections of the velocity wx , wy , wz on the , , d d d corresponding coordinate axes. Then

1  p p p    dx  dy  dz   gdz  wxdwx  wy dwy  wz dwz (1.36)   x y z  The terms on the right-hand side of this equation can be represented as

 wy  2  w2  , w dw  d  w z wx dwx  d  x , wy dwy  d   z z  2  2    2  2

consequently, their sum 19 

 

  (1.37) 

2 2 2 2  wx2   wy   wz2   wx  wy  wz   w2     d  , (1.38)   d    d  d   d   2   2   2   2 2          

where w  w 

is

the

velocity,

whose

components

along

the

corresponding axes are equal wx , wy , wz .

At the same time, the sum of the terms in parentheses on the right-hand side of the equation is the total differential of pressure dp (under the conditions that have been established, the pressure depends only on the position of the point in space, but does not change with time at any given point). Hence

 w2  dp    d   gdz .   2 

(1.39)

Dividing both sides of this equation by the acceleration of gravity g and transferring all its terms to the left-hand side, we find

 w 2  dp    dz  0 . d   2 g  g

(1.40)

For an incompressible homogeneous fluid p  const, therefore, the sum of the differentials can be replaced by the sum differential, hence  p w2  (1.41)   0 d  z   g g  2   whence

z

p w2   const. g 2g

Equation (1.42) is the Bernoulli equation for an ideal fluid. 20 

 

(1.42)

The quantity

is called the total hydrodynamic

pressure, or simply the hydrodynamic pressure. Consequently, according to the Bernoulli equation, the hydrodynamic pressure remains unchanged for all cross sections of the steady flow of an ideal fluid.  p  The sum  z  , called a full hydrostatic, or simply static  g   pressure, expresses the total specific potential energy at a given point (a given section). The quantity

is called the high-speed or dynamic pressure. The

velocity pressure characterizes the specific kinetic energy at a given point (of a given cross section). From the Bernoulli equation, in accordance with the energy sense of its terms, it follows that with the steady motion of an ideal fluid, the sum of the potential and kinetic energy of the fluid remains unchanged for each of the cross sections of the flow. All the summands in the Bernoulli equations are expressed in units of length /



/

,

∙ /

/



/

.

Thus, the Bernoulli equation is a special case of the law of conservation of energy and expresses the energy balance of the flow. The Bernoulli equations are used to determine the velocities and flow rates and time of the outflow of liquids from reservoirs [1-3,9].

21 

 

1.3.2. Forces acting in a real liquid

A fluid in a state of rest or motion is under the action of various forces, which can be divided into volumetric and superficial. Volumetric forces. These forces act on each element of the given volume of liquid and are proportional to the mass enclosed in a given volume. These include gravity forces, inertia forces and centrifugal forces. The characteristic of the intensity of gravity G acting on a given volume V is the specific gravity  of the liquid: lim

→

/

lim

/

→



/

.

The limit of the ratio of the mass of the liquid to the volume when it is contracted to a point is called the density of the liquid: lim

/

→

/

/

.

The specific gravity and density of the dropping liquids are usually determined experimentally, their values depend little on pressure or temperature. The density of gases at relatively low pressures can be calculated from the equation of state of ideal gases: /

/

,

(1.43)

where R is the universal gas constant.

At elevated pressures, the density of gases is calculated, for example, taking into account the compressibility factor (Z), which is determined as a function (represented by the graphical dependence) of the reduced temperature Tred and the reduced pressure Pred: /

,

,

.

(1.44)

Surface forces. They act on a surface that limits a given volume of fluid and separates it from the surrounding environment. These 22 

 

include the forces of pressure and the forces of internal friction (the force of viscosity). At equilibrium, the resting fluid is acted upon by gravity and pressure forces, while the laws governing the motion of liquids (real) are determined not only by the forces of gravity and pressure, but also to a very large extent by the forces of internal friction (viscosity forces). The characteristic of the intensity of the surface forces is the stress , which they create on the surface S, which limits the given volume V. This is the limit of the ratio of forces to the surface area when it tends to zero: lim

/∆

→

/

.

The normal component of these stresses is caused by the surface forces (Fs) acting perpendicular to the surface at a given point: lim∆

/∆ .

→

The parameter that reflects the effect of the pressure forces of the liquid on the bottom and the walls of the vessel in which it is located, as well as on the surface of any body immersed in it, is the hydrostatic pressure. Hydrostatic pressure is a scalar quantity related to the vector value of normal stresses in accordance with its definition as follows: .

(1.45)

where – the unit normal vector to the surface S.

In the system of SI units, the hydrostatic pressure is expressed in Pa (N/m2), while in engineering it is often in kgf/cm2 or in units of height (H) of the column of the gauge or working fluid. To recalculate the pressure, expressed in some units into others, one can use the formula P = gh, as well as the relations between different units of pressure: (one physical atmosphere 1 atm = 760 mm of the Hg column = ρgh = 13600∙9.81∙0.760 = 101.3∙103 Pa = 10.33∙103 kgf/m2 (mm of the H2O column) = 1.033 kgf/cm2. One technical atmosphere at = 23 

 

1 kgf/cm2 = 104 kgf/m2 (mm of the H2O column) = 98100 Pa = 735 mm of the Hg column). The surface forces also include the forces of internal friction (viscosity forces) Fs, directed along the tangent to the surface, delineating the layers of the fluid, moving relatively to each other. Tangential stresses created by forces of internal friction are called stresses of internal forces, or shear stresses: lim∆

→

/∆

/

.

Transmission of impulse from layer to layer is equivalent to the appearance of friction between layers, because, according to Newton’s second law, the force is equal to the derivative of the impulse with respect to time. This force prevents the mutual displacement of the adjoining layers of liquidity. Thus, the frictional force is equal to the flux density through the boundary surface between the layers of the flowing liquid. It has been experimentally established that for many liquids the magnitude of the tangential stresses of frictional forces  at a given point of a surface element that delimits the two moving layers of liquidity is proportional to the velocity gradient. In accordance with this, in the case of a one-dimensional fluid flow, the internal friction stress /

,

(1.46)

where the minus sign is explained by the fact that the normal is directed towards a decrease in the velocity.

In this case, a positive value of the flux density of impulse corresponds to a negative value of the velocity gradient, with the stream oriented in the direction of the normal, and the gradient in the opposite direction. If the normal is directed towards an increasing velocity, the minus sign in equation (1.46) will change by plus. Equation (1.46) expresses Newton’s law of internal friction. Fluids in which the stresses of internal friction obey this law are called Newtonian. Fluids in which the stresses of internal friction are not described by the equation (1.46) are called non-Newtonian. 24 

 

The coefficient of proportionality  in equation (1.46) is called the coefficient of dynamic viscosity, or dynamic viscosity; it has the dimension ∙ ∙

∙

∙

1

∙



∙

∙

10

10

;

.

Viscosity characterizes the resistance of the liquid to the displacement of its layers and is one of the basic physical properties of liquids. The viscosity of liquids, as a rule, decreases with increasing temperature due to the increase in the distance between molecules due to weakening of the forces of attraction between them. In addition, with the growth of temperature, the association of molecules of dropping liquids decreases. The viscosity of gases increases with increasing temperature, because the increasing rate of thermal motion intensifies the exchange of impulse between the layers of the flow. As the pressure increases, the viscosity of the gases also increases. Equation (1.46) can be written in the form relating the flux density of impulse to the impulse gradient of a unit volume of the liquid / (the flow is assumed to be plane-parallel, the environment is conditionally assumed to be incompressible):

/

.

(1.47)

The proportionality factor  = / (m2/s) is called the kinematic viscosity. Thus, the coefficients of dynamic () and kinematic () viscosity characterize the fluid resistance to the displacement of its layers and at the same time serve as a measure of the intensity of impulse transfer in the flowing fluid, since they are the ratio of the impulse flux density to the velocity or impulse gradient [1, 9]. 25 

 

Questions for self-control: 1. 2. tics? 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. other? 18. 19. 20.

Derive the basic equation of hydrostatics. What practical task can be solved using the basic equation of hydrostaWhat quantity is called the leveling height? What does it characterize? What is the hydrostatic head in terms of physical meaning? What is the meaning of Pascal’s law? What is the physical meaning of the Bernoulli equation for an ideal fluid? What quantity is called a full hydrostatic head? What is the magnitude of the velocity head? What forces act in a real fluid? Name and characterize the volume forces. Explain the nature of the forces acting on the surface. What is the hydrostatic pressure in the SI system? What does Newton’s law of internal friction express? What do the coefficients of dynamic and kinematic viscosity characterize? How does temperature increase affect the viscosity of liquids? How does temperature and pressure increase affect the viscosity of gases? What equation relates the dynamic and kinematic viscosity coefficients to each What is the unit for measuring the kinematic viscosity coefficient? What is the unit for measuring the dynamic viscosity coefficient? Name the known units for measuring viscosity coefficients.

1.4. Real liquid motion modes

Several researchers (Hagen – in 1869, Mendeleev – in 1880, Reynolds – in 1883) observed two fundamentally different modes of fluid motion. This question was investigated most fully by Reynolds on the device shown in Fig. 1.4. To the vessel 1, in which a constant water level is maintained, a horizontal glass tube 2 is connected. A thin stream of colored water (indicator) is introduced into this tube along its axis through the capillary tube 3. With a small water velocity in tube 2, the colored trickle drawn into a horizontal thread, which does not wash out, reaches the end of the pipe (Fig. 1.4, a). This indicates that the particle paths are rectilinear and parallel to each other. Such a motion, in which all particles of a fluid move along parallel trajectories, are called streamed, or laminar. 26 

 

Fig. 1.4. Reynolds experiment: a – laminar motion; b – turbulent motion

If the water velocity in pipe 2 is increased beyond a certain limit, the colored trickle first acquires a wavy movement, and then begins to blur, mixing with the bulk of the water. This is due to the fact that individual particles of the liquid move no longer parallel to each other and the axis of the tube, but are mixed in the transverse direction (Fig. 1.4,b). Such disordered motion, in which individual particles of liquid move along intricate, chaotic trajectories, while the entire mass of the liquid as a whole moves in one direction, is called turbulent. In the turbulent flow, velocity pulsations occur, under the action of which fluid particles moving in the main (axial) direction also receive transverse displacements, leading to intensive mixing of the flow across the section and requiring a correspondingly higher expenditure of energy for fluid motion than for a laminar flow. It has been experimentally established that the transition from the laminar to the turbulent regime depends not only on the flow velocity w, but also on the physical properties of the fluid: viscosity  or  and density , and determining the geometric size – pipe diameter d. The flow is accelerated with increasing w, , d and decreasing . The / , which includes the enumerated dimensionless complex quantities, allows to judge, by its value, the regime of fluid motion. 27 

 

This complex is called the Reynolds number (criterion) and is denoted by Re: /

/ .

(1.48)

The value of the Reynolds number for the transition conditions from the laminar regime of fluid to turbulent motion is called critical. When the fluid flows through straight smooth pipes 2300. At 2300, the fluid motion regime will be laminar, and at 2300 – turbulent. However, at 2300 10000, the fluid motion regime is still unstable turbulent; this range of values of Re is often called transitional. Therefore, it is believed that a stable (developed) turbulent regime, when liquids move through straight smooth pipes, is established for 10000. In case if the liquid moves along a channel (pipeline, apparatus) of complex configuration, in calculating Re instead of d, use the hydraulic radius rh or equivalent diameter deq. The hydraulic radius rh is the ratio of the flow area S of the flow to the wetted perimeter of the P channel (pipeline): / .

(1.49)

For a round tube

/ 4



/4.

(1.50)

The diameter expressed in terms of the hydraulic radius is called equivalent [1, 2, 9]:

4 .

(1.51)

1.4.1. Speed distribution and liquid flow with the laminar flow streaming

In the case of laminar motion of a viscous liquid in a straight round tube, the entire liquid can be mentally divided into a series of annular layers coaxial with the pipe (Fig. 1.5). 28 

 

Fig. 1.5. The distribution of velocities for a laminar mode of fluid motion

Due to the action of frictional forces between the layers, the layers will move with unequal velocities. The central cylindrical layer at the axis of the tube has the maximum velocity, as the distance from the axis increases, the velocity of the elementary ring layers will decrease. Directly at the wall, the liquid “sticks” to the wall, and its velocity here vanishes. We select a cylindrical layer of length l and radius r in the flow of a fluid laminarly moving along a tube of radius R. The motion of the layer occurs under the action of pressure forces P1 and P2 from , where both end sides of the cylinder: p 1 , p 2  hydrostatic pressures in sections 1-1 and 2-2. The motion of the cylinder is resisted by the force of internal friction, for which, according to Newton’s law, the expression can be written:

S    2lr where

dw r , dr

(1.52)

2lr is the outer surface of the cylinder,   is the dynamic coefficient of

viscosity of the liquid, the velocity of the fluid along the axis of the cylinder at a distance r from the axis.

The minus sign indicates a decrease in the velocity with increasing radius r (for , 0). In accordance with the laws of dynamics for steady motion, we can write the equation: P1  P2  S

or 29 

 

(1.53)

p1r 2  p2 r 2   2rl

dwr , dr

(1.54)

whence, after contraction and separation of variables, we obtain p rdr   dw r , 2 l

(1.55)

 p  p1  p 2 . Passing to the entire volume of the liquid in the tube, integrate this differential equation, taking into account that the radius on the left side of the equation varies from r to r = R, and the variable velocity on the right-hand side is from w = wr to w = 0 (near the wall, where r = R):

where

R

0

p rdr    dwr 2l r wr

(1.56)

Then wr 

p 2 R  r2 . 4 l





(1.57)

The speed has a maximum value on the pipe axis, where r  0 : w max 

p 2 R . 4 l

(1.58)

Comparing the expressions (1.57) and (1.58), it is possible to find

 r2  wr  wmax  1  2 . R  

(1.59)

Equation (1.59) is the Stokes law, expressing the parabolic velocity distribution in the pipeline cross section for laminar motion. 30 

 

According to this law, the velocity of fluid flow near the pipe wall is zero and is maximum along the axis of the tube. To determine the flow rate for laminar flow, consider an elementary annular cross-section (Figure 1.3) with an internal radius r and an outer radius r  dr  of the area equal to dS  2rdr . The volumetric flow rate of the liquid through this section is:

dV l  w r dS  w r 2  rdr ,

(1.60)

or taking into account equation (1.57) dV l 

p1  p 2 R 2  r 2 2 rdr . 4 l





(1.61)

Integrating the last equation, it is possible to obtain the total flow of liquid through the pipe:

Vl 

p1  p 2 4 l

R

 R

2



 r 2 2rdr 

0

p1  p 2  4 l

R   p  p2  2R 2  rdr  2  r 3 dr   1 R 4 .   8 l 0 0   R

(1.62)

Substituting for R the diameter of the tube d  2R and denoting  p1  p 2    p , we finally find Vl 

d 4 p . 128 l

(1.63)

Equation (1.62) or (1.63), which determines the flow rate of a liquid during its laminar motion along a round straight pipe, is called the Poiseuille equation. The relationship between the average speed w and wmax can be obtained by comparing the value Vl from equations (1.62) and (1.63): 31 

 

Vl  wS  wR2

R 2 w  whence

w

p1  p 2 R 4 8 l

p1  p 2 2 R . 8 l

(1.64) (1.65)

(1.66)

Comparing equations (1.57) and (1.66), we obtaine

w

wmax . 2

(1.67)

Thus, with a laminar flow in a pipe, the average fluid velocity is half the velocity along the axis of the tube [1-3, 9]. 1.4.2. Turbulent movement of the liquid

In industrial practice turbulent motion of liquids is most common. In turbulent motion, because of the chaotic motion of the particles, the velocities in the main mass of the flow are equalized and their distribution along the pipe section is characterized by a curve that differs in form from the parabola in Fig. 1.5; the curve has a much wider peak (Fig. 1.6).

Fig. 1.6. Velocity distribution under turbulent mode of fluid motion

32 

 

Conditionally distinguish the central zone, or the bulk of the fluid, called the core of the flow, in which the motion is a developed turbulent, and the hydrodynamic boundary layer near the wall, where the turbulent motion changes into a laminar one. Inside this layer there is a thin sublayer (near the pipe wall) of thickness δ, where the viscosity forces exert a predominant influence on the motion of the liquid. Therefore, the nature of its flow in the sublayer is mainly laminar. The velocity gradient in the laminar boundary sublayer is very high, and at the wall itself the velocity is zero. There is a transition zone between the core of the flow and the laminar sublayer, and the laminar sublayer and this zone are sometimes called the hydrodynamic boundary layer. Experience shows that the average velocity for turbulent motion is not half the maximum for laminar motion, but much larger, with w/wmax = f (Re). For example, at Re = 104 the velocity w = 0,8wmax, and at Re = 108 the value w = 0,9wmax. In connection with the complex nature of turbulent motion, it is not possible to obtain a strictly theoretical profile of the velocity distribution and the value w/wmax. In addition, under a turbulent flow, the velocity profile (Fig. 1.6) expresses the distribution of the velocities, which are not true, but are averaged over time. At each point of the turbulent flow, the true velocity does not remain constant in time because of the chaotic motion of the particles. Its instantaneous values are affected by fluctuations, or irregular pulsations, which have a chaotic character. The difference between the true and the averaged velocities is called the instantaneous pulsating velocity and is denoted by ∆ :

∆ .

(1.68)

The concept of averaged velocity should not be confused with the concept of the mean velocity introduced earlier. The latter is not a time average velocity at a given point, but a velocity averaged over the entire cross section of the pipeline. Despite the seeming randomness of the change in velocities under turbulent motion, the value of the averaged velocity remains constant 33 

 

for a sufficiently large time interval. In this sense, the turbulent motion can be regarded as quasi-stationary [1-3,9]. 1.4.3. Film current of liquids

In a number of processes of chemical technology (absorption, rectification, evaporation) devices are used in which the liquid moves on the surface in the form of thin films. The speed of these processes depends on the characteristics of the flow of films, their thickness and speed of motion. The hydrodynamic regime is determined by the Reynolds criterion for the film: Re film 

wdeq l

l

,

(1.69)

where w  the average speed of the film; d eq  the equivalent film diameter.

The equivalent diameter of a film of thickness δ is determined by the area of the film S  P and the perimeter of the surface P on which the film moves:

d eq 

4S  4 . P

(1.70)

When the film moves along the inner surface of the tube, P = πd, where d is the internal diameter. Substituting the value of the equivalent diameter in the expression for Refilm, we get: Re film 

w4l

l

.

(1.71)

Because of the difficulty in measuring the thickness and speed of the motion of the film, it is more convenient to use in the calculations 34 

 

the product w  l entering the expression for Refilm. This product can be written in the form

G

wP  l wS  l  , P P

(1.72)

The value of G [kg/(ms)] is called the linear mass density of irrigation. It is the mass of fluid passing per unit time through a unit of length of the perimeter of the surface along which the film flows. Upon substitution G  w  l into the expression Refilm, the following expression of the Reynolds criterion for the film is obtained:

Re film 

4G

l

.

(1.73)

The presence of three basic modes of motion of the film was established experimentally: 1) laminar, non-wavy (smooth) flow of a film with a smooth interface with gas (Refilm < ~12); 2) laminar with a wavy phase interface (~12 < Refilm < ~1600); 3) turbulent flow of the film (Refilm > ~1600). When the film of liquid flows along the inner surface of the vertical pipe, which is countercurrent to the liquid i.e. from below upwards, the gas flow (vapor) moves, the film speed and its thickness do not depend on the gas velocity until this speed is sufficiently small. When the gas velocity is increased to 5-10 m/s, an equilibrium is achieved between the gravity force, under the action of which the film moves and the frictional force at the surface of the film, which retards its movement. This leads to choking of the device. It is accompanied by the accumulation of liquid in the apparatus, its ejection and a sharp increase in the hydraulic resistance. Counter-current motion of phases at speeds above the flooding point is impossible. Therefore, the flooding point corresponds to the upper speed limit for countercurrent processes in any type of apparatuses. 35 

With a further increase in the gas velocity in the vertical pipe or apparatus, the motion of the liquid film reverses, and it begins to “slip” from the bottom upward. There comes the regime of ascending direct flow of gas and liquid. With an increase in the gas velocity above 15-40 m/s, mud sprays begin, at which the liquid detaches from the surface of the film and is carried away in the form of a spray. In the case of downward movement (downward flow), the gas entrains the film of the liquid, increasing the speed of the film and reducing its thickness. At the same gas velocities, the hydraulic resistance for the downstream flow is lower than for the ascending one. A stable regime of downward flow exists at gas velocities of about 15-30 m/s. Above which there is a sparger [1-3, 9]. Questions for self-control: 1. Explain the difference between the laminar and turbulent flow regimes of a viscous fluid. 2. What is the physical meaning of the Reynolds criterion? 3. What is the critical value of the Reynolds number? 4. Derive the Stokes law. What does it express? 5. What determines the Poiseuille equation? 6. What is the relationship between the average and maximum fluid velocities in the pipeline? 7. What speed is called instantaneous pulsation speed? 8. In what processes of chemical technology is the film motion of liquids observed? 9. What is the linear mass density of irrigation? 10. Name the main modes of motion of the film.

1.5. Modeling of chemical-technological processes

Many chemical-technological processes are so complex that one can only construct a system of differential equations for describing them and establish the conditions for single-valuedness. It is usually not possible to solve these equations by the methods known in mathematics. In such cases, a simulation method is used. In the broad sense, modeling means understanding the objects of cognition on 36 

 

their models, so modeling is inseparable from the development of knowledge. Modeling is widely used both in conducting scientific research and in solving a large number of practical problems in various fields of technology: in hydraulics and hydraulic engineering (determination of structural and operational characteristics of hydraulic structures, modeling of flowing rivers, waves, tides and outflows and others); in aviation, missile and space technology (determination of characteristics of aircraft and their engines, etc.); in shipbuilding (determination of hull characteristics, etc.); in heating engineering (in the construction and operation of various heaters), etc. Of great importance is modeling in the study of chemical-technological processes and the design of chemical industries. At the same time, modeling is understood as a method of research into chemical and technological processes on models differing from objects of modeling (nature) in the main scale. Simulation can be carried out by two basic methods – the method of generalized variables, or the method of the theory of similarity (physical modeling), and the method of numerical experiment (mathematical modeling) [1, 2, 9]. 1.5.1. The method of generalized variables

In physical modeling (scaling), the experimentally studied object (model) differs from nature in scale, while the physical nature of the phenomenon (process) remains the same. The study of the processes in order to obtain the equations necessary for their analysis and calculation can be carried out theoretically. However, such a path is often impossible. In such cases, it is necessary to resort to experiments and obtain empirical dependencies. However, such an implementation of experiments, which allows us to generalize the results of experiments and apply them to a wide range of issues and phenomena similar to the one being studied, but differing in numerical values of the parameters, is most fruitful. This is achieved by using the methods of similarity theory to process experimental data. The method of generalized variables forms the basis of the similarity theory [1, 9]. 37 

 

One of the basic principles of the theory of similarity is the separation from the class of phenomena (processes) described by the general law (the processes of motion of liquids, diffusion, heat conduction, etc.), a group of similar phenomena. Such phenomena are called similar for which the relations of similar and characterizing quantities are constant. There are the following types of similarity: a) geometric; b) temporary; c) physical quantities; d) initial and boundary conditions. Geometric similarity assumes that similar dimensions of nature and models are parallel, and their ratio is expressed by a constant value. Let’s assume that a complex phenomenon is studied – the motion of gas in a rotating cylinder (Fig. 1.7). In order to investigate the process in this apparatus, the model is constructed observing the geometric similarity (Fig. 1.7,b), i.e. equality of relations of similar linear dimensions of nature and the model.

Fig. 1.7. To the determination of the similarity conditions for nature (a) and the model (b)

If the system in question (nature, the sample) is in motion, then in the presence of a geometric similarity, all its points must move along similar trajectories of similar points of a similar system (model), i.e. pass geometrically similar paths (points A1 and A2). Geometric similarity is observed when the ratio of all similar sizes of nature and model is equal: ⋯ 38 

 

.

(1.74)

The dimensionless quantity is called the constant of geometric similarity, or a scale (transient) factor. The similarity constant characterizes the ratio of homogeneous similar quantities in such systems (in this case, the linear dimensions of the natural object and the model) and allows us to move from the dimensions of one system (model) to another (nature). The temporal similarity assumes that similar points or parts of geometrically similar systems (models and nature), moving along geometrically similar trajectories, pass geometrically similar paths in time intervals, the ratio of which is a constant value: ⁄

⁄

,

(1.75)

where Т1 and Т2 – the time of passage of similar parts of the whole apparatus, respectively, nature and model; 1 and 2 – the time of passage by similar particles of similar paths l1 and l2; а – the temporal similarity constant.

The similarity of physical quantities assumes that in the considered similar systems (nature and model) the ratio of the values of the physical quantities of any two similar points or particles, like those placed in space and time, is a constant value. For example, if in nature the particle passed the path L1 in time 1 (Fig. 1.7, a), and in the model - in the time 2 the path l2, then for similar points A1 and A2 we have: ⁄

;

⁄

; or

⁄

,

(1.76)

where и1 and и2 are the sets of physical quantities (but in the general case, а  а  аl  а, etc.).

The similarity of physical quantities includes the similarity not only of physical constants, but also of all values of physical quantities, or fields of physical quantities. Thus, if the geometrical and temporal similarity is observed, the similarity of the fields of velocities, temperatures, concentrations and other physical quantities will also be observed; w1/w2 = aw, t1/t2 = at; c1/c2 = ас – constants. The similarity of the initial and boundary conditions assumes that the original state and state at the boundaries of systems (nature and model) are similar, i.e. the ratios of the main parameters at the beginning and at the boundaries of the systems are constant. This is 39 

only true in cases where geometrical, temporal and physical similarities are maintained for the initial and boundary conditions of systems, i.e. L1/L2 = аl; 1/2 = а. 1.5.2. Invariants of similarity and criteria of similarity

If all similar quantities that determine the state of a given system (nature) and a similar system (model) are measured in relative units, i.e. take a similar ratio of quantities for each system, it will also be a constant and dimensionless value, for example: L1/D1 = L2/D2 = ... = inv = idem = il; T1/1 = T2/2 = ... = i.

(1.77) (1.78)

Values il, i, etc. do not depend on the ratio of the sizes of nature and model, i.e. for another model, also similar to nature, the values il, i … will be the same. Thus, the relationships of geometric dimensions, time and physical constants in a given system (nature) are equal to the ratios of the same quantities in a similar system (model). When passing from one system to another, similar to it, the numerical value of the quantities il, i … is preserved. Therefore, the dimensionless numbers i, which express the ratio of two homogeneous quantities in such systems, are called invariants of similarity (invariantis (lat.) - unchanged). Similarity invariants, which are relations of one-dimensional values, are called simplexes (simplex (lat.) – simple), or by parametric criteria (for example, the ratio L1/D1 – a geometric simplex). Invariants of similarity, expressed by the ratio of heterogeneous values, are called similarity criteria (kriterion (Greek) – a sign, a means for judging). Usually they are designated by the initial letters of the names of scientists who have made a significant contribution to this area of knowledge (for example, Re – number, or Reynolds criterion). Phenomena similar to each other are characterized numerically equal to similarity criteria. Equality of similarity criteria – the only quantitative condition for the similarity of processes. Hence it is 40 

 

obvious that the ratio of the criteria of one system to the curves of a similar system is always 1. For example, for nature and the model Re1 = Re2. Then /

1

/

(1.79)

or /

/

/

1.

/

(1.80)

If the ratio of the similarity constants is equal to 1, it is called the similarity indicator and indicates equality of similarity criteria. Consequently, in similar phenomena, the similarity indicators are equal to one (the first similarity theorem). The similarity criteria, which are composed only of the quantities entering into the uniqueness conditions, are called defining criteria. Criteria also include quantities that are not necessary for an unambiguous characterization of a given process, but are themselves dependent on these conditions called determinable. Any relationship between variables that characterize a phenomenon (that is, a system of differential equations) can be represented in the form of a dependence between the similarity criteria (the second similarity theorem): ⋯

0

(1.81)

This dependence is called the generalized (criterial) equation, and the similarity criteria Кi – generalized variable quantities. Thus, the similarity theory makes it possible to represent the solution of differential equations and to process the experimental data in the form of generalized criterial equations. Usually equation (1.81) is written in the form of the dependence of the determined criterion of similarity (which includes the sought value) from the determinants: ⋯ , 41 

 

(1.82)

for example, ⋯,

(1.83)

where К1 – the determined similarity criterion; the values of A, n, and m are found experimentally.

Similar phenomena are described by the same system of differential equations and in which the similarity of the single-valuedness conditions is observed (the third similarity theorem). Similar to the same uniqueness conditions for the identity of the differential equations describing the processes, there is an equality of the defining similarity criteria. Hence, the third similarity theorem can also be formulated: the phenomena are similar if their defining criteria are equal [1,9]. 1.5.3. Hydrodynamic similarity

In accordance with the general provision on the similarity of processes, the motion of liquids in two pipelines will be similar in the case when the relations of the forces acting in them are constant in such flows. In the flow of liquid, each particle is under the influence of pressure, gravity and friction forces. In addition, in the moving fluid, there is an inertia force equal in magnitude but inverse to the sign of the resultant forces of pressure, gravity, and friction. The force of inertia is defined as the product of the particle mass by the acceleration. The constant ratio of each of the acting forces to the force of inertia (or the inverse relation, which is used instead of the direct ratio of inertia forces to not deal with fractional quantities) is characterized by similarity criteria. The hydrodynamic similarity criteria can be obtained from the differential equation of the equation of motion of a real Navier-Stokes fluid. We write the Navier-Stokes equation for a real incompressible fluid of one-dimensional steady-state motion (for the z axis):  g 

w z  2 wz p .   2  z z 42 

 

(1.84)

We divide all the terms of equation (1.84) onto its right-hand side 

g p  2 w    2 z  1. z wz wz zwz

(1.85)

Carrying out a similar transformation of the equation (1.85), we multiply each of its elements by the corresponding similarity constants, and the factors as constants are taken out as the sign of the differential: C g C  C  g     C p C w    w z

C p C   p      C C C zw z z  w  

 C  C wC     C z2 C  C w

  2 w z   2  z w z

 (1.86) . 

Comparing equations (1.85) and (1.86), we obtain dimensionless complexes composed of similarity constants, which are called similarity indicators (with the same factors being canceled). For the terms of equation (1.86), taking into account the influence of gravity and body forces, we will have: Сg C Cw

 1.

(1.87)

 1.

(1.88)

Replacing it C  Cl , we get: Cw C g Cl Cw 2

For the terms of equation (1.86), which take into account the effect of pressure forces: С pC CzC Cw

1

or Сp CCw2 43 

 

 1.

(1.89)

For the terms of equation (1.86), which take into account the influence of internal friction forces: С  С С z2 C

1

or C  1. Cl C  C w

(1.90)

In the similarity indicators (1.88-1.90), instead of the scale factors, substituting the corresponding ratios of physical quantities Сw 

  w1 l p g ; Cl  1 ; C   1 ; C p  1 ; C   1 ; C g  1 . w l  p  g

(1.91)

(the physical quantities in the cognizant refer to the given system, and in the numerator to the similar one), we obtain dimensionless complexes or similarity criteria. 1. The Froude criterion Fr is the ratio of the forces of gravity to the inertia forces and is obtained from the similarity indicator (1.88), from g1 l1  СgCl g l  2  1, w1 Cw2 w2

(1.92)

g1l1 gl   idem w12 w2

(1.93)

or

gl  Fr . w2

(1.94)

To avoid fractional values, the inverse expression is usually used:

w2  Fr . gl 44 

 

(1.95)

2. Euler’s criterion Eu is the ratio of the pressure forces to the inertial forces, obtained from the similarity indicator (1.89): p1 p   1, 1 w12   w2

(1.96)

p1 p  2  idem 2 w1 1 w 

(1.97)

Сp C  Cw 2

whence

or p

w 2

 Eu .

(1.98)

Since for the theory of similarity it is not the absolute values that are important, but the relative ones, instead of the magnitude of the absolute pressure, the pressure difference is introduced at any two points, and the Euler’s criterion takes the form:

p  Eu . w 2

(1.99)

3. The Reynolds criterion Re is the ratio of the frictional forces to the inertia forces and determines the fluid motion regime. It turns out from the similarity indicator (1.90):

1

C    1, Cl C Cw l1  1  w1 l  w whence

1

1l1w1



  idem lw

45 

 

(1.100)

(1.101)

and

1    lw Re

or

l w



 Re .

(1.102)

(1.103)

If we consider unsteady motion, then, in an analogous manner, as well as for the derived hydrodynamic similarity criteria, we obtain a homochronality criterion Ho that takes into account the unsteady fluid motion:

w  Ho , l where

 

time;

w 

speed;

(1.104)

l  determining linear dimension.

Thus, the Navier-Stokes equation describing in general form the process of fluid motion, as a result of such a transformation, can be represented as a function of the similarity criteria: f Ho , Fr , Eu , Re   0 .

(1.105)

For steady motion, where Ho is excluded: f Fr , Eu , Re   0 .

(1.106)

For forced motion of a fluid, the influence of gravity is negligible, and the equality of Froude’s criteria in this case can be neglected. Then the relationship between the similarity criteria in the general form is expressed by a function: l  Eu  f  Re, , d  where

l  d

the ratio of linear dimensions, characterizing the geometric similarity.

46 

 

(1.107)

Euler’s criterion is undefined, because with the equality of the criteria of Froude and Reynolds it turns out by itself, since the pressure drop is a consequence of the velocity distribution in the flow. The form of the function (1.107) is represented in a power form: n

l Eu  A Re   . d  m

(1.108)

The value of the constant A and exponents m, n are determined experimentally. The basic criteria of hydrodynamic similarity Re and Fr sometimes are replaced by more complex criteria of Galileo Ga and Archimedes Ar, obtained by a combination of the main criteria: Galileo’s criterion

Ga 

Re2 gl 3  2 gl 3   2, Fr 2 

(1.109)

criterion of Archimedes

Ar  Ga

1   gl 3 1   gl 3  1    ,  2      2

where 1 and  are the densities of the liquid at two different points.

(1.110)

It is convenient to use the Ga criterion in those cases when it is difficult to determine the flow velocity (in Ga velocity is excluded). The criterion Ar characterizes the similarity in the motion of a fluid due to different densities at different points of the flow, i.e. in conditions of natural convection [1-3, 9]. Questions for self-control: 1. 2. 3. 4. 5. 6.

What is the principle of modeling physical and chemical processes? What phenomena are called similar? Name and characterize the types of similarity. What characterizes the similarity constant? What numbers are called similarity invariants? What are simplexes? Give examples.

47 

 

7. What is called similarity criteria? 8. Give the formulations of three similarity theorems. 9. Explain the physical meaning and structure of the criteria for hydrodynamic similarity. 10. In what cases are the criteria of Galileo and Archimedes used?

1.6. Resistance of flow

When the fluid flows through pipelines and apparatus, a pressure loss occurs, which is composed of various resistances that occur when the flow velocity changes, the flow direction is changed, and also due to frictional forces. In horizontal pipelines, the frictional pressure loss is determined from the functional relationship between the similarity criteria describing the forced motion of a viscous fluid (1.107): ,

.

(1.111)

We express the Euler’s criterion in terms of the corresponding physical quantities: ∆

,

,

(1.112)

from which the resistance, equivalent to the pressure drop ΔP, can be expressed as: ∆

2

.

(1.113)

Denoting the expression 2 in terms of the resistance coefficient (friction)  (dimensionless quantity), we obtain the formula (1.114), which is convenient for practical calculations. This expression is called the Darcy-Weisbach equation: , (N/m2),

∆ 48 

 

(1.114)

where  – the coefficient of friction; l  length of the pipeline, m; d  diameter of the pipeline, m; ρ –the density of the liquid, kg/m3; w – linear velocity of fluid motion, m/s.

The coefficient of friction is a function of the Reynolds criterion and, depending on the mode of motion, it is determined: When laminar flow of a liquid (Re 7200

  1, 26 .

(1.127)

The values of the Reynolds criterion are determined by the formula:

Re 

wd eq  l

 env



w f 4  l 4w f  l 4W     ,







where  l  the density of the liquid, kg/m3;





(1.128)

W  mass velocity, referred to the

2

whole section of the apparatus, kg/m ·s.

In equation (1.124), the value of the specific surface after simple transformations can be expressed in terms of the particle diameter. Let 1 m3 of the granular layer contain m particles with a porosity (free volume)  and a specific surface σ. The volume of particles in , and the average volume of 1 m3 of layer is obviously equal to 1 a particle Vp can be calculated by the formula: Vp 

1   d 3  , 6 m

(1.129)

And its surface will be

p 

 m



d 2 ф

,

(1.130)

where d  the diameter of the sphere having the same volume as the particle, m; ф  form factor.

52 

 

Dividing σp, by Vp, we obtain

p Vp

or

d 2

 

p Vp

m  ф 1  d 3 m 6



whence

 

 1 



6 , фd

6 1    . фd

(1.131)

(1.132)

(1.133)

Substituting the value (1.133) into equations (1.124) and (1.128), we obtain:

p 

2 l 61    w f 3 l 1    2  3  w f 8 фd 4 d p ф 3 

(1.134)

and Re 

4w f 





4w f  2 ф wf d p 2 ф Re 0 , (1.135)    61    3 1 3 1       фd

where Re0 – modified Reynolds criterion [2,3,9],

Re0 

wf d p 



.

(1.136)

Questions for self-control: 1. What causes a drop in pressure in the pipelines? 2. What is the physical meaning of the Darcy-Weisbach equation? 3. What equation is used to determine the pressure drop in meters of the fluid being transported?

53 

 

4. What causes the local resistance to the flow? 5. What is the total loss of head? 6. How are pressure losses in the coil calculated? 7. How is the equivalent diameter of the bulk material calculated? 8. Why are Raschig rings and granular material used in the apparatus? 9. List the main characteristics of the nozzle. 10. By what formula can the loss of fluid pressure be determined when it moves through the nozzles in the apparatus?

1.7. Mixing in liquid environments

Mixing of liquid environments, pasty and solid bulk materials is one of the most common processes of chemical technology. Most often in the technology there are processes of mixing liquid environments. The mixing of liquid media is understood as the process of multiple-fold relative mixing of macroscopic elements of the volume of a liquid environment under the action of a pulse transferred to the environment by a mechanical stirrer, a gas or liquid jet. Mixing of liquid media is used to solve the following main tasks: 1) the intensification of heat and mass transfer processes, including in the presence of a chemical reaction; 2) the uniform distribution of solid particles in the volume of the liquid (in the preparation of suspensions), as well as uniform distribution and crushing to a predetermined dispersion of liquid in the liquid (in the preparation of emulsions) or gas in the liquid (in bubbling). Apparatus with mixing devices are widely used in chemical technology to carry out such processes as evaporation, crystallization, absorption, extraction, etc. With mixing, the gradients of temperatures and concentrations in the environment filling the device tend to a minimum value. Therefore, agitators, for example, in the structure of the flows, are closest to the ideal mixing model. Mixing of liquid media can be carried out in various ways: rotational or oscillatory movement of the mixers (mechanical stirring); bubbling of gas through a layer of liquidity (pneumatic mixing); pumping the liquid through the turbulent nozzles; pumping of liquid by pumps in a closed circuit (circulation mixing). 54 

 

The process of mixing is characterized by intensity and efficiency, as well as energy consumption for its conduct. The intensity of mixing is determined by the amount of energy N supplied to a unit volume V of the stirred liquid per unit time (N/V) or to a unit mass of the stirred liquid (N/V). Intensification of the mixing process allows to increase the productivity of installed equipment or reduce the volume of the projected equipment. The efficiency of mixing is understood as the technological effect of the mixing process, which characterizes the quality of the process. Depending on the purpose of mixing, this characteristic is expressed in various ways. For example, when mixing is used to intensify thermal, mass-exchange and chemical processes, its efficiency can be expressed by the ratio of the kinetic coefficients for mixing and without mixing. When preparing suspensions and emulsions, the effectiveness of mixing can be characterized by the uniformity of phase distribution in suspension or emulsion [1,9]. 1.7.1. Mechanical mixing

In the industry, mechanical agitators with rotational motion are mainly used for mixing. When these agitators operate, a complex three-dimensional fluid flow (tangential, radial, axial) occurs with the prevailing circumferential velocity component. The tangential flow that forms during the operation of all types of mixers is primary. Usually the average value of the circumferential (tangential) component of the speed (wt) significantly exceeds the mean values of both the radial (wr), and the axial (or wa) components. For the rotational motion of a fluid, the system of Navier-Stokes equations can be written in the following form: ;

0;

where wt – the tangential component of the velocity.

,

(1.137)

In the case of a plane rotational motion about the z axis (wr = 0, wa = 0) the system (1.137) has a general solution: 55 

 

/ .

(1.138)

For r = 0, wt = 0 and C2 = 0 respectively. For the region located at the center of the rotating mass of the fluid, with the motion established, wt = r (where  – the angular velocity). Thus, along the axis of rotation of the liquid in the region 0 < r < rv, there exists a cylindrical vortex of radius rv. It follows from equation (1.138) that in the region outside the cylindrical vortex wt = C2/r, whence C2 = rv. Then for the peripheral region of the tangential velocity component / .

(1.139)

A comparison of the theoretical and experimental curves of the tangential velocities of a liquid in a rotating stirrer apparatus (Fig. 1.8) shows that there is some transition region II between the region of the central vortex I and the peripheral region III.

Fig. 1.8. Theoretical (1) and experimental (2) curves of the tangential velocities of the liquid in the apparatus with a rotating mixer: I – the region of the central cylindrical vortex, II – the transition region, III – the peripheral area

Under the influence of the centrifugal force arising when any type of agitator is rotated with a sufficiently high frequency, the fluid flows from the blades in the radial direction. Having reached the wall 56 

 

of the vessel, this flow is divided into two: one moves up, the other – down. The appearance of a radial flow leads to the formation of a zone of low pressure in the transition region, where the liquid rushes flowing from the free surface of the liquid and from the bottom of the vessel; there is an axial (central) flow moving in the upper part of the vessel from top to bottom to the mixer. Thus, a stable axial flow or steady circulation is created in the apparatus (Fig. 1.9). The volume of circulating liquid per unit time in a stirrer is referred to as the pumping effect, which is an important characteristic of the mixer: the greater the pumping effect, the better the mixing process takes place in this apparatus.

Fig. 1.9. Trajectories of the motion of particles of liquid in the apparatus with a stirrer (a) and a velocity diagram (b)

In the case of a predominantly radial flow created by the stirrer, the pumping effect Vr is determined by expression , where

the average radial velocity of the liquid, and

(1.140) ~

.

Since for geometrically similar mixers the ratio b/dm – a constant value, we can write: , where Сr – a constant for a given type of mixers.

57 

 

(1.141)

In the case of a predominantly axial flow created by a mixer, the pumping effect Vo is expressed by the following relationship: /4, where the average fluid velocity in the axial direction, with – the step of the stirrer).

Since for geometrically similar mixers / expression о

о

(1.142) ~

(where S

, we obtain

,

(1.143)

identical to equation (1.142). The values of the constants in equations (1.142) and (1.143) are determined experimentally, they are given in the special literature. Thus, the pumping effect is highly dependent on the design and speed of the mixer. The viscosity of the stirred liquid has a significant influence on it: with increasing viscosity, the pumping effect decreases, which reduces the efficiency of the mixing process. The modified Reynolds number for the Rem mixers in the case of mechanical mixing of the liquid medium is expressed in the following way (taking into account the fact that π = ωdmn): / where dm – the diameter of the mixer, m; n – the speed of the mixer, s-1.

(1.144)

With laminar motion (Rem 104), forced circulation provides an intensive three-dimensional flow of the entire mass of liquid in the apparatus. The region of the central cylindrical vortices 58 

develops, reaching (in order of magnitude) the dimensions of the transition and peripheral regions. When rotating mechanical mixers work on the surface of the liquid, a funnel appears, the depth of which grows with the speed of the mixer (in the limit it can reach the bottom of the vessel). This phenomenon adversely affects the efficiency of mixing and significantly reduces the stability of the mixer. The depth and shape of the funnel is greatly influenced by the diameter of the mixer and the frequency of its rotation [1,2,9]. 1.7.2. Energy consumption for mixing

Let us consider a blade that is streamlined by a liquid. The resistance force R, according to Newton’s law, is /2,

(1.145)

where the area of the blade, equal to the product of its width b by twice the radius r, i.e. 2 .

Assume that the liquid is stationary and w – the circumferential velocity of the rotating mixer, which varies along the length of the blade, where (where the angular velocity), or 2 . The resistance force dR on the surface element 2 is equal to: 2

2

/2.

Then the power consumed for mixing,

(1.146) , is

8

or 8

8

/4.

(1.147)

The value b can be expressed in fractions of the diameter of the (where a coefficient that depends on the mixer, i.e. 59 

 

geometric dimensions of the mixer). Taking into account the fact that /2, we get: /8. /8

We denote the ratio

(1.148)

. Then .

(1.149)

From here /

.

(1.150)

This value is usually called the power criterion, or the modified Euler’s criterion (for mixers); it is also called the Euler’s centrifugal criterion ∆ / , with ~ . Hydraulic resistance when rotating the mixer in a liquid environment ∆ ~ / . Then /

.

(1.151)

Then the generalized equation of hydrodynamics for the processes of mixing liquid environments will take the form: , where cess.

/

/

,

,⋯ ,

(1.152)

the Froude’s criterion for the mixing pro-

In cases where the action of gravity is negligible (the funnel is missing or has a small depth), equation (1.152) can be simplified and reduced to the form ,

,

,

, ⋯ or

⋯, (1.153)

where the values of A, m, n, q are determined experimentally.

For the most common types of mixers, the literature gives experimental curves for the dependence of KN from Rem [1,2,9]. 60 

 

1.7.3. Constructions of mixers

According to the speed of rotation, the mixers are conditionally divided into two groups: slow-moving (anchor, frame and others, whose circumferential velocity of blade ends is about 1 m/s) and high-speed (propeller, turbine and others, whose circumferential velocity is of the order of 10 m/s). Usually the apparatus for mixing is a vertical vessel with a mixer, the axis of rotation of which coincides with the axis of the apparatus (Fig. 1.10). Depending on the conditions for carrying out a particular process, the volume of the apparatus with a mixer can be from several parts to several thousand cubic meters. The main knots of such apparatuses are a cog, a drive and a shaft with a mixer.

Fig. 1.10. Apparatus with a stirrer: 1 – motor with drive; 2 – cover; 3 – the shaft of the mixer; 4 – connection for the supply of compressed gas; 5 – housing; 6 and 11 – inlet and outlet connections of the coolant; 7 – shirt, 8 – baffle plate, 9 – bottom, 10 – mixer; 12 – the outlet of the product, 13 – the pipe of extrusion

The body of the device usually consists of a vertical cylindrical shell 5, a lid 2 on which the mixer drive 1 and the bottom 9 are mounted. Apparatuses whose operating pressure differs from the atmospheric one have elliptical bottom and cover, and in apparatuses 61 

 

with a large diameter of the cover and the bottom are made integral (allwelded with the body), and for internal inspection and cleaning of such devices on the cover, hatches of a sufficiently large diameter are installed. On the cover are also the branches 4 and 11 for the supply and removal of substances, the supply of compressed gas, the installation of control-measuring devices, etc. For the supply and removal of heat, the housing of the apparatus is supplied with a shirt 7. The drive of the stirring device is usually performed by an electric motor connected to the mixer shaft by direct or downshifting. To reduce the rotational speed of the mixer shaft, various reducers are used in comparison with the motor shaft. A structural element, directly designed to drive the fluid, is a mixer 10. As practice shows, most mixing problems can be successfully solved by using a limited number of mixer designs. In this case, there are the most characteristic applications and ranges of geometric relationships of individual types of mixers. For example, ribbon, scraper and screw mixers are used for mixing high-viscosity media under laminar conditions (Fig. 1.11, a,b,c). Scraper mixers are used mainly for intensification of heat transfer; scrapers are attached with the help of springs, thereby ensuring a close fit to the wall of the apparatus. To mix liquids with a relatively low viscosity (usually with heat supply, ie in apparatus with a shirt) slow-speed mixers are used – anchor and frame mixers (Fig. 1.11, d,e). The ratio of Da/dm in these mixers is not great (1,05-1,25), so they are often used when mixing suspensions whose particles are prone to adherence to the walls.

Fig. 1.11. Mixers for mixing of high-viscous environments (a-c) and environments of medium viscosity (d, e): a – band; b – scraper; c – auger with guide pipe; d – anchoring; e – frame

62 

 

High-speed lobed, turbine, propeller mixers usually have a ratio Dа/dm  1,5 (Fig. 1.12). They differ in the ability to create an axial circulation flow. In apparatuses without internal devices, these mixers provide a pumping effect that is twice the pumping effect of conventional stirrers (for example, shown in Fig. 1.11,d,e). It should be noted that the appropriateness of using the mixers of these or other designs is often determined by the features of the technology of their manufacture. For example, when gumming, or enamelling mixers, the presence of sharp corners and edges prevents the formation of a reliable coating. For gumming, blade paddles are convenient, and for enamelling - mixers from flattened pipes. In recent years, only the enamelled mixers from solid pipes and milling have firmly entered the practice of mixing from the new mixer designs (Fig. 1.12, f). Milling stirrer is a disk with blades in the form of teeth. It provides a high difference in the speeds of the agitator blades and the flow of their fluid around them. Milling stirrers are used mainly for the preparation of finely divided suspensions.

Fig. 1.12. High-speed mixers: a – propeller, b – two-blade; c – three-blade; d – turbine open; e – closed turbine; f – milling

63 

 

The intensity of mixing depends to a large extent on the presence of such or other internal fixed devices. For functional purposes, these devices can be divided into three groups: 1) organization of the flow; 2) heat exchange; 3) technological pipelines (for supplying liquid and gaseous components) and pipelines for placing control-measuring devices. For the organization of the flow, reflective partitions are most often used, the main purpose of which is to reduce the circumferential velocity component with a corresponding increase in the axial and radial components. To increase the pump effect in the apparatus the guide tubes (diffusers) are served. They are used both for laminar and turbulent mixing, in the first case in combination with auger, and in the second – with propeller (screw) mixers. As internal heat exchangers in apparatuses with a volume of less than 5 m3, the coil is usually installed coaxially with the shaft of the mixer, and in the large-volume appara-tus, several coils located on the periphery may be used. The concentric arrangement of two or more coils is undesirable due to the deterioration of mixing and heat exchange in the intertubular space [1,2,9]. Questions for self-control: 1. What is mixing? 2. To solve what problems is mixing of liquid environments used? 3. List the main methods of liquid environments mixing. 4. Give the notion of intensity and effectiveness of mixing. 5. What is the pumping effect of mixers? What ways are used to increase the pumping effect? 6. Give a modified Reynolds number for mixers in the case of mechanical mixing of the liquid environments. 7. What flow regimes are observed in apparatus with a mixer? 8. What parameters does the power used for mixing liquids depend on? 9. Give a classification of mixer designs. 10. What is the difference between the basic mixer designs?

64 

 

1.8. Basics of the principle of fluidization

At present, a number of processes of chemical technology, in which gas or liquid interacts with finely divided solid material (drying, calcination, adsorption, catalytic processes) are carried out in devices with a so-called suspended (fluidized) or boiling layer. If a flow of gas or liquid passes through a fixed layer of solid particles, depending on the velocity of the gas or liquid, the granular layer can be in the following stationary states: 1. The gas flow velocity is below a certain critical velocity wcr, the solid particles of the granular layer are immobile. The hydraulic resistance of the layer increases with the gas velocity in accordance with equation (1.124). 2. After reaching a certain critical velocity of the gas flow, wcr the particles of the granular layer go into a suspended state (fluidized), move and mix. The fluidized state in Fig. 1.13 is represented by a horizontal section BC. It is characterized by the equality of the hydrodynamic pressure and the weight of the layer per unit area of its cross-section (N/m2). 3. At the velosity of the fluidizing agent, when the force of the hydrodynamic pressure begins to exceed the force of gravity, the particles are carried away from the layer. This velocity of the gas (liquid) flow is called the velocity of entrainment went.

Fig. 1.13. Dependence of the resistance of a layer of solid particles from the fictitious gas velocity: OB – the line segment of the fixed bed, BC – the line segment of fluidization,  – pressure peak, the moment of transition of the bed to a fluidized state

65 

 

The limits of existence of the fluidized bed are limited, from below by the critical velocity wfl and from above by the rate of entrainment or by the speed of free waving wf.w. The sharp transition from the fixed to the fluidized state of the granular layer is characteristic only of the layers of particles of the same dispersity. For polydisperse layers, there is not a fluidization rate, but a fluidization velocity region in which the transition from a fixed to completely fluidized bed begins and ends. The ratio of the working speed wo, the value of which must be in the range from wfl and wf.w, to the fluidization start velocity is called the fluidization number and is denoted by the symbol Kw: о

(1.154)

It has been experimentally established that the most intensive mixing of particles corresponds to a fluidization number of 2. With further increase Kw, the particle layer becomes nonuniform, i.e. the uniformity of the phase contact is broken. However, the optimum values Kw for each particular process are practically fixed and can vary within fairly wide limits [1-3,9]. 1.8.1. Technological parameters of the process of fluidization

The main technological parameters of fluidization are the pressure drop in the layer Р, the values of the critical velocity wcr, the rate of entrainment went and the permissible degree of polydispersity of the fluidizable mixtures of solid particles. The magnitude of the pressure drop can be found from the condition that the hydrodynamic resistance of the layer fP is equal to the weight of the particle layer G minus the Archimedes (lift) A force: f p  G  A,

(1.155)

where f  the cross-sectional area of the particle layer, m2; p  hydrodynamic pressure on the material layer, N/m2; lifting force.

G

weight of a layer of solid particles;

66 

 

A

We denote by the height of the layer of solid particles H in meters, through the free volume (porosity)  of the particle layer. Then the intrinsic volume occupied by a layer of solid particles can be expressed: V  fH 1   .

(1.156)

Multiplying expression (1.149) by the density of solid particles and by the acceleration due to gravity, we obtain the expression for the weight of a given layer of solid particles: G  V  p g   p gfH 1   .

(1.157)

The value of the lifting force A can be obtained by multiplying (1.156) by the density of the environment ρenv (gas or liquid) and by the acceleration due to gravity:

A  g  env fH 1   .

(1.158)

Substituting the values G and A found from equations (1.157) and (1.158) into equation (1.155), we obtain the pressure drop in the fluidized bed:  p  gH 1     

p

2   env  , N/m .

(1.159)

In practice, due to insufficiently fluidized, channeled, stagnant zones of solid material and other deviations from ideal fluidization, the value p is often 10-15% lower than calculated by formula (1.159). It follows from Fig. 1.12, on the section BC p remains constant with increasing gas velocity to the rate of entrainment. This phenomenon is easy to understand in the analysis of equation (1.159): with increasing speed, the free volume  , increases but the height H also increases. Consequently, the product H 1    does not change to the rate of entrainment, and therefore p remains 67 

 

constant on the section BC. The boiling layer exists so far   0 , 4  1, 0 . When   1, 0 the state corresponds to a single particle in the flow, and with went, the entrainment of particles by the gas flow occurs. The porosity of the layer can be determined from the approximate equation 0, 21

 18Re0  0,36Re02      Ar  

(1.160)

,

where Re0 – the modified Reynolds criterion

Re 0 

2 w 2f  env d p2 2  env

,

(1.161)

and the Archimedes criterion

Ar 

g env d 3p  p   env  2  env

.

(1.162)

The rate of entrainment of particles can be determined experimentally, and for an approximate calculation one can use the formula:

Reent env , denv

went 

(1.163)

in which the Reynolds criterion is determined by the formula:

Reent 

Ar . 18  0,61 Ar

(1.164)

Equivalent diameter of particles for polydisperse mixtures is calculated [1-3, 9]: 68 

 

d eq 

1 ,m xi 1 d i n

(1.165)

where n  the number of fractions; x i  mass content of the i-th fraction in fractions of a unit; d i  the average sieve size of the i-th fraction (i.e., the average between the sizes of the passing and non-flowing sieves).

1.8.2. Application of pseudofluidized layer in industrial practice

Fluidization is one of the most progressive methods for carrying out heterogeneous solid-state processes. Industrial application of the fluidized bed was initiated during the gasification of brown coal in the Winkler gas generator (1930), and in 1940 in the catalytic cracking of oil. Currently, the fluidization method is used in oil refining, chemical, metallurgical, food and medical industries. The wide introduction of the fluidization method into industrial practice is due to a number of its advantages: 1. The surface of the interfacial contact is increased due to the finer grinding of the solid material and continuous surface renewal. 2. Intensive mixing of the solid phase leads to an almost complete equalization of the temperatures, concentrations by volume of the fluidized bed. This eliminates the possibility of local overheating of solid particles. 3. Organization of continuous schemes of technological processes is facilitated. 4. Small hydraulic resistance of the fluidized bed, regardless of the speed of the fluidizing agent. The fluidization process is also characterized by significant drawbacks: 1. Large erosion of the walls of the apparatus of solid particles of the fluidized bed. 69 

 

2. The abrasion of solid particles and their large entrainment by gases, which requires additional devices (such as cyclones, dry electrostatic precipitators) to trap solid particles. 3. The emergence of charges of static electricity during the fluidization of particles of dielectric materials. Therefore, on the basis of technical and economic calculations, a conclusion is drawn on the application of the fluidization process [1-3,9]. Questions for self-control: 1. What processes are carried out in devices with a suspended layer? 2. What is the fluidization number? 3. What are the limits corresponding to the value of the free volume of a layer of particles in the process of fluidization? 4. By what equation is the pressure drop determined for the flow passing through the suspended layer of solid particles? 5. How is the bed porosity calculated for fluidization? 6. On what parameters does the volume occupied by solid particles in the apparatus depend? 7. List the main technological parameters of fluidization. 8. What determines the volume occupied by a layer of particles? 9. What criteria determines the porosity of the suspended layer? 10. List the advantages and disadvantages of fluidization.

1.9. Transportation of liquids

The fluids and gases used in chemical technology often need to be transported along vertical and horizontal pipelines both inside the enterprise (for supply to apparatuses and installations, from shop to shop, etc.) and outside (for supplying raw materials or finished products, etc.). This task can be solved quite simply if the liquid moves from a higher level to a lower level by gravity. But more often in engineering it is necessary to solve the inverse problem – transporting the liquid from a lower level to a higher level. For this purpose, hydraulic machines are used - pumps in which the mechanical energy of the engine is converted into the energy of the transported fluid due to an increase in its pressure. 70 

 

1.9.1. Pumps. Basic parameters

The wide use of pumps in a variety of working conditions led to the creation of numerous types of these machines, differing in both the principle of operation and constructive features. According to the principle of operation, the pumps are divided into volumetric and dynamic ones. In volumetric pumps, energy and pressure increase as a result of displacement of fluid from the enclosed space by bodies moving back and forth or rotationally. In accordance with this, in the form of movement of the working parts, they are divided into reciprocating (piston, plunger, diaphragm) and rotary, or rotary (gear, screw, etc.). In dynamic pumps, the energy and pressure of the fluid are increased by the centrifugal force generated by the rotation of the impeller wheels (for example, in centrifugal and axial pumps) or by frictional forces (for example, in jet and vortex pumps). Therefore, according to the form of the force action on the liquid, the dynamic pumps are divided into vane pumps and friction pumps. The most common dynamic pumps are lobed. These types of pumps are centrifugal and axial. The operation of these pumps is based on the general principle of the force interaction of the impeller blades with the flow of fluid flowing around them. However, the mechanism of this interaction in centrifugal and axial pumps is different, which, naturally, leads to significant differences in their design and performance. A large number of pump designs is due to the variety of problems of transporting liquids in the chemical industry. For example, the required capacity of a pump can in one case be several liters per hour (i.e., dm3/h), and in the other several tens of m3 per 1 second. Basic parameters of pumps. The main parameters of pumps include productivity, pressure (head), power. The capacity of the pump Q is the volume of liquid supplied by the pump to the injection pipeline per unit time (m3/s, m3/h). Typically, when choosing a pump for pumping liquids through a given system of pipelines and apparatus, the value of Q is known. The pressure (head) H (m) is the excess specific energy imparted by the pump to the unit mass of the liquid. When selecting a pump, the head is determined using the Bernoulli’s equation. 71 

 

The useful power of the pump Nu, spent by it for transmitting the energy liquid, is equal to the product of the specific energy H by the mass flow rate ρgQ of the liquid: (1.166) The actual power on the pump shaft is Na, i.e. the power consumed by the pump is greater than the useful power due to losses in the pump itself (hydraulic losses, fluid leakages through leaks, losses due to friction in bearings, etc.), which are taken into account by the efficiency of the pump p: (1.167) The value p characterizes the design perfection and economics of pump operation, reflects the relative power loss (in comparison with Np) in the pump and is the product of three factors: (1.168) In expression (1.168), v = Q/Qth – the feed rate, or the volume efficiency (Qth – theoretical pump productivity), taking into account the loss of pump performance (through gaps, oil seals, etc.). Hydraulic efficiency h = Н/Нth (Нth – the theoretical head) takes into account the pressure loss due to fluid flow through the pump. Mechanical efficiency mech characterizes the power loss for mechanical friction in the pump (in oil seals, etc.). The value of p depends on the pump’s capacity, its structure and degree of wear. For the most advanced centrifugal pumps of high efficiency, the value is higher and can be 0.93-0.95; for piston pumps 0,8-0,9; for centrifugal pumps 0,6-0,7. The power consumed by the engine, or the rated engine power Ne, is greater than the shaft power due to mechanical losses in transmission from the electric motor to the pump and in the motor itself. These losses are taken into account by introducing the 72 

 

efficiency in equation (1.168) the transmission efficiency tr and efficiency of engine e: д

(1.169)

The product is the total efficiency of pumping unit , which is defined as the ratio of the useful power Nu to the rated power of the motor Ne and characterizes the total power losses by the pumping unit: (1.170) From equations (1.168) and (1.170) it follows that the total efficiency of the pump installation can be expressed by the product of five quantities: (1.171) The installed power of the engine Ninst is calculated from the value Ne, taking into account possible overloads at the moment of pump start-up, arising in connection with the need to overcome the inertia of the resting mass of liquid: ,

(1.172)

where β – the power reserve factor.

The value of the power reserve factor is determined depending on the rated power of the engine: Neng < 1 kW β = 2 – 1,5; Neng = 1 ÷ 5 kW β = 1,5 – 1,2; Neng = 5 ÷ 50 kW β = 1,2 – 1,1; Neng > 50 kW β = 1,1 [1,2,9]. 1.9.2. Piston pumps

The most common type of volumetric pumps are piston pumps. In Fig. 1.14, and the scheme of the simplest installation of a piston 73 

 

pump which supplies liquid from the supply vessel 6 to a receiving vessel 8 is shown. The pump consists of a cylinder 1, inside which a reciprocating piston 2 moves, and two valves - a suction 3 and a discharge valve 4. A suction pipe is connected to the cylinder in the bottom, and a discharge pipe is connected to the top. When the piston moves from left to right (from the left end position to the right end position), a vacuum is created in the cylinder, so that the suction valve 3 rises and the liquid from the vessel 6 flows through the suction pipe 5 into the cylinder, fills it and moves behind the piston.

Fig. 1.14. Schemes of the simplest installation of a piston (a) and plunger (b) pumps

When the piston is reversed (from right to left), excessive pressure is created in the cylinder, the suction valve is lowered, the pressurized valve is lifted and liquid from the cylinder is forced out by the piston along the delivery line 7 into the vessel 8. Thus, with repeated reciprocating motion of the piston, carried out by means of a crank-and-crank mechanism, the liquid alternately is sucked from the vessel 6 and injected into the vessel 8. 74 

 

It is quite obvious that for the normal operation of the pump, the valves must tightly lock the suction line at the beginning of the discharge stroke (in order to avoid displacement of the liquid from the cylinder into this line) and the discharge line – at the beginning of the suction stroke (in order to avoid backflow of fluid into the cylinder from the discharge line). In addition, the piston must fit tightly to the inner surface of the cylinder, which is achieved by careful processing of this surface and the use of special sealing devices (elastic cuffs, piston rings). Since the reliable compaction of the piston at discharge pressures above 0.4-0.6 MPa is associated with structural complications and is not observable, at higher pressures the piston is replaced by a solid or hollow plunger 2' (rolling pin). The latter moves inside the cylinder without touching its walls, and is sealed with the help of an oil seal 10 at the point of exit from the cylinder (Fig. 1.14,b), accessible for observation. Being manufactured and structurally simpler, a plunger pump with the same cylinder diameter requires the displacement of an equal volume of liquid for a longer stroke length than a piston pump. The length of the piston path between its two extreme positions (S) is called the stroke of the piston. For one complete turnover of the pump shaft 9, the piston therefore makes two strokes. The considered pump for one complete turnover of the shaft once sucks the liquid (with a left-to-right motion) and once it pushes it (in the course from right to left); it is called a pump of simple action. For better use of the working volume of the pump cylinder, the latter is provided with a lid with an oil seal for the passage of the rod and another pair of valves are located on the right side of the piston (Fig. 1.15). In this case, the piston works with both sides: when it moves to the right, the liquid is sucked from the left side and injected from the right side, and when it is reversed, the suction takes place to the right and the discharge to the left. Thus, for a full revolution of the shaft, the pump sucks twice and doubles twice, giving approximately twice the amount of liquid, which is why it is called a double-acting pump. Intermittent liquid injection causes uneven performance of piston (plunger) pumps. This unevenness, obviously, is less for dual-action pumps than for simple-action pumps. 75 

 

Fig. 1.15. Schemes of pumps of double action: a – piston pump; b – plunger pump

To reduce the unevenness of the fluid supply, triple and quadruple pumps are used. The triple action pump is an aggregate consisting of three simpleaction pumps with common suction and discharge lines, as well as a common crankshaft, the cranks of simple pumps being shifted 120° relative to each other. The quadruple pump consists of two double acting pumps with common suction and discharge lines, as well as a common crankshaft, and the crankshafts of the double acting pumps being offset by 90° relative to each other (when the piston of one of the pumps is in any extreme position, the piston the second is in the middle of the turn). Pumps with greater multiplicity of action of practical application have not received. In addition to the multiplicity of the action and design of the piston, the piston pumps are classified according to the following features: according to the position of the working cylinder – horizontal and vertical; on the speed of rotation of the shaft – low-speed (40-60 rpm), normal (60-120 rpm), high-speed (120-180 and more rpm); for productivity - small (up to 15 m3/h), medium (15-60 m3/h), large (over 60 m3/h); on developed pressure - low (up to 1 MPa), medium (1-2 MPa) and high pressure (over 2 MPa). Pumps are most often driven by electric motors through an intermediate gear or steam machine, the piston of which is located on a common rod with the pump piston [1,2,9]. 76 

 

1.9.3. Piston pump productivity

The capacity, or feed rate, of the piston pump is the volume of fluid supplied to the discharge pipeline per unit time (Q, m3/s). If the stroke length of the piston is equal to S and its area (or cross-section of the plunger) is F, then the volume of fluid sucked by the pump in one half of the shaft rotation (left to right stroke) and pumped through the second half of the turn piston from right to left) is equal to FS. Thus, the theoretical performance of a single-acting pump ,

(1.173)

where n – the number of turnovers, s-1.

In the double-acting pump, the left side of the piston sucks in and pumps a volume of fluid equal to FS per turnover. For the same turnover of the shaft, the right side of the piston sucks in and pours out the volume of the liquid equal to (F-f)S, where f – the area of the transverse section of the rod. Consequently, the theoretical average performance of a double acting pump 2

(1.174)

It follows from expression (1.174) that if the volume of fluid displaced by the rod (f 3.0) to create high pressures. To create a pressure below atmospheric pressure (with gas suction), i.e. vacuum, any compressors can be used, but more often for this purpose, piston and rotary vacuum pumps are used, according to the principle of operation, not differing from compressors. Let’s consider the classification of compressors (Fig. 1.18). According to the principle of compression, compressors are divided into volumetric and dynamical ones.

Fig.1.18. Classification of the main types of compressors

88 

 

In volumetric compressors, compression occurs as a result of a periodic decrease in the volume occupied by the gas. They are subdivided into piston, membrane and rotor ones. In dynamic compressors, compression occurs as a result of a continuous buildup of accelerations in the gas flow. According to the principle of operation, they are subdivided into turbocompressors and jet. Depending on the created working pressure, all compressors are divided into vacuum (initial gas pressure below atmospheric), low pressure (final gas pressure 0.115-1.0 MPa), high (final pressure 10100 MPa) and ultrahigh (final pressure above 100 MPa). The final pressure can be created by a compressor with one stage (single-stage compressor) or with a series of several stages (multistage compressor). The main parameters characterizing the operation of the compressor are the volume flow (capacity or productivity) Q, the initial p2 and the final pressure p1, the compression ratio c, the power on the shaft of the compressor Ne. In order to better understand how these parameters depend on compression conditions and compressor design, let us consider the thermodynamics of the compressor process [1, 2, 9]. 1.10.1. Thermodynamics of the compressor process

Since the operation of compressor machines involves compression of the gas with a change in its volume, pressure and temperature, the theory of the compressor process is based on the thermodynamics of an ideal gas in accordance with the equation (1.191) When the outlet pressure of the compressor is more than 10 MPa, it is necessary to use the equation of state of a real gas (1.192) where z – the compressibility coefficient, the values of which are given in the reference literature. 89 

 

The joint use of the first law of thermodynamics and the equation of state of an ideal gas leads to the following equations of the processes taking place in compressors: for a polytropic process / for an adiabatic process / for an isothermal process /

, , ,

; ; ;

(1.193) (1.194) (1.195)

The polytropic process is a general type of thermodynamic process and takes place in compressors depending on external and internal conditions with a polytropic index n = 1.15 – 1.80. An adiabatic process is a process without heat exchange with the external environment; in such a process, an internal formation of heat is possible due to the work of gas friction and vortex formation. Strictly adiabatic process in compressors cannot be obtained as it is impossible to provide a complete thermal insulation of the gas stream from the environment. Sometimes we consider an isentropic process characterized by the constancy of entropy as a result of the lack of heat exchange with the environment and internal heat release due to friction in the gas stream. In real compressors, the isentropic process is impossible. These processes are conveniently depicted graphically in the coordinates S – Т (Fig. 1.19). This figure shows the main types of compressor processes: polytropic at n < k (k – the adiabatic exponent) characteristic of compressors with intensive water cooling (Fig. 19,a); polytropic at n > k, typical for centrifugal and axial compressors (Fig. 1.19,b); isoentropic with S = const (Fig. 1.19,c); isothermal with T = const (Fig. 1.19,d). The processes shown in Fig. 1.19,c and 1.19,d in compressors are not feasible and are used only to assess their energy efficiency. The compression process in all four cases is represented by lines 1–2. In Fig. 1.19,a and 1.19,b compression is accompanied by a change in entropy and an increase in temperature, while the enthalpy increases. In the polytropic compressor process for n < k (Fig. 1.19,a), line 1–2 represents the compression process occurring in the working cavity of the compressors; line 2–3 displays the process of isobar cooling of the compressed gas leaving the compressor. This process takes place in the compressor cooler. 90   

The energy consumed in the compressor process goes to the change in the enthalpy and kinetic energy of the gas, as well as to cover losses to the environment. This condition can be written in the most general form when the gas velocities at the inlet and outlet of the compressor are equal as the balance equation for the energy of the compressor process: Н1 + L = Н2 ± q, or L ± q = H2 – H1,

(1.196)

where H1 or H2 – the enthalpy of gas at the inlet and outlet of the compressor, respectively; q – the amount of heat supplied to the gas or released into the environment due to the cooling of the compressor.

Fig. 1.19. S-T Diagrams of compressor processes, described by equations (1.193) – (1.195)

91 

 

In an isothermal process, the gas contracts at a constant temperature, the internal energy of the gas does not change, and the equality р1V1 = р2V2 (equation 1.195) is observed. In this case, the enthalpy of the gas does not change under compression, so equation (1.196) takes the form: L + q = 0,

or L = – q.

(1.196 а)

A minus sign before q indicates a heat transfer, i.e. under isothermal compression, all the work expended turns into heat and is diverted from the gas. Therefore, the temperature, internal energy and enthalpy of the gas do not change. Obviously, with isothermal compression it is necessary to cool the compressor in order to divert heat equivalent to the work consumed. Under adiabatic compression, heat is not supplied to the gas and is not diverted from it, i.e., q = 0. Then L = Н2 – Н1,

(1.196 b)

i.e. all the work spent in the compressor is to increase the enthalpy of gas; while the gas temperature rises. Theoretical power Nt (W), spent for compressing the gas by the compressor, is defined as the product of the compressor capacity Q (kg/s) per specific compressive work L (J/kg): Nt = QL.

(1.197)

The power on the shaft of the compressor Ne can be calculated from the equation Nе = QL/(vmech)

(1.198)

where  – the density of the gas entering the compressor, kg/m3; Q – volumetric compressor capacity, m3/s; L – specific energy of the compressor process, J/kg; v – volume factor, taking into account the loss of gas volume due to leakage through the clearances of the compressor seals; mech – mechanical efficiency of the compressor, accounting for energy consumption on mechanical friction.

92 

 

Engine power Neng is greater than the power on the shaft of the compressor Ne due to power losses in the engine itself and in the transmission: Neng = Nе/(tre),

(1.199)

where tr и e – transmission and engine efficiency, respectively.

The installed engine power Nins is usually taken with a margin of 10 – 5 %, i.e. Nins = (1.1 - 1.15) Neng [1,2,9]. 1.10.2. Piston compressors

Piston compressors in the number of stages of compression are divided into one-step, two-stage and multistage, and by the nature of the action – on compressors of simple (single) and double action. The compression stage is called the part of the compressor machine where the gas is compressed to an intermediate (before entering the next stage) or final pressure. In piston compressors of simple action (Fig. 1.20,a), one suction and one injection occurs in one double stroke of the piston, and in the double-acting compressors (Fig. 1.20,b) – two suction and two injections. Single-stage compressors are manufactured horizontal and vertical. Horizontal compressors are usually dual-action machines, and vertical ones are simple actions.

Fig. 1.20. Schemes of single-stage piston compressors simple (a) and double (b) action

93 

 

The device of the single-stage piston compressor is similar to the piston pump arrangement (Fig. 1.20,a). The piston 2 moves reciprocatingly in the cylinder 1 equipped with a suction 3 and a delivery valve 4. The piston densely adjoins to carefully processed internal surface of the cylinder and divides hermetically its cavity on left and right parts. The movement of the piston is carried out by means of a crankand-crank mechanism, which transfers energy from the engine. When the piston is moved from left to right, the gas at the pressure p1 is sucked through valve 3; when moving in the opposite direction, the gas is first compressed to the required pressure p2 and then pushed through the valve 4 into the discharge pipeline. Since gas compression inevitably increases its temperature, coupled with the danger of burning lubricating oil and, as will be shown below, also with an increase in the specific energy consumption, the cylinder walls are usually cooled by a continuous flow of water (5 – water inlet, 6 – outlet). In Fig. 1.21,a a theoretical diagram of the compressor in the p–v coordinate system (pressure – specific volume of the gas) is shown. During the stroke of the piston AB, the gas, having a specific volume v1 and pressure p1, is sucked into the cylinder, in the reverse flight segment BC it is compressed to the required pressure p2 and specific volume v2, and on the CD path till the end of the stroke it is pushed into the discharge gas pipeline. In the described compressor scheme, the gas is compressed by one side of the piston once per two strokes, i.e. for one rotation of the shaft. The productivity of this single-cylinder compressor, called a simple action compressor, can almost be doubled, providing the cylinder with a second lid with a gland for the passage of the stock and another pair of valves (Fig. 1.20,b). In such a compressor, called a double-acting compressor, gas suction and compression will occur at each stroke of the piston, i.e. twice per rotation of the shaft. The work of gas compression in piston compressors. The diagram of the compressor operation, shown in Fig. 1.21,a, is theoretical, since it assumes that the entire compressed gas is completely pushed out of the cylinder at the end of the piston’s reverse stroke (point D), there are no energy losses in the valves and friction of the 94 

 

piston at an absolute density of its contact with the inner surface of the cylinder. Under these conditions, the theoretical work expense L for suction, compression and ejection of 1 kg of gas, as is known from technical thermodynamics, is expressed by the closed area ABCD.

Fig. 1.21. Theoretical working diagrams of a reciprocating compressor: a – the p-v diagram; b – i-S - diagram

The quantity L can be expressed by the following algebraic sum: (1.200) From this expression it can be seen that the value L depends, with other things being equal, on the law of the process of changing the state of the gas under compression. In the case of an ideal gas (pv = RT, where R – the gas constant and T – the temperature), the compression curve BC obeys the general equation pvm = const. Consequently, the work flow rate L (area ABCD) will be minimal under isothermal compression, when p1v1 = p2v2 = pv = RT and m = 1; it will be expressed as: (1.201) 95 

 

In this case the area of ABCD = the area of GHBC. In adiabatic compression, when m = k > 1 (curve BC1), the work expense (area ABC1D) is greater than in isothermal, and is: where

/

1 (1.202) is an adiabatic index.

Similarly, for the case of polytropic compression, we obtain: 1

(1.203)

where m is a polytropic index.

If by cooling of the cylinder only heat is removed, which is due to friction in the cylinder, then the compression of the gas is close to adiabatic. With the removal of more heat, the polytropic index has an intermediate value between the isotherm and adiabatic exponents: 1 < m < k (curve BC2 in Fig. 1.21,a). In the case of insufficient heat removal, the gas compression process will proceed with the polytropic index m > k (curve BC3 in Fig. 1.2,a). In real conditions, the process of gas compression never occurs with a constant value of polytropic m. At the beginning of compression, the gas is colder than the cylinder wall and does not heat up a bit. Further, because of the small difference in the temperatures of the gas and the cooling water of the compression polytrope, it approaches the adiabat and becomes even steeper than it. At the end of compression, the temperature difference between the gas and the cooling water increases and the compression curve approaches the isotherm (m  1). With some approximation, we can take m = 1.30-1.35 for practical calculations. (Recall, that R = 8300/M J/(kg∙K), where M – the molecular weight). An accurate calculation of the work of gas compression is possible using the known diagrams i–S (enthalpy-entropy). So, the 96 

 

work spent on adiabatic compression in a compressor of 1 kg of ideal gas will be: (1.204) Since

/

and

, we obtain for the ideal gas: . For real gases pv ≠ RT, and the specific heat capacities cp and cv are functions of pressure and temperature. The actual enthalpy values corresponding to each gas state can be taken from the diagram i–S, constructed from the true values of i. The required work expense will be expressed as follows (in J/kg): (1.205) where i1 and i2 – initial and final enthalpy (heat content) of gas, J/kg.

In Fig. 1.20,b the i–S – diagram of the compressor compressing the gas from the initial state (point A) to the final pressure p2 is presented. For adiabatic compression, S = const and the quantity i2 – i1 is expressed by the vertical segment AB. In cases of good cooling of the cylinder of the compressor, the process under polytropic compression will go along the line AB2, and Lpol = i2 – i1 < Lad, and in the absence or bad cooling - along the line AB1, where Lpol > Lad. The productivity of piston compressors. To determine the capacity of the compressor from its main dimensions (cross-sectional area of the cylinder or piston F (m2), the stroke of the piston S (m) and the shaft speed (n, rpm)), we consider the actual working diagram of the compressor. This is mainly due to the fact that not all of the compressed gas is displaced from the cylinder at the end of the working stroke of the piston. For design reasons, in the space between the working plane of the piston and the cylinder cover, called the harmful space, there always remains some amount of gas compressed to pressure p2. The absorption of a new portion of gas does not begin, obviously, until the remainder of the compressed gas expands to the pressure p1. Consequently, gas suction will not occur during the entire stroke of the piston S, but only along the path S1 < S (Fig. 1.22,а). 97   

Fig. 1.22. Actual working diagrams of a piston compressor: a – a real diagram; b – indicator diagram

The actual diagram of the compressor operation has the form shown in Fig. 1.22,a, where So is the reduced length of the harmful space proportional to its volume, line 4–1 is the suction section, 1–2 is the compression site, 2–3 is the ejection site, 3–4 is the expansion section of the gas remaining in the harmful space. Thus, the capacity (in m3/s) of a single-stage single-acting compressor, related to the intake air state, is as follows: V1 = FS1n/60. The ratio of the intake gas volume FS1 to the volume described by the piston in one stroke FS is called the volumetric efficiency of the compressor: o = S1/S. Thus /60

(1.206)

To determine the value 0, we express the ratio of the volumes of gases at points 4 and 3 for a polytropic expansion of the gas residue: /

/ /

/

/

/

1 (1.207)

Denoting the volume fraction of the harmful space by So/S = o and taking into account that S1/So = (S1/S) (S/So) = o/o, we get: 98 

 

1

/

/

1

(1.208)

It follows from expression (1.208) that the volumetric efficiency of the compressor decreases with increasing volume of the harmful space and with increasing compression ratio р2/р1. For this reason, when designing compressors, they tend to a possible decrease in the value 0; in practice, 0 = 0.03–0.08. Depending on the cooling intensity of the cylinder (especially its cover), m = 1.2–1.35. It should be noted that the work of expanding the remainder of the gas slightly exceeds the work of its compression, so the influence of the volume of harmful space on the energy consumption for compression of gases in compressors is usually neglected. Finally, high compression ratios of gas entail not only a fall of 0, but are also associated with an increase in the gas temperature and a deterioration in lubrication conditions of the working surface of the cylinder, and, as will be shown below, with a slight increase in energy consumption. The limiting degree of gas compression is usually chosen in such a way that its temperature does not exceed 150-160 °C (50-80 °C below the flash point of the oil). Denoting the cross-sectional area of the stock through f, we show the productivity of a double-acting compressor: 1/60

1/60

2

(1.209)

Note that the pressure in the compressor cylinder at suction p1 is always less than at the beginning of the suction gas pipeline p0, due to the hydraulic resistance of the latter and the suction valves (usually 5-10 %). For a similar reason, the pressure p2 is slightly higher than in the injection pipeline.

Energy consumption for gas compression in piston compressors. To assess the effeciency of the real process of gas compression in the compressor, and also to compare machines of different designs, compare the actual (polytropic) flow of work in a cylinder with an isothermal or adiabatic work expense. In this case, respectively, two efficiencies are obtained: isothermal – is = Lis/Lpol and adiabatic – ad = Lad/Lpol. 99 

 

The first coefficient is characteristic for well-cooled compressors, and the second is for those with insufficient cooling. The work of friction of the piston in the cylinder, the rod in the stuffing boxes, the shaft in the connecting rod heads and in the main bearings are accounted for by the mechanical efficiency of the compressor mech. Thus, with the hourly productivity of the compressor G (kg/s), the power on its shaft will be expressed as follows (in kW): (1.210) The rotational speed of the compressor shaft does not usually exceed 200 rpm, so when using an electric motor an intermediate gear is required, the efficiency of which will be denoted by tr. To determine the total efficiency factor of the compressor unit c, it is necessary to take into account the efficiency of the engine eng: or

(1.211)

Thus, the total power of the compressor unit (in kW) will be: (1.212) For a single-stage compressor, the values Lis and Lad can be found from formulas (1.201) and (1.202). In the case of a n–stage compressor for gases approaching the ideal, we have: ⋯

and

⋯

Here, isothermal and adiabatic specific works in separate steps are denoted by , ⋯, and , ⋯, . When the works are equal in all stages, and . For real gases and vapors, it is necessary to use the i–S – diagram, determining on it the adiabatic (or isothermal) compression work of 1 kg of gas (equation (1.203)) Then for a single-stage compressor 100 

 

(1.213) In the case of an n-stage compressor, the quantity (i2 – i1) is expressed by the sum of the heat differences in the individual stages, i.e. (i2 – i1) = (i2 – i1)1 + (i2 – i1)2 +  + (i2 – i1)n. If the work is equal in all stages, we get: i2 – i1 = n(i2 – i1)1. The values Nis and Nad mainly depend on the degree of compression of the gas and the cooling intensity of the compressor; on average, they fluctuate within the following limits: is = 0.75-0.85; ad = 0.85-0.95; mech = 0.85-0.95 [1, 2, 9]. 1.10.3. Vacuum pumps

The processes of chemical technology often have to be carried out not under atmospheric or excess pressure, but in a rarefied environment (in a vacuum). This is dictated in many cases by the conditions of chemical reactions, the need to lower the boiling point of thermolabile liquids, the possibility of using low-cost lowtemperature heat carriers, and so on. Residual pressures p0, used in chemical engineering, are rarely less, and in scientific studies, they are much lower than 1.35 mPa. The vacuum achieved is expressed in percent of the normal pressure pa, i.e. (ра – р0)/ра 100%. To create a vacuum, machines called vacuum pumps are used. Vacuum pumps are similar in design to the same compressors, but operate at pressures below atmospheric pressure. When vacuum technology is considered, the vacuum is divided into high, medium and low. In conditions of high vacuum, the residual pressure in the system is in the range 10-3÷10-8 mm Hg. Under medium vacuum conditions, the residual pressure in the system is in the range 1.0÷10-3 mm Hg, and at low vacuum the pressure in the system is equal to 1÷760 mm Hg. Piston vacuum pumps. The piston vacuum pump, having a device similar to a piston-type double-acting compressor, differs from the latter by a higher compression ratio. Thus, for example, when a residual pressure of 5 kPa (a rarefaction of 95 %) is created 101 

 

and the gas is compressed to a pressure of 0.1 MPa, the compression ratio is 1.05/0.05 = 21. In this case, as seen from expression (1.208), the compressor would work with a very low volumetric efficiency 0. To enhance the latter, vacuum pumps are supplied with so-called bypass facilities of various designs, equalizing the pressures on both sides of the piston at the end of its stroke. One of such devices is the bypass channels k in the cylinder of the machine (Fig. 1.23,a). In the absence of these channels, the remainder of the compressed gas from the harmful space, having pressure p2, expands as the piston moves from left to right (curve ea1 in Fig. 1.23,b) to the suction pressure p1 and о = V1/V. In the vacuum pump, when the piston comes to the left extreme position, the same remainder of the gas flows into the right cavity of the cylinder, where the pressure is p1. In this case, the pressure in the harmful space falls from p2 to pB, the remainder of the gas expands along the curve fa (Fig. 1.23,b), the suction begins almost at the very ′ beginning of the piston stroke and ′ / .

Fig. 1.23. Cylinder vacuum pump with bypass channels: a – a diagram of the cylinder; b – p–v – diagram

Similarly, the process takes place on the right side of the piston, i.e. when it moves from right to left. As a result, it is possible to increase the volume coefficient of the useful action ′ to 0,8–0,9. The presence of harmful space, constructively inevitable, is the reason why the piston vacuum pump is not only unable to create an absolute vacuum, but also has a theoretical limit of this value, which 102 

 

corresponds to a certain residual pressure pres. It is easy to see that in the absence of a bypass, the quantity ′ is greater than when pres is present. In fact, the vacuum pump will suck the gas until it reaches the limiting compression ratio when the volumetric efficiency factor reaches zero. For both variants of operation of the vacuum pump (without bypass and with a bypass), according to the expression (1.208), we get: 1

/

/

0;

(1.214)

1

в/

/

0

(1.215)

When maintaining a given vacuum in a continuous apparatus, the volume of the exhaust gas V0, equal to the volume of gases evolved during the process and sucked from outside through the leaks, does not change with time. The power on the shaft of the vacuum pump is also constant in time and is determined according to the formulas given earlier for compressors, and mech = 0.85-0.95. We note that this power is somewhat higher for machines with a bypass, since in this case the work of expanding the bypass amount of compressed gas is being performed. In the period of evacuation of the vessel due to a continuous change in the compression ratio of the gas, this power also changes. The regularity of this change can be established from the expression for the work of adiabatic compression of 1 m3 of gas from the current pressure in the apparatus p to the ejection pressure pk: /

1

/

/

1

(1.216)

Single-stage piston vacuum pumps usually create a vacuum of up to 96 %; to create a deeper vacuum (up to 99.9 %), two-stage reciprocating vacuum pumps are used [1,2,9]. Questions for self-control: 1. Give the classification of compressors by the compression ratio and the magnitude of the pressure created by them.

103 

 

2. Analyze the equations of compression and expansion processes occurring in compressors. 3. Draw the gas compression processes in the compressors on the S – T and P – V diagrams. 4. How is the energy consumed in the compressor process determined? 5. How is the power on the shaft of the compressor and engine determined? 6. Give the classification of volumetric compressors. 7. How are the piston compressors divided? 8. Define the performance of a piston compressor. What does it depend on? 9. What does the volumetric coefficient of the compressor о mean? 10. Describe the indicator diagram of the piston compressor. Draw an indicator chart at the compression limit of the compressor. 11. Formulate the principle of action of rotary, centrifugal and axial compressors. 12. What are the approximate pressures created by centrifugal fans, turbogasblowers, turbocompressors? 13. What are vacuum pumps used for? 14. Draw the processes of gas compression in vacuum pumps in the P – V diagram. 15. What parameters does the volumetric coefficient of efficiency depend on in the operation of piston vacuum pumps?

1.11. Hydromechanic separation of heterogeneous systems

Inhomogeneous, or heterogeneous, systems are systems consisting of two or more phases. Any inhomogeneous binary system consists of a dispersed (internal) phase and a dispersion medium, or a continuous (external) phase in which the particles of the dispersed phase are distributed. Depending on the physical state of the phases are distinguished: suspensions, emulsions, foams, dusts, smokes and fogs. Suspensions are inhomogeneous systems consisting of a liquid and suspended solids in it. Depending on the size of the solid particles (μ), the suspensions are subdivided into rough (more than 100), thin (0.5-100), dregs (0.1-0.5) and colloidal solutions (less than 0.1). Emulsions consist of immiscible liquids and can be stratified by gravity. However, emulsions can also be resistant to delamination if the droplet size of the dispersed phase is less than 0.5 microns. The method of separating inhomogeneous systems is chosen mainly based on the size of the suspended particles. In industry, the main methods of separating heterogeneous systems are: 1) upholding; 104   

2) filtering; 3) phase separation in the field of centrifugal forces (centrifugation). 1.11.1. Material balance of the separation process

Let a system consisting of substance a (continuous phase) and suspended particles of substance b (disperse phase) be subject to separation. We introduce the following notation: G m , G cl .l . , G sed  the masses of the initial mixture, the clarified liquid and the resulting sediment, kg; x m , x cl . l . , x sed  the content of the substance in the initial mixture, the clarified liquid and the sediment, the mass fraction. In the absence of loss of substance in the process of separation, the equation of material balance has the form: by total amount of substance

G m  G cl . l .  G sed

(1.217)

for the dispersed phase (substance b)

G m x m  G cl . l . x cl . l .  G sed x sed

(1.218)

The simultaneous solution of equations (1.217) and (1.218) makes it possible to determine the mass of the clarified liquid and the mass of the sediment obtained for a given content of substance b in the sediment and clarified liquid:

xsed  xm , xsed  xcl.l.

(1.219)

xm  xcl.l . . xsed  xcl.l .

(1.220)

Gcl.l.  Gm Gsed  Gm 105 

 

The content of suspended particles in the clarified liquid and in the sediment is selected depending on the specific technological conditions of the separation process. In this case, the content of the substance in the clarified liquid is usually limited to a certain lower limit [2,3,9]. 1.11.2. Upholding

Upholding is the process of precipitation under the action of gravity. The rate of free deposition of particles under the action of gravity in an unbounded volume is determined from the Reynolds criterion: (1.221) In industry precipitation processes are very often carried out in a limited volume at a high concentration of the dispersed phase, i.e. in conditions where the settling particles can affect the motion of each other. Precipitation in a limited volume at a high concentration of the solid phase is called constrained precipitation. With constrained deposition, the resistance to the motion of solid particles is composed of the resistance of the medium and the resistance due to friction and impacts of the solid particles against each other. Because of this, the rate of constrained deposition is always less than the rate of free deposition and is expressed by the following formula:                                       W0  where

 

d 2 g (  p   env ) 2 ф( ) 18

                (1.222)

the free volume;  – the coefficient of form.

According to the experimental data for a spherical particle, the value ф (  ) at   0 ,7 is determined from the equation 106 

 

ф ( )  10  1, 82 (1   )

(1.223)

For highly concentrated suspensions containing solid particles of spherical shape, with   0 ,7

1



ф ( )  0,123 .

(1.224)

Equation (1.222) in a more general form, for any deposition region, can be written in the following form:

W0  Wfree 2ф( ), where W

free

(1.225)

 the rate of free deposition in a given deposition region.

Accordingly, for suspensions, with   0 ,7 the expression (1.224) taken into account, the deposition rate will be

W 0  W free where

0,123 , 1 

(1.226)

  the volume fraction of liquid in the suspension, determined by the formula



Vl , Vl  Vsol

(1.227)

where V l  the volume of liquid in the suspension; V sol  the volume of solid particles in the suspension.

The volume fraction of solid particles in the suspension can be determined from the formula x q

 sol 1

 sus 107 

 



х sus

 sol

,

(1.228)

where х  the weight fraction of the solid phase in the suspension; density of solid particles;

 sus 

 sol 

the

the density of the suspension.

The density of the suspension is determined [2,3,9]

1

 sus



х

 sol



1 х

l

,

(1.229)

,

(1.230)

whence

 sus 

1 х

 sol



1 х

l

1.11.3. Filtration

Filtration is the process of separation of suspensions using porous partitions, which retard the solid phase of the suspension and pass its liquid phase. Filtration is a hydrodynamic process, the speed of which is directly proportional to the difference in pressure created on both sides of the filtering partition and inversely proportional to the resistance:

dV P  . Fd  R

(1.231)

The pressure difference on both sides of the filtering partition is created with the help of compressors, vacuum pumps and liquid pumps, and also using the hydrostatic pressure of the separable suspension itself. The resistance of the filtering partition increases strongly with the penetration of small particles of sediment into the pores. When filtering, both hydrodynamic factors (particle surface, sphericity, porosity) and physico-chemical factors act. As the particle size increases, the effect of hydrodynamic factors increases, and as the size of the particles decreases, the influence of physico-chemical factors increases. 108   

From the filtering conditions influencing its flow, the pressure difference on both sides of the filtering partitition and the temperature of the suspension are of greatest importance (the viscosity of the suspension decreases with increasing temperature). 1.11.4. Theory of filtering

The kinetic equation of filtration is written in the form (1.231):

dV P ,  Fd R

(1.231)

where R is the resistance composed of the resistance of the sediment Rs and the filtering partition Rf.p.

R  Rsed  Rf .p. .

(1.232)

The sediment resistance is proportional to its thickness δ

R sed  r  , where

(1.233)

r  the specific resistance of the sediment.

The specific resistance of the sediment is the resistance of a unit of the sediment volume of 1 m hight deferred on an area of 1 m2. The dimension of R is determined from equation (1.231):

R     PF     N 2m  V



s N s   3 . 3   m m   m  2

Accordingly, the dimension of the resistivity of the sediment is obtained from the dimension of R:

r    R    N  s / m  



m

109 

 

3

 N s    4 .   m 

The amount of sediment deposited on the filter can be expressed as the product of the filtering partition area F by the thickness of the precipitate . Denote the volume of sediment per 1 m3 of filtrate by u, then the volume of the sediment deposited after the formation of V m3 of the filtrate will be equal to uV. Hence we can write:

F  uV .

(1.234)

Hence the thickness of the sediment layer is:

 u

V . F

(1.235)

We denote by

V  q , [m3/m2] F as the volume of the filtrate obtained from the unit surface of the filtrate during the filtering time  (specific filter capacity), then the expression (1.235) will be written:

  uq .

(1.236)

The found value of  is substituted in (1.233), we obtain: R  ruq .

(1.237)

Taking (1.237) into account, the equation (1.232) takes the form:

R  ruq Rf .p..

(1.238)

With a constant value of the pressure difference on both sides of the filtering partition, equation (1.231) can be written in the form: 110 

 

V P  , F R

(1.239)

from which the velocity of the fluid through the layer at

V  q is F

equal to:

V q P 3 2 m /m ·s.   F  R

(1.240)

From equations (1.233) and (1.240) it is clear that the filtering resistance increases as  increases, and the filtering rate decreases. Therefore, equation (1.240) can be written in differential form:

w

dq P ,  d ruq  R f . p.

(1.241)

whence d 

ruq  R f . p . P

dq .

(1.242)

Integrating expression (1.242) in the range from 0 to τ and from 0 to q, we find the duration of filtering: q

 ruq

R



f . p. dq        P P  0 

(1.243)

or

 

ruq 2 R f . p .  q. P 2 P

(1.244)

Solving (1.244) with respect to q, we determine the specific productivity of the filtrate: 111 

 

2 R f . p. Rf . p .  2P , m3/m2.   q   ru     ru ru

(1.245)

Specific resistance of the sediment can be determined by calculation by the equation:

200ф2 1     . d 2 3 2

r

(1.246)

The resistivity and the resistance of the partition are determined experimentally, based on measuring the volume of the filtrate V obtained in time  from a certain filtration area, with a constant pressure drop and a constant temperature. In this case, the equation (1.244) is represented in the form:

 q

R f . p. ru q 2P P



(1.247)

or

 q

 К 1q  К 2 .

(1.248)

Since the experiments are carried out at constant values r, P, Rf . p. , u, , the dependence  on q is plotted, the slope of the q experimental line gives K1 (Fig. 1.24). ru From the equation К1  determine 2 P

r

2 PК 1 u

112 

 

(1.249)

Fig. 1.24. To the definition of K1 and K2 in equation 1.248

The segment of the straight line, cut off on the ordinate axis, gives the constant K2, R From the equation К 2  f . p . we find [2,9] P

Rf . p.  PК2 .

(1.250)

1.11.5. Construction of filters

According to the principle of material flows, the filters are divided into periodic and continuous filters. By pressure on the filters there are filters working under pressure, and the filters working under vacuum (under vacuum). The designs of the filter partitions can be cylindrical and flat. Batch filters. Devices of periodic action are nutch filters, filter presses, sheet (bag) filters, etc. Nutsch filters are cylindrical tanks with a porous filtering partition located at the bottom. These filters operate under hydrostatic pressure, under vacuum and under the pressure of the fluid created by the pump. Nutch filters are characterized by a significant filtration rate 113 

 

and the possibility of filtering liquids that emit toxic and flam-mable vapors. Filter presses are used to separate difficult-to-filter suspensions containing finely dispersed and colloidal particles. Sack filters. The filter elements in these filters are fabric bags (sheets), stretched over metal frames and placed in a horizontal or vertical housing. Continuous filters. In continuous filters, the following operations are automatically interleaved: filtration, washing, drying, discharge of sediment and filter cloth regeneration. These operations are continuous in each filter zone and independently of each other, so the entire filtration process also proceeds continuously. Constructions of continuous filters are distinguished by the shape of the filtering surface and subdivided into drum, disk and tape. The apparatuses of each of these groups are subdivided into filters operating under pressure. The vacuum varies from 0.2 to 0.8 at. The pressure is about 5 at. Filtering partitions. From the correct choice of the filtering wall depends the productivity of the filter equipment and the purity of the resulting filtrate. According to the principle of action, surface and depth filter partitions are distinguished. In the surface partitions, the solid particles of the suspension upon its separation are retained on their surface without penetrating the pores. Deep septa, which are used to clarify liquids containing solids in a small concentration, are characterized in that the particles of the suspension penetrate into their pores during the separation and stay there. On the materials from which they are made, the filtering partitions are divided into cotton, wool, synthetic, glass, ceramic and metal. By structure, the filter partitions are divided into flexible and inflexible [1,2,9]. 1.11.6. Centrifugation

Carrying out the process of separation of heterogeneous systems under the action of centrifugal forces, it is possible to substantially 114 

 

intensify it in comparison with sedimentation due to an increase in the driving force. To create a field of centrifugal forces, one of two methods is usually used: either provide rotational motion of the flow in a stationary apparatus, or the flow is directed to a rotating apparatus where it starts to rotate with the apparatus. In the first case, the process is carried out in cyclones, in the second case – in sedimentation centrifuges. In the first case, the separation is called a cyclonic process, in the second case - sedimentation (settling) centrifugation. Centrifuging is the separation of liquid heterogeneous systems under the action of centrifugal forces. Centrifugal forces exert a greater influence on the separating liquid than gravity and pressure. The intensity of the field of centrifugal forces is characterized by a separation factor, which is the ratio of acceleration center to acceleration due to gravity:

ф

 2r

,

g

(1.251)

where   angular speed of rotation of the drum, rad/s; r  radius of the drum, m; g  acceleration of free fall, 9.81 m/s2.

The angular velocity is determined by the expression:



2 n . 60

(1.252)

Taking into account (1.252), the separation factor (1.251) can be written as: 2  2n r n2r . ф 

602 g

900

(1.253)

The greater the value of the centrifuge separation factor, the higher its separation capacity. 115 

 

The product of the separation factor on the solid phase precipitation surface in the centrifuge drum is called the centrifuge productivuty index:   фF ,

(1.254)

where   the sedimentation surface of the settler or filter, in which the same productivity is achieved for the given slurry as the considered centrifuge.

Centrifuges. The main part of the centrifuges is a drum with solid or perforated walls, rotating at high speed on a vertical or horizontal shaft. The processes of separation of suspensions on centrifuges are as follows: centrifugal filtration, centrifugal upholding, centrifugal clarification. The separation of fine suspensions and emulsions requires the action of very significant centrifugal forces. In these cases, super centrifuges and liquid separators are used. Tubular supercentrifuges have a small diameter (up to 200 mm) for a long length and are characterized by n = 8000-45000 rpm. Liquid separators are used for separation of emulsions, as well as for clarification of liquid (d = 150-300 mm, n = 6500-10000 rpm). Centrifugal dust deposition. Cyclones are used to purify gases from dust. In these apparatus, the deposition of particles suspended in the gas stream occurs in the field of centrifugal forces. The centrifugal force is: C where m  the mass of the particle;

r

mw 2 , r

(1.255)

radius of the cyclone.

Therefore, the degree of gas purification in the cyclone can be increased by increasing the circumferential velocity w or by decreasing the rotation radius r of the gas [2,3,9]. Questions for self-control: 1. What is a suspension, an emulsion, an aerosol? 2. List the main methods of separation of heterogeneous systems.

116 

 

3. Under the action of which forces can precipitation occur? 4. Write the equations of the material balance of the separation process. 5. What is a constrained precipitation? 6. What is the driving force of filtering? 7. Derive a differential filtering equation. 8. What are the filtering constants? How are they determined and where are they used? 9. What are the main designs of periodic and continuous filters? 10. What is the separation factor in the processes of deposition under the action of centrifugal forces? 11. From which stages does the separation of suspensions consist in the filtering centrifuges? 12. What forces act on the particles in electrical cleaning of dusty gases? 13. Explain the principle of operation and list the main types of wet cleaning of dusty gases.

117 

 

2. THERMAL PROCESSES 2.1. General information

The transfer of energy in the form of heat, occurring between bodies having different temperatures, is called heat exchange. The driving force of any transfer of heat transfer is the difference in temperatures of the more heated and less heated bodies, in the presence of which heat spontaneously, in accordance with the second law of thermodynamics, passes from a warmer to a less heated body. Heat exchange between bodies is the exchange of energy between molecules, atoms and free electrons: as a result of heat exchange, the intensity of the motion of particles of a more heated body decreases, and less heated – increases. The bodies involved in heat exchange are called heat carriers. Heat transfer is the science of heat transfer processes. The laws of heat transfer form the basis of thermal processes – heating, cooling, condensation of vapor, evaporation – and are of great importance for carrying out many mass-exchange processes (processes of distillation, drying, etc.), as well as chemical processes that occur with the supply or removal of heat. There are three ways of spreading heat: thermal (heat) conductivity, convection and radiation. Thermal (heat) conductivity refers to the process of transfer of thermal energy by direct contact between particles of a body with different temperatures. Convection refers to the process of heat transfer by moving and mixing liquid or gas particles together. The transfer of heat by convection is always accompanied by thermal conductivity, since direct contact of particles with different temperatures is carried out. Simultaneous heat transfer by convection and thermal conductivity is called convective heat transfer; it can be free and forced. If the movement of the body is caused artificially (by a compressor, a fan, a mixer, etc.), then such convective heat transfer is called forced. If the motion of the working fluid arises under the influence of the difference in the densities of the individual parts of the liquid from heating, then such heat exchange is called free. 118 

 

Radiation (radiation) is the process of energy transfer in the form of electromagnetic waves. All three methods of heat exchange arise in the presence of a temperature difference of individual parts of the body, or several bodies. This temperature difference is the driving force under the action of which there is a transfer of heat [1-3,9]. 2.1.1. Thermal balances

The heat given out by the warmer heat carrier (Q1) is expended on heating the cooler heat carrier (Q2), and some relatively small amount of heat is expended to compensate for the heat loss to the environment (Qloss). The Qloss value in heat-exchanging devices covered with thermal insulation does not exceed ~3-5 % of the useful heat used. Therefore, it can be neglected in calculations. Then the heat balance is expressed by the equality ,

(2.1)

where Q is the thermal load of the apparatus.

Let the mass flow of the more heated coolant be G1, its enthalpy at the input to the apparatus I1in and at the output of the apparatus I1f. Accordingly, the cooler heat carrier flow rate is G2, its initial enthalpy I2in and the final enthalpy I2f. Then the heat balance equation: (2.2) If the heat exchange takes place without changing the aggregate state of the heat carriers, then the enthalpies of the latter are equal to the product of the heat capacity c by a temperature t: I1in = c1int1in; I1f = c1ft1f; I2f = c2ft2f; I2in = c2int2in. The values с1in and с1f are the average specific heat capacities of the more heated heat carrier within the temperature range from 0 to t1in (at the input to the apparatus) and to t1f (at the output of the apparatus), respectively. The quantities с2in and с2f – the average specific heat capacities of the colder heat carrier in the ranges 0 – t2in and 0 – t2f, respectively. 119 

 

In technical calculations, enthalpies are often not calculated, but their values at a given temperature are found from thermal and entropy diagrams or from reference tables. If the heat exchange takes place when the aggregate state of the heat carrier changes (condensation of steam, evaporation of liquid, etc.) or during the heat exchange, chemical reactions occur accompanied by thermal effects, then the heat released during physical or chemical transformation must be taken into account in the heat balance. Thus, in the case of saturated vapor condensation, which is a heating agent, the quantity I1in in equation (2.2) is the enthalpy of the vapor entering the apparatus, and I1f is the enthalpy of the removed steam condensate. In the case of using superheated steam, its enthalpy I1in is composed of the heat released by the steam upon cooling from the temperature tst to the saturation temperature tsat, the heat of condensation of the steam and the heat released during cooling of the condensate: , (2.3) where r is the specific heat of condensation, J/kg; сst and сc are the specific heat capacities of steam and condensate, J/(kg∙K); tc is the condensate temperature at the outlet of the apparatus.

When heating with saturated steam, if the condensate does not cool, i.e. tc = tst = tsat, the first and third terms of the right-hand side of equation (2.3) are excluded from the heat balance. The product of the heat carrier flow (G) by its average specific heat capacity (c) is conditionally called the water equivalent W. The numerical value W determines the mass of water, which in its thermal capacity is equivalent to the amount of heat needed to heat this heat carrier by 1 °C at a given flow rate. Therefore, if the heat capacities of the heat-exchanging fluids (c1 and c2) can be considered independent of temperature, then the heat balance equation (2.2) takes the form: (2.4) or ,

(2.5)

where W1 и W2 are water equivalents of the heated and cold heat carrier, respectively [2,9].

120 

 

2.1.2. Temperature field and temperature gradient

Among the basic problems of the theory of heat transfer is the establishment of a relationship between the heat flow and the distribution of temperatures in the environments. The set of instantaneous values of any quantity at all points of a given environment (body) is called the field of this quantity. Accordingly, the set of temperature values at a given instant of time for all points of the environment is called a temperature field. In the most general case, the temperature at a given point t depends on the coordinates of the point (x, y, z) and varies with a time , i.e. the temperature field is expressed by a function of the form: , , ,

(2.6)

This dependence is the equation of an unsteady (non-stationary) temperature field. If the temperature of the body is a function of only the coordinates and does not change with time, the temperature field will be stationary (steady-state). , ,

;

0.

(2.7)

Unlike the temperature, which is a scalar quantity, the heat flow associated with the direction of heat transfer is a vector value. The temperature in the body can vary in the direction of one, two and three coordinate axes. In accordance with this, the temperature field can be one-, two-, and three-dimensional. One-dimensional, for example, is the problem of heat transfer in a wall, in which the length and width are infinitely large in comparison with thickness. For this case, the equation of the temperature field for the nonstationary regime ,

; 121 

 

0.

(2.8)

For stationary mode ;

0 и

0.

(2.9)

For any temperature field in the body, there are always points with the same temperature. If we connect the points of the body with the same temperature, we obtain isothermal surfaces that never intersect each other. They either close to themselves, or end at the boundaries of the body. Consequently, the temperature in the body changes only in the direction crossing the isotherms. Let the temperature difference between two nearby isothermal surfaces be t (Fig. 2.1).

Fig. 2.1. To the determination of the temperature gradient to the expression of the Fourier’s law

The shortest distance between these surfaces is the distance along the normal n. On approaching these surfaces, the deviation t/n tends to the limit lim

∆ ∆

∆ →

grad t

(2.10)

The derivative of the temperature along the normal to the isothermal surface is called the temperature gradient. This gradient is a vector whose direction corresponds to an increase in temperature. The heat transfer takes place along the line of the 122 

 

temperature gradient, but is directed in the direction opposite to this gradient: q  (dt/dn) [2,3,9]. 2.1.3. Transfer of heat by heat conductivity

The condition for the transfer of heat through thermal conductivity is the presence of a temperature difference at various points in the body. The basic law of heat transfer by thermal conductivity is the Fourier’s law, according to which the amount of heat dQ transmitted by thermal conductivity through a surface element dF perpendicular to the heat flow during time d is directly proportional to the temperature gradient, surface and time: (2.11) or the amount of heat transmitted per unit surface per unit time (2.12) The quantity q is called the heat flow density. The minus sign in front of the right-hand side of equations (2.11) and (2.12) indicates that the heat moves toward a temperature drop. The coefficient of proportionality  in equations (2.11) and (2.12) is called the coefficient of thermal conductivity. It characterizes the ability of a substance to conduct heat. The dimension  is found from equation (2.11) ∙ ∙ ∙К

∙К

(2.13)

When Q is expressed in kcal/h ∙ ∙ ∙К

123 

 

∙ ∙К

(2.14)

Thus, the coefficient of thermal conductivity shows how much heat passes through heat conduction per unit of time through a unit of the heat exchange surface when the temperature falls by 1 degree per unit length of the normal to the isothermal surface. The value , which characterizes the ability of a body to conduct heat by thermal conductivity, depends on the nature of the substance, its structure, temperature and some other factors. At ordinary temperatures and pressures, the best heat conductors are metals, and the worst – gases. Thermal conductivity of solids is a linear function of temperature 1

,

(2.15)

where  is the thermal conductivity at a given temperature, (t, oC); o is the thermal conductivity at 0 °C; b is a constant for the given material.

With increasing temperature, the value of the thermal conductivity coefficient for most liquids decreases. The pressure practically does not affect the thermal conductivity of liquids. The value of the thermal conductivity coefficients (in W/(mK)) of dropping liquids at a temperature of 30 °C can be calculated from the ratio Ас

/М

/

,

(2.16)

where A is the size coefficient, which depends on the degree of association of the fluid; c, ρ and M are the thermal conductivity (J/(kg∙K), density (kg/m3) and molar mass (kg/kmol) of the liquid.

For associated fluids (for example, water) А = 3.5810-8; for nonassociated ones (for example, benzene) А = 4.2210-8. The value of the thermal conductivity of liquids at a temperature t, oC, can be calculated from the linear relationship 1

30 ,

(2.17)

where k is the temperature coefficient.

The value of the thermal conductivity of aqueous solutions at a temperature t, oC, can be calculated from the ratio 124 

 

р,

р,

∙

в,

/

в,

,

(2.18)

where sol and w are the thermal conductivities of the solution and water.

The value of the thermal conductivity of gases (in W/(m∙K)) at not too high pressures can be calculated through the viscosity of the gas μ, (Pa∙s), and its specific heat at constant volume сv, J/(kg∙K): ,

(2.19)

where B = (9k–5)/4; k = cp/cv is the adiabatic exponent; cp is the specific heat capacity of the gas at constant pressure, J/(kg∙K).

For gases of the same atomic number k = const, therefore, we can assume for all monatomic gases B = 2.5; for diatomic B = 1.9 and for triatomic B = 1.72 [2-4, 9]. 2.1.4. The equation of heat conductivity of a flat wall

Let us consider the transfer of heat by thermal conductivity through a plane wall of thickness  with the coefficient of thermal conductivity of the wall material  (Fig. 2.2). The temperature changes only in the direction of the x axis. The temperature on the external surfaces is maintained at a constant and .

Fig. 2.2. To the derivation of the equation of the thermal conductivity of a flat wall

125 

 

Under these conditions, the amount of heat that is transferred by thermal conductivity through the wall surface F in time , according to the Fourier’s law: (2.20) Dividing the variables, we get (2.21) Integrating equation (2.21) with the condition Q = const, we find с

(2.22)

The integration constant c is determined from the boundary conditions: at х = 0, ; at х = ,

,

whence ,W

(2.23)

Equation (2.23) can be used to calculate Q and in this form: , J (kcal)

(2.24)

The calculated formula for the steady heat flow through a multilayer flat wall is derived from the heat conductivity equation for individual layers. In general, the equation has the form:

⋯

where and

(2.25)

the thickness of the first layer, the thickness of the second layer, the thickness of the nth layer of the wall; respectively, the coefficients of

126 

 

,W

thermal conductivity of the layers are equal to , temperature of the outer surfaces of the wall [2,3,9].

,⋯,

;

и

the

2.1.5. Equation of heat conductivity of a cylindrical wall

Consider a homogeneous cylindrical wall of length l with inner diameter d1 and outer diameter d2. The coefficient of thermal conductivity of the material is constant and is equal to . The internal temperature t1 and external temperature t2 are kept constant, and t1 > t2 (Fig. 2.3). The temperature changes only in the radial direction. We select in the wall a ring layer with a radius r and thickness dr. According to the Fourier’s law, the amount of heat passing through such a layer is equal to 2

(2.26)

Dividing the variables, we get ∙

Fig. 2.3. To the derivation of the equation for heat conductivity of a single-layer cylindrical wall

127 

 

(2.27)

Integrating equation (2.27) in the range from t1 to t2 and from r1 and r2, (for  = const), we obtain t2

r2

Q dr  2  l r r1

(2.28)

 dt  

t1

or ∙

,

(2.29)

whence ,W

(2.30)

Expression (2.30) is the equation of the thermal conductivity of a homogeneous cylindrical wall for a steady heat flow. By analogy with the conclusion given for a single-layer wall, for a cylindrical wall consisting of n layers, the amount of heat transferred by thermal conductivity is ⋯

,

(2.31)

where d1 and d2, d2 and d3, d3 and d4, etc. – inner and outer diameters of each cylindrical layer [2,3,9].

Questions for self-control: 1. What types of heat transfer are involved in heat exchange? 2. What is the heat balance in the heat exchangers? 3. Explain the notion of an isothermal surface. 4. What is the temperature field? 5. Define the temperature gradient. 6. Write the Fourier’s law and explain the physical meaning of the coefficient of thermal conductivity. 7. Derive the heat equation for a single flat wall. 8. What is the thermal resistance of the wall? What is its dimension?

128 

 

9. What is the reason for the different temperature distribution over the thicknesses of the flat and cylindrical walls? 10. Derive the heat equation for a cylindrical wall.

2.2. Convective heat exchange

Heat exchange between the surface of a solid body and a liquid or gaseous environment when they are in direct contact is called heat emission or convective heat transfer. In convective heat emission, heat transfer from the surface of a solid to the core of a liquid environment or from a liquid environment to the surface of a solid is accomplished by heat conductivity and convection. The intensity of convective heat transfer is mainly determined by the presence and thickness of the laminar boundary layer b. Through this layer, heat is transferred only through thermal conductivity. The thickness of the laminar boundary layer b depends on the fluid motion regime. It decreases with increasing fluid velocity and decreasing viscosity. Therefore, the intensity of heat emission directly depends on the flow velocity and in the reverse one on the viscosity of the environment. The above diagram of the heat transfer mechanism (Fig. 2.4) only approximates the complex structure of the temperature field under conditions of convective heat transfer. With the complex mechanism of convective heat transfer, difficulties in calculating heat emission processes are associated. The exact solution of the problem of the amount of heat transferred from the wall to the environment (or from the environment to the wall) is associated with the need to know the temperature gradient at the wall and the profile of the temperature changes of the coolant along the heat exchange surface, the determination of which is very difficult. Therefore, for the convenience of calculating the heat emission, it is based on the equation of a relatively simple form, known as the heat transfer law, or Newton’s cooling law: (2.32) 129 

 

Fig. 2.4. The structure of the thermal and hydrodynamic boundary layers

According to this equation, the amount of heat dQ given in time dτ by the surface of the wall dF, having a temperature tw, of a liquid with temperature tl, is directly proportional to dF and the temperature difference tw – tl. With respect to the heat transfer surface of the entire apparatus F for the continuous heat transfer process, equation (2.32) takes the form (2.33) The proportionality coefficient  in equations (2.32) and (2.33) is called the heat emission coefficient. The value  characterizes the intensity of heat between the surface of the body, for example a solid wall, and the surrounding environment (a dropping liquid or gas). The heat emission coefficient is expressed as follows: ∙ ∙К

∙К

(2.34)

If Q is expressed in kcal/h, then ∙ ∙К

(2.35)

Thus, the heat emission coefficient  indicates how much heat is transferred from 1 m2 of the wall surface to the liquid (or from the 130 

liquid to 1 m2 of the wall surface) for 1 s with a temperature difference between the wall and the liquid of one degree. Due to the complex structure of the flows, especially under conditions of turbulent motion, the quantity  is a complex function of many variables. The heat transfer coefficient depends on the following factors: – the fluid velocity w, its density ρ and the viscosity μ, i.e. variables that determine the regime of fluid flow; – the thermal properties of the fluid (specific heat capacity cp, thermal conductivity λ), as well as the coefficient of volumetric expansion β; – geometric parameters – the shape and defining dimensions of the wall (for pipes – their diameter d and length L), as well as the roughness ε of the wall. In this case , , ,

, , , , ,

(2.36)

From this dependence of general form it can be concluded that the simplicity of the heat emission equation (2.32) is only apparent. In its use, the difficulties associated with determining the amount of heat transferred by convective heat transfer are in calculating the quantity . Due to the complex dependence of the heat emission coefficient on a large number of factors, it is impossible to obtain a calculated equation for , which is suitable for all cases of heat emission. Only by generalizing the experimental data with the help of the theory of similarity we can obtain a generalized (criterial) equation for the typical cases of heat emission, which makes it possible to calculate  for the conditions of a specific task. To determine the heat emission coefficient, it is necessary to know the temperature gradient of the liquid near the wall, i.e. distribution of temperatures in a liquid. The initial dependence for the generalization of experimental data on heat emission is the general law of temperature distribution in a liquid, expressed by the differential equation of convective-conductive heat emission [13,9]. 131 

 

2.2.1. Equation of convective-conductive transfer of heat

A mathematical description of the process of heat spreading in a moving environment simultaneously by thermal conductivity and convection is represented by the Fourier-Kirchhoff’s differential equation (2.37) More briefly, equation (2.37) can be written in the form ,



,

(2.38)

where the convective terms are represented by the scalar product of the velocity vectors and the gradient of temperature grad t, and the conductive terms are represented by the Laplace operator .

For solids 0 and equations (2.37, 2.38) are transformed into the differential equation of heat conductivity: (2.39) The coefficient of proportionality a in equations (2.37-2.39) is called the coefficient of thermal diffusivity: / /

∙К ∙

∙К

/ ∙ /

/

∙К ∙

∙К /

(2.40)

The coefficient of thermal diffusivity a characterizes the heatinertial properties of the body: all other things being equal, the body that has a large thermal diffusivity is heated or cooled faster [1,5,9]. 2.2.2. Criteria for thermal similarities

From the differential equation of convective-conductive heat transfer (2.38) it follows that the temperature field in a moving fluid 132 

 

is a function of various variables, including the velocity and density of the fluid. For practical use, equation (2.38) is similarly transformed taking into account the uniqueness conditions, i.e. represent as a function of the similarity criteria. Let us first consider the similarity of boundary conditions. As was pointed out, when the liquid is turbulent, the heat is at the boundary of the flow, i.e. in the immediate vicinity of the solid wall, is represented by thermal conductivity through the boundary layer L in a direction perpendicular to the direction of flow. Consequently, according to the Fourier’s law [equation (2.11)], the amount of heat passing through a boundary layer of thickness δ through the crosssectional area dF in a time dτ is (2.41) The amount of heat passing from the wall to the core of the flow is determined from the heat emission equation (2.32): (2.42) With a steady heat exchange process, the amounts of heat passing through the boundary layer and the core of the flow are equal. Therefore, equating the expressions (2.41) and (2.42) and reducing such terms, we obtain ∆

(2.43)

For a similar transformation of this equation, we divide (see page 4248) its right side by the left side and discard the signs of mathematical operators. In this case, we replace δ by a defining geometric dimension l. Then we obtain a dimensionless complex of quantities (2.44) which is called Nusselt’s criterion. The equality of Nusselt’s criteria characterizes the similarity of heat transfer processes at the boundary 133 

 

between the wall and the flow of a liquid. On the basis of a joint consideration of equations (2.41) and (2.42), it can be shown that Nu is a measure of the ratio of the thickness of the boundary layer δ and the determined geometric dimension (for a pipe, its diameter d). Thus, the Nusselt’s criterion is a conditional dimensionless form of the heat emission coefficient . Now consider the similarity conditions in the core of the flow, using a similar transformation of equation (2.37). In the left-hand side of the Fourier-Kirchhoff’s equation, the sum of terms reflecting the influence of the flow velocity on the heat transfer can be replaced by the quantity: ~

(2.45)

where l – the defining linear dimension.

The right-hand side of the same equation, characterizing the heat transfer by thermal conductivity, is also replaced by the quantity: ~

(2.46)

The term , which reflects the unsteady heat exchange regime, can be replaced by the ratio t/τ. Dividing the term t/τ by at/l2, we obtain a dimensionless complex of quantities l2/aτ. This complex is replaced by an inverse value in order to not operate with fractional numbers in the calculations. The latter complex is called the Fourier’s criterion: (2.47) The meaning of the Fourier’s criterion is a measure of the ratio of the intensity of conductive heat transfer to the rate of change in temperature at any internal point of the heat carrier flow or inside a solid body. The Fourier’s criterion serves as the dimensionless time for nonstationary thermal processes. The Fourier’s criterion is an analogue of the criterion of homochronicity Ho at a hydrodynamic similarity. 134 

 

The division of a convective summand into a convective summand gives an expression, which is called the Peclet’s criterion. The meaning of the Peclet’s criterion – a measure of the ratio of the intensities of convective and conductive heat transfer in the heat carrier flow: /

/

/

(2.48)

/

Since the heat transfer process depends on the component of the velocity of the heat carrier (equation (2.38)), then all the criteria of hydrodynamic similarity, on which the velocity components of the heat carrier can depend, in general should affect the heat emission intensity. These are the Reynolds criterion Re / , Froude’s criterion Fr / , Euler’s criterion Eu Δ / , Galileo’s crite/ , criterion of Archimedes Ar Δ / . rion Ga In heat-exchange processes, the difference in the density of the environment Δρ at various points of its volume is often a consequence of the temperature difference Δt of this environment: Δρ = ρβΔt. Substitution of the expression for Δρ into the Archimedes criterion gives Grashof’s heat criterion: Δ

where

,

(2.49)

the coefficient of volumetric thermal expansion, K-1.

Grashof’s criterion is a measure of the ratio of the product of inertia forces and Archimedean lifting force to the square of the viscous friction force. The Grasgof’s criterion determines the intensity of the natural thermal convection of the heat carrier in the field of gravity. The Peclet’s criterion can be represented as the product of two dimensionless complexes: ∙

∙

The dimensionless complex 135 

 

∙

(2.50)

(2.51) is called the Prandtl’s criterion, which is a measure of the ratio of the viscous and thermal diffusive properties of the heat carrier. Thus, the general relationship between the criteria that determine the intensity of the heat emission process between the flowing heat carrier and the heat exchange surface can be represented by the dependence of the Nusselt’s criterion on the criteria and simplices of geometric similarity G: ,

,

,

,

,

,

⋯

(2.52)

In the relation (2.52), there is no hydrodynamic criterion of homochronity / , since it is a product of the Pecle’s and Fourier’s criteria: / / / / . The Euler’s criterion defined in hydrodynamic problems is excluded from the set of influencing criteria, since in most cases its eigenvalue is a function of the criteria Re, Fr and geometric simplices G1, G2, ...,. For practically important processes of stationary heat exchange, the Fourier’s criterion, which contains the current time from the beginning of the thermal process, is excluded from the number influencing the Nu criteria. In the relation (2.52), the Ga or Ar criterion can be included as the influencing values if the archimedean lifting force does not arise due to the available uneven temperature of the heat carrier, but because of the difference in densities due to other causes – the presence of vapor bubbles or solid particles inside the drop liquid etc. Consequently, the most frequently encountered dependence of the criterion Nu on the dimensionless quantities that determine it has the form ,

,

,

,

,

⋯

(2.53)

The lack of the criterion Fr in the ratio (2.53) is explained by the fact that the influence of gravity is already taken into account by the Grasgof’s (Gr) and Galileo’s (Ga) criteria. 136 

 

The form of the functions (2.52) and (2.53) is determined experimentally, and they are usually given a power-law form. Thus, for example, equation (2.53) for flow in a pipe of diameter d and length l can be represented in the form ,

(2.54)

where C, m, n, p – the values determined from the experiment.

With free motion of the fluid and for heat emission processes under natural convection, equation (2.53) can be represented in the form ,

(2.55)

For gases Pr ≈ 1 = const and, therefore, the Pr criterion can be excluded from the generalized equations for determining the heat emission coefficient  [1-3,5,9]. 2.3. Thermal radiation

Thermal radiation is the result of intraatomic processes. The intensity of thermal radiation increases with increasing body temperature. Radiant energy spreads in the form of a stream of particles called quanta or photons, and has the properties of electromagnetic waves. Radiant heat exchange is radiation of electromagnetic waves by one body and absorption of radiation by another body. Thermal and light radiation are of the same nature, only differ in wavelength. The wavelengths of light rays are 0.4-0.8 μm, infrared rays are 0.8-400 μm. All bodies not only radiate, but also continuously absorb radiant energy. At the same temperature, the whole system of bodies is in mobile thermal equilibrium. The amount of energy radiated by the body per unit of time throughout the wavelength interval (from λ = 0 to λ = ) by the unit 137 

 

of the surface F of the body characterizes the radiant emissivity E of the body: (2.56) where Q – the energy radiated by the body.

Of the total amount of energy Qo falling on the body, part of it is absorbed QA, some is reflected QR and part passes through the bodies QD. Then the energy balance will be: (2.57) When dividing the equality by Qo, we get: ⁄ where

⁄

⁄

1,

(2.58)

characterizes the absorptive capacity of the body; characterizes the reflectivity of the body; characterizes the throughput of the body.

Consequently, the equality (2.58) can be represented as 1

(2.59)

If the body absorbs all the energy incident on it, A = 1, and R = D = 0, such a body is called absolutely black. In nature, absolutely black bodies do not exist. The greatest absorption capacity is possessed by petroleum soot, for which A = 0.9-0.96. If R = 1, then A = D = 0. This means that all energy falling on the body is reflected. Such a body is called absolutely white or mirror. For polished metals R reaches 0.06-0.88. If the body passes all the energy incident on it, such a body is called absolutely transparent or diathermic and D = 1, and A = R = 0. An example of such a body is pure air. The values A, R, D depend on the physical properties of the body, the state of their surface, the temperature and the wavelength of the incident radiation. 138 

Kirchhoff found that the ratio of the radiant power of any body to its absorptive capacity at the same temperature is a constant value equal to the emissivity of an absolutely black body: (2.60) where Ао – refers to an absolutely black body, Ао = 1.

The ratio of the emissivity of any body to the emissivity of absolutely black is called the degree of blackness: (2.61) The degree of blackness  varies within 0-1 and depends on the nature of the body, the state of its surface and temperature. According to the law of Stefan-Boltzmann, the emissivity of an absolutely black body Eo is proportional to the fourth power of the absolute temperature of its surface ,

(2.62)

where Ko=5.710-8 W/(m2К4) – the constant of emission of an absolutely black body.

To simplify the calculations, the Stefan-Boltzmann equation is applied in the form: ,

(2.63)

where Сo = Ko108 = 5.7 W/(m2К4) – the emissivity of an absolutely black body. The amount of heat transmitted by radiation depends on the temperature of the body, the state, shape, size and surface of the body, the location in space and the distance between the bodies participating in radiant heat exchange. Heat exchange between two unlimited parallel planes is determined by the equation (2.64) 139 

 

where red is the reduced degree of blackness of the system of bodies, equal to

,

(2.65)

where 1 и 2 are the degrees of blackness of the bodies participating in radiant heat exchange.

To calculate the radiant heat exchange between two surfaces in an enclosed space, when one of the surfaces F2 covers another F1 (Fig. 2.5), one can use formula (2.64). But since only part of the energy emitted by the second surface falls on the first surface, red is determined by a formula that takes into account the dimensions of the surfaces of both bodies:

(2.66)

Fig. 2.5. The scheme of heat exchange between bodies in a confined space

Radiation heat exchange between two bodies arbitrarily located in space is calculated by the formula (2.67)

р

where Fc is the conditional calculated heat exchange surface; 1–2 is the average angular coefficient of irradiation.

The angular coefficient takes into account the shape and dimensions of the surfaces, the relative position and distance between them and determines the energy radiated by the surface F1 to the surface F2 , where Q1 is the amount of energy radiated by the first body.

(2.68)

The radiation of gases differs significantly from the radiation of solids. Gases radiate and absorb energy not in the entire wave band, 140 

 

as is typical for solids, but only in certain intervals of waves, in so-called bands, and outside these bands they are transparent. Gases radiate and absorb by all volume, and solid bodies – only by the surface. The emissivity of gases somewhat deviates from the law of Stefan-Boltzmann. For example, for water vapor E ~ T3, for CO2 E ~ T3.5. However, in technical calculations it is assumed that the gases follow the law of Stefan-Boltzmann (the deviations are taken into account by the degree of blackness of the gas): ,

(2.69)

The coefficient of radiation C is variable and is determined from the relation С

гС

(2.70)

The calculated equation (approximate) for the radiant heat exchange between the gas and the body surface has the form: ,

. .

(2.71)

where e.b. is the effective degree of blackness taken as the average between red and unity [2,3,9]. . .

п

(2.72)

2.4. Heat emission at boiling and condensation

Boiling is an intensive process of evaporation occurring throughout the volume of the liquid when the pressure of a saturated vapor of the boiling liquid is equal to the external pressure. The boiling process is widely used in engineering (for example, in power engineering) and in chemical technology when evaporation of solutions in evaporators, separation of liquid mixtures by distillation and rectification, and evaporation of refrigerants. 141 

 

An obligatory condition for boiling of the liquid is a continuous supply of heat necessary for the vaporization process. Usually, heat is supplied from the heating surface in contact with the boiling liquid, and the temperature of the heating surface must exceed the temperature of the boiling liquid (tw  tboil). The centers of formation of small bubbles (smallest hillocks on a hard surface, particles of pollution) are called the centers of vaporization. The intensity of the formation of bubbles increases to a certain extent with increasing temperature difference between the wall and the boiling liquid (t = tw – tboil). With increasing t, the density of the heat flow q increases, i.e. the amount of heat transferred by the fluid per unit time by a unit of the wall surface. The resulting mixing of the liquid, caused by the growth, detachment and bubbling of the bubbles, leads to an increase in the heat transfer coefficient  (Fig. 2.6). This region in Fig. 2.6 corresponds to a bubbling or nuclear boiling regime, characterized by a relatively high rate of heat emision.

Fig. 2.6. Dependence of α and q on t for boiling water at p = 1 atm

With further increase of t = tcr, the number of vaporization centers increases so much that the vapor bubbles are merged and the 142 

 

heating surface is covered by a poorly conductive heat film of superheated steam. Despite the fact that this film is not stable, its formation leads to a significant decrease in the value . The corresponding regime at which a transition occurs from bubbling regime of boiling to film regime is called the boiling crisis, and it is depicted by the right descending branch  = f(t) in Fig. 2.6 is called film boiling. The value of the coefficient of heat transfer during the transition to the film boiling regime decreases by 20-40 times, which can lead to undesirable overheating of the heat exchange surface. The film boiling regime is always undesirable, and in the industry they try to organize a boiling process in the region of a developed bubbling regime of high intensity, but without the danger of switching to a film mode. The physical parameters of the liquid and vapor phases in the calculation formulas for heat transfer at boiling are taken at the boiling point (saturation), so it is often possible to represent these calculated ratios in a simple form, but with coefficients depending on the nature of the boiling liquid: (2.73) For water and most other liquids m  0.4 и n  0.7; the values of the coefficient A for various liquids are given in the reference literature. In order for boiling not to pass from an intense bubbling to a film regime, it is necessary to estimate the critical values of the heat flow qcr and the difference tcr. Experiments show that for many liquids qcr lies within the limits of 100–350 kW/m2, and tсr  20 – 25 К. For water, tсr = 25 К, cr  45103 W/(m2К) and qcr  106 W/m2. Condensation of vapors. In chemical equipment, heat emission from a condensing vapor is carried out, as a rule, under conditions of film condensation. In the case of film condensation, the thermal resistance is almost completely concentrated in the condensate film, the temperature of which on the wall side is assumed to be equal to the wall temperature tw, and on the steam side – to the saturation temperature tsat of the vapor (Fig. 2.7). Compared with the thermal resistance of the film, the corresponding resistance of the vapor phase is negligible. 143 

 

The film flow regime is a function of the Reynolds criterion: with increasing film thickness, the laminar flow of a film having a smooth surface goes into a wave, and then becomes turbulent. In addition to the physical properties of the condensate (density, viscosity, thermal conductivity), the heat transfer affects the wall roughness, its position in space, and the wall dimensions; in particular, with an increase in the surface roughness and height of the vertical wall, the condensate film thickens downward (Fig. 2.7).

Fig. 2.7. Temperature distribution in the condensate film

The generalized equation for determining the heat emission coefficient from condensing vapors has the form ,

,

(2.74)

This function, on the basis of processing experimental data, can be represented by the equation ∙ where

∆

∙

,

(2.75)

the criterion characterizing the change in the aggregate state, or

the condensation criterion (r is the heat of condensation, cl is the heat capacity of the condensate, and t = tsat – tw).

The Ga and Pr criteria included in (2.75) are assigned to the condensate film. The expression for the condensation criterion K is found by transforming the differential equation characterizing the boundary conditions. Criterion K should be considered as a measure 144 

 

of the ratio of the heat flow expended on the phase transformation to the heat of overheating or supercooling of the phase at the temperature of its saturation. When film condensation of a variable, laminating heat emission, is the thickness of the condensate film. The velocity of the vapor does not usually reach a value sufficient to disrupt the film, and does not enter the uniqueness conditions. The generalized equation for film condensation instead of the Re and Fr criteria includes the Ga = Re2/Fr = gl/2 derived criterion, which reflects the similarity of gravity forces acting on a heavier phase in a two-phase steam-condensate stream. The coefficients of heat emission during the film condensation of water vapor vary within the range (7-12)103 W/(m2К). With drop condensation, they are much higher, but stable dropping condensation in industrial heat exchange equipment can not be realized. Condensation of steam-gas mixtures. If even small impurities of air or other non-condensable gases are present in the vapor, the value  for the condensing vapor decreases sharply. Non-condensing gases gradually accumulate in the vapor space; at the same time, their partial pressure rises and, accordingly, the partial pressure of the vapor drops. In addition, the wall washing by the steam deteriorates and decreases t = tsat – tw. The coefficient of heat emission in this case depends on the intensity of the interconnected processes of mass and heat exchange, which are determined by the composition of the vapor-gas mixture, the nature of its flow, the physical properties of the components of the mixture, pressure, temperature, shape and size of condensation [1,2,9]. Questions for self-control: 1. What is the difference between the processes of convection and heat emission? 2. What factors determine the value of the heat emission coefficient in the heat emission equation? 3. What is the physical meaning of the heat emission coefficient? What is its dimension? 4. What is the physical meaning of the differential equation (2.37) of convectiveconductive heat transfer in a moving flow? 5. What is thermal similarity? Give the criteria of thermal similarity, the criterion equation of heat emission.

145 

 

6. What factors does the emissivity of the body depend on? How is it determined? 7. How do you determine the amount of heat that passes from a warmer body to a less heated body due to heat radiation? 8. Describe the mechanism of the processes of bubbling fluid boiling and the boiling crisis. 9. What is the criterion of condensation and on what parameters does it depend? 10. How does the process of vapor condensation on a solid surface occur and what is the criterial calculated dependence for the heat emission coefficient?

2.5. Heat transfer in heat exchanging devices

Heat transfer is the heat exchange between two environments through the partition separating them. Heat transfer is a complex kind of heat exchange, in which two environments and a body participate. In addition, it operates simultaneously and together all the elementary phenomena of heat transfer (heat conductivity, convection, radiation). Usually in the calculations one of the types of heat exchange is taken as the main one, and another type of heat exchange is secondary. For example, if the convective heat exchange is much higher than the radiant heat, it is taken as the main and the calculation formula for the general heat transfer is as follows: (2.76) where αc – heat emission coefficient by convection; αr – coefficient of heat emission by radiation; αо – total heat emission coefficient; tс – the temperature of the environment; ts – the temperature of the wall surface.

The amount of heat transferred by heat transfer under steady-state conditions is determined by the basic heat transfer equation: ∆

(2.77)

where Q – the amount of transmitted heat, W; t = th – tc, оС; th – the temperature of the hot heat carrier, oC; tc – the temperature of the cold heat carrier, оС; F – heat exchange surface, m2; K – the heat transfer coefficient, the dimension of which is obtained from the basic equation:

∆

∙

146 

 

∙К

∙К

(2.78)

The heat transfer coefficient is the amount of heat transferred per unit of surface per unit of time from one coolant to another with a temperature difference between them of one degree. The heat transfer coefficient connects each other the coefficient of thermal conductivity and heat emission [3,9]. 2.5.1. Heat transfer through a flat wall

Let us consider the case when two environments of different temperatures are separated by a homogeneous flat wall, the width and height of which are sufficiently large in comparison with its thickness (Fig. 2.8). The coefficient of thermal conductivity of the wall –  and its thickness – . The temperature – and , and . The temperature of the wall surfaces is unknown, we denote them as and . The total heat emission coefficient on the side of the hot heat carrier is 1, and on the cold one – 2. By the condition of the problem, the temperature field is onedimensional, the regime is stationary. In this case, all the heat transferred from the hot coolant to the surface of the wall passes through the wall and is released to the cool heat carrier, i.e. the indicated amounts of heat are equal to each other. Therefore, for a heat flow q, where , we can write a system of their three equations: , ,

(2.79) ,

Equations (2.79) contain partial temperature heads: , , . 147 

 

(2.80)

Fig. 2.8. To the derivation of the equation of heat transfer through a flat wall

After the left and right parts of equations (2.80) have been added, we obtain the expression for the total temperature head (2.81) from which the specific heat flow is determined: (2.82) The term

is the thermal resistance of the wall, and

and

are

the thermal resistances of heat transfer from the hot heat carrier to the cold one. According to formula (2.82), the heat flow is directly proportional to the temperature difference between the two heat carriers and inversely proportional to the sum of the thermal resistances. Introducing the notation: (2.83) in the expression (2.83), we obtain 148 

 

(2.84) The quantity K is called the heat transfer coefficient. It establishes the relationship between the elementary types of heat exchange through the coefficients of heat emission and the coefficient of thermal conductivity. The inverse value of the heat transfer coefficient is called the total thermal resistance of heat transfer: , where

(2.85)

the thermal resistance of the wall;

are the thermal resistance of

heat emission from the hot heat carrier to the cold one [2,3,9].

2.5.2. Heat transfer through the cylindrical wall

The cylindrical wall separates hot and cold liquids with temperatures and . The temperatures of the wall surfaces are unknown, we denote them by and . The total heat emission coefficient from the hot liquid flowing inside the pipe is 1, and to the cold one – 2. Under steady-state conditions, the amount of heat given off by the hot one and perceived by cold liquids is the same, and consequently, one can write: , ,

(2.86) .

Solving these equations for the temperature difference, we obtain: , , 149 

 

(2.87)

. Adding the equations (2.87), we obtain the total temperature head (2.88) Whence the value of the heat flow: (2.89) We introduce the following notation (2.90) After substituting this equality into (2.89), we finally obtain: (2.91) In contrast to K, the value Kl is a linear coefficient of heat transfer, per unit length of the tube, and not to the unit of its surface. Accordingly, Kl is expressed in W/(m2∙K) [2,3,9]. 2.5.3. Average temperature head

The processes of heat transfer at constant temperatures are relatively common. Such processes occur, for example, if steam condenses on one side of the wall, and on the other – boils up the liquid. Most often heat transfer in industrial equipment takes place at variable temperatures of heat carriers. The temperatures of the heat carriers usually vary along the surface that separates their walls. Heat transfer at variable temperatures depends on the mutual direction of motion of the heat carriers. In continuous processes of heat 150 

 

exchange, the following variants of the direction of motion of liquids relative to each other along the wall separating them are possible: 1) a parallel current, or direct flow, in which heat carriers move in the same direction; 2) a counter-current, in which heat carriers move in opposite directions; 3) a cross-current, in which heat carriers move mutually perpendicular to each other; 4) a mixed current, in which one of the heat carriers moves in one direction, and the other - both parallel (or direct) and counter-current to the first one. The driving force of heat transfer processes at variable temperatures varies depending on the type of the mutual direction of motion of the heat carriers. Therefore, in the heat transfer equation, the average value of the temperature head Δ

(2.92)

Let us consider the case of direct flow, when heat carriers move along the surface of heat exchange in the same direction (Fig. 2.9).

Fig. 2.9. To the derivation of the formula for the average temperature head

As the heat carriers flow along the wall, their temperatures will change due to heat transfer. Accordingly, the temperature difference t between the heat carriers will change. Through the element of the 151 

 

heating surface dF per unit time (per second) the amount of heat passes: (2.93) In this case, the temperature of the more heated liquid will decrease by ,

(2.94)

,

(2.95)

less heated one will increase by

where G1 – the amount of hot fluid flowing per unit time; c1 – its heat capacity; G2 – the amount of cold fluid flowing per unit time; c2 – its heat capacity.

The “minus” sign indicates a cooling of the warmer heat carrier during heat exchange. The product Gc is called the water equivalent and denoted by ;

(2.96)

and (2.97) The change in the temperature head is obtained by subtracting the value of the temperature change from the less heated liquid from the value of the temperature change of the more heated liquid —

,

(2.98)

whence (2.99) 152 

 

Substituting the value found (2.99) into equation (2.93), we obtain (2.100) We replace t1 – t2 by t and divide the variables by t ∆

(2.101)

∆

Equation (2.101) can be integrated in the range from tin to tf and from 0 to F (Fig. 2.9) ∆ ∆

∆

∆

∆

∆

,

(2.102)

where Δtin – the initial temperature difference; Δtf – the final temperature difference.

The heat balance equation for the surface element dF has the form: , and since

and

(2.103)

, from equation (2.103) we find and

(2.104)

Adding these expressions term by term, we obtain ,

(2.105)

whence, taking equation (2.97) ∆

∆

Substituting the value m into equation (2.102), we obtain 153 

 

(2.106)

∆

∆

∆

,

∆

(2.107)

whence ∆

∆

∆

∆

∆ ∆ ∆

∆

(2.108)

Comparing (1.104) with the basic heat emission equation (2.92), we obtain ∆

∆

∆

∆ ∆

(2.109)

After reducing both sides of the equation to KF, we obtain the value of the mid-temperature head ∆

∆

∆

(2.110)

∆ ∆

Equation (2.110) remains valid also for determining the average logarithmic temperature head when the fluid moves counter-current. If the temperature of the working fluids along the surface changes insignificantly, i.e. the condition is satisfied ∆

2,

∆

then the average temperature head can be calculated as the arithmetic mean of the extreme heads ∆

∆

∆

(2.111)

For mixed current and crosscurrent ∆

∆

∆

,

(2.112)

where t – the correction factor to the average temperature difference tcc, computed for the counter-current [2,3,9].

154 

 

2.5.4. Thermal insulation

To reduce heat transfer, it is necessary to increase the thermal resistance. This is achieved by applying a layer of thermal insulation to the wall. Thermal insulation is called any auxiliary coating, which helps to reduce the loss of heat to the environment. The choice and calculation of insulation is made taking into account considerations of an economic nature and the requirements of technology and sanitation. The thickness of insulation for flat walls is determined directly from formula (2.82), and for pipelines from formula (2.89) through d2, or the ratio , where d1 – the diameter of the bare and d2 – insulated pipelines. For pipelines, the determination of the insulation thickness is complicated by the fact that d2 enters the calculation equation not only in the form , but also in the form of the term . Thermal losses of insulated pipelines are reduced in proportion to the increase in insulation thickness. This circumstance is explained by the fact that as the thickness is increased, the thermal resistance of the insulation layer increases: ,

(2.113)

and the thermal resistance of heat emission to the environment is reduced: (2.114) To avoid a large thickness in the insulation of pipelines, materials with a low coefficient of heat conductivity are used. The maximum thermal losses are observed at a certain value of the diameter, which is called the critical diameter of the insulation: ,

(2.115)

where d2cr – critical insulation diameter at which there will be a maximum loss of heat, mm;  – thermal conductivity of insulation; 2 – coefficient of heat emission from the surface to the environment [3,9].

155 

 

Questions for self-control: 1. Give the basic heat transfer equation. 2. What is the physical meaning of the heat transfer coefficient? 3. Write the heat transfer equation through a flat wall. 4. What is the thermal resistance of heat transfer from a hot heat carrier to a cold one? 5. Write the heat transfer equation through the cylindrical wall. 6. List possible options for the direction of motion of liquids relative to each other along the wall separating them in continuous heat exchange processes. 7. Explain the physical meaning of the average temperature difference in the formula (2.110) in the calculation of heat exchangers. 8. What is called thermal insulation? 9. What equation can be used to calculate the thermal resistance of the insulation layer? 10. What value is called the critical diameter of insulation?

2.6. Evaporation

Evaporation is the process of concentrating solutions by removing the solvent by evaporation while boiling the liquid. Evaporation is used to increase the concentration of diluted solutions or to separate dissolved substances from them by crystallization. The peculiarity of the evaporation process is the transition to the vapor state of only the solvent. The boiling point of solutions is always higher than the boiling point of the solvents, it depends on the chemical nature of the solutes and solvents and grows with increasing solution concentration and external pressure. The difference between the boiling points of the solution ts and the pure solvent at the same external pressure is called the temperature depression td: ∆

(2.116)

The increase in the boiling point of the solution is also determined by hydrostatic and hydraulic depressions. The increase in the boiling point due to the hydrostatic pressure of the liquid column in the vertical pipe is called hydrostatic depression th.d.. The increase in the boiling point of the solution due to the increase in pressure in the apparatus due to hydraulic losses during 156 

passage of the secondary vapor through the trap and the outlet of pipeline is called hydraulic depression thd.d.. The vapor produced by evaporation of the boiling solution is called secondary. When boiling pure water (solvent), the temperature head is equal to the difference between the temperature of the heating steam and the temperature of the boiling water, which is equal to the saturation temperature of the secondary vapor. When the solution boils, the saturation temperature of the secondary vapor corresponding to the pressure in the apparatus does not change, and the boiling point of the solution increases by the amount of depression. Consequently, the same temperature is lowered by the same magnitude of depression. Thus, depression causes a loss of temperature head, as a result of which it is called a temperature loss. Total depression tt is equal to the sum of temperature, hydrostatic and hydraulic depressions: ∆

∆

∆

. .

∆

. .

(2.117)

Evaporation is accompanied by an increase in the density and viscosity of the solution, which leads to a decrease in the heat transfer coefficient [2,3,9]. 2.6.1. Ways of evaporation

Evaporation is made at the expense of heat from the outside, transmitted more often through the surface of heating and less often by direct contact of the solution with the heat carrier. Water vapor, flue gases, as well as high-boiling liquids and their vapors are used as heat carriers. The evaporation processes are carried out under vacuum, at elevated and atmospheric pressures. The choice of pressure is related to the properties of the solution to be evaporated and the use of secondary vapor heat. 157 

 

Evaporation under vacuum has certain advantages before evaporation under atmospheric pressure. When evaporated under reduced pressure, the vacuum in the apparatus is created by condensation of the secondary vapor in the condenser by a vacuum pump. The vacuum evaporation allows to lower the boiling point of the solution, and also to increase the temperature difference between the heating agent and the boiling solution, which makes it possible to reduce the heat exchange surface. When evaporated under elevated pressure, the resulting secondary steam can be used as a heating agent, for heating or other technological needs. In industry, both single-casing and multi-casing evaporators are widely used. Multi-casing evaporators consist of several (up to four) connected devices. Direct-flow units operate under pressure, dropping from the first housing to the last one. In such installations, the secondary vapor generated in each previous casing is used to heat the subsequent casing. Fresh steam is heated only by the first case. Secondary steam from the last housing is sent to the condenser (if this housing is under vacuum) or used outside the installation (if the latter housing is working under increased pressure). Practically the steam consumption (in kg) per 1 kg of evaporated water is: in a single-casing residue – 1.1; in a two-casing – 0.57; in a three-casing – 0,40; four-casing – 0.30; five-casing – 0,27. In multiple-unit plants, the same amount of heat is used repeatedly (the heat given off by the heating steam in the first casing), which significantly reduces the amount of fresh steam consumed, i.e. increase the technical and economic parameters of the installation [3,9]. 2.6.2. Evaporating devices

When evaporating small amounts of solutions, horizontal and vertical devices are used, which are boilers equipped with heating jackets and coils for steam and liquid heating or gas heating furnaces. In the chemical industry, vertical evaporators with natural and forced circulation, as well as film evaporators, were most widely distributed. 158 

 

The evaporator with a natural circulation of the solution consists of a heating chamber 1 where steam is supplied, plates 2 in which pipes 3 of 2 to 4 m in length are rolled up, a vapor space 4, a separator 5, a circulation pipe 6 (Fig. 2.10).

Fig. 2.10. Evaporator with natural circulation

The evaporated solution circulates through the tubes from the bottom upwards and descends down the circulation pipe. The circulation in the apparatus is due to the difference in the specific gravity of the liquid in the descending circulation pipe and the vaporliquid emulsion in the boiler tubes. The presence of a vapor space 4 above the solution to be evaporated must ensure a satisfactory separation of the spray of the evaporated solution from the secondary vapor. Insufficient separation of the spray leads to loss of the solution, and with multi-casing evaporation to contamination of the heating surface of the next housing and the condensate of the secondary vapor. A decrease in the speed of the secondary steam (i.e., an increase in the diameter of the apparatus) and an increase in the height of the vapor space lead to a decrease in the splashwater [3,9]. 159 

 

2.6.3. Material balance of the evaporation device

The material balance of the evaporation device can be represented by the total number of substances (2.118) and for the dissolved substance (2.119) where G1 and G2 – initial and final amount of solution, kg/s; a1 and a2 – initial and final concentration of solution in weight fractions; W - amount of evaporated water, kg/s.

The above equations (2.118) and (2.119) include five variables, of which some three quantities must be specified. In practical calculations, the following quantities are most commonly known: the consumption of the initial solution G1, its initial concentration a1 and the required final concentration a2 of the evaporated solution. Then by the equations (2.118) and (2.119) determine the productivity of the device: over evaporated solution (2.120) over evaporated water 1

(2.121)

If the flow rate of the initial solution G1, its initial concentration a1 and the amount of evaporated water W are set, then from the material balance equations (2.118) and (2.119), it is possible to calculate the final concentration of the solution (2.122) 160 

 

and the amount of the final solution (2.123) 2.6.4. Thermal balance of the evaporation device

The coming of heat in the evaporation device is composed of heat with the incoming solution and heat, which is given to the apparatus by the heating agent . The heat consumption for evaporation includes: heat carried away by the secondary steam ; the . . ; heat with a leaving solution heat expended for dehydration Qd; loss of heat to the environment Ql. Thus, we can write the heat balance equation: ,

. .

(2.124)

where cin and cf – the specific heat capacities of the incoming Gin and outgoing Gf solutions, J/(kgK); tin and tf – the temperatures of incoming and outgoing solutions, oC; is.v. – the specific enthalpy of the secondary vapor, at the outlet of the evaporator, J/kg.

The heat of dehydration is the heat input to increase the concentration of the solution and it is equal in magnitude and back to the sign of the heat of vaporization of the solution. Usually the heat of dehydration is low and therefore not taken into account. Considering the initial solution as a mixture of the evaporated solution and the water to be evaporated and assuming that the heat capacity cin of the initial solution within the temperature tin to tf remains constant, we will write down the heat balance of mixing at the boiling point of the solution in the apparatus: с

(2.125)

с

(2.126)

whence

where cw – the average specific heat of water (within the temperature range from 0 o C to tf), J/(kgK).

161 

 

Substituting the value (2.126) into the heat balance equation (2.124), we obtain, neglecting Qd: с

. .

(2.127)

or (2.128) In this equation, the term is the heat consumption for evaporation of water. The specific heat capacityof the solution entering into the heat balance equation can be calculated as a function of its concentration a according to the approximate formula 1

с

,

(2.129)

where csol – the specific heat of an anhydrous solid solute (for two-component solutions).

The heat capacity of solutions (multicomponent) can be calculated from the general formula с

с

,

(2.130)

where с1, с2, с3 – the heat capacities of the components; x1, x2, x3 – the mass fractions of the components. In the absence of direct experimental data, the specific heat capacity of a chemical compound can be calculated approximately by the additivity rule: ∑

,

/ ,

(2.131)

where ni and ca,i – the number of atoms and the atomic heat capacity of the i-th element (Table 2.1) entering into the chemical compound; M – the molar mass of the compound, kg/kmol.

Table 2.1 shows the heat capacities of the elements. For an approximate calculation of the specific heat capacity of diluted aqueous solutions 0.2 , the heat capacity of the dis162 

 

solved substance can not be taken into account because of its relative smallness: 4,19 ∙ 10 1

,

(2.132)

where 4,19 ∙ 10 J/(kg∙K) – the specific heat of water.

Table 2.1. Atomic heat capacity of elements

Element

C H B Si O

The atomic heat capacity of elements for chemical compounds, kJ/(kgatomK) in the in the solid state liquid state 7.5 11.7 9.6 18.0 11.3 19.7 15.9 24.3 16.8 25.1

The atomic heat capacity of elements for chemical compounds, kJ/(kgatomK) in the in the solid state liquid state 21.0 29.3 22.6 31.0 22.6 31.0

Element

F P S Rest

26.0

33.6

The required flow of heating water vapor (Gh.v.) for the evaporator is proportional to the required amount of heat: . .

"

′

.

,

(2.133)

where " и ′ the specific enthalpies of dry saturated heating steam and its condensate at the condensation temperature, J/kg; x – the degree of dryness (steam content) of the heating steam (in most cases x ≈ 0.95  0.98; rh.s. – specific heat of condensation of heating steam, J/kg.

Specific consumption of heating steam (d) characterizes the efficiency of the use of heating steam in relation to the amount of evaporated solvent [1-4,9]: . .

163 

 

(2.134)

2.7. Heat exchanging devices

Devices intended to transfer heat from one body to another are called heat exchangers. Bodies that give or perceive warmth are usually called heat carriers. Depending on the purpose, heat exchangers are called heaters, condensers, evaporators, steam generators and others. By the methods of heat transfer, there are two main groups of heat exchangers: surface and mixing. In surface heat exchangers, the transfer of heat between the heat exchanging environments takes place through the heat exchange surface that separates them – a blank wall. In turn, surface heat exchangers are divided into recuperative and regenerative. If heat exchange between different heat carriers occurs through the separation walls, the heat exchanger is called recuperative. In regenerative heat exchangers, heating of liquid environments occurs due to their contact with previously heated bodies – the nozzle filling the apparatus, periodically heated by another heat carrier. In the mixing apparatus, the transfer of heat occurs when it directly contacts and mixes the heat carriers. 2.7.1. Surface heat exchangers Apparatus with a jacketed heat exchange surface. In apparatuses with shirts, a closed space forms between the shell and the surrounding jacket-shirt. When heating from above, a heating heat carrier is introduced, when cooled, the heat carrier is fed from below (Fig. 2.11). The use of such devices is limited to a small heat exchange surface (up to 10 m2) and overpressure in the shirt (up to 10 atm). Coil heat exchangers. The heat exchange element – coil, is a pipe bent in any way. Coils are installed in refrigerators, condensers, evaporators, distillation devices. The velocity of heat carriers in such devices is somewhat lower than in straight pipes (up to 1 m/s), but the coefficient of heat emission of coils is somewhat higher than that of straight pipes. Casing tubular heat exchangers. These devices are the most common type of heat exchange equipment in chemical technology. Casing tubular heat exchangers are apparatus made of bundles of 164 

 

tubes assembled with pipe grids and bounded by casings and lids with fittings (Fig. 2.12, 2.13).

Fig. 2.11. The device with a jacket: 1 – the case of the device; 2 – shirt; 3 – condensation pot

Pipe and intertubular space in the apparatus are disconnected, and each of these spaces can be divided by partitions into several moves. Partitions are installed in order to increase the speed, and consequently, the coefficient of heat exchange of heat carriers. Casing tubular heat exchangers are used when a large heat exchange surface is required. In most cases, the steam (heating heat carrier) is introduced into the intertube space, and the heated liquid flows through the pipes.

Fig. 2.12. Casing tubular single-pass heat exchanger: 1 – casing; 2 – tube grid; 3 – tubes; 4 – camera (output, input); 5 – flange; 6 – choke

Fig. 2.13. Multu-hull casing tubular heat exchanger: 1, 3, 5, 7 – compartments of the lower chamber; 2, 4, 6, 8 – compartments of the upper chamber; 9 – transverse partitions

165 

 

Heat exchangers “pipe in the pipe”. Heat exchangers of this type are a battery of several heat exchange elements located one below the other. Each of the elements consists of an inner tube and an outer tube surrounding it (Fig. 2.14).

Fig. 2.14. Heat exchanger “pipe in pipe”: 1 – outer tube; 2 – inner tube; 3 – roll

Heat exchange between heat carriers is carried out through the walls of internal pipes. In two-tube heat exchangers, a high velocity of heat carriers and a high intensity of heat exchange are ensured. However, these heat exchangers are cumbersome and metal-laden. Irrigation heat exchangers are mainly used for cooling liquids and gases or condensing vapors. The irrigation heat exchanger consists of a series of pipes placed one above the other (Fig. 2.15).

Fig. 2.15. Irrigation heat exchanger: 1 – chute; 2 – roll; 3 – pipe; 4 – the pallet

166 

 

Outside, the pipes are watered. A coolant flows through the pipes. Irrigation water is fed to the upper pipe, which drains to the pipes below. In order to evenly irrigate the upper pipe, a chute with serrated edges is mounted on it. In the lower part there is a trough for collecting water. Heat exchangers of this type are used when the temperature of the cooled liquid is above 100 °C [2,3,9]. 2.7.2. Mixing heat exchangers

In mixing heat exchangers, the transfer of heat from one heat carrier to another one occurs when they are in direct contact and are mixed. Such apparatuses are used primarily for condensing vapors and cooling gases with water, and also for cooling water with air. Mixing heat exchangers in which condensation of any vapors with a cold liquid takes place are called mixing capacitors. By the method of outputting flows from the apparatus, wet and dry mixing capacitors are distinguished. In wet condensers, the cooling water, the condensate formed and the non-condensable gases are pumped out of the apparatus by the wet-air pump together. In dry condensers, cooling water and condensate are drained from the bottom of the apparatus by gravity through one pipe, and noncondensing gases are evacuated by a vacuum pump from the top of the apparatus through another pipe. Mixing devices can be direct-flow and counter-current, depending on the mutual direction of movement of water and vapors. In countercurrent, the temperature difference between the condensing steam and the outgoing water is 1-3 °C, and with a direct flow of 5-6 °C, and consequently the water flow in the direct-flow capacitors will be large. The main factor determining the operation of the mixing apparatus is the contact surface of the heat carriers, which should be as large as possible. Therefore, in the mixing apparatus, the contact surface is increased by arranging the shelves, spraying the liquid, and placing the nozzles. The consumption of cooling water is determined from the heat balance equation: 167 

 

,

(2.135)

where G – the amount of condensable vapor, kg/s; Ist – enthalpy of incoming steam, J/kg; cw – specific heat of water, J/(kgK); t2in and t2f – the initial and final temperatures of the cooling water.

As follows from equation (2.135) (2.136) The amount of aspirated air (in kg/s) is determined by the empirical formula 0,001 0,025

10

,

(2.137)

where W – the flow rate of the cooled water, kg/s; G – the amount of condensed steam, kg/s.

The volume of suction air is calculated ,

(2.138)

where tair – the air temperature, оС; pair – partial air pressure, N/m2; 288 – gas constant for air, J/(kgK) [2,3,9].

Questions for self-control: 1. Show the essence of evaporation and the area of its practical application. 2. Describe the methods of the evaporation process – under vacuum, at atmospheric pressure and under increased pressure. 3. Expand the features of single-casing and multi-casing evaporation, periodic and continuous evaporation. 4. What is meant by secondary steam and extra steam? 5. Explain the principle of operation and the device of the evaporator with natural circulation. 6. Give the equations of material balance of the evaporator. 7. What are the terms in the heat balance equation of the evaporator? 8. What equations calculate the consumption of heating steam and evaporated water? 9. Give the classification of heat exchangers. 10. Give a comparative description of surface and mixing heat exchangers.

168 

 

2.8. Heating processes

The substances involved in the heat transfer process are called a heat carriers. Heat carriers that have a higher temperature than the heated environment and give off heat are called heating agents. Flue gases, which are gaseous products of combustion of fuel, and electrical energy are used as direct heat sources in chemical technology. Substances that receive heat from these sources and transfer it through the wall of the heat exchanger to the heated environment are called intermediate heat carriers. Among the common intermediate heat carriers are water vapor and hot water, as well as high-temperature heat carriers – superheated water, mineral oils, organic liquids (and their vapors), molten salts, liquid metals and their alloys. The choice of the heat carrier depends primarily on the desired heating temperature. The industrial heat carrier should provide a sufficiently high intensity of heat exchange at low mass and volume consumptions. Accordingly, it must have a low viscosity, but high density, heat capacity and heat of vaporization. In chemical engineering, the following methods of heating are most common: by water vapor, by flue gases, by intermediate heat carriers, and by electric current. 2.8.1. Heating with water vapor

One of the most widely used heating agents is saturated water vapor. As a result of the condensation of steam, large amounts of heat are produced at a relatively low steam flow rate. The heat of condensation of steam is 2.26106 J/kg (540 kcal/kg) at P = 9.8104 N/m2 (1 atm). An important advantage of saturated steam is the constant temperature of its condensation, which makes it possible to accurately maintain the heating temperature. The main disadvantage of water vapor – a significant increase in pressure with increasing temperature. Because of this, the temperatures to which heating with saturated steam can be carried out, usually does not exceed 180-190 °С, which corresponds to a vapor 169 

 

pressure of 10-12 atm. At a pressure not exceeding 10 atm, heating with steam is performed to a temperature of 150-170 °C. Heating with “shap” steam. The hot steam is injected directly into the heated liquid in which it condenses, giving off the heat of condensation of the heated liquid, and the condensate is mixed with the liquid and their temperatures are equalized. Heating with “shap” steam is not suitable if mixing of condensate with heated liquid is impossible or its dilution. The flow rate of the “shap” steam is determined by taking into account the equality of the final temperatures of the heated liquid and condensate. Then, using the heat balance equation, we find (2.139) from where the steam consumption ,

(2.140)

where D – the flow rate of the “shap” steam, kg/s; G - flow rate of the heated environment, kg/s; c – the average specific heat capacity of the heated environment, J/(kgK); t1 and t2 – the initial and final temperatures of the heated environment, K; Qp – heat loss to the environment, J/s; Is – enthalpy of heating steam, J/kg; сw – the heat capacity of the condensate, J/(kgK).

Heating with a “deaf” steam. When heated by a “deaf” steam, heat is transferred to the liquid through the wall separating them. The steam, coming into contact with the colder wall, condenses on it, and the condensate film flows down on the wall surface. In order to facilitate the removal of condensate, steam is introduced into the upper part of the apparatus, and the condensate is withdrawn from its lower part. The temperature of the condensate film is close to the temperature of the condensing vapor, and these temperatures can be assumed to be equal to each other [2,3,9]. The consumption D of a deaf steam with continuous heating is determined from the heat balance equation:

where Ic – the enthalpy of condensate, J/kg.

170 

 

,

(2.141)

2.8.2. Heating with flue gases

Most often flue gases are used for heating through the wall of other heating agents – intermediate heat carriers. When heated with smoke or flue gases, temperatures of 1000 °C or more can be reached. However, for flue gas heating, the following significant drawbacks are typical: 1. Low coefficient of heat emission from gases to the walls of heated apparatus ( = 15-30 kcal/m2hgrad). 2. Small volumetric specific heat capacity of gases (Сv = 3,6 kcal/m3grad), which makes it necessary to pass significant volumes of gas. 3. Irregularity of heating due to cooling of gases when they give off heat. 4. Due to the high temperatures of the flue gases and the difficulty of their regulation, overheating of the heated products is possible. 5. Contamination of the product during the transfer of heat at direct contact. 6. Heating with flue gases of highly volatile and flammable materials is dangerous. Flue gases are formed by burning solid, liquid or gaseous fuels in furnaces or ovens of various designs [2,3,9]. 2.8.3. Heating with high-temperature heat carriers

For most chemical processes taking place at high temperature, it is required to conduct an even heating of the equipment. In this case, heating is carried out by high-temperature heat carriers. These heat carriers usually receive heat from flue gases or electric current, transfer it to the heated material and are, thus, like water vapor, intermediate heat carriers. Intermediate heat carriers are various liquids or vapors circulating in the system, absorbing heat from flue gases or electric current and transmitting it to the wall of the apparatus. The circulation of intermediate heat carries in the system can be natural or forced. 171 

 

The natural circulation is due to the difference in densities. The circulation speed is 0.2 m/s. To ensure circulation, the heat exchanger must be located above the furnace for 4-5 m. Due to the low circulation speed, the heat transfer coefficient is very low. Forced circulation is by means of a pump. As an intermediate heat carriers used mineral oils, superheated water, organic heat carriers, molten salts, mercury, etc. Heating with superheated water. Superheated water at a pressure close to critical (22.1 MN/m2 (225 atm)), is used to heat up to 300-350 °C by the circulation method. The entire system is filled with a hand pump with distilled water. Then the water is heated, the water expands upon heating, and the pressure in the system increases: the pressure is regulated, gradually releasing the water. Then the temperature is brought to the critical parameters – 374 °С. However, heating with superheated water is associated with the use of high pressures, which greatly complicates and increases the cost of the heating installation and increases the cost of its operation. Heating with mineral oils. Mineral oils are one of the oldest intermediate heat carriers used for uniform heating of various products. As heating agents, oils with the highest flash point – up to 310 °C (cylinder, compressor, cylinder heavy) are used. Therefore, the upper limit of heating by oils is limited to temperatures of 250 – 300 °C. Heating by means of mineral oils is produced either by placing a heat-using apparatus with a jacket filled with oil into an oven in which heat is transferred to the oil by flue gases or by installing electric heaters inside the oil jacket. Oils are the cheapest organic high-temperature heat carriers. However, they have significant drawbacks. In addition to the relatively low application temperature limits, mineral oils have low heat emission coefficients, which are further reduced by thermal decomposition and oxidation of oils. Heating with high-boiling organic liquids and their vapors. The group of high-temperature organic heat carriers includes individual organic substances: glycerin, ethylene glycol, naphthalene 172 

 

and its substituents, as well as certain aromatic hydrocarbon derivatives (diphenyl, diphenyl ether, diphenylmethane, etc.). The greatest industrial application was obtained by a diphenyl mixture consisting of 26.5 % diphenyl and 73.5 % diphenyl ether. At P = 1 atm, it is possible to heat up to 250 °C. In the vapor state, the diphenyl mixture is used to heat up to temperatures not exceeding 380 °C (for short-term heating – up to about 400 °C). At higher temperatures, an appreciable decomposition of the diphenyl mixture takes place. It is flammable, but almost explosion-proof and has only a weak toxic effect on the human body [2,3,9]. 2.8.4. Heating with electricity

With the help of electric current heating can be carried out in a very wide temperature range, accurately maintaining and easily adjusting the heating temperature in accordance with the specified technological regime. Heating by electric current is produced in electric furnaces. Depending on the method of converting electrical energy into heat, heating by electrical resistance, induction heating, high-frequency heating, and heating by an electric arc are distinguished. Electric resistance heating is the most common method of heating by electric current. In electric resistance furnaces, a temperature of 1000-1100 °C can be obtained with a uniform heating of the volume. The heating elements are mainly made of wire or nichrome tape – an alloy of nickel, chromium and iron. Passing current through a metal wire, the electric power is transformed into a thermal one. In this case, heat is released 860

,

(2.142)

where 860 – the amount of heat in kcal, equivalent to an electric power of 1 kWh; W – the power of the heater (kW), equal to the product of the current I (A) by the voltage U (V);  – time, h.

Arc furnaces allow to obtain a temperature of up to 2000 °С and higher [3,9]. 173 

 

Questions for self-control: 1. Name the types of heat carriers for supplying heat to heat exchange equipment. 2. List the main advantages and disadvantages of heating saturated steam. 3. When is “sharp” steam used for heating up? 4. How to determine the consumption of “sharp” steam for heating the cold heat carrier? 5. What is the peculiarity of heating by the “deaf” water steam? 6. Write the equation for the consumption of “deaf” water steam during continuous heating. 7. List the main advantages and disadvantages of heating with flue gases. 8. Give a comparative description of high-temperature heat carriers. 9. What are the main types of electric heating? 10. List the advantages and disadvantages of cooling of hot heat carriers with water and air. To what temperatures can the hot heat carrier be cooled with these cooling agents?

174 

 

3. MASS EXCHANGE PROCESSES 3.1. Basiсs of mass transfer

Technological processes, the rate of which is determined by the rate of transfer of a substance (mass) from one phase to another, are called mass-exchange processes. Such processes include: absorption, adsorption, rectification, extraction, drying, crystallization. The rate of these processes is determined by the rate of diffusion. Processes in which the transition of substance from one phase to another occurs by diffusion are called mass transfer processes. In the processes of mass transfer, two phases participate in which the third substance is distributed. The phases are carriers of the substance to be distributed and do not participate directly in the mass transfer process. 3.1.1. Phase equilibrium

The transition of substance from one phase to another occurs in the absence of equilibrium between the phases. At equilibrium, a definite relationship is established between the limiting, or equilibrium, concentrations of the distributed substance in the phases for the given temperature and pressure at which the mass transfer process takes place. In the most general form, the relationship between the concentrations of a distributed substance in phases at equilibrium is expressed by the dependence: ∗

(3.1)

∗

(3.2)

or

where x – the content of the substance distributed in one phase, y* – the equilibrium concentration of this substance in the other phase and vice versa (equation (3.2)).

175 

 

The equilibrium conditions (3.1) and (3.2) allow us to determine the direction of the process. If the working concentration of the distributed substance in this phase is above equilibrium, then it will leave this phase in a different phase. The equilibrium between the phases can be represented graphically on the у – x diagram (Fig. 3.1) [2,3,9].

Fig. 3.1. Diagram: ОС – equilibrium line; AB – working line

Fig. 3.2. To the derivation of equation line of working concentration

3.1.2. Material balance of mass-exchange processes

Diffusion (mass exchange) processes, as a rule, are carried out in countercurrent apparatuses, where the phases participating in the mass exchange flow towards each other. Therefore, to derive the equation for the material balance of mass exchange processes, let us consider the scheme of a mass-exchange apparatus operating in the ideal-displacement mode in countercurrent phases (Fig. 3.2). We denote the weight velocities of the phases of liquid L and gas G along the interface in kilograms per hour. The content of the distributed component in them will be denoted in kilograms per kilogram of phase: in phase L – through x and in phase G – through y. 176 

 

Let us assume that the working concentration of the distributed component is above its equilibrium concentration у > у*, and therefore the component will pass from phase G to phase L. The phases are carriers of the substance being distributed and do not participate in the mass exchange process. For an infinitely small surface element dF of the phase contact, the material balance with respect to the component distributed between the phases is expressed by the differential equation (3.3) Integrating the equation within the given limits of the concentrations of the distributed substance from yin to yf and from xin to xf (3.4) or (3.5) we obtain the equation of the material balance of mass exchange for the entire surface of phase contact in the apparatus under consideration. From the equation a the relationships between the weight flows of phases are found (3.6) and G

(3.7)

and specific consumption of solvent (3.8) 177 

 

For any arbitrarily taken section of the apparatus below the line MN (Fig. 3.2) with the phase concentration y and x, integrating the equation of material balance (3.3) in the range from y to yf and from xin to x, we obtain (3.9) we get (3.10) the equation of material balance for a part of the apparatus (below MN). From the equation (3.10) we find (3.11) This equation is called the equation of the working line of the mass exchange process. It expresses the relationship between the nonequilibrium compositions of the phases y, x in any section of the apparatus. The quantities G, L, yf, xin are known and are constant, therefore, introducing the notation and , we find (3.12) This equation of the straight line, from which it follows that the concentrations of the substance distributed in the phases G and L are connected by a linear relationship [2,3,9]. 3.1.3. Basic equation of mass transfer

The basic law of mass transfer can be formulated on the basis of the general kinetic laws of chemical-technological processes. The 178 

 

speed of the process is equal to the driving force divided by the resistance: ∆

(3.13)

where dM – the amount of substance passing from one phase to another, kg/s; dF – phase contact surface, m2; d – the time, s;  – the driving force of the mass transfer process; R – the resistance.

Denoting the inverse of the resistance 1/R by K and referring the amount of substance transferred from one phase to another dM to a unit time, equation (3.13) can be rewritten as follows: ∆,

(3.14)

where K – the mass transfer coefficient.

Equation (3.14) is called the basic mass transfer equation. For the entire surface of the phase contact F, equation (3.14) is written ∆

(3.15)

Thus, the amount of substance M, passing from one phase to another in a unit of time, is proportional to the contact surface of the phases F and the driving force Δ. The dimension of the mass transfer coefficient is determined from equation (3.15): / ∙

∆

.

.

(3.16)

The mass transfer coefficient is the amount of a substance passing from one phase to another per unit time through a unit of the phase contact surface at a driving force equal to unit. The driving force  can be expressed in any units used to express the phase composition. The driving force of process  can be expressed through concentrations in one of the phases: ∗

179 

 

,

(3.17)

∗

,

(3.18)

where y, x – the working concentrations of the component being distributed in the gas and liquid phases, respectively; у*, х* – the equilibrium concentrations.

If the working and equilibrium concentrations of the substance to be distributed are expressed in terms of relative weight compositions (kg/kg), the mass transfer coefficient will be: / ∙

∆

/

∙

(3.19)

When the driving force is expressed in terms of the difference in ∗ , N/m2: partial pressures, ∆ /

∙

∙ /

∆

∙

∙ ∙

∙

(3.20)

If the driving force of the process is expressed in terms of the difference in volume concentrations (kg/m3), then the dimension of the mass transfer coefficient will be [2,3,9]: / ∙

∆

/

(3.21)

3.1.4. Average moving force of the process of mass transfer

The driving force varies with the change in working concentrations. Therefore, for the entire process of mass transfer, which takes place within the limits of the change in concentrations from the initial to the final, the average driving force is determined. The expression for the average driving force depends on whether the equilibrium line (other things being equal) is a curve or a straight line. To determine the average driving force, we consider the process taking place in a countercurrent column apparatus under the following conditions: 1) the y* = f(x) dependence is a curve; 2) the phase consumptions are constant (G = const, L = const), i.e. the working line is 180 

 

straight; 3) the mass transfer coefficients do not change (Kx = const, Ky = const) along the height of the apparatus (Fig. 3.2). In our case, y > y*, therefore, the substance to be distributed passes from phase G to phase L. For the element of the phase contact surface, dF, the driving force can be expressed by the difference in working and equilibrium concentrations Δy = y – y*. The amount of substance will pass from phase G to phase L on the surface element dF equal to dM, which will be determined in accordance with the basic mass transfer equation: ∗

(3.22)

The same amount of substance can be expressed as (3.23) Comparing equations (3.22) and (3.23) and solving with respect to dF, we find ∗

∙

∗

(3.24)

Integrating equation (3.24) in the range from 0 to F and from yin to yf, we obtain ∗

(3.25)

or ∗

(3.26)

For the entire surface of the phase contact F, based on the basic mass transfer equation and the material balance equation, we can write: ∆ (3.27) where Δуm – the average driving force.

181 

 

From equation (3.27), the amount of phase G can be expressed as: (3.28) We substitute the found value of G into equation (3.26) and obtain: ∗

∗

(3.29)

or (3.30) ∗

Comparing the equations (3.27) and (3.30) ∆

(3.31) ∗

find the value of the average driving force ∆

(3.32) ∗

When the driving force is expressed through the concentration of the substance to be distributed in the liquid phase x, the expression for the average driving force is obtained ∆

(3.33) ∗

When the equilibrium line is straight (у* = mx), the average driving force is defined as the average logarithmic force between the driving forces at the beginning and at the end of the phase contact surface: 182 

 

∆ where ∆ surface; ∆

∗ ∗

∆

∆ ,

∆ ∆

(3.34)

the driving force at the beginning of the phase contact the driving force at the end of the phase contact surface [2,3,9].

Questions for self-control: 1. List the main mass-exchange processes. 2. What is the driving force of all mass-exchange processes? 3. Why are mass-exchange processes, as a rule, carried out in countercurrent devices? 4. Give the differential and integral equations of mass transfer for the entire surface of the phase contact. 5. What is the physical meaning of equation (3.11) of the working line of a continuous mass-exchange process. 6. Formulate the basic law of mass transfer. 7. What is the mass transfer coefficient? 8. Indicate all possible dimensions of the mass transfer coefficient. 9. By what equation is the average driving force of the mass transfer process calculated? 10. What happens to the mass-exchange process in establishing the equilibrium state?

3.2. Modified equation of mass transfer

In many cases of computational practice, the basic mass transfer equation is used in a modified form. Since the phase contact surface is not determined by a simple geometric calculation. In this case, the main technical characteristic of the apparatus can be the volume, height or number of stages of phase contact. To derive a modified mass transfer equation, when the main technical characteristic of the apparatus is taken to be its height, the phase contact surface in the entire volume of the apparatus can be represented by the expression: , m2, 183 

 

(3.35)

where f – the sectional area of the apparatus, m2, H – the height of the apparatus, m2,  – the specific surface area of the phase contact per unit volume of the apparatus, m2/m3.

Substituting the found values of the phase contact surface (3.35) into the basic mass transfer equation (3.30), we obtain (3.36) ∗

Replacing from (3.5),

(3.37)

will have ,

(3.38)

∗

Whence (3.39)

∗

If the driving force is expressed through the concentration of the distributed substance in the liquid phase, the modified mass transfer equation (3.39) will have the form: (3.40)

∗

where L and G – the flows of liquid and gas entering to the treatment.

The multipliers in equations (3.39) and (3.40)

,

repre-

sent the height of the apparatus section corresponding to one transport unit and are called the transfer unit height (TUH = h). The integral is the change in the working concentration per unit of driving force in a given section and is called the number of transfer units – n. The number of transfer units is determined by the method of graphical integration. One transfer unit n = 1 corresponds to the 184 

 

section of the apparatus in which the change in operating concentrations is equal to the average driving force in a given section. Equations (3.39) and (3.40) after the introduction of a certain height of transfer units and the number of units of transfer are written down [2,3,9]. (3.41) 3.2.1. Mass transfer exchange between phases

The transfer of substance between phases is carried out simultaneously by molecular and convective diffusion. In the mass of the phase, due to intensive mixing, the concentration of the distributed substance in each section of the system is almost identical, and therefore the transport of substance is carried out predominantly by convective diffusion, i.e. moving particles of the carrier and the substance being distributed. In the boundary layer, substance is transported by both by molecular and convective diffusion. At the phase interface, the role of molecular diffusion increases. If mass transfer occurs between a solid phase and a liquid or gas, then the substance is transported inside the solid phase by mass conductivity. The law of mass conductivity is analogous to the law of molecular diffusion. The transfer of substance by molecular diffusion is determined by Fick’s first law, according to which the amount of substance diffused through the layer is proportional to the concentration, time, and surface gradient of the layer perpendicular to the direction of the diffusion flow, ,

(3.42) с

where M – the amount of diffused substance, kg (kgf); concentration gradient in 3 2 the diffusion direction (kg/m )/m ; F – the area of the layer through which the substance diffuses, m2;  – the time, s (h); D – the diffusion coefficient.

The proportionality coefficient D in the Fick’s law expression is called the molecular diffusion coefficient, or simply the diffusion coefficient. The minus sign in front of the right-hand side of Fick’s first 185 

 

law indicates that molecular diffusion always proceeds in the direction of decreasing the concentration of the distributed component. The dimension of the diffusion coefficient is determined from the Fick’s equation (3.42): ∙ ∙

/

(3.43)

∙

or in the MKGSS system ∙ ∙

/

∙

(3.44)

The diffusion coefficient shows how much subsctance diffuses per unit time through a unit surface with a concentration gradient of unity. Returning to the analogy with the processes of heat distribution, it can be noted that the diffusion coefficient D is an analog of the coefficient of temperature conductivity a. The molecular diffusion coefficient is a physical constant that characterizes the ability of a given substance to penetrate due to diffusion into a stationary environment. The value D thus does not depend on the hydrodynamic conditions in which the process proceeds. The value of the diffusion coefficient D is a function of the properties of the substance being distributed, of the properties of the environment through which it diffuses, temperatures and pressures. Usually, the values D increase with increasing temperature and a decrease in pressure (for gases). In each specific case, the value of the diffusion coefficient is determined from experimental data or from theoretical and semiempirical equations, taking into account the temperature and pressure at which the diffusion process takes place [2,3,9]. 3.2.2. Convective diffusion

In convective diffusion, substance is transported by moving particles of the carrier and the substance being distributed. With convective diffusion, the amount of the transferred substance from the phase giving up the substance to the phase interface 186 

 

is proportional to the surface of the phase contact, time, the particular driving force, i.e. the difference in the concentration of the distributed substance in the phase and at the interface: ∆ ,

(3.45)

where F – the phase contact surface, m2;  – the time, s; c – the private driving force of the process;  – the mass emission coefficient.

The mass emission coefficient shows how much mass of substance passes from the interface of phases to the core of the phase (or in the opposite direction) through unit of surface per unit time with a driving force equal to unity. The mass emission coefficient is not a physical constant, but a kinetic characteristic that depends on the physical properties of the phase (density, viscosity, etc.) and the hydrodynamic conditions in it (laminar or turbulent flow regime), which in turn are related to the physical properties of the phase, factors determined by the design and dimensions of the mass exchange apparatus. In terms of meaning, the mass emission coefficient is an analog of the heat emission coefficient in heat transfer processes, and the basic mass emission equation is identical in structure to the basic heat emission equation. The mass emission coefficient can be expressed in various units, depending on the choice of units for the mass of the substance to be distributed and the driving force. The dimension of the mass emission coefficient is determined from the equation of convective diffusion (3.45): ∙ ∙

∆

.

(3.46)

.

If the working and equilibrium concentrations of the substance to be distributed are expressed in terms of relative weight compositions (kg/kg), then the mass emission coefficient dimension will be: ∙ ∙

∆

187 

 

/

∙

(3.47)

When expressing the driving force (for the gas or vapor phase) ∗ through the difference in partial pressures ∆ , N/m2: ∙ ∆

∙ ∙ /

∙

∙ ∙

(3.48)

∙

If the driving force of the process is expressed in terms of the difference in volume concentrations (kg/m3), then the dimension of the mass emission coefficient will be [2,3,9]: ∙ ∙

∆

(3.49)

/

3.2.3. Criteria of diffusional similarity

Criteria for diffusion (mass-exchange) similarity are obtained from the basic equation of convective-diffusion mass transfer of a component in a single-phase flow: (3.50) or in compact vector form ,



D

,

(3.51)

where the convective terms are represented by the scalar product of the velocity vector and the gradient of concentration grad С, and the diffusion ones – by the Laplace operator С.

To derive the similarity criteria from equation (3.50), this equation is written in a simplified, one-dimensional form with the notation of the spatial coordinate replaced by l. Then, instead of (3.50), we write , 188 

 

(3.52)

where the principal physical content of the equation (3.50) and its individual terms is completely preserved.

The right-hand side of equation (3.52), corresponding to the transport intensity of the target component due to molecular diffusion, is divided into the first term of the left side, which reflects the overall rate of change of the component concentration at an arbitrary point of the carrier stream: ~

,

(3.53)

where Ci – the concentration of the component at the interface; C0 – the concentration of the component in the bulk of the carrier stream.

In this case we obtain a dimensionless complex of quantities ,

(3.54)

which is called the diffusion Fourier’s criterion. The diffusion Fourier’s criterion is a measure of the ratio of the rate of change in concentration caused by molecular diffusion to the total overall rate of change in concentration at any point of the moving environment. By analogy with non-stationary processes of conductive-convective heat transfer, the diffusion Fourier’s criterion is often called the dimensionless time of the nonstationary diffusionconvective mass transfer of the component. The division of the convective term of (3.52) into a diffusion term and the analogous replacement of the derivatives with respect to the coordinate by the ratio of finite differences gives another independent criterion for diffusion similarity, known as the Peclet’s diffusion criterion: ~

(3.55)

The Peclet’s diffusion criterion is a measure of the ratio of the intensity of transfer of a component by convection and the transfer by molecular diffusion. By multiplying and dividing by the kinematic viscosity of the environment, the Peclet’s diffusion criterion can be represented in 189 

 

terms of the Reynolds criterion and a new criterion – the Prandtl’s diffusion criterion (Schmidt’s criterion): (3.56) The Prandtl’s diffusion criterion is a measure of the ratio of the viscosity and diffusion properties of the environment carrier: (3.57) Prandtl’s diffusion criterion includes only quantities reflecting the physical properties of the flow. Thus, this criterion formally expresses the constancy of the ratio of the physical properties of the liquid (gas) at similar points of similar flows. However, its physical meaning is deeper, as the viscosity is determined, with all other conditions being equal, the velocity profile in the flow, and the concentration distribution depends ultimately on the value D. Another criterion of diffusion similarity, important for practical calculations, is obtained from an analysis of the mass exchange conditions at the phase interface. Since the amount of substance moving from the phase to the phase boundary is determined by the convective diffusion equation (3.45), at the interface of the phases the same amount of substance moves to another phase due to molecular diffusion and is determined by the molecular diffusion equation (3.42). The mathematical formulation of the boundary conditions can be written in the form: /

,

(3.58)

where n – the direction along the normal to the wall.

The left-hand term is divided by the right, then the unknown value of the derivative С/ is replaced by the proportional ratio of the concentration difference С С to the characteristic geometrical dimension of the system l: /

~

(3.59) 190 

 

Diffusion criterion of Nusselt (Sherwood): (3.60) is a measure of the ratio of the mass emission rate from the surface to the intensity of diffusion transfer. In its structure, the Nusselt’s diffusion criterion is completely analogous to the Nusselt’s heat criterion (2.44), which characterizes the heat exchange at the boun-dary. Experimental data on the determination of the mass emission coefficients β are processed and represented as a dependence of the Nusselt’s diffusion criterion on the defining Reynolds criteria, the Prandtl’s diffusion criterion, and for nonstationary processes – also on the diffusion Fourier’s criterion: ,

,

(3.61)

For stationary processes, a Fourier’s criterion consisting of the current time τ is excluded from the set of defining criteria: ,

(3.62)

If there are zones or points with different densities Δρ in the volume of the environment, then the Archimedes’s criterion is introduced into the set of defining criteria, and for geometrically inconvenient systems geometric simplices G1, G2, ... are added. Thus, the experimental data on the intensity of mass exchange are presented in the form of a dependence of the Nusselt’s number on the determining criteria and simplices of geometrical similarity:

,

,

,

,

,⋯

(3.63)

The dependence (3.63) can be represented in power form: ,⋯ 191 

 

(3.64)

The numerical values A, m, n, k in the criterion equation (3.64) are found experimentally, and the mass emission coefficient is determined from the Nusselt’s diffusion criterion [1,2,5,9]. (3.65) Questions for self-control: 1. Derive the modified mass transfer equation if the driving force is expressed through the concentration of the substance distributed in the liquid phase. 2. Formulate Fick’s first law. 3. What does the coefficient of molecular diffusion depend on? What is its physical meaning? What is its dimension? 4. What are the main differences in the transport of substance by convection and mass emission? 5. Explain the physical meaning of the mass-emission coefficient. 6. Give all possible dimensions of the mass-emission coefficient. 7. What is the physical content of the equation (3.50) for the convective-diffusion transfer of a component in a single-phase flow? 8. Describe the similarity of mass-exchange processes. 9. Write down the criterial mass emission equation for unsteady and steady mass transfer processes. 10. Expand the physical meaning of the similarity criteria for mass-exchange processes.

3.3. Absorption

Absorption is the process of selective extraction of one or several components from a gas mixture with a liquid absorber (absorbent). The reverse process – the release of dissolved gases from the absorbent is called desorption. Absorption processes involve two phases – liquid and gas. When they are in contact, one component (or several) passes from one phase to another. In the presence of a component (components) practically insoluble in the liquid phase in the gas phase, they are called an inert, or carrier gas. A dissolving component – an absorbed component. In the absence of chemical interaction between the absorbed component and the absorbent, the process is called physical absorption, and in the presence of such interaction – chemisorption. 192 

 

Absorption is very widely used in the chemical and allied industries. Absorption is used to extract valuable (target) components from the gas mixture, and to purify gas mixtures from impurities before using them in technological processes or before their release into the atmosphere. In modern industrial practice, the importance of the absorption process is very great for the creation of wasteless technologies. The main problems in the implementation of absorption are associated with the selection of absorbent and the creation of rational conditions for contacting gas and liquid. When choosing an absorbent, there are a number of requirements: 1) selectivity, i.e. the ability to selectively absorb the extracted component with the possible minimum solubility in it of the carrier gas; 2) high absorptivity, otherwise high solubility of the absorbed component in the liquid phase under operating conditions (reduces absorbent consumption); 3) possibly lower volatility, i.e. low elasticity of absorbent vapors at operating temperature in order to avoid its losses with the outgoing gas; 4) stability in operation, i.e. the absorbent should not be subjected to changes – decomposition, oxidation, molding, etc.; 5) convenience in work – non-toxicity, incombustibility, low corrosive effect on the equipment; 6) availability and cheapness; 7) easy regenerability during desorption. Industrial absorbents do not fully meet all of these requirements at the same time. Therefore, in practice, the absorbents are selected from the process conditions (properties and composition of the gas mixture, gas temperature and pressure, the required degree of purification, etc.) [6,9]. 3.3.1. Physical bases of the process of absorption

In the processes of physical absorption, at least three components are involved: two carrier – substances (gas and liquid) and a component that goes from one phase to another. The system of two phases ( = 2) with the total number of components k = 3 according 193 

 

to the phase rule has three degrees of freedom applied to the equilibrium state:  2 3 2 2 3 (3.66) With complete insolubility of the inert in the absorbent and low volatility of the latter, the composition of the phases will be completely characterized by the concentrations of the absorbed component in each of the phases: x – in the liquid phase and y – in the gas phase. The parameters of the equilibrium state of the system are also the temperature and pressure at which this system is located. Thus, the total number of variables of the equilibrium system is 4. For  = 3, three variables can be chosen arbitrarily – according to the conditions of the technological process, and the fourth one will be dependent. For example, you can arbitrarily choose the temperature and pressure, as well as the concentration of the absorbed component (AC) in the liquid (x). Then for such a system the equilibrium concentration of this component in the gas phase (yeq) will be quite definite. Such a dependence of y on x at a certain temperature and pressure is called the equilibrium curve – the equilibrium line, or the curve of equilibrium (Fig. 3.3). ∗

(3.67)

Let a point A characterizing the working (nonequilibrium) state of the contacting phases lie above the equilibrium lines. Then, when the system approaches equilibrium (in the direction of arrow 1), the concentration of the absorbed component in the gas phase will decrease, and in the liquid phase – it will increase. Such a change in the concentration of AC in the phases corresponds to the absorption process. This means that all points lying above and to the left of the equilibrium line form the absorption region. Now let the operating state of the system be characterized by a point D (of concentration and ) located below the equilibrium line. Here, on the contrary, when it tends to the equilibrium state (in the direction of the arrow 2), the concentration of the absorbed component in the liquid phase decreases and its increase in the gas phase, i.e. there 194 

 

is a desorption process. The working area, located below and to the right of the equilibrium line, is called the desorption region.

Fig. 3.3. Phase-balance diagrams of gas – liquid: a – for p = const, b – for t = const

These curves are also called absorption isotherms. If the temperature of the system t is changed to t1, then the new AC value in the liquid x will correspond to a new value у1eq, to the value ′ – ′ the value . With increasing temperature (t1 > t), the solubility of the absorbed component (gas) in the liquid decreases. If the point characterizing the operating state of the system lies between two isotherms 3 and 4, for example point E (Fig. 3.3), then in such a system absorption will take place – at temperature t (absorption region under isotherm 3) or desorption – at temperature t1 (desorption region under isotherm 4). Therefore, by affecting the temperature of the system, it is possible to change the direction of the “absorption-desorption” process. Let us now consider the effect of the total pressure P in the gasliquid system on the equilibrium distribution of the components between the phases. For small concentrations of the solution (when the gas in the liquid dissolves poorly), Henry’s law can be applied, according to which the equilibrium partial pressure of the component in the gas phase above the liquid is proportional to the content of the dissolved gas in the liquid: 195 

∗

,

(3.68)

where p* – the equilibrium partial pressure of the component in the gas, mmHg; ψ – the Henry constant (having the dimension of pressure); x – the dissolved gas content in the solution (kg/kg absorber).

Henry’s constant characterizing the solubility of gases in a liquid, it depends on the properties of the dissolved gas and absorber, and also on the temperature. The temperature dependence with some approximation is expressed by the equation: ,

(3.69)

where q – the heat of dissolution of the gas, kcal/kgfmole of dissolved gas; R – the gas constant; c – the experimental constant.

If the gases are highly soluble and form solutions of high concentration, and gases are under pressures measured in tens of atmospheres, the equilibrium does not follow Henry’s law. For technical calculations, the values of the equilibrium partial pressure of the gas P* obtained from the experiment are used and the equilibrium content of the component in the gas mixture is calculated from formula ∗

∙

∗ ∗

,

(3.70)

where Mc – the molecular weight of the component; Mcar – the molecular weight of the carrier; P – the total gas pressure over the liquid, mmHg [2,3,6,9].

3.3.2. Influence of temperature and pressure on the process of absorption

With increasing temperature, the concentration of the absorbed component (AC) increases in the gas phase at the same concentration in the liquid phase, which leads to a shift of the equilibrium line upwards. The driving force is thereby reduced and the absorption conditions deteriorate. Therefore, it is advantageous to carry out absorption at a lower temperature. 196 

 

At a constant value of the concentration (AC) in the liquid phase (for example, at x = x3 in Fig. 3.3b), the equilibrium concentration of AC in the gas phase decreases with increasing pressure . At a constant concentration of AC in the gas phase, its solubility in the liquid increases with increasing pressure (x1 > x2 > x3 at р1 > р2 > р3). Therefore, absorption is advantageous at an elevated pressure [6,9]. 3.3.3. Material balance and kinetic laws of absorption

The material balance and the working line of the absorption process are characterized by the equations of the material balance of mass exchange (3.5) and the working line of the mass exchange process (3.11). Kinetic regularities correspond to the general mass transfer equation for two-phase systems ∗

,

(3.71)

,

(3.72)

∗

where y, x – the mass emission coefficients for the gas and liquid phases; p – the partial pressure of the absorbed component in the gas mixture; p* – the equilibrium partial pressure of the absorbed gas at the interface; C – the concentration of dissolved gas in the liquid; C* – the equilibrium concentration of the absorbed component in the liquid at the interface; F – the phase interface; M – the amount of gas absorbed.

For systems that obey Henry’s law, the equilibrium values p* and C* according to Henry’s law are related by the relation ∗

∗

, then

∗

С

(3.73)

Solving jointly equations (3.71) and (3.72), we obtain the mass transfer equation for the expression of the driving force through the pressure difference: ∗

197 

 

,

(3.74)

where Ky – the total mass transfer coefficient associated with the mass emission coefficients y and x by the following relation

(3.75) Similarly, expressing the driving force through the difference in concentrations, we obtain ∗

,

(3.76)

where (3.77)

3.3.4. Absorption devices

Apparatus, in which absorption processes are carried out, are called absorbers. When absorbed, the mass transfer process takes place at the interface of the phases. Therefore, the absorbers must have a developed contact surface between the liquid and the gas. By the way this surface is formed, the absorbers can be conditionally divided into the following groups: 1) surface and film; 2) packed; 3) bubbling (poppet); 4) spraying. Surface and film absorbers. In absorbers of this type, the contact surface of the phases is a mirror of a stationary or slowly moving liquid, or the surface of a current liquid film. In surface absorbers, the gas passes over the surface of a stationary or slowly moving liquid (Fig. 3.4). Surface absorbers are used to absorb highly soluble gases (for example, to absorb hydrogen chloride with water). Since the contact surface in such absorbers is small, several sequentially connected apparatuses are installed in which the gas and liquid move countercurrent to each other. Surface absorbers have limited application due to their low efficiency and cumbersomeness. 198 

 

Fig. 3.4. Surface absorber

Film absorbers are more efficient and compact than surface absorbers. In film absorbers, the contact surface of the phases is the surface of the current liquid film. Еhe following types of apparatus of this type are distinguished: 1) tubular absorbers; 2) absorbers with a plane-parallel or sheet nozzle; 3) absorbers with an upward movement of the liquid film. The tubular absorber (Fig. 3.5) is similar in structure to the vertical casing tubular heat exchanger.

Fig. 3.5. Tubular film absorber: 1 – housing; 2 – tubes; 3 – partitions

199 

 

The absorbent enters the upper tube plate, is distributed along the tubes 2 and drains along their inner surface in the form of a thin film. In apparatuses with a large number of pipes, special distribution devices are used to distribute the allocation of liquid more evenly through the pipes. The gas moves along the pipes from below upwards towards the flowing liquid film. To remove the heat of absorption through the intertubular space, water or another cooling agent is passed through. Absorbers with a plane-parallel nozzle (Fig. 3.6). This apparatus is a column with a sheet nozzle 1 in the form of vertical sheets of various materials (metal, plastic masses, etc.) or tightly stretched materials from the fabric. In the upper part of the absorber there is a distribution device 2 for uniform wetting of the sheet nozzle on both sides. Absorbers with an upward movement of the film (Fig. 3.7) consists of pipes 1 fixed in tube grids 2. The gas from chamber 3 passes through pipes 4 arranged coaxially with tubes 1. The absorbent enters the tubes through the slits 5. The gas moving at a sufficiently high velocity drags the liquid film in the direction of its movement (from the bottom up), i.e. the device operates in the mode of ascending direct flow. On leaving the pipe 1, the liquid is drained onto the upper tube plate and discharged from the absorber. A coolant is passed to remove heat of absorption through the intertube space. In apparatus with an upward movement of the film, due to the high velocities of the gas flow (up to 30-40 m/s), high values of the mass transfer coefficients are achieved, but, at the same time, the hydraulic resistance of these devices is relatively large. Packed absorbers. The packed absorbers have found the greatest application in the industry with the absorption of gases by liquids. They are columns loaded with a nozzle, solid bodies of various shapes, through which the liquid flows down from above, towards the rising gas. As a nozzle, the so-called Raschig rings (thin cylinders, whose height is equal to their diameter) are widely used in the size of 15150 mm. The rings are made of ceramics, porcelain and less often of steel. In the apparatus, Rashig rings are laid in bulk or in regular rows (with a diameter d > 50 mm). The main characteristics of the nozzles are the specific surface area  (m2/m3) and free volume  (m3/m3). 200 

 

Fig. 3.6. Absorber with plane-parallel nozzle: 1 – sheet nozzle; 2 – distributive device

Fig. 3.7. Absorbers with ascending motion of a liquid film: 1 – pipes; 2 – pipe grid; 3 – the chamber; 4 – a branch pipe for gas supply; 5 – slot for absorbent supply

To prevent the liquid from spreading to the walls, the nozzle is covered in separate layers (the height of each layer is 1.5-3 m), between which the guide cones are installed. 201 

 

The packed absorbers, depending on the fluid and gas flow regime, can operate in different hydrodynamic regimes. These modes are visible from the graph (Fig. 3.8), which expresses the dependence of the hydraulic resistance of the irrigated nozzle on the fictitious gas velocity in the column.

Fig. 3.8. Dependence of the hydraulic resistance of the nozzle on the gas velocity in the column (L = const): 1 – dry nozzle; 2 – irrigated nozzle

The first mode – film mode – is observed at low irrigation densities and low gas velocities. The amount of liquid retained in the nozzle under this regime is practically independent of the gas velocity. The film mode ends at the first transition point (point A, Fig. 3.8), called the hang point. The second mode – the hang-up mode. When the phases are counter-current due to an increase in the frictional forces of the gas against the liquid, there is a brake of a liquid by a gas stream. As a result, the flow velocity of the liquid decreases, and the thickness of its film and the amount of liquid retained in the nozzle increases. In the hang-up mode with increasing gas velocity, the moistened surface of the nozzle increases and, accordingly – the intensity of the mass transfer process. This mode ends at the second transition point (point B, Fig. 3.8), and in the suspending mode the calm flow of the film is disturbed: vortices appear, splashes appear, i.e. conditions for the transition to bubbling are created. All this contributes to an increase in the intensity of mass exchange. 202 

 

The third mode – the emulsification mode. In these conditions, the liquid occupies the entire free volume of the nozzle, which is not occupied by gas. The liquid is a continuous phase, and the gas is a dispersion phase. The role of the nozzle is reduced to the fragmentation of gas vortices into a large number of small vortices piercing the liquid, to distribute them throughout the entire column section, and the swirling of the liquid itself. By carefully adjusting the gas supply, the emulsification mode can be set at the entire height of the nozzle. The hydraulic resistance of the column thus increases sharply (in Fig. 3.8, this mode is characterized by an almost vertical segment BC). The fourth mode – the mode of entrainment, or reversed motion of the liquid, carried from the apparatus by a gas stream. This mode is not used in practice. Bubbling (poppet) absorbers. In bubbling absorbers, the gas is distributed in the liquid in the form of bubbles, on the surface of which absorption takes place. The most common absorbers are in the form of columns with cap and sieve plates (Fig. 3.9 and 3.10). Captive plates are equipped with nozzles, covered with caps. Gas passes through a layer of liquid, the level of which on the plate is supported by overflow tubes. The lower ends of the overflow tubes are lowered to the level of the liquid of the next plate, so that a hydraulic seal is created to prevent the passage of gas through the overflow tubes. The liquid from the plate to the second plate flows over the overflow pipes. The number of caps on a plate is not the same in different columns. Sieve plates have holes (2-5 mm in diameter) through which gas flows. The liquid on plates with a height of about 25-30 mm is determined by the position of the upper ends of the overflow tubes, is supported from below by gas pressure and flows to the next plate only over the overflow pipes. Bubbling absorbers are complex in design and have high hydraulic resistance caused by a large amount of gas being passed. Therefore, bubble absorbers are used mainly in those cases when absorption is carried out under increased pressure, since at the same time high hydraulic resistance is insignificant. In bubbler absorbers, the removal of the heat of absorption can be carried out with the help of coils installed on the plates of the column, through which the coolant is passed. 203 

 

Fig. 3.9. Column with cap plates: 1 – plates; 2 – branch pipes; 3 – caps; 4 – overflow pipes

Fig. 3.10. Column with perforated plates: 1 – holes; 2 – overflow pipes

Spraying absorbers. In spray absorbers, the contact surface of the phases is created by spraying the liquid into small droplets in the mass of the gas. Spraying the liquid is done from above, and the gas moves from the bottom up. Spraying absorbers are used to absorb highly soluble gases. Spraying of liquid is carried out by mechanical or pneumatic nozzles or centrifugal sprayers. Pneumatic injectors operate under the influence of compressed air or steam under excess pressure up to 5 atm. Centrifugal sprayers are made in the form of discs rotating at high speed. The speed of the discs is 4000-20000 rpm. The injection absorbers operate at low gas velocities (1-1.5 m/s) and irrigation densities of at least 0.003 m3/(m2s) [2,3,9]. 3.4. Adsorption

Adsorption is the process of selective absorption of one or several components of a gas or liquid mixture by the surface of a solid absorber (adsorbent). 204 

The absorbed component (AC) contained in a continuous environment (gas, liquid) is called the adsorbtive contained in the sorbent – adsorbate. The adsorption process is accompanied by the release of heat, the value of which depends on the nature of the interaction of adsorbed molecules with the surface. According to this, physical and chemical adsorption are distinguished. Physical adsorption is due to the action of van der Waals forces. The amount of heat released during adsorption roughly corresponds to the evaporation heat values (1-5 kcal/mol for simple molecules and 10-20 kcal/mol for large molecules). Physical adsorption – a reversible process. Chemical adsorption – an irreversible process. The amount of heat released during chemical adsorption is close to the amount of heat of the chemical reaction (10-100 kcal/mol). Chemical adsorption increases with increasing temperature, physical adsorption decreases with increasing temperature – desorption occurs. Adsorption is used to purify gas (liquid) mixtures from undesirable impurities or to isolate this impurity as a target product; optimal is the realization of both objectives together, i.e. approach of technology to wasteless. Due to selectivity of absorption of various components, adsorption is one of the effective separation processes. At the same time, it constitutes one of the stages of carrying out a heterogeneous chemical reaction, catalytic or non-catalytic. After adsorption, the adsorbent is desorbed. This allows you to extract AC (often – the target product) from the sorbent and reuse the sorbent released from it. To do this, it is necessary to activate the sorbent to restore its adsorption properties. The stages of desorption and activation of the adsorbent are its regeneration. Adsorption is widely used in chemical technology: – for drying of gases and their purification with allocation of target components; – for extraction (regeneration) of solvents from gas or liquid mixtures; – for clarifying solutions; – for cleaning gas emissions and waste water; – for analytical purposes (chromatography method). 205 

 

The success of the adsorption process is largely determined by the choice of adsorbent. Basic requirements for adsorbents: – selectivity; – possible high absorption capacity; – acceptable cost and availability; – ease of desorption and regeneration; – high mechanical strength; – convenience in work; – incombustibility, low erosive impact on the elements of equipment. In accordance with the requirement of high absorptivity, adsorbents – most often highly porous solids used in the form of grains ranging in size from a fraction of a millimeter to several millimeters. Depending on the size, micropores, intermediate pores (mesopores), macropores are distinguished. Micropores include pores with a radius of up to 20 Å (1 Å = 10-10 m), they are commensurable with the size of AC molecules. The specific surface area ranges from several hundred to 2000 m2/h. Intermediate pores with a radius of 20 to 1000-2000 Å are considered; the specific surface area is from 10 to 500 m2/h. It is believed that the mesopores perform two roles: the proper adsorption and transport (transfer of AC molecules to micropores). Macropores (their radius exceeds 2000 Å) differ by a small specific surface (up to several square meters per gram). Their main role – transport: the transfer of AC to micro- and mesopores. The most common industrial sorbents include: activated carbons (AC), silica gels and alumogels, zeolites, ion exchangers [2,3,6,9]. 3.4.1. Equilibrium between phases

During adsorption, gas or vapor molecules concentrate on the surface of the adsorbent under the influence of molecular forces of attraction. This process is often accompanied by chemical interaction, as well as condensation of steam in the capillary pores of the solid adsorbent. There is no generally accepted theory of adsorption. 206 

 

According to the widespread view, adsorption occurs under the action of electrical forces caused by interaction of charges of molecules of the adsorbent and the substance being placed. According to another theory, adsorption forces are of a chemical nature, and their nature is explained by the presence of free valences on the surface of the adsorbent. Regardless of the nature of the forces that cause adsorption, with sufficient contact time of the phases, an adsorption equilibrium occurs, at which a definite relationship is established between the concentration of the adsorbed substance X (in kg/kg of the adsorbent) and its Y concentration in the phase contacting with the adsorbent: /

,

(3.78)

where Y – the equilibrium concentration (kg/kg of the inert part of the vapor-gas mixture or solution); A and n – coefficients determined experimentally, with n  1.

Dependence (3.78) corresponds to a certain temperature and is depicted by a curve, which is called the adsorption isotherm. The adsorption isotherms of some substances are shown in Fig. 3.11. The concentration of the adsorbed substance in the mixture at constant temperature is proportional to its pressure. Therefore, the equation (3.78) can be represented in the form /

,

(3.79)

where A1 – the proportionality coefficient; P – the equilibrium pressure of the absorbed substance in the vapor-gas mixture.

The main factors influencing the course of the adsorption process are: the properties of the adsorbent, temperature, pressure, properties of the substances absorbed and the composition of the phase from which they are adsorbed. The equilibrium concentration X decreases with increasing temperature and increases with increasing pressure. Thus, adsorption accelerates with decreasing temperature or with increasing pressure. The same factors influence the desorption process, which is usually carried out after adsorption, in the opposite direction. Desorption is accelerated with an increase in the temperature of the 207   

adsorbent and a decrease in the pressure above it, as well as when passing through the adsorbent the vapors that displace the absorbed substance.

Fig. 3.11. Adsorption isotherms (at 20 oC): 1 – for ethyl ether; 2 – for ethyl alcohol; 3 – for benzene

Adsorbents are characterized by static and dynamic activity. After a certain period of work, the adsorbent ceases the completely absorb the extracted component and begins to “slip through” the component through the adsorbent bed. From this moment, the concentration of the component in the off-gas vapor mixture increases until equilibrium is reached. The amount of substance absorbed by a unit of weight (or volume) of the adsorbent during the time from the beginning of adsorption to the onset of a “slip through” determines the dynamic activity of the adsorbent. The amount of substance absorbed by the same amount of adsorbent during the time from the onset of adsorption to the establishment of equilibrium, characterizes the static activity. The activity of the adsorbent depends on the gas temperature and the concentration in it of the absorbed component. The consumption of adsorbent is determined by its dynamic activity, since dynamic activity is always less than static activity [7,9]. 208 

 

3.4.2. Material balance of adsorption process

Adsorption processes are carried out periodically or continuously. If the adsorbent moves through the apparatus, adsorption occurs continuously and the material balance of the process is expressed by equation (3.5), which is common for all mass transfer processes. Adsorption in a layer of a fixed adsorbent is a periodic (batch) process in which the concentration of the absorbed substance in the adsorbent varies in time and in space. Assume that the gas (in the amount G per unit time), passing through the time d, the adsorbent layer with a height dh, changes its concentration by a value dy and, consequently, gives the substance in an amount (3.80) At the same time, the concentration of the absorbed substance in the layer element increases by dx, and the amount of subtance absorbed by the layer with a height dh at the cross-sectional area of sorbent S will be ,

(3.81)

where bulk – the bulk weight of the adsorbent.

Then the equation of material balance will have the form [3,9]: (3.82)

or (3.83)

3.4.3. Kinetics of adsorption

Adsorption refers to the processes of mass exchange occurring with the participation of the solid phase. Within the solid phase, the substance moves due to mass conductivity. But experience shows that the internal diffusion resistance of the sorbent can be neglected, the calculation of the process of mass exchange during adsorption 209 

 

can be carried out using the equation of convective diffusion (3.45). The mass emission coefficient in equation (3.45) can be determined from the following equations: 1) for a granular adsorbent under laminar motion (Re 0. Such mixtures are called zeotropic. Konovalov’s first law retains the sense characteristic of ideal mixtures: in an equilibrium state, the vapor phase is enriched in the low-boiling component in comparison with the liquid phase. The equilibrium phase compositions using the diagrams t – x – y and х – у are determined graphically – by the same construction as for ideal binary systems.

Fig. 3.15. The diagram P(x) for real binary mixtures: 1 – the straight line following Raoult’s law; (–) and (+) – negative and positive deviations from Raoult’s law

Great deviations from ideality. For some mixtures, deviations from ideality are so great that the curves P(x) pass through an extremum. The specific value x for the extremum point depends on the properties of the components. The diagrams P(x) with the extreme pressure (maximum or minimum) are shown in Fig. 3.16, a,d. Mixtures with an extreme deviation of ideality follow the second law of Konovalov (see Fig. 3.16, a,b,d,e): the maximum on the pressure curve corresponds to a minimum on the boiling curve; the minimum on the pressure curve corresponds to a maximum on the boiling temperature curve. Since systems with a maximum pressure and a minimum boiling point are encountered more often, we consider in more detail. There are two branches on the curve Р(х) (Fig. 3.16,a): the ascending dP/dx > 0 for it and the descending dP/dx < 0, and also the maximum point, where the tangent is horizontal and dP/dx = 0. In the diagram t – x, y (Fig. 3.16,b), the first region, as in the case of zeotropic mixtures, is characterized in the equilibrium state by the 216 

 

inequality у > х. However, for the second region у < х, i.e. the vapor phase in comparison with the liquid is enriched in HBC. If for dP/dx > 0 the у > х is fair, and for dP/dx < 0 the у < х is true, then the equation dP/dx = 0 corresponds to у = х, i.e. equality of equilibrium concentrations in the liquid and vapor phases for a certain composition of the liquid mixture xaz. A mixture of such a composition is called azeotropic or inseparably boiling, and a mixture of components having an azeotropic point A at a certain concentration xaz – is azeotrope-forming. In the diagram у – х (Fig. 3.16,c), for such a mixture there are also regions у > х and у < х; the point of intersection of the equilibrium line with the diagonal corresponds to azeotrope (y = x).

Fig. 3.16. The diagrams P – x (a, d), t – x, y (b, e) and x – y (c, f) for azeotrope-forming mixtures

217 

 

Compositions of azeotropic points, depending on the properties of the components, are mixed with a change in pressure in accordance with the rule of Vrevsky: in the case of mixtures with a minimum of boiling points, with increasing pressure, the concentration of the component with a higher molar heat of vaporization increases, and in the case of mixtures with a maximum boiling point – a smaller one. The displacement of the point of the azeotrope with a change in pressure can be used to separate the azeotrope-forming mixtures, including mixtures of an azeotropic composition, into very pure components. Mixtures of mutually insoluble components. Practically mutually insoluble are liquids with negligible solubility in each other. Such mixtures form two layers and can be separated by upholding. A system consisting of two mutually insoluble components and three phases (two liquid and one vapor), according to the phase rule, has one degree of freedom. It follows that each temperature of the mixture corresponds to a strictly defined pressure, and each component of the mixture behaves independently of the other. Accordingly, the partial pressure of each component does not depend on its content in the mixture and is equal to the vapor pressure of the pure component at the same temperature. In the P – x diagram (Fig 3.17,a), the partial pressure and total pressure lines are straight lines parallel to the abscissa. In Fig. 3.17 also shows the phase diagrams t – x – y (b) and х – у (c) for binary mixtures of mutually insoluble components. In the diagram t – x – y, the values tA and tB – the boiling points of the pure components A and B, and S – the boiling point of the mixture. The boiling point of the mixture is always below the boiling point of the pure components that make up the mixture. This property is used in the technique to separate water-insoluble liquids by distillation with water vapor. Mixtures of liquids that are limitedly soluble in each other. For such systems, when one liquid is added to another (for example, phenol to water), they first completely dissolve into each other, then form two layers at certain concentrations and behave like insoluble 218 

 

liquids: their amounts change, but the liquid phase remains constant. Such mixtures are called heteroazeotropic. Heterozeotropic mixtures can be considered as general, including as a partial mixture with both an azeotrope and mutually insoluble components. As shown in Fig. 3.18 when the points ′ and ′′ are shifted to the point S (i.e., when the horizontal plateau ′ ′′ is contracted at the point), an azeotropic mixture is obtained. When the point ′ is shifted to the vertical x = 0 and the point ′′ to the vertical x = 1, we have a mixture of mutually insoluble components [2,6,9].

Fig. 3. 17. Diagrams Р – х (а), t – x, y (b) и х – у (c) for mutually insoluble components

Fig. 3.18. The diagrams Р – х (а), t – x, y (b) и х – у (c) for the mixtures with a limited mutual solubility

219 

 

3.5.3. Material balance of simple distillation

When considering the processes of distillation, it is assumed that the vaporization takes place very slowly and that equilibrium is established between the liquid and the vapor. Consider the material balance of simple distillation. We denote by G – the amount of liquid in the cube, and by x – its composition. The content of the low-boiling component in the liquid is Gx. When a small amount of liquid dG having a composition x evaporates, the liquid concentration decreases by dx and the remainder of the liquid in the cube is expressed by the quantity (3.93) and its composition will be (3.94) The content of the low-boiling component in the liquid residue is (3.95) The amount of the distillate is equal to the amount of the evaporated liquid dG, and the composition of its y is in equilibrium with x. The material balance of the volatile component can be represented by the time interval under consideration in the following form (3.96) or (3.97) Neglecting the product dGdx as an infinitesimal second-order quantity, we obtain 220 

 

(3.98) or (3.99) We denote the amount of liquid in the cube after distillation through G1 and its composition through x1, equation (3.99) can be integrated in the range from G1 and x1 to G and x. We get (3.100) or 2,3

(3.101)

The integral of the right-hand side of equation (3.101) is determined graphically. To do this, plot the x values on the abscissa and the corresponding values along the axis and find the area bounded by the curve, the x axis, and the vertical ones drawn through the abscissas x1 and x. This area is equal to the desired integral (Fig. 3.19).

Fig. 3.19. To the calculation of simple distillation

221 

 

The amount of distillate G – G1 = Geq obtained and its composition xeq are determined from the equation of material balance of the volatile component (3.102) whence (3.103) A simple distillation is carried out at atmospheric pressure or under vacuum, connecting the distillate collectors to a vacuum source. The use of vacuum makes it possible to separate thermally low-stable mixtures and, due to a decrease in the boiling point of the solution, to use for the cube heating a steam of lower parameters [2,3,9]. 3.5.4. Distillation with water vapor

The boiling point of an inhomogeneous mixture of insoluble liquids is always below the boiling point of the lowest boiling point. It follows that if water is added to a liquid that is immiscible with water and boiled at high temperatures, the boiling point of such a mixture at atmospheric pressure will be below 100 °C. The total vapor pressure over the mixture is equal to the sum of the elasticities of the components in pure form at the same temperature ,

(3.104)

from which the partial pressure of water vapor over the mixture (3.105) At atmospheric pressure, p = 760 mm Hg. col. the partial pressure of water vapor will be 760 222 

 

(3.106)

and a saturated water vapor with a pressure of less than 760 mm Hg.col. is below 100 °C. Due to the low boiling point of water with water vapor, liquids are easily distilled in a pure form having a very high boiling point at which the substance can partially decompose. In this way, with water vapor under atmospheric pressure at temperatures below 100 °C, fatty acids, aniline, nitrobenzene, turpentine, etc. are distilled. Distillation with water vapor is usually carried out in distillation cubes equipped with a steam jacket to preheat the original mixture to the distillation temperature and a bubbler through which the hot steam is supplied. If the initial mixture contains water, the “sharp” steam is started to pass only after the water distillation from the mixture. The distillable product after condensation is separated from the water with which it is not mixed, by sedimentation or centrifugation. The steam flow rate for distillation is theoretically determined from the relationship ∙

(3.107)

∙

In practice, the water vapor leaving the distillation apparatus is not completely saturated with the vapors of the distilled component. Therefore, practical GB is always more theoretically determined. Taking this into account, the saturation factor  ∙ ∙

(3.108)

The value  depends on the hydrodynamic mode of distillation [3,9]. 3.5.5. Rectification

The rectification is the process of separating liquid homogeneous mixtures into constituent substances as a result of the counter-current interaction of a mixture of vapors and a liquid resulting from the condensation of vapors. When the vapor rising in the column with 223 

 

the downward flowing liquid partially condensed vapor and partial evaporation of the liquid take place. In this case, the high-boiling component (HBC) predominatly is condensed from the vapor phase, and the low-boiling component (LBC) evaporates from the liquid. Thus, the flowing liquid is enriched with a high-boiling component, and the vapors are enriched by the LBC. At the top of the column (Fig. 3.20) there are vapors consisting of one LBC, and with their condensation a rectificate is formed.

Fig. 3.20. Scheme of rectification column

Part of the rectificate enters the top of the column for irrigation and is called phlegm. From the bottom of the column a liquid flows, consisting mainly of the HBC, it is called the vat residue. The interaction of vapor and liquid on the distillation column plate can be followed on the t–x–y diagram for the binary mixture (Fig. 3.21). The vapors A from the bottom plate n 1 are mixed on the overlying plate n with the liquid (phlegm) B. Par A and phlegm B are not equilibrium, and therefore their figurative points do not lie on the isotherm. The temperature of the steam tA is above the phlegm temperature tB, so the steam is partially condensed when mixed with reflux, and 224 

 

due to the heat of condensation, part of the liquid evaporates. The LBC predominantly evaporates from the liquid, but from the vapor mainly the HBC condenses. The steam is enriched by the LBC, and the figurative point A is shifted along the condensation line and at the moment of equilibrium it will take the position D.

Fig. 3.21. To the analysis of the process of rectification on a plate: diagram t–x–y for a binary mixture

At the moment of equilibrium, the temperature of the vapor and liquid is the same, then the figurative phlegm point, equilibrium to vapor of composition D, is located on the isotherm tD, which is denoted by g. On the considered plate, n vapors will be enriched with a volatile component, changing their composition from yA to yD, and phlegm will be enriched by a higher-boiling component, according to which its composition changes from xB to xg [3,9]. 3.5.6. Calculation of the number of plates of the rectification column of continuous action for separation of binary liquid mixtures

The degree of separation of the liquid mixture into constituent components and the purity of the resulting distillate and vat residue depend on the phase contact surface. The surface of the phase contact is determined by the amount of irrigated phlegm and the design of the apparatus. The number of phlegm fed for irrigation is determined by the number of theoretical plates in the column. 225 

 

Several methods for calculating the number of theoretical plates have been developed, of which the graphical method of Mac Cab and Thiele (since 1925) is widely used for binary mixtures. The method is based on the following assumptions: 1. The molar heat of evaporation of both components is the same. 1 kmol of condensed vapor evaporates 1 kmol of liquid. Therefore, the amount of vapor and liquid in the column height does not change, but only their composition changes. 2. The initial mixture and phlegm have a temperature equal to their boiling point. 3. The composition of phlegm is equal to the composition of steam rising from the top of the column, i.e. in the dephlegmator there is no change in the composition of the vapor. 4. The composition of the liquid draining from the last plate and the bottom column is equal to the composition of the steam rising from the boiler, i.e. the cube does not produce a separating action. The equations of the working lines of the rectification process, necessary for calculating the number of theoretical plates, are deduced, as for the mass exchange process, from the equation of material balance. In general, the equation has the form: (3.109) In the case under consideration, we express the quantities G and L. The amount of steam rising up the column V after the reflux condenser gives a liquid to the top of the column (phlegm) P and the distillate Gr (3.110) By introducing dimensionless relations, we obtain 1

The dimensionless ratio

is – called the reflux ratio.

Thus, the equation (3.109) takes the form: 226 

 

(3.111)

1

(3.112)

In the continuous column, the amount of vapor and the amount of liquid remain unchanged, so we take the quantities R + 1 and R out of the integral sign and for any plate in the upper part of the column with which the vapor with composition y leaves and on which the liquid has composition x, taking into account the presence of a counterflow, we get 1

,

(3.113)

whence 1

(3.114)

and after the transformation, taking into account by the condition yeq = хeq, (3.115) The resulting equation establishes a relationship between the composition of the vapor and the composition of the liquid in any section of the upper part of the column for given irrigation values (phlegm ratio R) and composition of rectificate xr. Dependence (3.115) is the equation of the working line of the upper (strengthening) part of the rectification column. Similarly, we obtain the equation of the working line of the lower part of the column, taking into account that the amount of flowing liquid in this part of the column increases by the amount of feed F. We write the equation of material balance for the lower part of the column: 1



(3.116)

We integrate it within the limits of the change in the vapor composition from yw to y and the liquid from x to xw: 227 

 

1

,

(3.117)

whence 1

,

(3.118)

where уw – the composition of steam rising from the boiler, хw – the composition in mole fractions of the bottom liquid.

After the transformation, taking into account the condition that хw=уw, we obtain (3.119) Dependence (3.119) is the equation of the working line of the lower (exhaustive) part of the distillation column. For a continuous column, the following quantities remain constant: ,

,

,

,

(3.120)

then the equations of the working lines of the process are the equations of straight lines [2,3,9]: ,

(3.121) (3.122)

3.5.7. Rectification under different pressures

Depending on the boiling point of the separated liquids, the rectification is carried out under various pressures. At tboil = 30-150 oC, the rectification is usually carried out at atmospheric pressure. When the high-boiling liquids are separated to reduce their boiling points, the rectification is carried out under vacuum. Pressure rectification is carried out in the separation of liquids with a low boiling point, when the separated mixture is at atmosphe228 

 

ric pressure in the gaseous state (an example is the separation of liquefied gases). The pressure in the cube is always greater than the pressure at the top of the column by the amount of its hydraulic resistance. Therefore, the hydraulic resistance of columns operating under vacuum should be as small as possible [3,9]. Questions for self-control: 1. What is meant by simple distillation? What are the types of simple distillation? 2. Show the scheme of the distillation process with dephlegmator, expand its advantages over simple distillation. 3. Give the rule of phase and equilibrium in liquid-vapor systems. 4. What is the difference between real and ideal mixtures? 5. Formulate Konovalov’s first and second laws. 6. Describe the diagrams P – x, t – x, y and x – y for azeotropic mixtures. 7. Give a comparative analysis of the diagrams P – x, t – x, y and x – y for mutually insoluble components and for mixtures with limited mutual solubility. 8. Expand the principle of drawing up the material balance of simple distillation, determining the amount of vat residue, distillate and its composition at simple distillation. 9. What is the essence of steam distillation? 10. Expand the principle of rectification. Draw a diagram of the distillation column and indicate the flow of liquid and vapor on it. 11. What physical content is contained in the equations of working lines of the process of continuous rectification? 12. Give the assumptions of the graphic method of Mac Cab and Thiele to calculate the number of theoretical plates. 13. How does the phlegm number affects the number of required theoretical plates? 14. What factors determine the required diameter of the rectification column? 15. When is rectification performed under pressure?

3.6. Extraction

Extraction is the process of extracting one or more components from a mixture of substances by treating it with a liquid solvent that has the ability to selectively dissolve only recoverable components. In the chemical industry, extraction in liquid-liquid systems is most common. Liquid extraction involves two technological operations: 229 

 

– contacting the initial mixture with the solvent, during which the actual mass-exchange process is carried out, i.e. transition of a component through the interface from one phase to another; – separation of the resulting solution from the remaining liquid mixture. Thus, liquid extraction assumes incomplete mutual solubility of the initial mixture and solvent – otherwise the second operation is unworkable. The operation of contacting the phases is usually carried out by distributing (splitting) one phase in the form of drops in the volume of the other. Separation of liquid mixtures by extraction is carried out at low temperatures, which makes it possible to separate a mixture consisting of thermally unstable components. Extraction can be divided into azeotropic mixtures, as well as mixtures consisting of closely-boiling components. An extract is called an extragent containing the recovered component and a portion of the starting solvent. The initial mixture, depleted by the extractable component and containing a certain amount of extragent, is called a raffinate. The extragent must have selectivity, easy regenerability, differ from the initial solution in density and viscosity, providing the process of phase separation. In addition, the extragent should, if possible, be low-volatility, non-toxic, affordable and low-cost. Extraction includes the following basic operations: 1) mixing of the initial mixture of substances and extragent for the purpose of closer contact between them; 2) mechanical separation of two immiscible phases into so-called extract and raffinate; 3) removal and regeneration of the extragent from the extract and raffinate. Separation of the formed phases can occur due to the difference in densities, or under the action of the field of centrifugal forces. Regeneration of the extragent from the raffinate and extract can be carried out by distillation, rectification, evaporation and other methods. Industrial methods of extraction can be carried out in the apparatus of periodic and continuous action. In the first, the initial mix230 

 

ture and the solvent are charged periodically, and during the extraction process, only one component of the initial mixture can be continuously released. In continuous installations, loading of the initial mixture and the solvent is carried out continuously, and both components of the separated initial mixture are continuously separated. Currently, liquid extraction is used in chemical technology, hydrometallurgy, analytical chemistry for extraction, separation, concentration and purification of substances. Extraction processes are used in the production of organic products, antibiotics, food products, rare earth elements, a number of rare, non-ferrous and noble metals, in nuclear fuel technology, in wastewater treatment [2,3,9]. 3.6.1. Physical basics of the extraction process

The physical essence of extraction consists in the transition of the extracted component from one phase to another – the phase of the extragent – upon mutual contact of the initial mixture and the extragent, as a result of the system’s striving for a state of equilibrium. In a state of equilibrium at a certain temperature, the concentrations of the dissolved substance in the extract and in the raffinate are in a functional relationship (3.123) This dependence on the diagram in the х–у coordinate system can be represented as a curve whose course is determined experimentally on the basis of simple measurements (Fig. 3.22). Sometimes equilibrium can be depicted in the х–у diagram as a straight line or by the equation ,

(3.124)

where kd – a constant at a given temperature, is called the distribution coefficient.

In this case, the system obeys the law of equilibrium distribution of matter between the extract and the raffinate. Equation (3.124) is valid under the condition that the initial solvent and the extragent are mutually completely insoluble, there 231 

 

is no association or dissociation of the molecules of the extracted substance and there is no chemical interaction between the phases. The extraction processes obey the general laws of mass transfer. The equation of material balance for the extraction process in general form can be written as: (3.125) Equation (3.125) is integrated within the limits depending on the extraction conditions. Let us consider the case when the liquids are mutually insoluble. The solvent is used as a pure, not used, and therefore the initial content of the dissolved substance in it is y0 = 0. Let x0 denote the initial content of the extracted component in the initial mixture, and let x1 denote the final content of the extracted component in the same mixture, the final content of the extractable component in the extragent as y1. Then, with a single contact of liquids (the initial mixture and the extragent), the material balance equation is integrated in the range from xo to x1 and from 0 to y1, i.e. ,

(3.126)

whence (3.127) From equation (3.127), the working line on the diagram in the х–у coordinates will be a straight line with a negative tangent of the slope angle (Fig 3.23):

(3.128)

In Fig. 3.23 the straight line of the working line FE crosses the equilibrium curve at the point E, determining the composition of the extract y1 and raffinate x1. 232 

 

Fig. 3.22. Extraction equilibrium at complete mutual insolubility of solution and extragent

Fig. 3.23. The position of the working line with a single contact

If the distribution law is valid, then the combined solution of the equilibrium equation (3.124) and equation (3.127) leads to the relation: (3.129) or ,

(3.130)

whence (3.131) Equation (3.131) makes it possible to calculate the composition of the liquid after extraction [3,9]. 3.6.2. Triple systems

With the partial mutual solubility of the phases A and C, each of the phases during extraction will be a three-component solution whose composition cannot be depicted in the diagram with the coordinates x – y. It is convenient to represent the compositions of 233 

 

such three-component phases in a triangular coordinate system – on the so-called triangular diagram (Fig. 3.24). The vertices of an equilateral triangle A, B and C are pure components: the solvent of the initial solution – A, the extragent C and the distributable substance B. Each point on the sides AB, BC and CA corresponds to the composition of two-component solutions (Fig. 3.24).

Fig. 3.24. Triangular equilibrium diagram of a three-component mixture

Each point on the area inside the diagram corresponds to the composition of a three-component solution (or a triple mixture). To measure the content of each component in the solution, scales are plotted on the sides of the diagram, with the length of each side taken as 100 % (by weight, by volume or by mole) or per unit. The composition of the solution or mixture is determined by the length of the segments drawn parallel to each side of the triangle before crossing with the other two. For example, point g characterizes a triple mixture consisting of 70 % of solvent A, 10 % of solvent C and 20 % of the distributable substance B to be distributed. The lengths of the perpendiculars dropped from point g to the sides of an equilateral triangle are 234 

 

proportional to the content of the corresponding components in the mixture. The rays Aa, Bb, Cc drawn from the vertices of the triangle (see Fig. 3.24) are the geometric locus of the figurative points of the mixtures with a constant ratio of the content of the other two components хВ/хС, хА/хС, хА/хВ, respectively. The lines dd, ee, ff, parallel to the sides of the triangle AC, BC, AB, are the geometrical place of the figurative points of mixtures with a constant content of components B, A, C, respectively. Mixing processes on a triangular diagram. The rule of the lever. When mixing two solutions whose compositions are characterized in the diagram by any points a and b, the total composition of the mixture is expressed by the point c lying on the line ab, connecting these points (Fig. 3.25). The position of point c on the straight line is determined by the rule of the lever if the quantities of the taken solutions are known. The segments ac and bc are inversely proportional to the masses of the solutions taken (Fig. 3.25): (3.132) Then ;

/

/

(3.133)

; ;

/

/

/

,

(3.134)

where Ga, Gb, Gc – the mass of the components of mixture a, b and c, kg; xa, xb, xc – the mass fractions of any component (A, B and C) in mixture a, b and c,%. ′ ′ ′ ′ In Fig. 3.26: the line the boundary (binodal) curve. The field inside this curve is the region of mixtures that are stratified into two coexisting phases whose composition is expressed by points on the curve. The field outside the boundary curve is the region of non-dissipating (homogeneous) solutions. The point K is a critical point.

235 

 

Fig. 3.25. Rules of the lever in the relations of material balance during extraction

Fig. 3.26. Isothermal equilibrium diagram of liquid-liquid systems

Material balance of extraction. The material balance of extraction is expressed by the equation (3.125) common to mass-exchange processes. In the case of partial mutual solubility of t h e phases A and C, their values will no longer be constant in the height of the apparatus, and consequently, the ratio A/C will be variable. In case of partial mutual phase solubility, the working extraction line in the x – y coordinate system will not be a straight line. The equation of material balance by general flows in this case will have the form

,

(3.135)

where F and R are respectively the quantities of the initial solution and the resulting raffinate, kg/s; S and E are respectively the amounts of extragent and extract obtained, kg/s.

If equation (3.135) is rewritten in the form , the equation of material balance can be represented graphically on a triangular diagram (Fig. 3.27) as a process of mixing the initial flows F + S (with the formation of a triple mixture represented by a point M, and the subsequent separation of this triple mixture M into final flows R + E). 236 

Fig. 3.27. To drawing up a material balance of the extraction process

From the diagram according to the rule of the lever (3.136) you can find the amount of extragent required for the process (3.137) or the ratio between the amounts of the raffinate and extract streams obtained (3.138) as well as the composition of any of the flows, if the compositions and quantities of the other three streams are given [2,4,8,9]. Questions for self-control: 1. Explain the meaning of the process of liquid extraction. Show the scheme of the process, the scope of application. 2. How is the equilibrium composition and phase state of the three-component liquid mixture determined by the triangular phase diagram? 3. List the main requirements for the extragent.

237 

 

4. What is the physical meaning of the rule of the lever for the processes of periodic extraction? 5. Formulate the distribution law and explain the extraction isotherms. 6. Explain the triangular diagrams and the construction of equilibrium (binodal) curves. 7. What are the stages of the extraction process? 8. Explain the physical content of the material balance equations for the mixingslopping stage of continuous extraction. 9. What processes are used to regenerate the extragent? 10. What devices are used in chemical technology for extraction?

3.7. Drying 3.7.1. General information

Drying is the process of removing moisture from damp materials by evaporating it. Moisture can be removed from materials by mechanical ways (spinning, upholding, filtering, centrifugation). However, more complete dehydration is achieved by evaporation of moisture and evacuation of formed vapors, i.e. with the help o f thermal drying. By the method of supplying heat to the dried material, the following types of drying are distinguished: 1) convection drying – by direct contact of the dried material with a drying agent, which is usually heated air or flue gases; 2) contact drying – by transferring heat from the heat carrier to the material through the wall separating them; 3) radiation drying – by transferring heat by infrared rays; 4) dielectric drying – by heating in the field currents of high frequency; 5) freeze-drying – drying in a frozen state with a deep vacuum. The last three types of drying are relatively rare and are called special types of drying. The dried material under any drying method is in contact with wet gas (air), i.e. in the drying process, the main role belongs to drying agents. In industrial conditions, air is mainly used as the heat carrier for convective drying [2,3,9]. 238 

3.7.2. Main parameters of wet air

Air always contains some moisture. A mixture of dry air and water vapor is wet air. Wet air is characterized by the following basic parameters: absolute and relative humidity, moisture content and enthalpy (heat content). Absolute humidity is the amount of water vapors contained in 1 m3 of humid air (g/m3, kg/m3). Air with the maximum content of water vapor at a given temperature is called saturated. The amount of water vapor is determined by the temperature of the air. Relative humidity or degree of air saturation  is the ratio of the mass of water vapor Mw.v., located in 1 m3 of wet air, to the maximum mass of vapor Mm.v.v. that can be contained in 1 m3 of humid saturated air at a given temperature and pressure: М . . М . . .

∙ 100

∙ 100%,

(3.139)

where v – the vapor density, kg/m3; s.v. – density of saturated vapor, kg/m3.

The vapor density is proportional to its partial pressure, therefore, the relative humidity can be expressed by the ratio of pressures ,

(3.140)

where pv – the partial pressure of water vapor corresponding to its density; ps – the saturated vapor pressure at the same temperature.

If air is cooled, then its relative humidity increases. The temperature corresponding to the saturated state of vapor in air ( = 100 %) at a given partial pressure is called the dew point (td.p.). When the air is cooled below the dew point, condensation of water vaporы occurs. The amount of water vapor in humid air, referred to 1 kg of dry air, is called the moisture content (kg/kg): ∙ 239 

 

(3.141)

Substituting in the last equation (from equation (3.140)), 18, 29, we obtain the dependence of the moisture content of air on its relative humidity ∙

(3.142)

The enthalpy of humid air (I) refers to 1 kg of absolutely dry air and is determined at a given air temperature t (oC) as the sum of the enthalpies of absolutely dry air and water vapor: с

. .

,

(3.143)

where сd.a. – specific heat of dry air, J/kgK; t – the air temperature, K; iv – enthalpy of superheated vapor, J/kg.

The enthalpy of steam is determined by the empirical formula: 2493

1,97 ∙ 10

(3.144)

where ro = 2493∙103 – constant coefficient, approximately equal to the enthalpy of vapor at 0 oC; сv = 1,97103 – specific heat of vapor, J/kgК.

Representing the value iv in expression (3.144) and accepting сd.a. = 1000 J/kgK as a constant value, we find the enthalpy of humid air 1000

1,97 ∙ 10

2493 ∙ 10

,

(3.145)

where x – the moisture content, kg/kg of dry air [2,3,9].

3.7.3. Statics of drying

The statics of the process is the consideration of the equilibrium data, on the basis of which the direction and possible limits of the process are determined. Wet material gives off moisture by evaporation into the environment. Environment is wet air. Therefore, the drying process will only take place if the vapor pressure of moisture at the surface of the dried material pm is greater than the partial pressure of water 240 

 

vapor in air pw.v.. That is, the condition for drying is the inequality pm > pw.v.. When pm = pw.v. – the drying process stops. Each material can be dried only to an equilibrium moisture content (under atmospheric drying conditions). The equilibrium humidity is determined by the property of the material to be dried, the nature of the connection with it of moisture and the parameters of the environment. According to the theory of Academician P.A. Rebinder, there are three forms of the connection of moisture with the material: 1) chemical; 2) physico-chemical; 3) physico-mechanical. A chemical bond is characterized by a strictly defined molecular ratio (hydrate or crystallization water). The physicochemical connection of moisture with the material does not imply a strictly defined ratio (adsorption moisture, osmotic moisture, etc.). With the help of a physico-mechanical bond, water is held by the material in undefined proportions. The physico-mechanical form includes the structural bond, the capillary bond, and the wetting bond. When drying, first free moisture is removed, then the bound one. The boundary between free and bound moisture is called the critical moisture content of the material. The equilibrium humidity depends on the water vapor pressure, it is higher the more relative humidity of air [3,9]. 3.7.4. Material balance of drying

If the wet material is supplied to the drying in an amount of G1 kg/s with a humidity of u1 parts by weight, after drying, G2 kg/s of dried material with a moisture content of u2 parts by weight is obtained and wherein the moisture W kg/s is evaporated, then the material balance is expressed by the equality: for the whole quantity of the substance (3.146) for absolutely dry substance: 241 

 

1

1

(3.147)

From these equations, the amount of dried material G2 and evaporated moisture W is determined. For heat balance, it is necessary to know the air consumption for drying, which can be determined from the moisture balance. The moisture balance can be expressed by equality ,

(3.148)

from where the air flow is ,

(3.149)

where L – the amount of dry air, kg; xo – moisture content of humid air at the inlet to the dryer, kg/kg; x2 – moisture content of humid air at the dryer outlet, kg/kg; W – amount of moisture evaporated, kg.

Specific air consumption will be: (3.150) It follows from expression (3.150) that the air flow will be the greater, the higher the initial moisture content xo, which is determined by the temperature and relative humidity of the air. Other things being equal, the air flow will increase with increasing initial temperature and the initial relative humidity of the air. Consequently, the air consumption for drying in summer will be greater than in winter [2, 3, 9]. 3.7.5. Kinetics of drying

Drying is a complex diffusion process, the speed of which is determined by the rate of diffusion of moisture from the depth of the material to be dried into the environment. The drying process is a combination of the processes of heat and mass transfer (moisture exchange) associated with each other. 242 

 

By measuring the loss of the mass of the dried sample over time, it is possible to determine the change in moisture content ua as a function of time . The dependence of absolute humidity on time is called the drying curve. It follows from Fig. 3.28 that in the initial stage (section AB) the moisture content of the material decreases slowly and the heat is expended on heating the material from the initial temperature v1 to the temperature of the wet thermometer v = tw.t.. This is the heating stage of the material. In the BK section, the moisture content of the material falls linearly, the drying is characterized by a constant velocity with a constant surface temperature of the material, v = tw.t.. Starting from point K, the drying proceeds along the curve KC. The temperature of the surface of the material then continuously increases and, once the equilibrium moisture reaches equilibrium, becomes equal to the heating air temperature v = tair. Thus, the drying process is composed of a period of constant drying speed and a period of falling drying speed. The moisture content of the material at the point K is called the critical moisture content ucr.

Fig. 3.28. Curve of drying the material and changing its temperature during the drying process: v – surface temperature of the material; v1 – initial temperature of the material; tw.t. – the temperature of a wet thermometer; tair – air temperature; uin – initial humidity of the material; ucr – the critical humidity of the material; ueq – equilibrium humidity of the material

243 

 

The drying rate is determined by external diffusion (diffusion of moisture vapor from the surface of the material to the environment), i.e. by the temperature, humidity and rate of drying agent, but it does not depend on the moisture content of the material. The basic equation for the rate of evaporation is given in the following form: ′

∆

,

(3.151)

where С – the difference in the vapor concentration at the evaporation surface and in the ambient air; F – the evaporation surface;  – the evaporation coefficient, taking into account the aerodynamic conditions of evaporation and the physical properties of the liquid.

The coefficient  can be determined by knowing the value of the Nusselt diffusion criterion

′

,

(3.152)

where l – the length of the sample in the direction of air movement, m.

At forced motion of air to determine the diffusion Nusselt’s criterion the dependence (3.153) is used, ′

′

∙

(3.153)

The duration of a period of constant drying speed can be determined by the equation: ∙

′ ′

′

,

(3.154)

where K – the rate constant of the drying process (can be determined experimentally or through the mass emission coefficient to the gas phase); ′ , ′ , initial, critical, equilibrium moisture content of the material.

The speed of the second drying period is determined by internal diffusion, depends on the moisture content and temperature of the material and is practically independent of the speed and humidity of the air. The drying time of the material can be set exactly only by experienced specialists [3, 9]. 244 

 

3.7.6. Vacuum drying

Removal of moisture from materials poorly enduring the effects of high temperatures is carried out at low temperatures. Therefore, for the purpose of intensification, the drying process is carried out under vacuum. Advantages of vacuum drying are: 1) the driving force of the process increases, since with the pressure decrease in the dryer, the difference in vapor pressure of moisture over the material and in the environment increases; 2) complete removal of moisture is achieved; 3) valuable volatile solvents are captured; 4) the release of harmful gases and vapors from the dryer into the surrounding space is excluded; 5) due to the tightness of the system, contamination of the material is avoided. Vacuum drying technique: the dried material is placed in a hermetically sealed chamber, from which air is pumped out with the air pump together with moisture vapor. The moisture vapor is detected in the capacitors. Capacitors are barometric or superficial. Inside the chamber, there are coils, or plates, through which hot water or steam is maintained at a constant temperature during drying. Under the influence of a temperature gradient, moisture diffusion occurs in the direction toward the evaporation surface and its steam generation. Vacuum drying is a thermal diffusion process. The process of vacuum drying is a series of simultaneously proceeding complex processes – boiling, evaporation, condensation occurring in the pores and capillaries of a moist body, as well as an unsteady process of heat transfer, then the mathematical description of this process is very difficult [3,9]. 3.7.7. Drying of gases

Removal of water vapors from gases is necessary when the multicomponent gases are deeply cooled in order to separate them into fractions when transporting flammable gases through pipelines. 245 

During transportation, even at normal temperature, the gas can produce complex compounds with water, while paraffinic hydrocarbons are precipitated as complex compounds with water. Therefore, natural gas must be dried to a temperature of -10 °C before transporting them. Dehydration of gases is carried out by physicochemical (absorption, adsorption) and physical methods. Absorption methods are based on the absorption of moisture from gases by liquid substances, whose aqueous solutions have a low water vapor pressure (glycerin, diethylene glycol 85 %). Adsorption methods are based on the absorption of moisture from gases by solid substances – adsorbents. As adsorbents the solid CaCl2, NaOH, KOH, bauxite, alumogel, silica gel, molecular sieves are applied. Physical methods are based on cooling the drying gas in surface coolers with water or refrigerant, cooling after gas compression and sudden expansion of the compressed gas. The condensate which is then released from the gas is discharged through the separator [3,9]. Questions for self-control: 1. What methods of thermal drying are used in industry? 2. What are the main parameters of the steam-air mixture? How are they determined from the H – x diagram of the humid air state? 3. List and describe the types of connection of moisture with the material. 4. What is the form of recording the equations of material balance in terms of moisture in the material and in the drying agent? 5. What is the physical meaning of the specific consumption of the drying agent? 6. What is the type of typical drying curves and drying speed of wet materials? 7. What equation is used to calculate the duration of the constant drying rate period? 8. What is accepted as the driving force of the drying processes and how is their average value determined? 9. List the advantages of vacuum drying. 10. What are the special ways of drying? What is the scope of their

3.8. Crystallization

Crystallization is the process of formation of the crystalline phase from melts, solutions and the gas phase. This process is used in chemical, petrochemical, coke chemical, metallurgical, food, phar246 

maceutical and other industries. With the help of crystallization the following tasks are solved: – production of solid products in the form of blocks, granules, etc.; – separation of various mixtures into fractions enriched with one or another component; – separation of various substances from technical and natural solutions; – deep purification of substances from impurities; – concentration of diluted solutions by freezing the solvent; – growth of single crystals; – production of substances with certain physical and mechanical properties; – application of various coatings to the surface of solids, etc. Crystals are solid, chemically homogeneous bodies of regular shape that have anisotropy properties. Anisotropy is the dependence of some macroscopic properties of crystals on the direction. Depending on the nature of the dissolved substance and the crystallization temperature, anhydrous crystals or crystalline hydrates with a different number of water molecules can be released from aqueous solutions. Crystalline hydrates have a certain elasticity of water vapor. If the elasticity of their vapor exceeds the elasticity of water vapors in the air, then when crystals are stored in air they lose the crystallization water, weathered, if the elasticity of water vapor over the crystals is less than their elasticity in the ambient air, then, on the contrary, the crystals attract moisture from the ambient air [2,3,6,9]. 3.8.1. Physical basics of the crystallization process

The process of crystallization from solutions is based on the limited solubility of solids in liquid solvents. The solubility of substances depends on their chemical nature, solvent properties and temperature. A solution containing an excess of dissolved substance with respect to the saturation state at a given temperature is called supersaturated. A solution that contains the maximum possible 247 

 

amount of a substance at a given temperature is called saturated. The supersaturated solution is unstable, a solid phase can be isolated from it, i.e. to carry out the process of crystallization. Thus, one of the main factors that determine the crystallization process is the ability of the crystallized salt to form supersaturated solutions. The measure of the stability of supersaturated solutions is the value of the maximum supersaturation , determined by the relation С С

∆С

С

С

,

(3.155)

where C is the maximum possible concentration of the substance in the metastable supersaturated solution; Co is solubility of the substance at a given temperature.

The stability of supersaturated solutions increases with decreasing temperature with an increase in the cooling rate of the solution and the intensity of its mixing. The crystallization process consists of two stages – the formation of crystal nuclei and the growth of crystals. Both processes proceed simultaneously. If the rate of germinal crystal formation is very high, and the rate of their growth is small, a fine crystalline precipitate is formed and vice versa. Thus, in order to obtain a coarse crystalline product, the process must be carried out with a slight supersaturation, which is possible, all other things being equal, only by reducing the cooling rate of the solution (with isohydrogen crystallization) or the rate of evaporation (in isothermal crystallization) [3,9]. 3.8.2. Methods of crystallization and crystallizers

The centers of crystallization arise in a supersaturated solution in which the equilibrium is disturbed. In the production conditions, two methods are used to disturb the equilibrium and form a supersaturated solution: evaporation of a part of the liquid (crystallization with removal of the solvent particles) and cooling of the solution. The first method is used for substances in which the solubility depends little on temperature, or even increases with decreasing temperature. The second method is used for substances in which 248 

 

solubility decreases with decreasing temperature. The third, combined method, is simultaneous cooling and evaporation of part of the solvent (cooling under vacuum). According to the crystallization method, crystallizers can be divided into two groups: crystallizers requiring removal of a portion of the solvent and crystallizers operating without removal of the solvent, in turn, they are divided into batch (periodic) and continuous apparatus. To remove part of the solvent, cooling of the solution is carried out with air, or crystallization is carried out in a vacuum. In crystallizers operating without removing the solvent, water cooling is used. There is a rotary crystallizer, a tower-type crystallizer and vacuum crystallizers of various designs of periodic and continuous action. In vacuum crystallizers, a part of the solvent is simultaneously removed and the solution is cooled [3,9]. 3.8.3. Material balance of crystallization Crystallization by removing a portion of the solvent. The equation of material balance for the whole amount of substance

(3.156) Balance for an absolutely dry dissolved substance: ,

(3.157)

where Gi.sol. is the amount of initial solution, kg; Gcr is the number of crystals, kg; Gm is the amount of mother liquid, kg; W is the amount of evaporated solvent, kg; bsol is the concentration of the crystallizing substance in the initial solution, wt. parts; a is the concentration of the crystallizing substance in crystals, weight. %; bm is the concentration of the crystallizing substance in the mother liquid, wt. parts.

The weight of the crystals obtained is found by solving equations (3.156) and (3.157) (3.158) 249 

 

At a = 1 we have 1

(3.159)

Crystallization without solvent removal (W = 0). The number of crystals obtained

(3.160) At a = 1 we find (3.161) When the solvent evaporates into the gas (air), the gas flow rate (in kg) is determined from the equation ,

(3.162)

where L is the amount of dry gas (air), kg; x1, x2 is the initial and final moisture content of gas (air), kg moisture/kg dry gas [2,3,9].

3.8.4. Thermal balance of the crystallization process

When a solid crystalline substance dissolves, the heat qcr is absorbed to destroy the crystal lattice (the heat of fusion) and the release of heat during the chemical interaction of the substance with the solvent qsol (hydrate formation). Depending on the values qcr and qsol, the thermal effect of crystallization will be positive or negative. The equation of the thermal balance of continuous crystallization contains unequal terms for isothermal and isohydric crystallization. In isothermal crystallization, the heat balance equation is analogous to that for continuous evaporation (see Chapter 2): 250 

 



,

. .

(3.163)

where сin, сcr, cm are heat capacities of the initial solution, crystals and mother liquor, J/(kg∙K); tin, tcr, tm are the temperatures of the initial solution, crystals and mother liquid, оС; rcr is the heat of crystallization of the substance, J/kg; is.v.is the enthalpy of the solvent vapors removed, J/kg; is the heat supplied with the heat carrier, W; is the loss of heat to the environment, Wt.

When using a saturated water vapor as the heat carrier . .,

(3.164)

where D is the consumption of heating steam, kg/s; rh.s. is the heat of condensation of the heating steam, J/kg.

In isohydric crystallization (W = 0), the solution is cooled, and the heat balance equation has the form:

в.н



. .

,

(3.165)

where Gw and сw are consumption (kg/s) and heat capacity (J/(kg∙K)) of cooling water; tw.in., tw.f. are initial and final temperatures of water, оС [2,3,5,9].

Questions for self-control: 1. What does crystallization mean? For what purposes is crystallization used? 2. What is the basis of the crystallization process? 3. What is the difference between saturated solutions and supersaturated solutions? 4. Describe the methods of disturbance of equilibrium and formation of a supersaturated solution. 5. Describe the processes of nucleation and growth of crystals. 6. List the main factors that determine the rate of crystallization. 7. Give the differential and integral equations for the speed of the crystallization process. 8. Which summands are included in the equations of material balances of the processes of continuous crystallization? 9. What is the difference between the heat balance equations for the continuous processes of isohydric and isothermal crystallization? 10. Which industrial crystallizers are used for the crystallization process?

251 

 

BIBLIOGRAPHIC LIST 1. 2. 3. 4. 5. 6. 7. 8. 9.

Дытнерский Ю.И. Процессы и аппараты химической технологии. – М.: Химия, 1992. Часть 1. – 416 с. Касаткин А.Г. Основные процессы и аппараты химической технологии. – М.: Химия, 1973. – 752 с. Кривошеев Н.П. Основы процессов химической технологии. – Минск: Вышэйшая школа, 1972. – 304 с. Романков П.Г., Фролов В.Ф., Флисюк О.М. Примеры и задачи по курсу процессов и аппаратов химической технологии. – Санкт-Петербург: ХИМИЗДАТ, 2009. – 544 с. Фролов В.Ф. Лекции по курсу «Процессы и аппараты химической технологии». – Санкт-Петербург: ХИМИЗДАТ, 2003. – 608 с. Общий курс процессов и аппаратов химической технологии / Под ред. В.Г. Айнштейна. – М.: Университетская книга, Логос, Физматкнига, 2006. Кн. 2. – 872 с. Дытнерский Ю.И. Процессы и аппараты химической технологии. – М.: Химия, 1992. Часть 2. – 384 с. Плановский А.Н., Николаев П.И. Процессы и аппараты химической и нефтехимической технологии, – М.: Химия, 1972. – 496 с. Ешова Ж.Т., Акбаева Д.Н. Лекции по курсу «Основные процессы и аппараты химической технологии». – Алматы: Қазақ университеті, 2017. – 392 c.

252 

 

THE TEST TASKS HYDRODYNAMIC PROCESSES: Test tasks (1-30) (Topic 1.2): 1. The hydrodynamic processes are: A) Movement of gases and liquids. B) Heating of gases and liquids. C) Cooling of gases and liquids. D) Distillation of liquids. E) Condensation of vapors. F) Evaporation of liquids. 2. The volumetric flow of liquid or gas can be expressed in: A) m3/s. B) kg/h. C) m3/m3. D) dm3/h. E) kg/s. F) kg/m3. 3. The mass flow of liquid or gas can be expressed in: A) m3/s. B) dm3/h. C) m3/m3. D) kg/s. E) m2/m3. F) kg/m3. 4. The equation of continuity of a flow is expressed by the formula: . А) 0.785 B) ⋯ C) . D) 0.785 . E) . F) /. 5. The equation for the volumetric flow rate of a fluid for a round pipe is given by: А) 0.785 . ⋯. B) C) . D) 0.785 .

253 

 

E) F)

. /.

6. The equation for the mass flow rate of a fluid for a round pipe is given by: А) 0.785 . ⋯. B) C) . D) 0.785 . E) . F) /. 7. The equation of equivalent diameter of the pipe is expressed by the formula: A) deq = P/S. B) deq = 4P/S. C) deq = S/P. D) deq = 4S/P. E) deq = S/4P. F) deq = P/2S. 8. The hydraulic radius for a rectangle is calculated by the formula: A) Dd/4. B) ab/2(a+b). C) d/4. D) a/4. E) h/6. F) d/2. 9. The equivalent diameter for a ring section is calculated by the formula: A) Dd. B) ab/2(a+b). C) d/4. D) a/4. E) h/6. F) d/2. 10. The hydraulic radius for a square section is calculated by the formula: A) D  d/4. B) ab/2(a+b). C) d/4. D) a/4. E) h/6. F) d/2. 11. The hydraulic radius for a round section is calculated by the formula: A) а/4.

254 

 

B) d/4. C) Dd/4. D) ab/2(a+b). E) h/6. F) d/2. 12. The ratio of Q/S means: A) The average velocity of a liquid or gas. B) The mass flow of liquid. C) The mass flow of gas. D) The volumetric consumption of liquid. E) The volumetric consumption of gas. F) The specific volume of gas. G) The mass fluid velocity. 13. The volumetric flow rate of fluid flowing through the hole at a constant liquid level is calculated by the formula: A) V = f0(2gH)1/2. B) V = (2gH)1/2f0. C) V = (2gH)1/2. D) V = f0(2gH)1/2. E) V = f0(2gH)1/3. F) V = (2gH)1/2. G) V = f0(2gH)1/2. 14. The diameter of the round pipeline is calculated by the formula: A) d = 4P/S. B) d = S/P. C)

.

.

D) d = S/4P. E) d = 4rh. F) . . G) d = rh. 15. The volume flow of liquid flowing through a hole at a constant level of liquid in the vessel is expressed by the formula: A) 0.785 . B) C) V

. 0.785

.

2

D)

2

E)

0.785

. 2

.

255 

 

F)

0.785

2

.

G)

0.785

2

.

16. The volumetric flow rate, measured with a normal diaphragm and a differential pressure gauge connected to it, is expressed by the formula: 2

A) B)

0.785

C)

.

. .

D) V E)

0.785 0.785

2

.

F)

0.785

2

.

G)

0.785

2

.

2

.

17. The time τ during which the level of liquid in an open vessel of constant cross-sectional height f drops from the initial height to the level of the hole of area f0 can be calculated by the equation: /

A) B)

√

D)

√

E)

√

G)

. /

C)

F)

.

√

. .

. . .

18. The equation for the continuity of the flow includes the following parameters: A) Viscosity. B) Cross-sectional area. C) Pressure. D) Speed. E) Weight. F) Temperature. G) Concentration.

256 

 

19. The values in the expression for calculating the volumetric flow rate of the liquid flowing through the hole at a constant liquid level: A) Coefficient of kinematic viscosity. B) Speed coefficient. C) Speed. D) Surface tension. E) Dynamic viscosity coefficient. F) Compression coefficient of the jet. G) Time. 20. The volumetric flow rate of a liquid or gas depends on: A) The density of the liquid or gas. B) The coefficient of local resistance. C) The average flow velocity. D) The average specific heat. E) The boiling points. F) The inner diameter of the pipe. G) The surface tension. 21. The equivalent diameter of the channels of the granular layer is calculated by the formula: A) ∑ / . B) 4 . C) . D) 4 / . E) / . F) / . G) . 22. The equation for determining the mass flow rate of liquid and gas includes the following quantities: A) Viscosity. B) Pressure. C) Cross-sectional area. D) Concentration. E) Weight. F) Density. G) Temperature. H) Speed. 23. To calculate the equivalent diameter, we must know the following values: A) Hydraulic radius. B) Pressure. C) Cross-sectional area. D) Concentration.

257 

 

E) Weight. F) Density. G) The moistened perimeter. H) Speed. 24. The pressure in the system was 3 technical atmospheres (at). Its expression in pascals will be within the following limits: A) 29.42104 – 29.45104. B) 29.47104 – 29.49104. C) 29.38104 – 29.41104. D) 29.41104 – 29.44104. E) 29.46104 – 29.48104. F) 29.48104 – 29.51104. G) 29.40104 – 29.43104. H) 29.49104 – 29.53104. 25. A pipe with a diameter of 202 mm passes air at a speed of 9 m/s. The air volume flow (in m3/s) will be within the limits of: A) 0.00183 – 0.00185.. B) 0.00180 – 0.00182. C) 0.00182 – 0.00184. D) 0.00179 – 0.00182. E) 0.00184 – 0.00186. F) 0.00178 – 0.00183. G) 0.00175 – 0.00177. H) 0.00177 – 0.00179. 26. Hydrogen at a speed of 15 m/s and a density of 0.09 kg/m3 passes through a pipe 483 mm in diameter. Mass flow of hydrogen (in kg/s) will be within the limits of: A) 1.9610-3 – 1.9810-3. B) 1.8610-3 – 1.8810-3. C) 1.9410-3 – 1.9610-3. D) 1.8110-3 – 1.8410-3. E) 1.8510-3 – 1.8910-3. F) 1.9110-3 – 1.9410-3. G) 1.8610-3 – 1.8810-3. H) 1.8910-3 – 1.9210-3. 27. Nitrogen passes through a pipe with a diameter of 546 mm. The volume flow of nitrogen was 0.0125 m3/s. The nitrogen velocity (in m/s) will be within the limits of: A) 9.02-9.06. B) 8.01-9.01. C) 8.91-8.97.

258 

 

D) 8.91-9.09. E) 8.08-9.01. F) 8.53-8.59. G) 8.93-9.04. H) 9.07-9.08. 28. Hot air is passed into the ring space of the “pipe-in-pipe”: heat exchanger made of pipes with diameters of 1005 mm and 361.5 mm. The equivalent diameter for the ring section will be within the limits of: A) 0.056-0.058. B) 0.053-0.055. C) 0.055-0.057. D) 0.052-0.056. E) 0.051-0.053. F) 0.049-0.052. G) 0.048-0.051. H) 0.051-0.054. 29. A methane with a density of 0.72 kg/m3 and a mass flow of 24 kg/h passes through a pipe with a diameter of 355 mm. The rate of methane (in m/s) will be within the limits of: A) 18.8-19.2. B) 18.1-18.4. C) 18.7-19.1. D) 18.3-18.6. E) 18.2-18.5. F) 18.7-18.9. G) 18.4-18.7. H) 19.1-19.3. 30. Through the pipe with an internal diameter of 152 mm, water flows at a speed of 1.3 m/s. The volume flow of water (in m3/s) will be within the limits of: A) 0.0231-0.0233. B) 0.0234-0.0237. C) 0.0232-0.0234. D) 0.0230-0.0232. E) 0.0235-0.0238. F) 0.0237-0.0239. G) 0.0233-0.0239. H) 0.0233-0.0235. Test tasks (31-60) (Topic1.3): 31. Ideal solutions are: A) The solutions that move without friction.

259 

 

B) The viscous solutions. C) The colloidal solutions. D) The saturated solutions. E) The unsaturated solutions. F) The supersaturated solutions. 32. The differential equation of motion of an ideal fluid for a steady flow is called: A) The Bernoulli equation. B) The Euler’s equation. C) The Navier-Stokes equation. D) The Newton’s equation. E) The Fourier’s equation. F) The equation of continuity of a flow. 33. The Bernoulli equation describes: A) The law of conservation of mass. B) The law of conservation of energy. C) The law of composition. D) The law of conservation of impulse. F) The Avogadro’s law. F) The Fourier’s law. 34. The ratio of the dynamic viscosity coefficient to the density is called: A) The kinematic coefficient. B) The diffusion coefficient. C) The coefficient of efficiency. D) The coefficient of friction. E) The distribution coefficient. F) The coefficient of consumption. 35. The unit of measurement of the kinematic viscosity coefficient is: А) Pаs. В) m2/s. C) m3/s. D) Nm2/s. E) m/s. F) Pa. 36. The unit of measurement of the dynamic viscosity coefficient is: А) Pаs. В) m2/s. C) m3/s. D) kg/s. E) m/s. F) Pa.

260 

 

37. The energy balance makes it possible to determine: A) Mass flow rate. B) Concentration rate. C) Consumption of the whole substance. D) Heat consumption. E) Consumption of components. F) Flow volume flow. 38. In the basic equation of hydrostatics value of Z is: A) The piezometric pressure. B) The high-speed pressure. C) The hydrostatic head. D) The geometric pressure. E) The rush of pressure. F) The full pressure.

/

/

the

39. The unit of measurement of viscosity in the absolute system of units of mechanical quantities (SGS) is: A) Poise. B) g/cm3. C) N/m2. D) m/s. E) m3/s. F) kgf/cm2. 40. The Bernoulli equation for an ideal fluid: A) Z1  P1/g  W21/2g = Z2  P2/g  W22/2g. B) P1/g + W21/2g = P2/g + W22/2g. C) Z1 + P1/g = Z2P2/g. D) P1/g  W21/2g = P2/g  W22/2g. E) Z1 + P1/g + W21/2g = Z2 + P2/g + W22/2g. F) Z1 + W21/2g = Z2 + W22/2g. 41. The volumetric forces include: A) Viscosity. B) Gravity. C) Surface tension forces. D) Capillary forces. E) Forces of internal friction. F) Centrifugal forces. G) Pressure forces. 42. Surface forces include: A) Frictional forces.

261 

 

B) Gravity. C) Surface tension forces. D) Capillary forces. E) Forces of inertia. F) Centrifugal forces. G) Pressure forces. 43. To calculate the absolute pressure at excess pressure it is necessary to know: A) Partial pressure. B) Critical pressure. C) Osmotic pressure. D) Diffusive pressure. E) Differential pressure. F) Atmospheric pressure. G) Manometric pressure. 44. To calculate the absolute pressure under vacuum, we must know: A) Atmospheric pressure. B) Partial pressure. C) Critical pressure. D) Osmotic pressure. E) Diffusive pressure. F) Excessive pressure. G) Pressure of rarefaction. 45. In the basic equation of hydrostatics ratio / is called: A) Piezometric pressure. B) Kinematic pressure. C) Full pressure. D) Geometric pressure. E) Dynamic pressure. F) Rush of the pressure. H) Hydrodynamic pressure.

/

46. The quantity W2/2g in the Bernoulli equation is called: A) Hydrostatic pressure. B) Hydrodynamic pressure. C) Geometric pressure. D) High-speed pressure. E) Static pressure. F) Kinetic energy. G) Rush of the pressure. 47. The value of W2/2g in the Bernoulli equation characterizes: A) The specific static energy.

262 

 

/

, the

B) The specific potential energy of pressure. C) The specific potential energy of the position at a given point. D) The specific kinetic energy at a given point. E) The specific kinetic energy. F) The total specific energy. 48. The Bernoulli equation Z + P/g + W2/2g characterizes: A) The static pressure. B) The dynamic pressure. C) The high-speed pressure. D) The geometric pressure. E) The energy balance of the flow. F) The law of conservation of energy. G) The piezometric pressure. 49. The forces acting on the moving real liquid are forces of: A) Atmospheric pressure. B) Hydrodynamic pressure. C) Capacity. D) Rarefaction. E) Speed. F) Internal friction. G) Density. H) Gravity. 50. Theoretical foundation of science on the processes and apparatuses of chemical technology are the following basic laws of nature: A) The Avagadro’s law. B) The laws of conservation of mass, energy and impulse. C) The Pascal’s law. D) The laws of thermodynamic equilibrium. E) The Stokes law. F) The laws of mass, energy and impulse transfer. G) The Fourier law. H) The Stefan-Boltzmann law. 51. The technological process consists of: A) Physiological processes. B) Hydromechanical processes. C) Physical processes. D) Thermal processes. E) Biophysical processes. F) Biological processes. G) Mass-exchange processes. H) Geochemical processes.

263 

 

52. The substance is: A) Mass. B) Temperature. C) Speed. D) Pressure. E) Energy. F) Volume. G) Area. H) Impulse. 53. For substances involved in the chemical-technological process, material balances refer to: A) The parts of the process element. B) The general for all substance. C) The total element of the apparatus. D) The private – for one component. E) The total production. F) The elemental – for the chemical element. G) The parts of production. H) Many productions. 54. According to the hierarchical structure of production, material balances are divided on: A) The parts of the apparatus. B) The general for all substance. C) Of the apparatus. D) The private. E) Of the setup. F) The elemental. G) For one component. H) For the chemical element. 55. The conditions of equilibrium in the processes of heat, impulse and mass transfer are: A) dT = 0. B) dV = 0. C) dM = 0. D) dP = 0. E) dR = 0. F) dμi = 0. G) dN = 0. H) dF = 0. 56. In the technique for measuring pressure, it is widely used: A) Voltmeters. B) Ammeters.

264 

 

C) Manometers. D) Colorimeters. E) Vacuum meters. F) pH-meters. G) Piezometers. H) Potentiometers. 57. Determine the magnitudes of the kinematic viscosity coefficient (in m2/s) of carbon dioxide at 30 оС and Рabs = 5.28 kgf/cm2, if it is known that the dynamic coefficient of viscosity of carbon dioxide was 15 mPas. A) 1.76·10-6-1.79·10-6. B) 1.65·10-6-1.68·10-6. C) 1.74·10-6-1.77·10-6. D) 1.75·10-6-1.78·10-6. E) 1.63·10-6-1.67·10-6. F) 1.62·10-6-1.64·10-6. G) 1.71·10-6-1.73·10-6. H) 1.64·10-6-1.69·10-6. 58. The relative density of oil is 0.89, then the density of oil in the SI system (in kg/m3) will be in the range: A) 881-885. B) 889-892. C) 883-886. D) 884-889. E) 887-893. F) 892-895. G) 893-896. H) 885-895. 59. The pressure on the manometer was 2 kgf/cm2, and the barometric pressure was 740 mm Hg, then the absolute pressure (in Pa) will be in the range: А) 3948·102 – 3951·102. В) 2946·102 – 2952·102. С) 3942·102 – 3945·102. D) 3945·102 – 3948·102. E) 2942·102 – 2949·102. F) 3946·102 – 3949·102. G) 2942·102 – 2946·102. H) 2944·102 – 2949·102. 60. The pressure at the vacuum meter is 60 cm Hg. The barometric pres‐  sure is 748 mm Hg. The absolute pressure in Pa will be within the following va‐  lues: A) 185·102 – 188·102.

265 

B) 195·102 – 198·102. C) 187·102 – 192·102. D) 191·102 – 195·102. E) 188·102 – 199·102. F) 183·102 – 189·102. G) 182·102 – 186·102. H) 196·102 – 199·102. Test tasks (61-90) (Topic 1.4): 61. The regime in which the fluid particles in the pipeline move at high speed and in different directions is called: A) Laminar. B) Turbulent. C) Accelerated. D) Transitional. E) Film. F) Self-similar. 62. The Reynolds criterion, which characterizes the hydrodynamic regime, is inversely proportional to: A) The flow rates. B) The gas pressure. C) The diameter of the pipe. D) The viscosity of the liquid. E) The density of the liquid. F) The length of the pipe. 63. The average speed for a laminar flow regime is calculated by the for‐  mula: A) Wav = 0.85Wmах. B) Wav. = 0.25Wmах. C) Wav = Wmах. D) Wav = 0.Wmах. E) Wav = 0.75Wmах. F) Wav = 0.35Wmах. 64. With laminar flow of liquids ... A) The fluid particles move randomly in different directions. B) The liquid particles move in parallel layers. C) The fluid particles in the pipeline move haphazardly. D) The velocity of the fluid is minimal at the center of the pipeline. E) The velocity of the liquid through the pipeline is maximal at any point. F) The velocity of the fluid at the walls of the pipeline is not zero.

266 

 

65. With turbulent flow of liquids ... A) The fluid particles move randomly in different directions. B) The liquid particles move in parallel layers. C) The velocity of the fluid at the walls of the pipeline is zero. D) The velocity of the fluid is minimal at the center of the pipeline. E) The liquid retains a certain pattern of its particles. F) The velocity of the fluid through the pipeline is minimal at any point. 66. The average velocity in the turbulent regime of fluid motion is calculated by the formula: A) Wav = 0.85Wmах. B) Wav = 0.25Wmах. C) Wav = Wmах. D) Wav = 0.5Wmах. E) Wav = 0.75Wmах. F) Wav = 0.35Wmах. 67. The Reynolds criterion for a laminar flow of a film with a smooth phase interface can have the following values: A) Refilm < 12. B) 12  Refilm   1600. C) Refilm   12. D) Refilm   1600. E) Refilm   1600. F) Refilm = 1600. 68. The Reynolds criterion for laminar flow of a film with a wavy phase interface can have the following values: A) Refilm   12. B) 12  Refilm   1600. C) Refilm   12. D) Refilm   1600. E) Refilm  12. F) Refilm = 1600.   69. The Reynolds criterion for turbulent flow of a film can have the following values: A) Refilm   12. B) 12  Refilm   1600. C) Refilm   12. D) Refilm   1600. E) Refilm  12. F) Refilm = 1600.

267 

 

70. The viscosity of liquids and gases is a physicochemical constant and is determined by: A) The volume of liquid and gas. B) The temperature of the liquid and gas. C) The concentration of liquid and gas. D) The density of the liquid and gas. E) The refractive index of a liquid and a gas. F) The specific gravity of liquid or gas. 71. In the turbulent flow occurs: A) Flow attenuation. B) Velocity deceleration. C) Slow particle movement. D) Transverse particle displacements. E) Weak mixing of the stream. F) Intensive stirring of the stream. G) Parallel motion of the flow particles. 72. The critical value of the Reynolds criterion is divided into regions: A) The flash mode. B) The steady laminar flow. C) The pulsation mode. D) The transverse mode. E) The turbulent regime. F) The intensive mode. G) The parallel mode. 73. In a laminar flow occurs: A) Acceleration of velocities. B) Velocity pulsations. C) Chaotic motion of particles. D) Weak mixing of the stream. E) Transverse particle displacements. F) Intensive stirring of the stream. G) Parallel motion of particles. 74. The transition from laminar to turbulent motion is characterized by the critical value of the Reynolds criterion: A) Re ≈ 2320. B) Re < 2320. C) Re > 2320. D) Re > 10000. E) Re > 100000. F) Re < 2000. G) Re < 1000.

268 

 

75. The structure of the turbulent flow differs in the zones: A) The core of the flow. B) Jet layer. C) Non-stationary flow layer. D) Non-intermixing flow layer. E) Non-pulsating flow layer. F) Laminar boundary sublayer. G) Stationary flow layer. 76. The hydrodynamic regime of film motion is determined by the Reynolds criterion for a film: A) Re  wl  l .

l

B)



C)



D)



E)



F)



G)



. . . . . .

77. The linear mass density of irrigation of the film is expressed by the formula: . A) B)



C)



.

D)



.

.

E) Re  wS .

l

F) G)



. .

78. The main modes of motion of the film include: A) Laminar-non-wavy flow of the film. B) Turbulent-non-wavy flow of the film. C) Laminar-wavy flow of a film. D) Turbulent-wavy flow of a film. E) Turbulent flow of a film.

269 

 

F) Laminar flow of the film. G) Pulsating film flow. H) Stationary film flow. 79. The Reynolds criterion, which characterizes the hydrodynamic regime, is directly proportional to: A) The flow rates. B) The gas pressure. C) The diameter of the pipe. D) The viscosity of the liquid. E) The density of the liquid. F) The volume of the liquid. G) The temperature of the liquid. H) The concentrations of liquid. 80. The linear mass density of irrigation is directly proportional to: A) The film speed. B) The gas pressure. C) The diameter of the pipe. D) The viscosity of the liquid. E) The density of the liquid. F) The thickness of the film. G) The temperature of the liquid. H) The concentrations of the liquid. 81. The linear mass density of irrigation depends on: A) The average speed of the film. B) The coefficient of friction. C) The pressure. D) The film thickness. E) The volume. F) The specific heat capacity. G) The density of the liquid. H) The coefficient of friction. 82. The Reynolds criterion for film flow, which characterizes the hydrodyna‐ mic regime, is directly proportional to: A) The viscosity of the flow. B) The fluid velocities. C) The flow pressure. D) The thickness of the film. E) The concentration of liquid. F) The density of the liquid. G) The volume of the liquid. H) The temperature of the liquid.

270 

 

83. Two-phase flows, gas (or liquid) – a solid phase, where solid particles do not change their shape and mass, include the processes such as: A) Adsorption. B) Precipitation. C) Absorption. D) Pseudo-liquefaction. E) Rectification. F) Pneumatic transport. G) Crystallization. H) Extraction. 84. Elements of disperse phases in gas–liquid and liquid–liquid systems flow include: A) Bubbles. B) Gases. C) Drops. D) Suspensions. E) Solid particles. F) Film. G) Suspensions. H) Emulsions. 85. The gas velocity is known to be 0.01 m/s, its density is 1.91 kg/m3, the viscosity is 8.3510-6 Pas. The pipe diameter is 0.75 m. Specify the range for the Reynolds number. A) 1814 – 1818. B) 1714 – 1718. C) 1815 – 1819. D) 1713 – 1717. E) 1813 – 1817. F) 1715 – 1719. G) 1811 – 1814. H) 1711 – 1714. 86. The fluid velocity is known to be 0.77 m/s, its density is 1150 kg/m3, viscosity is 1.210-3 Pa s. The diameter of the pipe is 25 mm. Indicate the range of values for the Reynolds number. A) 18443-18455. B) 18452-18455. C) 18446-18448. D) 18453-18456. E) 18440-18442. F) 18451-18457. G) 18442-18458. H) 18444-18466.

271 

 

87. The average speed for the laminar flow regime was 10 m/s. Specify the limits for the maximum fluid velocity (in m/s). A) 22-25. B) 15-25. C) 15-18. D) 18-22. E) 14-19. F) 17-23. G) 16-19. H) 23-26. 88. Fluid velocity is known to be 2 m/s, its density is 1200 kg/m3, viscosity is 2.0510-3 Pas. The diameter of the pipe is 0.88 m. The value of the Reynolds test lies within the limits of: A) 1028103-1035103. B) 1022103-1029103. C) 1023103-1028103. D) 1021103-1027103. E) 1032103-1036103. F) 1027103-1036103. G) 1025103-1034103. H) 1034103-1036103. 89. The average speed in the turbulent regime of fluid motion was 15 m/s. Calculate the maximum fluid velocity (in m/s) and determine the range of its values: A) 17.61-17.71. B) 18.61-18.71. C) 17.59-17.69. D) 18.59-18.69. E) 18.55-18.65. F) 18.53-18.63. G) 17.53-17.63. H) 17.62-17.72. 90. The pipe diameter is 0.046 m, the air density is 1.2 kg/m3 and its dynamic coefficient is 0.018 mPas. Calculate the air velocity (in m/s) during the transition period (Re = 2320) and determine the range of its values: A) 0.853-0.858. B) 0.753-0.758. C) 0.751-0.759. D) 0.851-0.859. E) 0.855-0.865. F) 0.759-0.764. G) 0.859-0.864. H) 0.755-0.765.

272 

 

Test tasks (91-120) (Topic 1.5): 91. The Reynolds criterion characterizes: A) Film motion. B) Vortex motion. C) Constant motion. D) Motion mode. E) Bubble motion. F) Wave motion. 92. The Reynolds criterion for flows passing through straight pipes under laminar flow has the following values: А) Re ≤ 2320. В) Re ≥ 2320. С) Re > 10000. D) Re = 10000. E) Re > 100000. F) Re = 20000. 93. The Reynolds criterion for flows passing through straight pipes under steady-state turbulent flow has the following values: А) Re ≤ 2320. В) Re > 10000. C) Re = 2320. D) Re > 1000. E) Re ≥ 2320. F) Re  10000. 94. The ratio of the forces of friction to the forces of inertia and the determining mode of motion of the liquid is called: A) Reynolds criterion. B) Froude’s criterion. C) Euler’s criterion. D) Nusselt’s criterion. E) Grashof’s criterion. F) Criterion of Archimedes. 95. The ratio of pressure forces to inertial forces is called: A) Euler’s criterion. B) Froude’s criterion. C) Reynolds criterion. D) Nusselt’s criterion. E) Grashof’s criterion. F) Criterion of Archimedes.

273 

 

96. The ratio of the forces of gravity to the forces of inertia is called: A) Froude’s criterion. B) Nusselt’s criterion. C) Euler’s criterion. D) Reynolds criterion. E) Grashof’s criterion. F) Criterion of Archimedes. 97. Criterion of homochronity: A) Characterizes the ratio of inertial forces to frictional forces. B) Characterizes the ratio of the change in the hydrostatic pressure force to the inertia force. C) Characterizes the ratio of the force of inertia to gravity. D) Considers the unsteady nature of the movement. E) Characterizes the ratio of the particle acting on the particle to the force of inertia. F) This is a simplex of geometric similarity. 98. Newton’s criterion: A) Characterizes the ratio of the force acting on a particle to the inertia force. B) Characterizes the ratio of the force of inertia to gravity. C) Characterizes the ratio of the change in the hydrostatic pressure force to the inertia force. D) Characterizes the ratio of inertial forces to frictional forces. E) Takes into account the unsteady nature of the movement. F) This is a simplex of geometric similarity. 99. The Reynolds criterion is expressed by the formula: A) / . B) ∆ / . C) / . D) / . E) / . F) / . 100. Euler’s criterion is expressed by the formula: A) / . B) ∆ / . C) / . D) / . E) / . F) / . 101. The Froude’s criterion is expressed by the formula: A) / .

274 

 

B) ∆ / . C) / . / . D) E) / . F)

/

.

102. The criterion of Galileo is expressed by the formula: A) / . . B) ∆ / C) / . / . D) E) / . F) / . 103. The criterion of Archimedes is expressed by the formula: A) / . B) ∆ / . C) / . / . D) E) / . F) / . 104. Newton’s criterion is expressed by the formula: A) ∆ / . B) / C) / . D) / E) / . F) ) / . 105. Geometric similarity is the ratio: A) D1/D2. B) T1/T2. C) 1/2. D) L1/L2. E) u1/u2. F) 1/2. G) µ1/µ2. 106. The similarity of physical quantities is the ratio: A) µ1/µ2. B) T1/T2. C) D1/D2. D) 1/2. E) 1/2.

275 

 

F) L1/L2. G) l1/l2. 107. Parametric criteria is the ratio: A) T1/1. B) u1/u2. C) L1/D2. D) 1/2. E) 1/2. F) L1/L2. G) µ1/µ2. 108. The relations of various similar quantities in nature and in the model are called: A) Simplexes. B) Physical parameters. C) The chemical constant. D) Diffusion criteria. E) Parametric criteria. F) Similarity coefficients. G) Properties of substances. 109. The functional dependence , A) Equations in generalized variables. B) Physical parameters. C) Generalized equations. D) The similarity constant. E) Parametric criteria. G) Properties of substances. H) Diffusion criteria.

,

,

is called:

110. The criterion equation of hydrodynamics is described by the equation: A) Е , , , , … . B) Е , , . C) Е , , , … . D) Е , . E) Е , , , . F) Е , , . G) Е , , . 111. The Reynolds criterion is described by the following physical parameters: A) Speed. B) Viscosity. C) Density. D) Diameter.

276 

 

E) Time. F) Volume. G) Temperature. 112. The criterion of homochronicity is described by the following parameters: A) Speed. B) Viscosity. C) Density. D) The height or length of the apparatus. E) Time. F) The coefficient of thermal conductivity. G) Heat emission coefficient. H) Heat transfer coefficient. 113. The Froude’s criterion is described by the following parameters: A) Speed. B) Viscosity. C) Density. D) The height or length of the apparatus. E) The time. F) Gravity. G) Concentration. H) Temperature. 114. The Euler’s criterion is described by the following parameters: A) Pressure. B) Viscosity. C) Density. D) The height or length of the apparatus. E) Speed. F) Gravity. G) Concentration. H) Temperature. 115. The gas density is 1.25 kg /m3, the gas velocity is 7 m/s and the pressure difference is 5×103 Pa. Calculate the Euler’s number and specify the limits for it. A) 80.2-81.2. B) 80.7-81.7. C) 80.3-81.3. D) 81.1-81.8. E) 71.1-71.8. F) 70.3-71.3. G) 70.2-71.2. H) 79.5-82.5.

277 

 

116. The fluid velocity is 15 m/s and the length of the pipe is 10 m. Calculate the Froude’s number and specify the limits for it. A) 2.25-2.35. B) 2.35-2.45. C) 2.28-2.31. D) 2.31-2.35. E) 2.36-2.38. F) 2.25-2.28. G) 2.23-2.27. H) 2.27-2.36. 117. The gas velocity is 5 m/s, its density is 0.925 kg/m3, the viscosity is 0.01510-3 Pas, and the pipe diameter is 0.25 m. Calculate the Reynolds number and specify the limits for it. A) 78.1·103-78.4·103. B) 76.5·103-77.7·103. C) 78.4·103-78.9·103. D) 78.5·103-78.7·103. E) 76.8·103-77.8·103. F) 78.2·103-78.6·103. G) 76.9·103-77.5·103. H) 77.8·103-78.5·103. 118. The gas density is known to be 0.925 kg/m3, the gas velocity is 7.48 m/s and the pressure difference is 7×104 Pa. Calculate the Euler’s number and specify the limits for it. A) 1449-1452. B) 1349-1354. C) 1445-1455. D) 1345-1355. E) 1447-1457. F) 1442-1448. G) 1342-1348. H) 1347-1357. 119. The gas velocity is 9 m/s and the length of the pipe is 15 m. Calculate the Froude’s number and specify the limits for it. A) 0.549-0.552. B) 0.649-0.652. C) 0.547-0.557. D) 0.647-0.657. E) 0.651-0.661. F) 0.652-0.662. G) 0.548-0.558. H) 0.555-0.565.

278 

 

120. The fluid velocity is known to be 0.5 m/s, its density is 998 kg/m3, the viscosity is 1110-3 Pas, and the pipe diameter is 0.018 m. Calculate the Reynolds number and specify the limits for it. A) 715-725. B) 815-825. C) 712-719. D) 812-819. E) 811-821. F) 711-721. G) 825-835. H) 725-735. Test tasks (121-150) (Topic 1.6): 121. The mass velocity, referred to the whole section of the device can be expressed in: A) kg/m2. B) kg/(m2s). C) kg/s. D) kg/m3. E) kg/min. F) kg/h. 122. The value indicating how many times the pressure, lost on friction, differs from the high-speed pressure, is called: A) The coefficient of thermal diffusivity. B) The coefficient of thermal conductivity. C) The coefficient of resistance. D) The coefficient of dynamic viscosity. E) The coefficient of kinematic viscosity. F) The coefficient of consumption. 123. In a turbulent flow, the coefficient of friction depends on: A) The pressure. B) The dynamic viscosity. C) The thermal diffusivity. D) The mode of liquid flow. E) The kinematic viscosity. F) The volume. 124. The ratio of pressure loss for a given local resistance to a high-speed pressure in it is called: A) The coefficient of thermal conductivity. B) The coefficient of local resistance. C) The coefficient of friction resistance.

279 

 

D) The coefficient of dynamic viscosity. E) The coefficient of kinematic viscosity. F) The coefficient of consumption. 125. The porous environment through which the liquid moves in the apparatus can be created by: A) The melts of salts. B) The granular material. C) The metal salts. D) The fluid solutions. E) The metal oxides. F) The solutions of salts. 126. The friction coefficient for laminar motion is calculated by the formula: A) 64/ . , B) 0,316/ . C) 128/ . , D) 0,158/ . E) 32/ . F) 16/ . 127. The friction coefficient for turbulent motion is calculated by the formula: A) 64/ . , B) 0,316/ . C) 128/ . , D) 0,158/ . E) 32/ . F) 16/ . 128. The pressure loss due to the Darcy-Weisbach equation is found by the formula: /2 . A) B) 0,316/Re , . C) 64/ / . E) 0,316/√ . , D) 0,158/ . E) 32/ . F) 16/ . 129. Loss of pressure due to local resistance is found by the formula: /2 . A) B) 0,316/Re , . C) 64/ / . , D) 0,158/ .

280 

 

E) F)

/2 . 32/ .

130. The equivalent diameter of the channels in the granular layer is expressed by the ratio: A) 4 / . В) / . С) 4/ . 4 / . D) E) / . F) /4 . 131. Loss of pressure in apparatus with granular material is found by the formula: A) Δ B) Δ

. 1

С) ∆

F) Δ

.

.

.

D) ∆ E)

∙ .

. .

Δ

. .

132. The coefficient of friction is directly proportional: A) The fluid velocity. B) The length of the pipeline. C) Density of the liquid. D) The diameter of the pipe. E) Dynamic viscosity coefficient. F) The volume of the liquid. 133. The loss of pressure on friction in straight pipes and channels can be expressed in: A) m2/m2. B) N/m2. C) kg/m3. D) m/s. E) kgf/m. F) m/s2. G) m. 134. The Euler’s criterion for forced motion of a viscous liquid depends on: A) The Reynolds criterion. B) Cross-sectional areas of the pipeline.

281 

 

C) The length and diameter of the pipeline. D) The coefficient of flow. E) Mass flow of a viscous liquid. F) Density of a viscous liquid. G) Volumetric flow of a viscous liquid. 135. When liquid flows through a granular layer, the equivalent diameter of the nozzle is characterized by the following parameters: A) Free volume. B) Viscosity. C) Specific surface. D) Speed. E) Pressure. F) Volume. G) Density. 136. The equivalent diameter of the channels in the granular layer depends on: A) Average perimeter. B) Heights. C) Specific surface area. D) The total volume. E) Free volume. F) Inner diameter. G) Outer diameter. 137. The pressure loss in the coil is calculated by the formula: . А) Δ Δ В) Δ Δ 1 3,54 . C) Δ D) Δ

. 1

E) ∆

.

F) Δ G) Δ

∙

.

.

. .

138. The coefficient of friction is inversely proportional to: A) The flow rates. B) The dynamic viscosity coefficient. C) The kinematic viscosity coefficient. D) The density of the liquid or gas. E) The roughness of pipes. F) The volume flow of liquid or gas. G) The diameter of the pipe. H) The mass flow of liquid or gas.

282 

 

139. Resistance to the flow in the pipeline arises due to: A) Friction force. B) Reduction in the viscosity of the liquid. C) Flow direction change. D) Increase in the viscosity of the liquid. E) Change in flow velocity. F) Increase in the temperature of the liquid. G) Lowering in the temperature of the liquid. H) Increase in density. 140. Local resistance to flow in the pipeline occurs: A) As a result of a decrease in the viscosity of the liquid. B) As a result of temperature increase. C) When changing direction or flow rate. D) As a result of an increase in the viscosity of the liquid. E) Due to cranes, latches and valves. F) With a sudden contraction and expansion of the pipes. G) As a result of a decrease in the temperature of the liquid. H) As a result of an increase in the density of the liquid. 141. The Darcy-Weisbach equation includes the following parameters: A) Coefficient of friction. B) Fictitious speed. C) Geometrical dimensions. D) Pressure. E) High-speed pressure. F) Volume. G) Temperature. H) Concentration. 142. The Reynolds number was 1700. Calculate the coefficient of friction and specify the limits for it. A) 0.0276-0.0286. B) 0.0277-0.0284. C) 0.0367-0.0377. D) 0.0381-0.0391. E) 0.0371-0.0381. F) 0.0275-0.0285. G) 0.0361-0.0371. H) 0.0368-0.0378. 143. The Reynolds number was 15000. Calculate the coefficient of friction and specify the limits for it. A) 0.0277-0.0287. B) 0.0377-0.0387. C) 0.0281-0.0288.

283 

 

D) 0.0381-0.0388. E) 0.0384-0.0394. F) 0.0381-0.0384. G) 0.0279-0.0289. H) 0.0273-0.0283. 144. The diameter of the steel pipe is 432.5 mm, the diameter of the coil winding is 1 m, the density of the liquid is 1200 kg/m3, the flow rate of the liquid through the pipe is 1 m/s and the coefficient of friction is 0.03. Calculate the pressure loss for overcoming friction in a straight pipe (in Pa) and specify the limits for it. A) 482-487. B) 483-488. C) 472-477. D) 481-488. E) 471-478. F) 488-498. G) 465-475. H) 461-471. 145. The pipe diameter is known to be 0.025 m, the pipe length is 10 m, the flow velocity of the liquid through the pipe is 1.8 m/s and the coefficient of friction is 0.04. Calculate the head loss in friction in a straight pipe (in m) and specify the limits for it. A) 2.58-2.68. B) 2.68-2.78. C) 2.61-2.67. D) 2.71-2.79. E) 2.56-2.66. F) 2.66-2.76. G) 2.52-2.62. H) 2.51-2.54. 146. The diameter of the coil winding is 1 m, the internal diameter is 39 mm, and the pressure loss in the straight pipe was 13.1 kPa. Calculate the loss of pressure on the friction in the coil (in Pa) and specify the limits for it. A) 14.90103-14.92103. B) 15.89103-15.93103. C) 15.85103-15.96103. D) 14.88103-14.98103. E) 14.83103-14.88103. F) 15.84103-15.94103. G) 14.86103-14.96103. H) 15.83103-15.87103.

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147. The loss of friction pressure in the coil is known to be 14.91 kPa and the dimensionless correction factor is  = 1.138. Calculate the loss of pressure on friction in a straight pipe (in Pa) and specify the limits for it. A) 135102-138102. B) 130102-135102. C) 125102-128102. D) 128102-134102. E) 124102-129102. F) 125102-132102. G) 133102-136102. H) 134102-138102. 148. The solution passes through the pipe space at a speed of 0.3 m/s. Calculate the high-speed pressure in the pipes (in N/m2), if the density of the solution is 1100 kg/m3, and specify the limits for it. A) 49.2-49.7. B) 48.3-48.6. C) 48.4-48.7. D) 49.7-49.9. E) 48.7-48.9. F) 48.9-49.6. G) 48.8-49.3. H) 49.4-49.8. 149. The pipe diameter is known to be 0.034 m, the pipe length is 2 m, the gas flow velocity is 5 m/s along the pipe and the friction coefficient is 0.035. Calculate the pressure loss on friction in a straight pipe (in m) and specify the limits for it. A) 2.67-2.69. B) 2.59-2.64. C) 2.52-2.56. D) 2.61-2.67. E) 2.64-2.68. F) 2.56-2.59. G) 2.55-2.58. H) 2.62-2.65. 150. Gas passes through the pipe space at a speed of 9 m/s. Calculate the high-speed pressure in the pipes (in m) and specify the limits for it. A) 4.19-4.23. B) 4.08-4.17. C) 4.24-4.28. D) 4.09-4.16. E) 4.05-4.08. F) 4.03-4.07. G) 4.16-4.19. H) 4.11-4.15.

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Test tasks (151-180) (Topic 1.7): 151. Multiple pumping of liquid or gas through pumps through the working area is called: A) Mechanical mixing. B) Circulation mixing. C) Mixing with compressed air. D) Mixing with an inert gas. E) Pneumatic mixing. F) Bubbling mixing. 152. Mixing with rotary devices is called: A) Mechanical mixing. B) Pneumatic mixing. C) Circulation mixing. D) Mixing with fans. E) Mixing with compressed air. F) Rapid pneumatic mixing. 153. Internal circulation mixing with propeller pumps is called: A) High-speed mechanical mixing. B) High-speed pneumatic mixing. C) Slow mechanical mixing. D) Mixing with fans. E) Mixing with lobed mixers. F) Mixing with compressed air. 154. Internal circulation mixing with lobed mixers refers to: A) High-speed mechanical mixing. B) High-speed pneumatic mixing. C) Low-speed mechanical mixing. D) Mixing with fans. E) Mixing with propeller pumps. F) Mixing with compressed air. 155. The Euler’s criterion for the mixing process is calculated by the formula: A) nd ρ/μ. B) ndρ/μ. C) n d/g. D) ΔP/ρ nd . E) N/ρn d . F) n dρ/μ.   156. The Reynolds criterion for the mixing process is calculated by the formula: A) nd ρ/μ.

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B) ndρ/μ. C) n d/g. D) ΔP/ρ nd . E) N/ρn d . F) n dρ/μ. 157. The Froude’s criterion for the mixing process is calculated by the formula: A) nd ρ/μ. B) ndρ/μ. C) n d/g. D) ΔP/ρ nd . E) N/ρn d . F) n dρ/μ 158. The power criterion for the mixing process is calculated by the formula: A) nd ρ/μ. B) ndρ/μ. C) n d/g. D) ΔP/ρ nd . E) N/ρn d . F) n dρ/μ. 159. The mixing in liquid environments is carried out for: A) The intensification of mass transfer processes. B) The uniform distribution of solid particles in the volume of the liquid. C) The decrease in the process speed. D) The increase in the process speed. E) The pressure reduction. F) The uniform crushing of solid particles in the volume of the liquid. G) The increase in viscosity. H) The decrease in viscosity. 160. With mixing in liquid environments, the following objectives are achieved: A) The intensification of heat transfer processes. B) The uniform distribution of solid particles in the volume of the liquid. C) The decrease in the process speed. D) The increase in the process speed. E) The pressure reduction. F) The uniform crushing of solid particles in the volume of the liquid. G) The increase in viscosity. H) The decrease in viscosity. 161. Mixing in liquid environments is carried out for: A) The uniform gas distribution in the volume of the liquid.

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B) The preparation of suspensions. C) The decrease in the process speed. D) The increase in the process speed. E) The pressure reduction. F) The increase in viscosity. G) The decrease in viscosity. 162. Mixing in liquid environments ... A) Accelerates the chemical process. B) Increases pressure. C) Improves the heat transfer process. D) Increases density. E) Increases the diffusion process. F) Changes the temperature. G) Increases viscosity. H) Reduces viscosity. 163. Mixing in liquid environments ... A) Accelerates the diffusion process. B) Increases pressure. C) Improves the preparation of emulsions. D) Increases density. E) Increases the diffusion process. F) Changes the temperature. G) Increases viscosity. H) Reduces viscosity. 164. The mixing process is characterized by the following basic parameters: A) Intensity. B) Efficiency. C) Energy consumption. D) Pressure. E) Density. F) Viscosity. G) Temperature. H) Concentration. 165. Euler’s criterion for the mixing process is: A) Inversely proportional to the density of the liquid. B) Directly proportional to the diameter of the agitator. C) Directly proportional to the pressure difference. D) Directly proportional to the mixer stirring frequency. E) Directly proportional to the rate of mixing of the liquid. F) Directly proportional to the temperature of the liquid. G) Inversely proportional to the viscosity of the liquid.

288 

 

166. Froude’s criterion for the process of mixing is: A) Inversely proportional to the density of the liquid. B) Directly proportional to the diameter of the mixer. C) Directly proportional to the pressure difference. D) Directly proportional to the mixer stirring frequency. E) Directly proportional to the rate of mixing of the liquid. F) Directly proportional to the temperature of the liquid. G) Inversely proportional to the viscosity of the liquid. 167. The Reynolds criterion for the mixing process is: A) Inversely proportional to the density of the liquid. B) Directly proportional to the diameter of the mixer. C) Directly proportional to the pressure difference. D) Directly proportional to the mixer stirring frequency. E) Directly proportional to the rate of mixing of the liquid. F) Directly proportional to the temperature of the liquid. G) Inversely proportional to the viscosity of the liquid. 168. The criterion equation of hydrodynamics for the processes of mixing liquid media takes the form: A) , , , … . B) , , . C) , , , , … . D) , . E) , , , . F) , , . G) , , . 169. Intensification of chemical, thermal and diffusion processes by mixing in liquid environments of heterogeneous systems leads to: A) The delivery of reacting substances to the reaction zone. B) Cooling of the environment. C) The delivery of substances to the phase interface. D) Heating of the environment. E) The delivery of substances to the heat transfer surface. F) The change in the volume. G) The pressure change. H) The change of the pressure. 170. When mechanical mixers work, a complex three-dimensional flow of liquid arises: A) Film. B) Ascendant. C) Tangential. D) Descending. E) Sinusoidal.

289 

 

F) Radial. G) Cosinusoidal. H) Axial. 171. For geometrically similar mixers, it is true: A) b/dm = const. B) u1/u2 = const. C) H/dm = const. D) T1/T2 = const. E) 1/2 = const. F) µ1/µ2 = const. G) D/dm = const. H) L1/L2 = const. 172. When rotating in a mixer, there are: A) Area of entrainment. B) The region of the central vortex. C) Fixed layer area. D) Transition area. E) Fluidized bed area. F) Velocity decay region. G) Speed ramp area. H) Peripheral area. 173. The bubbling of gas or steam through a liquid environment is called: A) Mechanical mixing. B) Pneumatic mixing. C) Circulation mixing. D) Mixing with nozzles. E) Mixing with pumps. F) Mixing with compressed air. G) Mixing with an inert gas. H) Mixing with agitators. 174. From the method of mixing liquid environment are distinguished: A) Dynamic mixing. B) Mechanical mixing. C) Kinematic mixing. D) Pneumatic mixing. E) Uniform mixing. F) Periodic mixing. G) Circulation mixing. H) Continuous mixing. 175. The rotational speed of the normalized mixer is 3.0 rps, its diameter is 0.3 m, the density of the acid mixture is 1600 kg/m3. The pressure difference

290 

 

was 2 kPa. Calculate the Euler’s criterion for the process of mixing the acid mixture and specify the limits for the mixture. A) 1.63-1.67. B) 1.53-1.56. C) 1.51-1.53. D) 1.52-1.58. E) 1.62-1.68. F) 1.61-1.63. G) 151-1.55. H) 1.56-1.58. 176. The rotational speed of the normalized stirrer is 3.5 rps and its diameter is 0.35 m. Calculate the Froude’s criterion for mixing the acid mixture and specify the limits for the mixture. A) 0.436-0.438. B) 0.456-0.458. C) 0.452-0.457. D) 0.431-0.441. E) 0.439-0.449. F) 0.458-0.462. G) 0.453-0.459. H) 0.435-0.445. 177. The power consumed by the stirrer was 21 kW, the diameter of the stirrer was 0.7 m, and the density of the mixture of substances was 1300 kg/m3. The power criterion was 7.3. Determine the speed of the mixer (in rps) for the preparation of a mixture of substances and specify the limits for it. A) 2.32-2.42. B) 2.41-2.45. C) 2.31-2.41. D) 2.25-2.31. E) 2.33-2.37. F) 2.37-2.45. G) 2.41-2.46. H) 2.42-2.44. 178. The rotational speed of the normalized mixer is 3.5 rps, its diameter is 0.4 m, the density of the acid mixture is 1600 kg/m3, the dynamic coefficient of viscosity is 2010-3 Pas. Determine the hydrodynamic regime for the process of mixing the acid mixture and specify the limits for the mixture. A) 48.5·103-48.9·103. B) 44.6·103-44.9·103. C) 48.2·103-48.7·103. D) 44.2·103-45.2·103. E) 48.6·103-49.2·103. F) 44.5·103-45.4·103.

291 

 

G) 48.4·103-49.4·103. H) 44.2·103-44.5·103. 179. The rotational speed of the normalized mixer is 3.5 s-1, its diameter is 0.4 m, the density of the stirred mixture of acids is 1600 kg/m3. The power criterion was 0.27. Calculate the power consumed by the mixer (in W), and specify the limits for it. A) 185-195. B) 195-205. C) 187-197. D) 182-188. E) 188-198. F) 181-185. G) 193-203. H) 196-206. 180. The power consumed by the mixer was 16.5 kW, the rotation speed was 4.0 s-1, the density of the mixture of substances was 1200 kg/m3. The power criterion was 6.9. Determine the diameter of the mixer (in m) for the preparation of a mixture of substances and specify the limits for the mixture. A) 0.6-0.9. B) 0.3-0.4. C) 0.1-0.4. D) 0.4-0.7. E) 0.1-0.3. F) 0.3-0.6. G) 0.6-0.8. H) 0.2-0.9. Test tasks (181-210) (Topic 1.8): 181. The motion of particles in a fluidized bed is characterized by: A) The velocity of fluidization. B) The change in concentration. C) The temperature difference. D) The change in volume. E) The pressure change. F) The increase in temperature. 182. The surface of the elements or particles of material in a unit of volume is: A) Specific surface. B) Fraction of the free volume. C) Porosity. D) Specific volume.

292 

 

E) Surface area. F) Cross-sectional area. 183. The ratio between the quadruple fraction of the free layer and its specific surface, determines: A) Equivalent diameter for the granular layer. B) Fraction of the free volume. C) Porosity. D) Specific volume. E) Surface area. F) Cross-sectional area. 184. The relation of the volume flow rate of the liquid to the entire cross-sectio‐ nal area of the layer is called: A) Equivalent diameter. B) Fictitious velocity. C) Porosity. D) Specific volume. E) Free volume. F) The fraction of the volume occupied by the solid particles. 185. Limits corresponding to the value of the free volume of a layer of particles in the process of fluidization: A)  = 1.0 – 2.0. B)  = 1.5 – 2.0. C)  = 0.5 – 1.0. D)  = 2.5 – 3.0. E)  = 3.0 – 3.5. F)  = 2.0 – 3.5. 186. The pressure drop for the flow passing through the suspended layer of solids is determined by the equation: .

A) Δ B) Δ

1

C) Δ D) Δ E) F) Δ

∙

.

.

. .

∆

. /2 . .

187. The ratio of the working speed of the gas, referred to the total section of the apparatus, to the critical velocity is called: A) Equivalent diameter. B) The pseudo-liquefaction number. C) Porosity.

293 

 

D) Specific volume. E) Free volume. F) Wetted perimeter. 188. The fluidization number is calculated by the formula: w/w . A) K B) w w/ε. ε h . C) h ε D) ε 1 ρ /ρ . 4ε/σ. E) d F) d Reμ/wρ. 189. The actual flow velocity with a free (live) cross section between the particles of the layer is determined by the equation: A) K w/w . B) w w/ε. ε h . C) h ε D) ε 1 ρ /ρ . 4ε/σ. E) d F) d Reμ/wρ. 190. The porosity of the bed during fluidization is calculated by the formula: / . A) B) / . C) 4 / . D) 1 . E) 1 . F) 1 / 1 . 191. The volume occupied by solid particles in the apparatus is calculated by the formula: A) / . B) / . C) 4 / . D) 1 . E) 1 . F) 1 / 1 . 192. The porosity of the suspended layer depends on: A) Reynolds сriterion. B) Criterion of Galileo. C) Froude’s criterion. D) Criterion of Archimedes. E) Euler’s criterion.

294 

 

G) Newton’s criterion. H) Weber’s criterion. 193. Granular layers can be: A) Monodisperse. B) Uniform. C) Polydisperse. D) Different. E) Inhomogeneous. F) Polylayer. G) Monolayer. 194. The volume of free space between particles per unit volume occupied by the layer expresses: A) Specific surface. B) Fraction of the free volume. C) Porosity. D) Specific volume. E) Surface area. F) Fictitious speed.  

195. For a fixed layer of solid particles, porosity is determined by the equation: / . A) B) / . С) / . D) 4 / . ⁄ . E) 1 F) 1 / 1 . G) 1 . 196. The main technological parameters of fluidization are: A) Temperature difference. B) Pressure difference. C) Change in volume. D) The rate of entrainment. E) Viscosity. F) Heat capacity. G) Critical speed. H) Density. 197. In the process of fluidization, the volume occupied by a layer of solid particles is directly proportional to: A) The cross-sectional area of the particle layer. B) The viscosity. C) The height of the layer of solid particles. D) The velocity of entrainment.

295 

 

E) The free volume of the particle layer. F) The heat capacity. G) The transition state speed. H) The size of the particles. 198. In the fluidization process, the pressure drop for the flow is directly pro‐ portional to: A) The velocities of particle collisions. B) The differences in the densities of particles and the environment. C) The height of the particle layer. D) The velocity of entrainment. E) The free volume of the particle layer. F) The heat capacity. G) The transition state speed. H) The size of the particles. 199. The volume occupied by a layer of particles depends on: A) The cross-sectional area of the layer. B) The velocity of entrainment. C) The free volume of the particle layer. D) The lifting force. E) The heights of the layer of solid particles. F) The hydrodynamic pressure on the material layer. G) The fictitious speed. H) The volume occupied by solid particles. 200. The hydrodynamic pressure on the material layer depends on: A) The density of solid particles. B) The weight of the layer of solid particles. C) The particle shapes. D) The gravity. E) The lifting force. F) The frictional forces. G) The cross-sectional area of the particle layer. H) The centrifugal force. 201. The shapes and dimensions of the elements of the granular layers can be: A) In the form of granules. B) Uniform. C) As a tablet. D) Different. E) Inhomogeneous. F) In the form of large packed bodies. G) Polylayer. H) Monolayer.

296 

 

202. The granular layer is characterized by: A) The size of its particles. B) The volume. C) The temperature. D) The specific surface. E) The pressure. F) The free volume fraction. G) The concentration. H) The height. 203. Advantages of the fluidized bed are: A) The decrease in the interface between the phases. B) The abrasion of solid particles. C) The increase in the interface between the phases. D) The uneven distribution of temperature and concentration. E) The uniform temperature distribution. F) The erosion of the walls of the apparatus. G) The entrainment of solid particles by gases. H) The uniform concentration distribution. 204. The disadvantages of the fluidized bed are: A) The decrease in the interface between the phases. B) The abrasion of solid particles. C) The increase in the interface between the phases. D) The uneven distribution of concentration and temperature. E) The uniform temperature distribution. F) The erosion of the walls of the apparatus. G) The entrainment of solid particles by gases. H) The uniform concentration distribution. 205. The bulk density of silica gel is known: bulk = 650 kg/m3, particle density  = 1100 kg/m3. Calculate the porosity of the fixed layer and specify the limits for it. A) 0.44-0.47. B) 0.47-0.49. C) 0.39-0.42. D) 0.33-0.37. E) 0.37-0.43. F) 0.31-0.35. G) 0.38-0.45. H) 0.45-0.48. 206. The height of the fixed bed is known to be 0.2 m, the porosity of the fixed layer is 0.4. The density of the particles was 1200 kg/m3. Calculate the hydraulic resi‐ stance of the suspended particle layer (in Pa) and specify the limits of the values for it. A) 1410-1420.

297 

 

B) 1416-1421. C) 1421-1425. D) 1419-1426. E) 1407-1409. F) 1409-1418. G) 1418-1424. H) 1411-1417. 207. The height of the fixed bed is 0.2 m, the porosity of the fixed layer is 0.4. The thickness of the weighed layer was 0.47. Calculate the height of the weighted layer (in m) and specify the limits of the values for it. A) 0.228-0.232. B) 0.224-0.229. C) 0.223-0.225. D) 0.222-0.228. E) 0.231-0.235. F) 0.232-0.236. G) 0.221-0.231. H) 0.219-0.221. 208. The cross-sectional area of the layer of particles of 0.5 m2 is known, the height of the solid particle layer is 0.6 m and the free volume of the particle layer is 0.4. Calculate the volume occupied by a layer of solid particles (in m3), and specify the limits for values. A) 0.09-0.11. B) 0.11-0.21. C) 0.21-0.25. D) 0.24-0.27. E) 0.15-0.19. F) 0.12-0.16. G) 0.11-0.17. H) 0.17-0.23. 209. The volume occupied by a layer of solid particles of 0.37 m3 is known, the particle density is 1400 kg/m3. Calculate the weight (in kgf) of a given layer of solid particles and specify the range of values for it. A) 6160-6180. B) 6175-6195. C) 5065-5085. D) 6145-6165. E) 5070-5090. F) 5045-5065. G) 5075-5095. H) 6125-6145.

298 

 

210. The working air speed is 0.36 m/s and the porosity of the weighed layer is 0.43. Calculate the actual air velocity in the free section of the layer (in m/s) and specify the limits of the values for it. A) 0.828-0.838. B) 0.846-0.856. C) 0.815-0.825. D) 0.829-0.843. E) 0.843-0.853. F) 0.819-0.829. G) 0.835-0.845. H) 0.825-0.835. Test tasks (211-242) (Topic 1.9): 211. In technological operations, machines for transporting liquids are: A) Pumps. B) Compressors. C) Vacuum pumps. D) Fans. E) Cyclones. F) Scrubbers. 212. The volumetric coefficient of efficiency of the pump characterizes: A) The theoretical productivity. B) The number of shaft turnovers in one minute. C) The theoretical pressure. D) The suction height. E) The power loss due to mechanical friction. F) The useful power. 213. Hydraulic efficiency of the pump characterizes: A) The theoretical productivity. B) The number of shaft turnovers in one minute. C) The theoretical pressure. D) The suction height. E) The power loss due to mechanical friction. F) The useful power. 214. Mechanical efficiency of the pump characterizes: A) The theoretical productivity. B) The number of shaft turnovers in one minute. C) The theoretical pressure. D) The suction height. E) The power loss due to mechanical friction. F) The static height of the fluid supply.

299 

 

215. The pump productivity is measured in: A) m3/s. B) m2/s. C) m/s2. D) m3. E) m/s. F) m2. 216. The specific increment in the mechanical energy of the fluid flowing through the pump is: A) Productivity. B) Heat capacity. C) Power. D) Volume. E) Head. F) Weight. 217. The unit of measurement of the pump capacity is: A) kW. B) m3/s. C) N/m. D) kg/m3. E) m2/s. F) m3/h. 218. The productivity of a piston pump is determined by the formula: A) Q fsn. B) Q fs. C) Q fn. D) Q fsλ. E) Q fsnλ. F) Q 2fsλ. 219. The power of the piston pump is determined by the formula: ρ A) N . η

B) N

Δ

C) Q D) Q E) N

fsn. fsnλ.

F) N

η

.

∙ ∙

η η

.

.

220. The pump head is expressed by the equation: . A) H h ρ

300 

 

D) H C) H

hn. ρg

D) H

ρg

E) H

h

F) H

h

. . .

ρ ρ

.

221. Values of efficiency for centrifugal pumps are: A) 0.6 – 0.7. B) 0.8 – 0.9. C) 0.93 – 0.95. D) 0.8 – 0.95. E) 0.6 – 0.8. F) 0.75 – 0.85. 222. Values of efficiency for piston pumps are: A) 0.6 – 0.7. B) 0.8 – 0.9. C) 0.93 – 0.95. D) 0.8 – 0.95. E) 0.6 – 0.8. F) 0.75 – 0.85. 223. Values of efficiency for centrifugal pumps of high capacity are: A) 0.6 – 0.7. B) 0.8 – 0.9. C) 0.93 – 0.95. D) 0.8 – 0.95. E) 0.6 – 0.8. F) 0.4 – 0.5. F) 0.75 – 0.85. 224. The ratio between the real productivity to the theoretical one is called: A) The volume coefficient of efficiency. B) The transmission efficiency. C) The hydraulic efficiency. D) The efficiency of the engine. E) The mechanical coefficient of efficiency. F) The efficiency of the pump. G) The giving cofficient. H) The total efficiency. 225. The volume of fluid delivered by the pump to the delivery pipeline per unit time is determined by: A) Productivity.

301 

 

B) Pressure. C) Power. D) Giving. E) Installation power. F) Useful power. G) Power on the shaft. H) Nominal engine power. 226. The energy of a fluid when it is moved by piston pumps changes as a result of an increase: A) Pressure. B) Temperature. C) Power. D) Head. E) Density. F) Heat capacity. G) Amount of heat. 227. The volume of liquid sucked by the pump depends on: A) The number of turnovers per minute. B) The piston stroke. C) The piston section area. D) The density of the pumped liquid. E) The boiling point of the pumped liquid. F) The atmospheric pressure. G) The free fall acceleration. 228. The main parameters of the pumps are: A) Productivity. B) Temperature. C) Power. D) Viscosity. E) Density. F) Head. G) Amount of heat. H) Heat capacity. 229. The coefficient of efficiency of the pump is composed of: A) Theoretical efficiency. B) Volumetric efficiency. C) Practical efficiency. D) Hydraulic efficiency. E) Relative efficiency. F) Mechanical efficiency. G) Thermal efficiency. H) Pressure head efficiency.

302 

 

230. With the change in the number of rotations of the wheel of the centrifugal pump changes: A) Productivity. B) Volume. C) Temperature. D) Head. E) Area. F) Speed. G) Pressure. H) Consumed power. 231. For transportation of liquids by means of compressed gas use: A) Gas-lifts. B) Piston pumps. C) Monte-jus. D) Compressors. E) Gas-blowing. F) Fans. G) Centrifugal pumps. H) Air-lifts. 232. The efficiency of the pump is expressed by the product of: A) Volumetric efficiency. B) Transmission efficiency. C) Hydraulic efficiency. D) The coefficient of efficiency of the engine. E) Mechanical efficiency. F) Useful power. G) Power on the shaft. H) Nominal engine power. 233. The full efficiency of the pumping unit is expressed by the product of: A) Volumetric efficiency. B) Transmission efficiency. C) Hydraulic efficiency. D) The coefficient of efficiency of the engine. E) Mechanical efficiency. F) The coefficient of efficiency of the pump. G) Power on the shaft. H) Nominal engine power. 234. The pump power is divided into: A) Mechanical power. B) Transmission efficiency. C) Hydraulic efficiency. D) The coefficient of efficiency of the engine.

303 

 

E) Mechanical efficiency. F) Useful power. G) Power on the shaft. H) Rated engine power. 235. The pump head is equal to the sum of three terms: A) The height of the fluid in the pump. B) The coefficient of efficiency of the pump. C) Differences in the piezometric head in the pump discharge and suction pipelines. D) The supply rate. E) Differences in dynamic head in the pump discharge and suction pipelines. F) The useful power. G) The power on the shaft. H) The nominal engine power. 236. In the pumping system, the pump head is expended on: A) Movement the fluid to the geometric height of its rise. B) Efficiency of the pump. C) Differences in the piezometric head in the pump discharge and suction pipelines. D) Pump supply ratio. E) Differences in dynamic pressure in the injection and suction pipelines. F) To overcome the difference in pressure in the pressure and receiving tanks. G) Power on the shaft. H) Total hydraulic resistance in the suction and discharge pipelines. 237. The main parts of the piston pump are: A) The height of the pump. B) The efficiency of the pump. C) The piezometric head difference. D) The supply rate. E) The cylinder. F) The useful power. G) The piston. H) The suction and discharge pipelines. 238. The productivity of a piston pump is 5·10-3 м3/с, the pump’s full head is 24 m, efficiency of the pump 0.64, the density of the pumped liquid is 1120 kg/m3. Calculate the power consumed by the pump (in kW) and specify the limits for the pump. A) 1.9-2.1. B) 1.5-1.8. C) 1.3-1.7. D) 1.7-2.3. E) 2.5-2.8. F) 2.8-3.2.

304 

 

G) 2.6-2.9. H) 1.5-2.5. 239. With a single-acting piston pump with a piston diameter of 160 mm and a piston stroke of 200 mm, it is necessary to supply 7·10-3 m3/с from the collector to the apparatus. What speed of rotation should be given to the pump (in rps), if the total efficiency of pump installation is adopted as 0.72. Indicate the limits for the speed. A) 2.33-2.38. B) 2.37-2.46. C) 2.34-2.37. D) 2.44-2.48. E) 2.41-2.47. F) 2.46-2.52. G) 2.40-2.50. H) 2.48-2.54. 240. Known efficiencies: pump 0.8, transmission and electric motor to 0.95. Calculate the total efficiency of the pump unit and specify the limits for it. A) 0.68-0.74. B) 0.74-0.78. C) 0.78-0.82. D) 0.69-0.76. E) 0.64-0.68. F) 0.71-0.75. G) 0.62-0.67. H) 0.78-0.88. 241. Pressures in the suction spaces of 73 kPa and a discharge of 474 kPa are known. The density of the pumped liquid is 1600 kg/m3. Calculate the total head, developed by the pump (in H), and specify the limits for the values. A) 25.2-26.2. B) 23.3-24.3. C) 24.8-25.8. D) 23.5-24.5. E) 25.1-26.1. F) 26.2-27.2. G) 24.5-24.8. H) 23.3-23.7. 242. Calculate the performance of the piston pump (in m3/s) if the crosssectional area of the pump is 0.0201 m2, the stroke of the piston is 200 mm, and the shaft speed is 126 rpm. Specify the limits for the piston pump performance. А) 8.34·10-3- 8.38·10-3. В) 8.38·10-3- 8.48·10-3. С) 8.46·10-3- 8.56·10-3.

305 

 

D) 8.42·10-3- 8.52·10-3. E) 8.54·10-3- 8.64·10-3. F) 8.55·10-3- 8.65·10-3. G) 8.42·10-3- 8.49·10-3. H) 8.53·10-3- 8.58·10-3. Test tasks (243-272) (Topic 1.10): 243. Machines designed to move and compress gases are called: A) Pumps. B) Compressors. C) Centrifuges. D) Piston pumps. E) Centrifugal pumps. F) Hydrocyclones. 244. The compressor output is measured in: A) m3/s. B) m2/s. C) m/s2. D) kg/s. E) kg/m3. F) m2/min. 245. The theoretical work consumed by a multi-stage compressor during gas compression is measured in: A) J/kg. B) J/s. C) kW. D) kJ. E) J. F) J/h. 246. The compression ratio at which the compressor volume factor becomes zero is called: A) The harmful space. B) The limit of compression. C) The exponent of the gas expansion polytrope. D) The productivity. E) The indicator power. F) The coefficient of efficiency. 247. The ratio of the capacity of an isothermal machine to the actual power of a given machine operating with gas cooling is called: A) Thermodynamic efficiency.

306 

 

B) Isothermal efficiency. C) Adiabatic efficiency. D) Isentropic efficiency. E) Complete isothermal efficiency. F) Volumetric efficiency. 248. The product of isothermal and mechanical efficiency is called: A) Thermodynamic efficiency. B) Isothermal efficiency C) Adiabatic efficiency. D) Isentropic efficiency. E) Full isothermal efficiency. F) Hydraulic efficiency. 249. The compressor productitvity is calculated by the formula: A) QρgH/1000η. B) fsn. C) QγH/102η. D) fsnλ. E) ρgQH. F) ρg . 250. The values of the system residual pressure under high vacuum conditions are within the following limits: A) 10-3  10-8 mm Hg column. B) 1.0  560 mm Hg column. C) 1.0  10-3 mm Hg column. D) 560  760 mm Hg column. E) 1.0  760 mm Hg column. F) 460  660 mm Hg column. 251. The values of the system residual pressure under middle vacuum condi‐ tions are within the following limits: A) 10-3  10-8 mm Hg column. B) 10-8  mm Hg column. C) 1.0  10-3 mm Hg column. D) 560  760 mm Hg column. E) 1.0  760 mm Hg column. F) 460  660 mm Hg column. 252. The values of the system residual pressure under low vacuum conditions are within the following limits: A) 10-3  10-8 mm Hg column. B) 10-8  mm Hg column. C) 1.0  10-3 mm Hg column.

307 

 

D) 10-3  mm Hg column. E) 1.0  760 mm Hg column. F) 1.0  10-2 mm Hg column. 253. The ratio of the compression power of an isoentropic machine to the capacity of a given compressor operating without gas cooling is called: A) Thermodynamic efficiency. B) Isothermal efficiency. C) Adiabatic efficiency. D) Isoentropic efficiency. E) Complete isothermal efficiency. F) Mechanical efficiency. F) Hydraulic efficiency. 254. Gas compression can be a process: A) Isobaric. B) Isothermal. C) Theoretical. D) Physical. E) Chemical. F) Polytropic. G) Absorption. F) Isentropic. 255. In order to calculate the number of compression steps it is necessary to know: A) The initial and final gas pressure. B) The initial temperature of the gas. C) The polytropic index. D) The compression ratio in one stage. E) The final temperature of the gas. F) The adiabatic exponent. G) The volumetric efficiency compressor. 256. To calculate the theoretical value of the work consumed by a single-stage compressor in the adiabatic compression of 1 kg of gas, it is necessary to know: A) The polytropic index. B) The final temperature of the gas. C) The adiabatic index. D) The number of compression steps. E) The power. F) The initial and final gas pressure. G) The volumetric efficiency compressor. 257. According to the principle of operation, compressor machines are divided into: A) Piston.

308 

 

B) Volumetric. C) Centrifugal. D) Fans. F) Double action. G) Simple action. H) Vacuum pumps. 258. According to the principle of operation, compressor machines are divided into: A) Vacuum pumps. B) Volumetric. C) Axial. D) Fans. E) Rotary. F) Double action. G) Simple action. 259. In terms of the number of steps, piston compressors are divided into: A) Single stage. B) Volumetric. C) Isothermal. D) Multistage. E) Isotropic. F) Adiabatic. H) Isothermal. 260. Piston compressors in the number of suction and discharge in one double stroke of the piston are divided into compressors: A) Simple action. B) Multistage. C) Multi-cylinder. D) Single action. E) Adiabatic. F) Double action. G) Isothermal. 261. The main parameters characterizing the operation of the compressor are: A) Head. B) Productivity. C) Coefficient of friction. D) The polytropic index. E) Degree of cooling. F) Power. G) Heat capacity.

309 

 

262. Depending on the created operating pressure, all compressors are divided into: A) Two-stage. B) Multi-cylinder. C) Single action. D) Low pressure. E) Multistage. F) Simple action. G) High pressure. 263. In compressors, the movement of gas occurs as a result of: A) Suction of gas into the compressor cylinder. B) Transport of liquids. C) Gas compression by a moving piston. D) Suction of liquids by pumps. E) Gas expansion in harmful space. F) Separation of the suspension. G) Precipitation. H) Cooling of liquids. 264. Compression of a real gas is accompanied by a change in it: A) Concentrations. B) The volume. C) Entropy. D) Pressure. E) Weight. F) Temperature. G) Density. H) Viscosity. 265. The volumetric coefficient of the compressor depends on: A) Relative volume of dead space. B) Power. C) Degree of compression. D) Productivity. E) Coefficient of efficiency. F) The polytrope indicator of the gas expansion. G) Indicator power. H) Indicator pressure. 266. Compression machines, depending on the degree of compression are divided into: A) Precipitators. B) Fans. C) Pumps. D) Gas-blowes.

310 

 

E) Cyclones. F) Mixers. G) Compressors. H) Centrifuges. 267. Kinetic energy is predominantly converted into pressure energy: A) In centrifugal compressors. B) In rotary compressors. C) In piston compressors. D) In axial compressors. E) In volumetric compressors. F) In dynamic compressors. G) In jet compressors. H) In vacuum pumps. 268. Centrifugal compressors, depending on the developed pressure, are divided into: A) Turbochargers. B) Rotary. C) Piston. D) Turbo gas blowers. E) Turbofans. F) Piston vacuum pumps. G) Diffusion vacuum pumps. H) Vacuum pumps. 269. In a single-stage reciprocating compressor, air is compressed from 1 to 9 kgf/cm2. The initial air temperature is 20 °C, the adiabatic index for air is 1.4. Calculate the air temperature after compression (in °C) and specify the limits of the values for it. A) 272-278. B) 282-287. C) 285-288. D) 275-285. E) 261-271. F) 273-283. G) 257-267. H) 264-268. 270. The piston compressor compresses ammonia from 2.5 to 12 kgf/cm2. The harmful space was 8.5%, the polytropic index was 1.29. Calculate the volumetric efficiency of compressor and specify the limits for it. A) 0,65-0,75. B) 0,75-0,85. C) 0,63-0,73.

311 

 

D) 0,72-0,78. E) 0,78-0,88. F) 0,88-0,98. G) 0,85-0,95. H) 0,77-0,83. 271. The piston area is known to be 0.1 m2, the length of the piston stroke is 200 mm, the speed is 250 rpm, the gas supply factor is 0.725. Calculate the compressor productivity (in m3/s) and specify the limits for it. A) 50510-4-52510-4. B) 52410-4-53410-4. C) 59510-4-61510-4. D) 51810-4-52310-4. E) 60110-4-62110-4. F) 52310-4-53310-4. G) 53310-4-53810-4. H) 59010-4-61010-4. 272. The piston compressor compresses nitrogen from 98.1 to 9810 kPa (absolute pressure). The compression ratio was 3. Calculate the number of compression steps and specify the limits for it. A) 2-4. B) 3-7. C) 8-10. D) 4-8. E) 2-3. F) 3-5. G) 5-9. H) 8-11. Test tasks (273-305) (Topic 1.11): 273. The separation of liquid heterogeneous systems is: A) Mass exchange process. B) Heat exchange process. C) Chemical process. D) Physical process. E) Hydromechanical process. F) Diffusion process. 274. For cleaning gases from dust, ... are used: A) Cyclones. B) Centrifuges. C) Filter presses.

312 

 

D) Pumps. E) Compressors. F) Vacuum pumps. 275. The resistance of the filtering partition is calculated by the formula: ΔP/μh . A) r B) r ΔP/μ. C) R . . ΔP/μh w. D) R . . ΔP/μw. E) r0 ΔP/hос w. F) R . . ΔP/μ . 276. Specific resistance of the sediment is calculated by the formula: A) r0 ΔP/μh . B) r ΔP/μ. C) R . . ΔP/h w. D) R . . ΔP/μw. E) r ΔP/μh w. F) R . . ΔP/μ . 277. The separation factor is calculated by the formula: A) FK . B) Gw2 /gr. C) 2πn/60r. D) w /gr. E) G/gr. F) 2πn/180r. 278. In the process of filtration, the sediment resistance is determined by the formula: A) R rδ. B) R R R . .. C) R uq. D) R ΔPK. E) R ru. F) R R R , .. 279. For the filtration process, the specific resistance of the sediment is of the following dimension: А) Ns/m3. B) Ns/m2. C) Ns/m. D) Ns/m4. E) Nh/m3. F) Nh/m2.

313 

 

280. At centrifugation, the separation factor is determined by the equa‐  tion: A) 

.

B) ΔP

.

C) 

. .

D) C .

E) C F) 

.

281. When centrifuging, centrifugal force is determined by the equation: A) 

.

B) ΔP

.

C) 

. .

D) C .

E) C F) 

.

282. In cyclones, the value of the centrifugal force is determined by the equation: A) 

.

B) ΔP

.

C) 

.

D) C

.

E) C F) 

. .

283. The material balance of the separation process according to the total number of substances is determined by the equation: A) Gm = Gc.l. + Gsed. B) Gm xm = Gc.l. xc.l. + Gsed xsed. C) G = Gm xsed – xm/xsed – xc.l.. D) G = Gm xm – xc.l./xsed – xc.l.. E) G = Gc.l. xc.l. – xm/xsed – xc.l.. F) Gm = Gc.l. - Gsed.

314 

 

284. The material balance of the separation process in the dispersed phase is determined by the equation: A) Gm = Gc.l. + Gsed. B) Gm xm = Gc.l. xc.l. + Gsed xsed. C) G = Gm xsed – xm/xsed – xc.l.. D) G = Gm xm – xc.l./xsed – xc.l.. E) G = Gc.l. xc.l. – xm/xsed – xc.l.. F) Gm = Gc.l. - Gsed. 285. The separation of liquid non-uniform systems under the action of gravity forces is called: A) Upholding. B) Filtration. C) Crystallization. D) Drying. E) Centrifugation. F) Precipitation. G) Distillation. 286. When filtering suspensions on a filter, the following operations are per‐ formed: A) Sediment compaction. B) Separation of sediment. C) Sediment washing. D) Chemical cleaning of the sediment. E) Drying of a precipitate. F) Distillation of the filtrate. D) Preparation of the filtrate. 287. The separation of liquid heterogeneous systems under the action of centrifugal forces is called: A) Filtration. B) Precipitation. C) Centrifugation. D) Drying. E) Cleaning. F) Separation. G) Distillation. 288. The pressure difference on both sides of the filtering partition is created by: A) Centrifuge. B) Mixers. C) Compressors. D) Separators. E) Vacuum pumps.

315 

 

F) Heat exchangers. G) Pumps. 289. Machines in which the centrifugation is carried out are called: A) Precipitators. B) Centrifuges. C) Separators. D) Filter presses. E) Adsorbers. F) Absorbers. 290. The constrained deposition is characterized by ... A) Separating in a limited volume. B) High deposition rate. C) Separating in an unlimited volume. D) Low concentration of solid phase. E) Velocity, higher speed of free precipitation. F) High concentration of solid phase. G) Speed equal to the rate of free deposition. 291. The following hydrodynamic factors influence the process of filtering suspensions: A) The surface of particles. B) Particle weight. C) Temperature. D) Sphericity. E) Viscosity. F) Pressure. G) Porosity. H) Heat capacity. 292. The separation processes of suspensions on centrifuges include: A) Filtration. B) Stirring. C) Upholding. D) Evaporation. E) Crystallization. F) Clarification. G) Absorption. H) Adsorption. 293. Air-dispersed systems include: A) Foams. B) Dusts. C) Emulsions. D) Fogs.

316 

 

E) Smokes. F) Slurries. G) Dregs. H) Suspensions. 294. Depending on the size of the solid particles, suspensions are conditionally divided into: A) Foams. B) Dusts. C) Emulsions. D) Fogs. E) Smokes. F) Thin. G) Dregs. H) Rough. 295. Suspended in a liquid or gas, solid or liquid particles are separated from the continuous phase under the action of ... A) Gravity. B) Repulsive force. C) The force of attraction. D) Electromagnetic forces. E) Friction force. F) The inertia force. G) Electrostatic forces. H) Centrifugal forces. 296. The main methods of separation of heterogeneous systems are ... A) Filtration. B) Distillation. C) Crystallization. D) Drying. E) Rectification. F) Upholding. G) Distillation. H) Centrifugation. 297. Non-homogeneous systems include ... A) Suspensions. B) Aqueous solutions of acids. C) Aqueous solutions of salts. D) Alloys of metals. E) Foams. F) Aqueous solutions of bases. G) Emulsions. H) Salt melts.

317 

 

298. The material balance of the separation process according to the total number of substances consists of ... A) The mass of the initial mixture. B) The mass of the mother liquid. C) The volume of the initial mixture. D) The amount of clarified liquid. E) The volume of the obtained precipitate. F) The mass of clarified liquid. G) The mass of the obtained precipitate. H) The volume of the mother liqiuid 299. The dynamic coefficient of the liquid phase of the suspension is 2810-3 Pas, the filtration rate is 0.0410-3 m3/(m2s) and the pressure difference is 3103 Pa. Calculate the resistance of the filtering partition (in m-1) and specify the limits of the values for it. A) 2.52109 – 2.58109. B) 2.63109 – 2.69109. C) 2.51109 – 2.56109. D) 2.54109 – 2.59109. E) 2.65109 – 2.72109. F) 2.57109 – 2.63109. G) 2.61109 – 2.64109. H) 2.67109 – 2.71109. 300. The dynamic coefficient of the liquid phase of the suspension is 2510-3 Pas, the filtration rate is 0.0510-3 m3/(m2s), the pressure difference is 3.5103 Pa and the height of the sediment is 0.01 m. Calculate the resistance sediment (in m-2) and specify the limits of values for it. A) 261010- 311010. B) 211010- 251010. C) 271010- 291010. D) 221010- 271010. E) 331010- 361010. F) 321010- 351010. G) 251010- 321010. H) 351010- 381010. 301. The dynamic coefficient of the filtrate is 2010-3 Pas, the mass of the dry solid is 0.1 kg/m3 and the specific resistance of the sediment is 7.6109 m/kg of dry sediment. The pressure drop across the filter was 3103 Pa. Calculate the filtering constant (in m2/s) and specify the limits for it. A) 0.38210-3- 0.38610-3. B) 0.38510-3- 0.38810-3. C) 0.39010-3- 0.39710-3.

318 

 

D) 0.38310-3- 0.38510-3. E) 0.39410-3- 0.39810-3. F) 0.38710-3- 0.39710-3. G) 0.39110-3- 0.39410-3. H) 0.38710-3- 0.38910-3. 302. The specific resistance of the filtering wall is 2.7108 m/m2, the specific resistance of the sediment is 7.6109 m/kg of dry sediment and the mass of dry solid to 1 m3 of the filtrate is 0.1 kg/m3. Calculate the filtering constant (in m3/m2) and specify the limits of the values for it. A) 0.351-0.358. B) 0.451-0.458. C) 0.346-0.356. D) 0.456-0.459. E) 0.453-0.458. F) 0.452-0.455. G) 0.357-0.359. H) 0.353-0.357. 303. The mass of a sediment and liquid located in the centrifuge drum is found to be 400 kg, the rotational speed of the centrifuge is 1200 rpm, the diameter of the drum is 800 mm. Calculate the centrifugal force (in N), developed during centrifugation, and specify the limits of the values for it. A) 2.61106- 2.64106. B) 2.66106- 2.69106. C) 2.62106- 2.67106. D) 2.65106- 2.68106. E) 2.50106- 2.58106. F) 2.53106- 2.57106. G) 2.49106- 2.59106. H) 2.51106- 2.54106. 304. After filtering 5 kg of the suspension, 1.5 kg of a wet sediment is formed. Determine the mass of the filtrate (in kg) and specify the limits for the quantities. A) 2.9 – 3.9. B) 2.2 – 2.8. C) 3.7 – 3.9. D) 2.8 – 3.2. E) 2.5 – 2.9. F) 3.3 – 3.8. G) 2.8 – 3.6. H) 2.3 – 2.7.

319 

 

305. After filtering 15 kg of the suspension, 5.0 kg of wet sediment is formed. Determine the mass of the filtrate (in kg) and specify the limits for the quantities. A) 5 – 8. B) 7 – 15. C) 12 – 18. D) 14 – 19. E) 16 – 22. F) 9 – 12. G) 8 – 16. H) 7 – 9.

320 

 

THERMAL PROCESSES: Test tasks (1-25) (Topic 2.1): 1. The transfer of heat energy between the system under consideration and the environment is: A) The hydromechanical process. B) The heat exchange process. C) The mass exchange process. D) The physical process. E) The chemical process. F) The diffusion process. 2. The process of heat energy transfer by direct contact between particles of a body with different temperatures is called: A) Convection. B) Thermal conductivity. C) Radiation. D) Heat exchange. E) Heat emission. F) Heat transfer. 3. If the temperature is a function of only spatial coordinates, then such a temperature field is called: A) Stationary. B) Non-stationary. C) Unsteady. D) True. E) Average. F) Periodic. 4. The set of temperature values at a given time for all points of the environment under consideration is called: A) Temperature field. B) Thermal field. C) Thermal conductivity. D) Heat emmision. E) Heat exchange. F) Temperature gradient. 5. The derivative of the temperature along the normal to the isothermal surface is called: A) Temperature field. B) Thermal field.

321 

 

C) Thermal conductivity. D) Heat emmision. E) Temperature gradient. F) Heat transfer. 6. The basic law of thermal conductivity is called: A) Newton’s law. B) The law of Navier-Stokes. C) The law of of Stefan-Boltzmann. D) Fourier’s law. E) Kirchhoff’s law. F) Avogadro’s law. 7. If the temperature is a function of spatial coordinates and time, then such a temperature field is called: A) Stationary. B) Non-stationary. C) Steady. D) True. E) Average. F) Continuous. 8. The unit of measurement of the coefficient of thermal conductivity is: A) W/(mK). B) W/(m2K). C) J/(kgK). D) J/kg. E) kW. F) (m2K)/W. 9. Dimension of heat quantity: A) J/(kgK). B) J. C) W/(m2K). D) J/kg. E) W/(mK). F) (m2K)/W. 10. The driving force of the heat exchange process is: A) Temperature field. B) Temperature difference. C) Temperature head. D) Thermal diffusivity. E) Thermal conductivity. F) Temperature gradient.

322 

 

11. The amount of heat transferred through thermal conductivity through a surface element perpendicular to the heat flow in time  is directly proportional to the temperature gradient, surface and time. This dependence is called: A) Newton’s law. B) The law of Navier-Stokes. C) Fourier’s law. D) Kirchhoff’s law. E) The law of Stefan-Boltzmann. F) The basic law of heat transfer by thermal conductivity. 12. The thermal conductivity of a flat wall under steady-state thermal conditions is given by: . A) B)

.

,

C)

.

D)

. .

E) Δ

F)

.

∑

13. The thermal conductivity of a cylindrical wall in the steady-state process of heat exchange is determined by the formula: . A) B)

.

,

.

C) D) E)

. π ∑

.

,

F)

.

14. The basic law of heat transfer by thermal conductivity is described by the equation: . A) B) С) D)

. ,

. .

323 

 

.

E) F)

π ∑

.

,

15. The nonstationary temperature field is described by the equation: A) t = f(x, y, z). B) t = f(x, y, z, ). C) t = f(x, y, ). D) t = f(x, y). E) t = f(y, z). F) t = f(x, z). 16. The stationary temperature field is described by the equation: A) t = f(x, y, z). B) t = f(x, y, z, ). C) t = f(x, y, ). D) t = f(x, y). E) t = f(y, z, ). F) t = f(x, z, ). 17. The differential equation of thermal conductivity in a stationary environment under steady-state thermal conditions is described by the equation: A) . B)

.

С)

.

,

0.

D) E) F)

. t

0.

18. There are three fundamentally different elementary modes of heat sprea‐ ding: A) Thermal conductivity. B) Thermal diffusivity. C) Thermal radiation. D) Heat emission. E) Heat transfer. F) Convection. G) Mass conductivity. H) Mass emmision.

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19. The amount of heat transmitted through thermal conductivity is directly proportional: A) To the emperature gradient. B) To the mass transfer coefficient. C) The the heat exchange surfaces. D) To the mass transfer coefficient. E) To the the time of heat exchange. F) Heat emission coefficient. G) Heat transfer coefficient. H) Emission ability of the body. 20. Depending on the temperature change in the direction of the axis of coordinates, the temperature field can be: A) One-dimensional. B) Straight line. C) Unsteady. D) Two-dimensional. E) Unsteady. F) Three-dimensional. G) Average. H) True. 21. The coefficient of thermal conductivity of a 25% solution of sodium chloride at 30 °C was 0.548 W/(mK), and the coefficients of thermal conductivity of water at 80 and 30 °C were 0.674 and 0.615 W/(mK), respectively. The coefficient of thermal conductivity of the solution (in W/(mK)) at 80 °С will be in the range: A) 0.2-0.9. B) 0.7-0.8. C) 0.4-0.7. D) 0.8-0.9. E) 0.8-1.0. F) 0.5-0.7. G) 0.9-1.0. H) 0.7-0.9. 22. The value B = 1.9 is known, the specific heat at constant volume c = 0.748103 J/(kgK) and the dynamic coefficient of air viscosity at 300 °С  = 2,9710-5 Pas. The coefficient of thermal conductivity of dry air (in W/(mK)) at 300 °С will be within the limits of: A) 0.0422-0.0425. B) 0.0427-0.0430. C) 0.0428-0.0432. D) 0.0420-0.0423. E) 0.0425-0.0426. F) 0.0429-0.0433.

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G) 0.0432-0.0435. H) 0.0421-0.0426. 23. Convective heat transfer occurs due to the movement of water at a velocity of w = 1.2 m/s at 80 °C. If the water density at 80 °C is known to be 972 kg/m3 and the specific heat capacity of water is cw = 4.19103 J/(kgK), then the heat flow density (in W/m2) transferred by convection in the direction of motion water will be within: A) (390-392)106. B) (391-393)106. C) (395-398)106. D) (394-397)106. E) (393-396)106. F) (396-399)106. G) (389-394)106. H) (397-398)106. 24. The device is covered with a layer of thermal insulation made of asbestos 75 mm thick. The coefficient of thermal conductivity of asbestos is 0.151 W/(mK). The wall temperature of the apparatus is 146 °C, and the temperature of the outer surface of the insulation is 40 °C. If the average area through which heat passes is 38.8 m2, then the heat flow (in W) through the isolation layer will be in the range: A) 8288-8320. B) 8279-8281. C) 8287-8295. D) 8280-8282. E) 8289-8297. F) 8278-8283. G) 8291-8298. H) 8290-8296. 25. The coefficient of thermal conductivity of nitrobenzene at 30 °C is known to be 30 = 0.149 W/(mK), the temperature coefficient is  = 1.010-3 °С-1. The coefficient of thermal conductivity (in W/(mK)) of nitrobenzene at 120 °C will be in the range: A) 0.135-0.137. B) 0.138-0.144. C) 0.134-0.136. D) 0.140-0.141 E) 0.139-0.143. F) 0.137-0.141. G) 0.136-0.138. H) 0.139-0.142.

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Test tasks (26-50) (Topics 2.2-2.4): 26. Simultaneous transfer of heat by convection and thermal conductivity is called: A) Convective heat exchange. B) Thermal conductivity. C) Radiation. D) Heat transfer. E) Heat emission. F) Thermal diffusivity. 27. The dependence in which the radiant ability of an absolutely black body is proportional to the fourth power of the absolute temperature of its surface is called the law of: A) Newton. B) Navier-Stokes. C) Fourier. D) Kirchhoff. E) Stefan-Boltzmann. F) Avogadro. 28. The unit of measurement of the heat emission coefficient is: A) W/(m2K). B) J/(kgK). C) J/kg. D) W/(mK). E) kW. F) (m2K)/W. 29. The amount of energy radiated by a unit of surface per unit time is called: A) Emission ability of the body. B) The absorptive capacity of the body. C) Ray-reflecting ability of the body. D) Radiant transmissivity of the body. E) Radiation of the body. F) Luminous ability of the body. 30. If the body absorbs all the energy falling on it, then such a body is called: A) Absolutely white. B) Gray. C) Absolutely black. D) Absolutely transparent. E) Absolutely colorless. F) White.

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31. If the body reflects all the energy falling on it, then such a body is called: A) Absolutely white. B) Gray. C) Absolutely black. D) Absolutely transparent. E) Absolutely colorless. F) Transparent. 32. If the body passes all the energy falling on it, then such a body is called: A) Absolutely white. B) Gray. C) Absolutely black. D) Absolutely transparent. E) Absolutely colorless. F) White. 33. The emission ability of a body is determined by the formula: A) . ⁄100 . B) C) / . D) ∆ . Е) ∆ . F) ∆ . 34. The amount of heat given off by a unit of surface per unit time with a difference in temperature between a solid surface and the environment of one degree is called the coefficient A) Heat transfer. B) Thermal conductivity. C) Heat emission. D) Viscosity. E) Diffusion. F) Thermal diffusivity. 35. In convective heat exchange, heat transfer occurs simultaneously by: A) Thermal conductivity. B) Thermal radiation. C) Convection. D) Temperature gradient. E) Mass transfer. F) Mass exchange. 36. The process of spreading of electromagnetic oscillations with different wavelengths, caused by the thermal motion of atoms or molecules, is called: A) Thermal conductivity.

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B) Thermal radiation. C) Convection. D) Temperature gradient. E) Radiant heat exchange. F) Heat transfer. 37. The amount of heat transferred from the heat exchange surface to its environment, or, conversely, from the environment to the heat exchange surface, is directly proportional to the heat exchange surface area, the tempera‐ ture difference between the heat surface and the environment and time. This definition is called: A) Newton’s law. B) The law of Navier-Stokes. C) Fourier’s law. D) Kirchhoff’s law. E) The law of Stefan-Boltzmann. F) Heat emission law. 38. Convective heat exchange is described by the equation: . A) ⁄100 . B) C) . D) ∆ . Е) . F) . 39. The law of Stefan-Boltzmann is expressed by the equation: . A) ⁄100 . B) C) . D) ∆ . Е) ∆ . F) . 40. The Nusselt criterion is expressed by the formula: A) / . B) / . C) / . D) / . E) / . F) / . 41. The generalized equation of convective heat exchange has the form: A) Nu f Re, Pr, Fo, Fr, Gr, G, G … . B) Nu f Re, Eu, Fr .

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C) Nu D) Nu E) Nu F) Nu

f Re, Pr, Gr, Ga, G , G … . f Re, Er, Fr, Ho . f Re, Fr . f Re, Eu .

42. The generalized equation for determining the coefficient of heat emission from condensing vapors is: A) Nu f Re, Pr, Fo, Fr, Gr, G , G … . B) Nu f Ga, Pr, K . C) Nu f Re, Pr, Gr, Ga, G , G … . D) Nu f Re, Eu, Fr, Ho . E) Nu f Re, Fr, Eu . F) Nu C Ga ∙ Pr ∙ K , . 43. The coefficient of heat emssion depends on the following factors: A) The Reynolds criterion. B) The Euler’s criterion. C) The Froude’s criterion. D) Thermal properties of a liquid. E) Criterion of homochrony. F) Geometric parameters. G) Power criterion. H) Weber’s criterion. 44. According to Newton’s law, the amount of heat in convective heat exchange for a continuous process is directly proportional to: A) The difference in wall and liquid temperatures. B) The mass emission coefficient. C) The heat exchange surfaces. D) The mass transfer coefficient. E) The coefficient of thermal conductivity. F) The heat emission coefficient. G) The heat transfer coefficient. H) The emissivity of the body. 45. Nusselt’s criteria include the following parameters: A) The diameter of the pipe. B) Mass emission coefficient. C) Heat transfer surface. D) Mass transfer coefficient. E) Coefficient of thermal conductivity. F) Heat emission coefficient. G) Heat transfer coefficient. H) Heat capacity.

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46. Reynolds criteria of 23,000, Prandtl’s criterion for alcohol 6.3 and Prandtl’s criterion of the wall of 5.94 are known. For l = 1, the Nusselt’s criterion will be within the limits of: A) 143-146. B) 147-157. C) 144-147. D) 146-148. E) 147-148. F) 148-149. G) 141-149. H) 148-151. 47. The specific heat capacity of benzene at 55 °C was c = 1800 J/(kgK). The dynamic viscosity coefficient of benzene at 55 °C is  = 0.41310-3 Pa·s, and the coefficient of thermal conductivity of benzene at this temperature is  = 0.14 W/(mK). The value of the Prandtl’s criterion will be in the range: A) 5.31-5.33. B) 6.37-6.39. C) 5.29-5.32. D) 6.36-6.38. E) 6.35-6.37. F) 5.33-5.36. G) 5.27-5.32. H) 5.32-5.34. 48. The Nusselt’s criterion was 7.24, the brine thermal conductivity  = 0.467 W/(mK) and the internal diameter of the tubes was 21 mm. The heat emission coefficient (in W/(m2K)) of the brine will be in the range: A) 159-162. B) 162-164. C) 163-165. D) 161-163. E) 163-166. F) 155-158. G) 156-159. H) 158-163. 49. The height of the pipes in the vertical casing tubular heat exchanger was 1.25 m, the density of carbon tetrachloride was 1560 kg/m3 and the dynamic viscosity coefficient of CCl4 at 37 °C was 0.7710-3 Pas. The value of the Galileo’s criterion will be within: A) (78.4-78.7)1012. B) (78.1-78.3)1012. C) (78.2-78.4)1012.

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D) (78.3-78.5)1012. E) (78.2-78.9)1012. F) (78.4-78.5)1012. G) (78.5-79.5)1012. H) (78.6-78.9)1012. 50. Galileo’s criteria Ga = 78.61012, Prandtl’s Pr = 6 and Reynolds Re = 5660 are known. For turbulent run-off of a film, the Nusselt’s criterion will be within the limits of: A) 11000-13000. B) 13500-13958. C) 12500-13500. D) 13957-13959. E) 13891-13898 F) 11500-12500. G) 13100-13200. H) 11900-12300. Tests tasks (51-75) (Topic 2.5): 51. The transfer of heat along the normal to the contact surface is called: A) Heat emission. B) Thermal conductivity. C) Heat transfer. D) Convective heat emission. E) Thermal radiation. F) Temperature gradient. 52. The analysis and calculation of heat transfer along the normal to the heat transfer surface is based on: A) Heat emission equation. B) Equation of heat conductivity. C) Heat transfer equation. D) Equation of convective heat emission. E) The equation of thermal radiation. F) Differential equation of heat condustivity. 53. The amount of heat transferred per unit time through a unit of surface at a single unit temperature head in 1 degree is: A) Heat emission coefficient. B) Coefficient of thermal conductivity. C) Heat transfer coefficient. D) Coefficient of temperature conductivity.

332 

 

E) Coefficient of heat emission by radiation. F) Flow coefficient. 54. The heat balance equation for the heat transfer process is expressed by the equation: A) Q = G1· (I1in + I1f) = G2·(I2in + I2f). B) Q = G1·(I1f – I1in) = G2·(I2f – I2in). С) Q = G1·(I1in – I1f) = G2·(I2f – I2in). D) Q = G1·(I1in - I1f) = G2·(I2in - I2f). E) Q = G1·(I2f – I2in) = G2·(I1f – I1in). F) Q = G1·(I1in - I1f) = G2·(I2in + I2f). 55. Any auxiliary coating that helps to reduce heat loss to the environment is called: A) Thermal insulation. B) Heat emission. C) Thermal conductivity. D) Heat transfer. E) Heat carrier. F) Radiation. 56. The inverse of the heat transfer coefficient is called: A) Wall resistance. B) The total thermal resistance. C) Thermal resistance of the environment. D) Thermal resistance. E) Thermal resistance of the wall. F) Thermal resistance of impurities. 57. Thermal resistance of the insulation layer is expressed by the formula: . A) ⁄ ⁄ ⁄

B) ⁄ . C) ⁄

.

D) E) F)

.

⁄

. ⁄

⁄

.

58. The thermal resistance of heat emission to the environment is expressed by the formula: . A) ⁄ ⁄ ⁄ B) ⁄ .

333 

 

C)

⁄

.

D) E) F)

.

⁄

. ⁄

⁄

.

59. The thermal resistance of a flat wall is determined by the formula: . A) ⁄ ⁄ ⁄

B) ⁄ . C) ⁄

.

D) Е) F)

.

⁄

. ⁄

⁄

.

60. The main equation of heat transfer is expressed by the formula: A) . ⁄100 . B) C) . /100 . D) E) Q KF∆t . F) Q KF∆t τ. 61. The unit of measurement of the heat transfer coefficient is: A) J/(kgK). B) J. C) W/(m2K). D) J/kg. E) W/(mK). F) kcal/(m2hK). 62. The heat transfer equation for a flat wall at constant temperatures of heat carries has the form: . A) ⁄100 . B) C) . /100 . D) E) . . F) 63. The total thermal resistance consists of: A) Thermal resistance of a more and less heated environment.

334 

 

B) Coefficient of thermal conductivity. C) Heat emission coefficient. D) Thermal resistance. E) Thermal resistance of the wall. F) Thermal resistance of the multilayer wall. 64. The linear heat transfer coefficient per unit length of the pipe is expres‐  sed in: A) W/(mK). B) kcal/(mhK). C) W/(m2K). D) J/kg. E) J/s. F) kcal/(m2hK). 65. The application of a layer of thermal insulation to the wall allows us to: A) Increase heat transfer. B) Reduce the thermal resistance. C) Increase the thermal resistance. D) Increase heat transfer and reduce thermal resistance. E) Increase the loss of heat to the environment. F) Reduce the loss of heat to the environment. 66. For a tubular heat exchanger consisting of several pipes, the heat transfer equation can be represented as: A) Q K nL∆t . ∆ ∆ B) Q K nL ∆ ⁄∆ . C) D) E) F)

. /100 . . .

67. The heat transfer coefficient is expressed by the equation: . A) ⁄ ⁄ ⁄ B) C)

⁄ .

⁄

⁄

.

D) Е) F)

.

. .

335 

 

68. According to the basic equation of heat transfer, the amount of heat transferred is a product of: A) Differences in temperatures of hot and cold heat carriers. B) Temperature differences of cold and hot heat carriers. C) Coefficient of friction. D) Heat transfer coefficient. E) Heat emission coefficient. F) Area of the heat exchange surface. G) Interphase contact surface. H) Temperature of heat carrier. 69. In the continuous processes of heat exchange, the following variants of the direction of motion of liquids relative to each other along the wall separating them are possible: A) Parallel current. B) Downward current. C) Ascending current. D) Counter-current. E) Constant current. F) Alternating current. G) Cross-current. H) Stationary current. 70. The total thermal resistance consists of: A) Thermal resistance of a more heated environment. B) The amount of heat given off by the wall to a less heated environment. C) The amount of heat transferred from a more heated environment to the wall. D) Thermal resistance of a less heated environment. E) The amount of heat passing through the wall layer. F) The amount of heat transferred by convection. G) Thermal resistance of the multilayer wall. H) The amount of heat transmitted by thermal radiation. 71. The initial and final temperatures of the cracking residue are known tin = 300 °C, tf = 200 °C and oil tin = 25 °C, tf = 175 °C. Both liquids move in one direction. The average temperature difference (in °C) in the heat exchanger between the heating cracking residue and the heated oil will be in the range: A) 101-107. B) 100-102. C) 103-106. D) 101-103. E) 98-102. F) 93-101. G) 102-112. H) 105-106.

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72. The initial and final temperatures of the cracking residue are known tin = 300 °C, tf = 200 °C and oil tin = 25 °C, tf = 175 °C. Both liquids move in opposite directions. The average temperature difference (in °C) in the heat exchanger between the heating cracking residue and the heated oil will be in the range: A) 150-154. B) 154-156. C) 153-157. D) 149-152. E) 154-156. F) 152-154. G) 148-151. H) 155-156. 73. The heat transfer coefficient was 400 W/(m2K). The surface area of heat transfer is 95 m2, the average temperature difference between hot and cold heat carriers is 37.5 °C. The value of the heat flow (in W) will be in the range: A) (1420-1428)103. B) (1434-1436)103. C) (1417-1427)103. D) (1435-1438)103. E) (1431-1434)103. F) (1421-1423)103. G) (1422-1426)103. H) (1431-1433)103. 74. The heat transfer coefficient is 400 W/(m2K) and the average temperature difference between hot and cold heat carriers is 37.5 °C. Specific heat load (in W) will be in the range: A) (150-152)102. B) (165-168)102. C) (164-167)102. D) (167-169)102. E) (148-151)102. F) (158-168)102. G) (149-153)102. H) (155-165)102. 75. The coefficient of heat emission for hot and cold heat carriers are 10000 and 1630 W/(m2K), the sum of the thermal resistances of all layers of which the wall consists, including layers of contamination 3.9210-4 W/(m2K). The value of the heat transfer coefficient (in W/(m2K)) will be in the range: A) 904-906. B) 899-901.

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C) 903-907. D) 902-904. E) 898-901. F) 897-899. G) 902-912. H) 895-897. Test tasks (76-100) (Topics 2.6, 2.7): 76. Devices for transfer of heat from the hot environment to the cold one are called: A) Heat exchangers. B) Heat emission. C) Thermal conductivity. D) Heat transfer. E) Heat carrier. F) Mixers. 77. The overall material balance of the evaporaton device is expressed by the equation: A) G1 = G2 + W. B) G1a1 = G2a2. C) G2 = G1·а1/а2. D) W = G1(1– а1/а2). E) G2 = G1 – W. F) G1 = G2·а2/а1. 78. The material balance of an absolutely dry substance in solution is expressed by the equation: A) G1 = G2 + W. B) G1a1 = G2a2. C) G2 = G1·а1/а2. D) W = G1(1– а1/а2). E) G2 = G1 – W. F) G1 = G2·а2/а1. 79. The material balance of the evaporation device according to the evaporated solution is expressed by the equation: A) G1 = G2 + W. B) G1a1 = G2a2. C) G2 = G1·а1/а2. D) W = G1(1– а1/а2). E) G2 = G1 – W. F) G1 = G2·а2/а1.

338 

 

80. The material balance of the evaporation device on evaporated water is expressed by the equation: A) G1 = G2 + W. B) G1a1 = G2a2. C) G2 = G1·а1/а2. D) W = G1(1– а1/а2). E) G2 = G1 – W. F) G1 = G2·а2/а1. 81. If the transfer of heat from the hot heat carrier to the cold one takes place by direct mixing of them, then such devices are called: A) Casing tubular. B) Coiled. C) Regenerative. D) Spiral. E) Mixing. F) Recuperative. 82. The process of concentrating solutions by removing the solvent by evaporation during boiling is called: A) Evaporation. B) Upholding. C) Absorption. D) Adsorption. E) Rectification. F) Condensation. 83. The difference between the boiling points of the solution and the pure solvent at the same external pressure is called: A) Hydrostatic depression. B) Hydraulic depression. C) Total depression. D) Incomplete depression. E) Temperature depression. F) Complete depression. 84. An increase in the temperature of solution rolling due to the increase in pressure in the apparatus due to friction and local resistance is called: A) Hydrostatic depression. B) Hydraulic depression. C) Total depression. D) Incomplete depression. E) Temperature depression. F) Complete depression.

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85. Surface heat exchangers include: A) Casing tubular heat exchangers. B) Coil heat exchangers. C) Mixing heat exchangers. D) Barometric capacitors. E) Scrubbers. F) Regenerators. 86. Contact heat exchangers include: A) Casing tubular heat exchangers. B) Coil heat exchangers. C) Mixing heat exchangers. D) Irrigation heat exchangers. E) Scrubbers. F) Regenerators. 87. The steam used during evaporation is called: A) Secondary steam. B) Heating steam. C) Primary steam. D) Sharp steam. E) Dry steam. F) Wet steam. 88. Upon evaporation under vacuum, it becomes possible to carry out the process: A) At higher temperatures. B) At atmospheric pressure. C) At lower temperatures. D) With a smaller heating surface. E) At a pressure above atmospheric. F) With a larger heating surface. 89. Multi-casing evaporators are distinguished by the pressure of the secondary steam in the last case and, according to this characteristic, are divided into the following: A) At higher temperatures. B) With a larger heating surface. C) At lower temperatures. D) With a smaller heating surface. E) Under vacuum. F) Under overpressure. 90. In the heat balance equation of the evaporator, the heat input is com‐ posed of: A) Loss of heat to the environment. B) Heat received from the heat carrier.

340 

 

C) Heat of the initial solution. D) Heat of evaporated solution. E) Heat of secondary steam. F) Heat of dehydration of solute. 91. The equation of the material balance of the evaporator consists of: A) The heat of evaporated solution. B) The heat of the evaporated solvent. C) The amount of evaporated solution. D) The amount of evaporated solvent. E) The heat of secondary steam. F) The heat of dehydration of solute. 92. In terms of the way heat is supplied, evaporators are distingui-shed: A) Heating through the heat transfer surface. B) Heating by direct contact of the heating agent and solution. C) Working under increased pressure. D) Working under underpressure. E) Working under atmospheric pressure. F) Working under vacuum. 93. The following types of heat exchangers are distinguished by the ways of contact of hot and cold heat exchangers: A) Recuperators. B) Regenerators. C) Contact. D) Condensers. E) Reflux condensers. F) Compressors. G) Classifiers. H) Separators. 94. The evaporator generates temperature losses that reduce the temperature difference between the heating steam and the evaporated solution. They are composed of: A) The temperature depression. B) The hydraulic depression. C) The hydrostatic depression. D) The boiling point of solution. E) The boiling point of the solvent. F) The secondary vapor temperature. G) The heating vapor temperature. H) The primary vapor temperature.

341 

 

95. In the equation of the heat balance of the evaporator, the heat consumption is composed of: A) The loss of heat to the environment. B) The heat obtained from the heat carrier. C) The heat of the initial solution. D) The heat of evaporated solution. E) The heat of secondary steam. F) Thr primary steam heat. G) The heat of heating steam. H) The heat of the solution to be evaporated. 96. A mass flow of the initial solution of 1000 kg and the mass fractions of the dissolved substance in the initial and final solutions of 0.0733 and 0.54 are known. For 1 ton of initial solution, the amount of evaporated water (in kg) will be in the range: A) 864-868. B) 875-878. C) 874-779. D) 863-865. E) 876-781. F) 861-862. G) 873-876. H) 862-866. 97. The heat consumption for evaporation was 763.22 kW. The specific enthalpy of dry saturated vapor is 2753103 J/kg and the specific enthalpy of condensate at a condensation temperature of 633103 J/kg. The dryness of the heating steam was 0.95. The flow rate of the heating steam (in kg/h) evaporator is in the range: A) 1366-1368. B) 1364-1366. C) 1367-1369. D) 1363-1365. E) 1365-1367. F) 1361-1362. G) 1362-1367. H) 1360-1361. 98. The consumption of heating steam was 2.4 kg/s. The evaporated water flow rate was 2.22 kg/s. Specific steam consumption (in kg/s) for evaporation will be in the range: A) (106-109)10-2. B) (102-106)10-2. C) (107-108)10-2. D) (101-105)10-2.

342 

 

E) (103-104)10-2. F) (105-110)10-2. G) (98-106)10-2. H) (99-105)10-2. 99. The amount of heat transferred from the heating steam to the boiling solution of 5120103 J/(kgK) is known, the heat transfer coefficient is 1000 W/(m2K), the useful temperature difference is 22.4 K. The heating surface area (in m2) of the evaporator will be within: A) 227 – 231. B) 221 – 224. C) 223 – 225. D) 224 – 226. E) 225 – 227. F) 220 – 223. G) 225 – 232. H) 228 – 233. 100. The amount of heat transferred from the heating steam to the boiling solution was 5120103 J/(kgK), and the specific heat of vaporization of heating steam at   pabs = 1.4 kgf/cm2 is equal to 2237103 J/(kgK). The dryness of the heating steam was 0.95. The flow rate of the heating steam (in kg/s) in the evaporator will be in the range: A) 2.41-2.44. B) 2.52-2.54. C) 2.39-2.42. D) 2.51-2.53. E) 2.50-2.56. F) 2.44-2.48. G) 2.38-2.43. H) 2.54-2.58. Test tasks (101-125) (Topic 2.8): 101. Substances involved in the heat transfer process are called: A) Heat carriers. B) Heat exchangers. C) Heat emission. D) Thermal conductivity. E) Heat transfer. F) Thermal diffusivity. 102. Heat carriers that have a higher temperature than the heated environment and give off heat are usually called: A) Heating agents.

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B) Cooling agents. C) Thermal conductivity. D) Heat transfer. E) Heat exchangers. F) Refrigerants. 103. Heat carriers with a lower temperature than the environment from which they receive heat, it is customary to call: A) Heating agents. B) Cooling agents. C) Thermal conductivity. D) Heat transfer. E) Heat exchangers. F) Heating agents. 104. Substances that receive heat from direct heat sources and transmit it through a heat exchanger wall to a heated environment are commonly referred to as: A) Intermediate heat carriers. B) Cooling agents. C) Heating agents. D) Dielectrics. E) Heat exchangers. F) Heaters. 105. Indicate the heat carrier, which is used when heated to 150-170 °С: A) Flue gases. B) Water vapor. C) Electric current. D) Diphenyl mixture. E) Mineral oils. F) Diphenyl ether. 106. Indicate the heat carrier, which is used when heated to 1000 °С and above: A) Flue gases. B) Water vapor. C) Overheated water. D) Diphenyl mixture. E) Mineral oils. F) Diphenyl ether. 107. Indicate the heat carrier, which is used when heated to 250-300 °С: A) Flue gases. B) Water vapor.

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C) Electric current. D) Diphenyl mixture. E) Mineral oils. F) Diphenyl ether. 108. Indicate the heat carrier, which is used when heated to 260-380 °С: A) Flue gases. B) Water vapor. C) Electric current. D) Diphenyl mixture. E) Mineral oils. F) Natural gas. 109. The main disadvantage of water vapor as a heating agent: A) Significant increase in pressure with increasing temperature. B) Provides uniform heating. C) High energy intensity. D) High intensity of heat emission. E) Has a significant enthalpy. F) Decrease in pressure with increasing temperature. 110. Water vapor, used as a heating agent, is called: A) Secondary steam. B) Sharp steam. C) Primary steam. D) Deaf steam. E) Dry steam. F) Wet steam. 111. Essential shortcomings of metallic coolants (lithium, potassium, sodium, mercury) are: A) Chemical activity. B) Toxicity. C) Soot formation. D) Ash formation. E) Increase in pressure. F) Uneven heating. 112. The essential disadvantages of flue gases, as heating heat carrier, are: A) Chemical activity. B) Toxicity. C) Soot formation. D) Ash formation. E) Increase in pressure. F) Uniformity of heating.

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113. The advantages of flue gases in comparison with other heating heat carriers are: A) Their cheapness. B) High temperature. C) Constant condensation temperature. D) High intensity of heat emission. E) Increase in pressure. F) Uneven heating. 114. The advantages of water vapor over other heating agents are: A) Their cheapness. B) High temperature. C) Uniformity of heating. D) High intensity of heat emission. E) Increase in pressure. F) Uneven heating. 115. The advantages of vapors of high boiling organic heat carriers compared to other heating agents are: A) Higher heating temperature. B) Low pressure. C) Chemical activity. D) Toxicity. F) Uneven heating. F) Increase in pressure. 116. Intermediate heat carriers are: A) Water vapor. B) Hot water. C) Flue gas. D) Electric current. E) Electric arc. F) Alternating electric field. 117. Intermediate heat carriers include: A) Overheated water. B) Mineral oils. C) Flue gas. D) Electric current. E) Electric arc. F) Alternating electric field. 118. The industrial heat carrier must have: A) High viscosity. B) High density.

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C) High heat capacity. D) High heat of vaporization. E) Low heat of vaporization. F) Low density. G) Low heat capacity. H) Chemical activity. 119. Depending on the method of transformation of electrical energy into heat, we distinguish: A) Heating with flue gases. B) Electrical resistance heating. C) Heating with deaf steam. D) Induction heating. E) High-frequency heating. F) Sharp steam heating. G) Heating with superheated water. H) Heating with high-temperature heat carriers. 120. The advantages of using electricity from other heat sources are: A) Compactness of the equipment used. B) Extremely high temperatures. C) Chemical activity. D) Toxicity. E) Uneven heating of substance. F) Absence of sources of contamination of heated substances. G) High cost. H) Cheapness. 121. The heat of condensation of steam is 2.26106 J/kg. This value in kcal/kg will be in the range: A) 538-541. B) 546-548. C) 537-539. D) 545-547. E) 546-549. F) 536-538. G) 536-542. H) 544-546. 122. The coefficient of heat emission from gases to the walls of heated apparatus was 15 kcal/(m2hgrad). This value in J/(m2sgrad) will be in the range: A) 17.44-17.49. B) 17.42-17.48. C) 17.54-17.59. D) 17.52-17.58. E) 17.53-17.61.

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F) 17.48-17.53. G) 17.43-17.51. H) 17.58-17.63. 123. The pressure, under which the superheated water is located, is close to the critical one and is 225 atm. This value will be in the range: A) 231-234. B) 245-248. C) 232-235. D) 244-247. E) 243-246. F) 228-230. G) 230-236. H) 238-241. 124. The flow rate of the heated environment is 0.22 kg/s, the specific heat of the solution is 2.5103 J/(kgK). The initial and final temperatures of the solution were 10 and 94 °C, and the enthalpies of heating steam and condensate were 2710 and 502.4 kJ/kg, respectively. The loss of heat to the environment is an average of 2030 watts. The consumption of deaf steam (in kg/s) will be in the range: A) 0.021-0.024. B) 0.015-0.018. C) 0.019-0.023. D) 0.016-0.019. E) 0.018-0.025. F) 0.016-0.017. G) 0.024-0.026. H) 0.025-0.028. 125. The flow rate of the heated environment is 0.22 kg/s, the specific heat capacity of the solution is 2.5103 J/(kgK). The initial and final temperatures of the solution were 10 and 94 °C, and the enthalpy of heating steam was 2710 kJ/kg, respectively. The loss of heat to the environment is an average of 2030 watts. The heat capacity of water at 94 °C was 4.19103 J/(kgK). The consumption of sharp steam (in kg/s) will be in the range: A) 0.038-0.043. B) 0.046-0.054. C) 0.032-0.045. D) 0.048-0.056. E) 0.030-0.047. F) 0.047-0.058. G) 0.035-0.038. H) 0.034-0.036.

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MASS EXCHANGE PROCESSES: Test tasks (1-25) (Topic 3.1): 1. In chemical technology, the process of transferring substance from one phase to another is called: A) Hydromechanical process. B) Mechanical process. C) Chemical process. D) Heat exchange process. E) Mass-exchange process. F) The hydrodynamic process. 2. The transfer of substance by molecular diffusion is determined by the law of: A) Newton. B) Navier-Stokes. C) Stefan-Boltzmann. D) Fourier. E) Fick. F) Kirchhoff. 3. The unit of measurement of the diffusion coefficient is: A) m3/kg. B) m2/s. C) m3/s. D) m/s. E) kg/s. F) m/h. 4. If the concentration of the substance to be distributed is expressed in terms of the difference in volume concentrations, the mass transfer coefficient will be: A) kg/(m2s). B) s/m. C) m/s. D) m2/s. E) kg/(m2s (mole fractions)). F) kg/s. 5. If the driving force of the process is expressed through the difference of partial pressures, the dimension of the mass transfer coefficient will be: A) s/m. B) m/s.

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C) kg/(m2s). D) m2/s. E) kg/(m2s (mole fractions)). F) kg/s. 6. If the driving force of the process is expressed in terms of relative weight compositions, the dimension of the mass transfer coefficient will be: A) m/s. B) s/m. C) kg/(m2s). D) m2/s. E) kg/(m2s(mole fractions)). F) kg/s. 7. The unit of mass transfer coefficient measurement is: A) kg/(m2s(unit.s)). B) W/(m2grad). C) J/(kggrad). D) m2/s. E) W/(mgrad). F) kg/s. 8. The speed of mass-exchange processes is limited by: A) Molecular diffusion. B) Convective diffusion. C) Mass transfer. D) Mass emission. E) Mass transference. F) Longitudinal diffusion. 9. Mass-exchange processes, as a rule, are carried out in: A) Counterflow devices. B) Straight-through devices. C) Mixed devices. D) Parallel apparatus. E) Heat exchangers. F) Evaporators. 10. The working lines of mass-exchange processes are expressed by the equa‐ tions: . A) B) C) ̅ ̅ .

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D) E) F)

̅

̅ . ̅ .

̅

̅ .

11. The basic equation of mass transfer is expressed by the formula: . А) ∗ В) . С) D) E) F G) hn.

. ∗

. .

12. Molecular diffusion is described by Fick’s first law and is expressed by the equation: A) ∆. B) . ∗ C) . D) E) F) hn.

. ∗

.

13. The relative mass fraction of the distributed component in the phases is determined by the equations: A) . B) ̅

.

C)

.

D)

.

E)

.

F)

.

14. The relative molar fraction of the distributed component in the phases is determined by the equations: . A) B) ̅

.

C) D)

. .

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E)

.

F)

.

15. The mass fraction of the distributed component in the phases is determined by the equations: A) . B) ̅

.

C)

.

D)

.

E)

.

F)

.

16. The molar fraction of the distributed component in the phases is determined by the equations: . A) B) ̅

.

C)

.

D)

.

E)

.

F)

.

17. The driving force of the mass transfer process in relative molar fractions is expressed by the equations: ∗ . A) ∆ B) ̅ C) ∆ D) E) ∆ F) ∆

. ∗

.

. ∗ ∗

. .

18. The molar flow of a component passing from one phase to another is directly proportional to: A) Mass transfer coefficient. B) Surface area of mass transfer. C) Mass emission coefficient. D) Coefficient of mass conductivity. E) The gradient of the volumetric concentration of the target component. F) The driving force of the mass transfer process.

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G) The diffusion coefficient. H) Mass volume concentration of the target component. 19. Chemical production includes three main stages: A) Preparation of raw materials. B) Chemical transformations. C) Separation of products. D) Filtration. F) Precipitation. F) Dispersion of liquids and gases. G) Processes of mixing liquid systems. H) Centrifugal deposition. 20. Processes with direct contact of the phases exchanging by substance include processes in systems: A) The liquid – steam. B) Liquid – gas. C) Liquid – liquid. D) Gas – solid. E) Liquid – solid. F) Solid – gas. G) Solid – liquid. H) Solid – steam. 21. The mass air flow rate was 646 kg/h. The initial moisture content in the air is 0.016 kg/kg of dry air, the final content is 0.006 kg/h of dry air. The initial water content in the acid is 0.6 kg/kg of monohydrate, the final content is 1.4 kg/kg of monohydrate. The drying is carried out at atmospheric pressure. The con-sumption of sulfuric acid (in kg/h) for air drying will be in the range: A) 8.0-8.2. B) 7.4-7.8. C) 7.9-8.3. D) 7.5-7.7. E) 7.0-7.2. F) 7.1-7.3. G) 7.8-8.4. H) 8.3-8.5. 22. The driving force of absorption at the bottom of the scubber was 0.0246 kmoles of acetone/kmol of air, and the driving force of absorption at   the top of the scubber was 0.00128 kmoles of acetone/kmol of air. The average driving force (in kmol of acetone/kmol of air) absorption will be in the range: A) 0.0078-0.0082. B) 0.0075-0.0078. C) 0.0076-0.0081.

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D) 0.0074-0.0077. E) 0.0072-0.0075. F) 0.0073-0.0076. G) 0.0077-0.0083. H) 0.0081-0.0084. 23. The amount of acetone absorbed is 3.9 kmol/h, the mass transfer coefficient is Ky = 0.4 kmol of acetone/(m2h(kmol of acetone/kmol of air)) and the average absorption force of 0.0079 kmol of acetone/kmol of air. The required surface (in m2) of mass transfer will be in the range: A) 1228-1237. B) 1223-1227. C) 1221-1239. D) 1224-1226. E) 1225-1228. F) 1226-1229. G) 1229-1236. H) 1230-1233. 24. The mass of absorbed carbon dioxide by water in 1 hour was 2630 kg. The total surface of all ceramic rings in the water scrubber is 5212 m2, the average driving force for the entire process is 57.4103 Pa. The mass transfer coefficient (in kg/(m2hmmHg)) will be in the range: A) 0.0011-0.0014. B) 0.0013-0.0015. C) 0.0009-0.0015. D) 0.0014-0.0016. E) 0.0016-0.0018. F) 0.0017-0.0018. G) 0.0010-0.0013. H) 0.0015-0.0017. 25. In the mass-exchange apparatus operating under the pressure of the pabs = 3.1 kgf/cm2, the mass emission coefficients have the following values: y = 1.07 kmol/(m2h(y = 1)), x = 22 kmol/(m2h(x = 1)). In equilibrium condition, y* = 35.1x. The mass transfer coefficient (in kmol/(m2h(y = 1)) for the gas phase will be in the range: A) 0.394-0.397. B) 0.384-0.387. C) 0.386-0.388. D) 0.392-0.396. E) 0.397-0.399. F) 0.396-0.398. G) 0.383-0.386. H) 0.393-0.398.

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Test tasks (26-51) (Topic 3.2): 26. If the transfer of substance is carried out by moving particles of the carrier and the substance being distributed, the process is called: A) Convective diffusion. B) Molecular diffusion. C) Mass transfer. D) Mass emission. E) Mass transference. F) Axial diffusion. 27. If at the interface of phases the transfer of substance is carried out by molecules, mass exchange is called: A) Convective diffusion. B) Molecular diffusion. C) Mass transfer. D) Mass emission. E) Mass transference. F) Radial diffusion. 28. The unit of measurement of the diffusion coefficient in the system of units of mechanical quantities (MKGSS) is: A) m2/h. B) m2/s. C) kg/s. D) m/s. E) m/h. F) kg/h. 29. Specify the basic mass transfer equation: A) ∆. B) ∆ . C) . D) . E) . F) ∆ . 30. The transfer of substance by molecular diffusion is determined by Fick’s law and is described by equation: A) ∆. B) ∆ . C) . D) . E) . F) ∆ .

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31. The modified mass transfer equation is described by the equation: A) ∆. B) ∆ . C) . D) . E) . F) ∆ . 32. In convective diffusion, the amount of the transferred substance from one phase to another is described by equation: A) ∆. B) ∆ . C) . D) . E) . F) ∆ . 33. If the driving force of the process is expressed through the difference in volume concentrations, then the dimension of the mass emission coefficient will be: A) s/m. B) m/s. C) kg/(m2s). D) m2/s. E) kg/(m2s (mole fractions)). F) kg/(m2h). 34. If the concentration of the substance to be distributed is expressed through relative weight compositions, the dimension of the mass emission coefficient will be: A) s/m. B) m/s. C) kg/(m2s). D) m2/s. E) kg/(m2s(mole fractions)). F) kg/(m2h(mole fractions)). 35. The total transport of substance due to convective transfer and molecular diffusion is called: A) Molecular diffusion. B) Convective diffusion. C) Convective mass transfer. D) Desorption. E) Absorption. F) Adsorption.

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36. The Nusselt’s diffusion criterion is expressed by the formulas: A) / . B) / . C) / . D) / . E) / . F) / . 37. The diffusion Fourier’s criterion is expressed by the formulas: A) / . B) / . C) / . D) / . E) / . F) / . 38. The diffusion criterion of Peclet is expressed by the formulas: A) / . B) / . C) / . D) / . E) / . F) / . 39. The diffusion criterion of Prandtl is expressed by the formulas: A) / . B) / . C) / . D) / . E) / . F) / . 40. The tions: A) Nu B) Nu C) Nu D) Nu E) Nu F) Nu

generalized dependence of mass emission is expressed by the equaf Pe′ , Re, Fr, G , G … . f Ga, Pr, K . f Re, Pr, Gr, Ga, G , G … . f Re, Eu, Fr, Ho . f Re, Fr, Eu . f Re, Pr ′ , Ga, G , G … .

41. The equations for the additivity of phase resistances are: . A)

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.

B)

.

C) ∆ ∗

D) ∆

. ∗

E) F)

.

∆ ∆

.

42. The average driving force of the mass transfer process is expressed by the equations: . A) .

B)

.

C) ∆ ∗

D) ∆

. ∗

E) F)

.

∆ ∆

.

43. The number of units of transfer is expressed by the A) . .

B) C) ∆

. ∗

D) ∆

. ∗

E) F)

∆ ∆

. .

44. The Nusselt’s diffusion criterion includes: A) Mass transfer coefficient. B) Characteristic linear dimension for the carrier stream. C) Mass emission coefficient. D) Coefficient of mass conductivity. E) The velocity of the carrier stream. F) The driving force of the mass transfer process. G) The diffusion coefficient. H) Mass volume concentration of the target component.

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45. The Prandtl’s diffusion criterion includes: A) Mass transfer coefficient. B) Characteristic linear dimension for the carrier stream. C) Mass emission coefficient. D) Coefficient of mass conductivity. E) The velocity of the carrier stream. F) Density of liquid or gas. G) The diffusion coefficient. H) Dynamic coefficient of viscosity. 46. The Peclet’s diffusion criterion includes: A) Mass transfer coefficient. B) Characteristic linear dimension for the carrier stream. C) Mass emission coefficient. D) Coefficient of mass conductivity. E) The velocity of the carrier stream. F) Density of liquid or gas. G) The diffusion coefficient. H) Dynamic coefficient of viscosity. 47. The Reynolds criterion for the gas phase is 2210 and the Prandtl’s diffusion criterion is 1.32. In the packed absorber for the gas phase, the Nusselt’s diffusion criterion will be in the range: A) 67-71. B) 71-73. C) 68-72. D) 72-75. E) 73-76. F) 75-78. G) 69-73. H) 74-77. 48. The Nusselt’s diffusion criterion was 69. In the packed absorber, the mass emission coefficient for gas is within the limits, if the diffusion coefficient of the absorbed component in the gas is 11.4510-6 m2/s and the equivalent diameter of the packed material in the 55 mm absorber. A) 0.0142-0.0145. B) 0.0146-0.0148. C) 0.0145-0.0147. D) 0.0148-0.0149. E) 0.0143-0.0147. F) 0.0141-0.0146. G) 0.0141-0.0142. H) 0.0142-0.0143.

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49. The dynamic coefficient of viscosity of sulfur dioxide was 0.017510-3 Pas. If the density of sulfur dioxide is 1.16 kg/m3 and the diffusion coefficient of the absorbed component in the gas is 11.4510-6 m2/s, then in the packed absorber the Prandtl’s diffusion criterion for the gas phase will be in the range: A) 1.31-1.35. B) 1.27-1.31. C) 1.29-1.33. D) 1.24-1.34. E) 1.34-1.36. F) 1.35-1.38. G) 1.28-1.30. H) 1.26-1.29. 50. In a scrubber with a nozzle made of ceramic rings, carbon dioxide is absorbed by water from the gas. The equivalent diameter of the packing material in the scrubber is 0.0359 m, the Reynolds criterion for the gas phase is 1920, and the Prandtl’s diffusion criterion is 0.575. The height of the transport unit (in m) for the gas phase will be in the range: A) 0.208-0.209. B) 0.205-0.208. C) 0.201-0.203. D) 0.204-0.208. E) 0.202-0.204. F) 0.204-0.207. G) 0.203-0.205. H) 0.207-0.209. 51. In a scrubber with a nozzle made of ceramic rings, carbon dioxide is absorbed by water from the gas. The reduced thickness of the liquid film was 4.5510-5 m. If the Reynolds criterion for the liquid phase 3060 and the Prandtl’s diffusion criterion of 512 are known, then the height of the transport unit (in m) for the liquid phase will be in the range: A) 0.89-0.92. B) 0.87-0.89. C) 0.88-0.94. D) 0.86-0.88. E) 0.93-0.95. F) 0.94-0.96. G) 0.95-0.97. H) 0.87-0.93. Test tasks (52-76) (Topic 3.3, 3.4): 52. The process of absorption of gas or vapor by liquids is called: A) Adsorption.

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B) Absorption. C) Extraction. D) Crystallization. E) Drying. F) Distillation. 53. If a gas is passed over a free surface of a stationary or slowly flowing liquid, then such absorption apparatuses are called: A) Film. B) Spraying. C) Surface. D) Bubbling. E) Packed. F) Foam. 54. If the gas is in contact with a liquid moving in the form of a thin film, then such absorption apparatuses are called: A) Film. B) Spraying. C) Surface. D) Bubbling. E) Foamy. F) Packed. 55. If the gas is distributed in the liquid in the form of bubbles and jets, then such absorption devices are called: A) Film. B) Spraying. C) Surface. D) Bubbling. E) Foamy. F) Packed. 56. Indicate the transfer equation for the absorption process in the expression of the driving force through the difference in the concentrations of the gas phase: A) М = Кy F (C* – C). B) М = Кх F (C – C*). C) М = Kу F(Р – Р*). D) М = Kх F(Р – Р*). E) М = КFΔ. F) М = КFΔ. 57. Specify the transfer equation for the absorption process when expressing the driving force through the pressure difference between the gas phase: A) М = Кy F (C* – C). B) М = Кх F (C – C*).

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C) М = Kу F(Р – Р*). D) М = Kх F(Р – Р*). E) М = КFΔ. F) М = КFΔ. 58. Define the law of Henry: A) р* = Еx. B) Ф + С = К + 2. C) р* = Px. D) у* = mx. E) p = Py. F) х* = my. 59. Determine the phase rule: A) р* = Еx. B) Ф + С = К + 2. C) р* = Px. D) у* = mx. E) p = Py. F) х* = my. 60. Determine the law of Dalton: A) р* = Еx. B) Ф + С = К + 2. C) р* = Px. D) у* = mx. E) p = Py. F) х* = my. 61. During the absorption process the solubility of gas in a liquid increases: A) With increasing pressure. B) With decreasing pressure. C) With decreasing temperature. D) As the temperature rises. E) With decreasing volume. F) With increasing volume. 62. If there is a component in the gaseous phase that practically does not dissolve in the liquid phase, it is called: A) Inert. B) Carrier gas. C) Absorbable component. D) The absorbed component. E) Active component. F) The target component.

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63. In the course of absorption, the dissolving component is called: A) Inert. B) Carrier gas. C) Absorbable component. D) The absorbed component. E) Absorbent. F) Adsorbent. 64. According to the method for creating a developed phase contact surface between a carrier gas and a liquid absorber, the absorption apparatus can be classified as: A) Single-section. B) Multisection. C) Regenerative. D) Semicontinuous. E) Film. F) Spraying. 65. According to the method for creating a developed phase contact surface between the carrier gas and the liquid absorber, the absorption apparatus can be classified as: A) Single-section. B) Multisection. C) Regenerative. D) Semicontinuous. E) Packed. F) Poppet. 66. Adsorbers of continuous action with a fluidized bed of a sorbent are: A) Single-section. B) Multisection. C) Film. D) Spraying. E) Packed. F) Poppet. 67. The regeneration of the adsorbent consists of the step of: A) Desorption. B) Activation. C) Adsorption. D) Chemisorption. E) Absorption. F) Capillary condensation. 68. During the adsorption process, the substance absorbed is called: A) Adsorbate.

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B) Adsorbtive. C) Adsorbent. D) Absorbent. E) Absorbent. F) Sorbent. 69. The most important areas of application of absorption processes are: A) Preparation of finished products in the form of saturated absorbents. B) Separation of gas mixtures using selective absorbers. C) Cleaning of gases from undesirable impurities. D) Preparation of solid products in the form of granules. E) Isolation of various substances and solutions. F) Application of various coatings to the surface of solids. G) Preparation of substances with special physical and mechanical properties. H) Concentration of diluted solutions. 70. Adsorption is widely used in chemical technology: A) For drying of gases and their purification with allocation of valuable components. B) To remove solvents from gas or liquid mixtures. C) For cleaning gas emissions and sewage. D) For the preparation of solid products in the form of granules. E) For the isolation of various substances and solutions. F) For the application of various coatings to the surface of solids. G) For obtaining substances with certain physical and mechanical properties. H) To concentrate diluted solutions. 71. The most common industrial sorbents are: A) Activated carbons. B) Silicagels. C) Aluminogels. D) Calcined soda. F) Caustic soda. G) Table salt. H) Baking soda. 72. The coefficient of the sorbent protective layer is known to be 5600 min/m, the height of the active carbon layer as a sorbent is 0.1 m and the loss of the protective action time of the sorbent layer is 159 min. The duration of absorption of   chloropicrin vapor (in minutes) by a layer of active carbon according to Shilov’s equation will amount to: A) 401-403. B) 398-400. C) 400-402. D) 397-398. E) 396-397. F) 403-405.

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G) 398-402. H) 404-406. 73. The amount of adsorbed steam per kg of coal is 93 liters/kg. The constants for ethyl alcohol are m = 3.65103 and n = 0.928. The heat of adsorption (in kJ/kg) will be in the range: A) 244-247. B) 242-244. C) 243-246. D) 241-243. E) 246-248. F) 247-249. G) 242-245. H) 248-249. 74. A gas-vapor mixture passes through the adsorber of continuous operation. The active carbon entering the adsorption zone contains a1 = 4 kg/m3 of the adsorbed component, when it leaves the content of the adsorbed component reaches up to 30 kg/m3. The concentration of the vapor-gas mixture entering the adsorber

С 0 = 0.105 kg/m3. The linear velocity of the gas-vapor mixture was 0.415 m/s. The speed (in m/s) of coal movement will be within: A) 0.00127-0.00132. B) 0.00124-0.00127. C) 0.00126-0.00131. D) 0.00130-0.00132. E) 0.00129-0.00133. F) 0.00133-0.00135. G) 0.00128-0.00133. H) 0.00125-0.00126. 75. The adsorption temperature is 20 °С, atmospheric pressure. The diffusion coefficient for diethyl ether in air is 0.028 m2/h. The diffusion coefficient (in m2/s) for diethyl ether will be in the range: A) (8.64-8.66)10-6. B) (8.74-8.76)10-6. C) (8.63-8.68)10-6. D) (8.73-8.78)10-6. E) (8.75-8.78)10-6. F) (8.76-8.79)10-6. G) (8.62-8.67)10-6. H) (8.67-8.69)10-6. 76. The diffusion coefficient of hydrogen sulphide in water at 20 °C was 1.9310-9 m2/s. The temperature coefficient is b = 0.02. At 40 °C the

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diffusion coefficient (in m2/s) of hydrogen sulfide in water will be in the range: A) (2.6-2.9)10-9. B) (2.4-2.6)10-9. C) (2.5-2.8)10-9. D) (2.2-2.5)10-9. E) (2.3-2.6)10-9. F) (2.1-2.3)10-9. G) (2.4-2.7)10-9. H) (2.3-2.6)10-9. Test tasks (77-101) (Topic 3.5): 77. The process of redistribution of components between phases as a result of the contact between the liquid and the vapor phase is called: A) Absorption. B) Adsorption. C) Extraction. D) Distillation. E) Crystallization. F) Drying. 78. The process of single partial evaporation of the liquid mixture and condensation of the formed vapors is called: A) Absorption. B) Adsorption. C) Extraction. D) Rectification. E) Distillation. F) Drying. 79. The process of separating liquid homogeneous mixtures into constituents of a substance as a result of countercurrent interaction of a mixture of vapors and a liquid resulting from the condensation of vapors is called: A) Absorption. B) Adsorption. C) Extraction. D) Rectification. E) Distillation. F) Drying. 80. The process of single partial evaporation of the boiling liquid mixture and condensation of the formed vapors is called: A) Rectification.

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B) Simple distillation. C) Equilibrium distillation. D) Extraction. E) Absorption. F) Drying. 81. The process, accompanied by the evaporation of part of the liquid and the continuous contact of the formed vapors with the unevaporated liquid to achieve phase equilibrium, is called: A) Rectification. B) Simple distillation. C) Equilibrium distillation. D) Extraction. E) Absorption. F) Condensation. 82. During rectification from the top of the column, the vapor condenses and is released as: A) Distillate. B) Extract. C) Filtrate. D) Rectificate. E) Vat rest. F) Mother solution. 83. The degree of separation of binary mixtures into constituent components and the purity of the rectificate and residue obtained depends: A) On the mixture concentration. B) From the boiling point. C) From the parts of the column. D) From the phase contact surface. E) From the condensation of vapors. F) From the surface of heat exchange. 84. Indicate the correct temperature range at which the rectification process is carried out at atmospheric pressure: A) 30 – 60 °С. B) 30 – 90 °С. C) 30 – 120 °С. D) 30 – 150 °С. E) 30 – 180 °С. F) 30 – 100 °С. 85. The rectification process under vacuum is carried out for separation of: A) Viscous liquids. B) Low-boiling liquids.

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C) High-boiling liquids. D) Liquids containing gases in the composition. E) Concentrated liquids. F) The water layer from the organic one. 86. During of the distillation of a binary liquid mixture, the resulting vapor contains a relatively large amount of: A) Light-volatile component. B) Difficult-volatile component. C) Low boiling point component. D) High-boiling component. E) The vat rest. F) The equilibrium component. 87. The lowering of the boiling point of the separated mixture can be achieved: A) At the distillation under vacuum. B) At the distillation with water vapor. C) At the distillation with reflux. D) At the fractional distillation. E) At the simple distillation. F) At the distillation of a binary mixture. 88. The simple distillation carried out to produce the final product of a different composition is called: A) Distillation under vacuum. B) Distillation with water vapor. C) Distillation with reflux. D) Fractional distillation. E) Splitted distillation. F) Distillation with an inert gas. 89. In the rectification unit, the ascending steam flow is created by: A) Reflux condenser. B) Boiler. C) Cube. D) The refrigerator. E) Divisor of phlegm. F) Condenser. 90. In the rectification unit, the downward flow of liquid is created by: A) Reflux condenser. B) Boiler. C) Cube. D) The refrigerator. E) Divisor of phlegm. F) Heat exchanger for partial condensation of steam.

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91. By the nature of the interaction of the vapor and liquid phases, rectification columns can be divided into two main groups: A) With stepped phase contact. B) With continuous phase contact. C) With fluidised bed. D) With a fixed layer. E) With a moving layer. F) Semicontinuous action. 92. Methods based on the introduction into the separated mixture of an additional separating agent include: A) Extractive rectification. B) Azeotropic rectification. C) Molecular distillation. D) Periodic rectification. E) Simple distillation. F) Equilibrium distillation. 93. Equations of the material balance of a continuous rectification column heated by a deaf steam have the form: . A) B) . C) . D) . E) н . к F) . 94. The main streams of the rectification unit are: A) Initial mixture. B) Distillate. C) Vat residue. D) Condenser. E) Reflux condenser. F) Boiler. G) Cube evaporator. H) Refrigerator. 95. The main parts of the rectification unit are: A) Initial mixture. B) Distillate. C) Vat residue. D) Condenser. E) Reflux condenser. F) Column. G) Phlegm. H) Vapor.

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96. The main parts of the rectification column are: A) Feeding plate. B) Strengthening part. C) Extensive part. D) Condenser. E) Reflux condenser. F) Boiler. G) Divisor of phlegm. H) Cube evaporator. 97. After distillation of the aqueous solution of ethyl alcohol weighing 200 kg, 5% (by weight) of alcohol is contained in the vat residue. The quantity (in kg) of the vat residue will be in the range: A) 11-13. B) 12-14. C) 9-13. D) 8-9. E) 8-12. F) 7-8. G) 7-11. H) 13-15. 98. In a simple distillation cube, distillation of 1000 kg of a mixture containing 68% (by weight) of ethyl alcohol is carried out. After distillation the vat residue contains 23 kg of ethyl alcohol. The weight of ethyl alcohol (in kg) in the distillate will be in the range: A) 658-661. B) 656-658. C) 659-662. D) 655-659. E) 660-662. F) 654-657. G) 661-663. H) 653-656. 99. After distillation 800 kg of a mixture of ethyl alcohol and water, a distillate with a mass of 590 kg is formed. The mass fraction (in %) of ethyl alcohol in the distillate will be in the range: A) 73.6-73.9. B) 72.6-72.9. C) 73.2-74.1. D) 72.5-72.8. E) 72.1-72.5. F) 72.8-73.1. G) 73.5-74.2. H) 73.1-73.5.

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100. The mole fraction of the volatile component in the distillate is 0.975, in the initial liquid of the distillation column is 0.675 and in the vapor equilibrated with the supply liquid is 0.315. The minimum number of phlegm in the continuous distillation column will be in the range: A) 0.832-0.835. B) 0.830-0.832. C) 0.831-0.834. D) 0.835-0.839. E) 0.836-0.838. F) 0.837-0.839. G) 0.833-0.836. H) 0.834-0.837. 101. Contaminated turpentine is distilled in a current of saturated water vapor under atmospheric pressure. The amount of water vapor leaving with the turpentine vapor was 2330 kg. The leaving steam with distilled turpentine is cooled from 110,7 to 96 °С. Specific heat capacity of water vapor was 1.97103 J/(kgK). The allocated amount of heat (in kJ) will be within: A) 67470-67478. B) 67510-67515. C) 67471-67480. D) 67509-67511. E) 67512-67516. F) 67514-67517. G) 67472-67482. H) 67476-67479. Test tasks (102-126) (Topic 3.6): 102. The process of extracting one or more components from a mixture of substances by treating it with a liquid solvent is called: A) Absorption. B) Adsorption. C) Extraction. D) Crystallization. E) Rectification. F) Drying. 103. The solvent used in the extraction process for the treatment of a mixture of substances is called: A) Reagent. B) Extragent. C) Sorbent. D) Sorbate. E) Extract. F) Vat residue.

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104. During extraction, the initial solution and the extragent must: A) Mutually react in each other. B) Dissolve into each other. C) Be insoluble in each other. D) Mix with each other. E) Form a sediment. F) Be limitedly soluble in each other. 105. During the extraction process, the extragent from the solution should differ by: A) The volume. B) The concentration. C) The density. D) The temperature. E) The molecular weight. F) The thermal conductivity. 106. When carrying out the extraction process, the extragent from the solution should differ by: A) The volume. B) The concentration. C) The viscosity. D) The temperature. E) The molecular weight. F) The thermal conductivity. 107. The solution of the target component in the extragent is called: A) Reagent. B) Raffinate. C) Extract. D) Distillate. E) Rectificate. F) Vat residue. 108. The residual initial solution, from which, with some degree of completeness, the components are extracted, is called: A) Reagent. B) Raffinate. C) Extract. D) Distillate. E) Rectificate. F) Vat residue. 109. For the regeneration of the extragent from the raffinate and the extract, a process is used: A) Filtering.

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B) Upholding. C) Evaporation. D) Drying. E) Centrifugation. F) Condensation. 110. For the regeneration of the extragent from the raffinate and the extract, a process is used: A) Filtering. B) Upholding. C) Rectification. D) Drying. E) Centrifugation. F) Precipitation. 111. The extraction process consists of the following stages: A) Mixing of the original mixture and the extragent. B) Addition of extragent. C) Separation of the extragent. D) Mechanical separation into extract and raffinate. E) Separation into raffinate. G) Heating of the original mixture. 112. The extraction process consists of the following stages: A) Mixing of the original mixture and the extragent. B) Addition of extragent. C) Separation of the extragent. D) Raffinate separation. E) Regeneration of the extragent from the raffinate. F) Cooling of the original mixture. 113. The extraction process consists of the following stages: A) Addition of extragent. B) Extragent separation. C) Mechanical separation into extract and raffinate. D) Regeneration of the extragent from the raffinate. E) Heating of the original mixture. F) Cooling of the original mixture. 114. The extragent must: A) Possess difficult recyclability. B) Have selectivity. C) Be non-selective. D) Be volatile. E) Have an easy regeneration. F) Be expensive.

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115. The extragent must: A) Possess difficult recyclability. B) Have selectivity. C) Be non-selective. D) Be volatile. E) Be expensive. F) To be non-volatile, non-toxic and affordable. 116. Extragents can serve as ... A) Ethyl alcohol. B) Alkalis. C) Acetone. D) Acids. E) Salts. F) Oxides. 117. Depending on the conditions of the extraction, the extraction may be: A) Reversible. B) Irreversible. C) Periodic. D) Physical. E) Chemical. F) Continuous. 118. Depending on the conditions of the extraction, the extraction may be: A) Reversible. B) Physical. C) Chemical. D) Continuous. E) Physicochemical. F) Countercurrent. 119. The extraction of substances by organic solvents is affected by: A) Nature of the substance to be extracted. B) Pressure difference. C) Head. D) Nature of the extragent. E) The time. F) Current mode. G) Temperature. H) Presence of mechanical impurities. 120. Differential-contact devices in chemical technology during extraction are divided into: A) Spray columns. B) Shelf columns.

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C) Packed columns. D) Drum columns. E) Columns under pressure. F) Continuous columns. D) Periodic columns. H) Foam columns. 121. The material balance of the extraction process is determined by the equation: А) . B) . C) . D) . E) . F) . G) . H) . 122. As a result of extraction of acetone with chlorobenzene from a mixture with a mass of 1730 kg, an extract of 1682 kg was obtained. The amount of raffinate (in kg) will be in the range: A) 44-46. B) 46-49. C) 47-51. D) 45-52. E) 51-53. F) 49-52. G) 43-45. H) 42-44. 123. As a result of acetone extraction by benzene chloride from initial mixture weighing 1630 kg the mixture was obtained weighing 1682 kg. The amount of extract after removal of solvent from it (in kg) will be in limits: A) 50-53. B) 51-54. C) 53-55. D) 49-53. E) 47-49. F) 53-54. G) 48-51. H) 46-50. 124. To extract acetone from a mixture of 100 kg chlorobenzene was used with a mass of 1630 kg. The amount (in kg) of the mixture obtained will be in the range: A) 1732-1735.

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B) 1733-1736. C) 1729-1732. D) 1727-1729. E) 1728-1733. F) 1732-1734. G) 1727-1734. H) 1735-1737. 125. Extraction of dioxane with benzene from a mixture weighing 150 kg produced an extract of 138 kg. The amount of raffinate (in kg) will be in the range: A) 10-13. B) 13-15. C) 11-15. D) 14-15. E) 15-16. F) 13-16. G) 12-13. H) 13-14. 126. To extract phenol from a mixture of 120 kg weight, benzene with a mass of 1430 kg was used. The amount (in kg) of the mixture obtained will be in the range: A) 1548-1555. B) 1552-1556. C) 1547-1549. D) 1547-1552. E) 1552-1555. F) 1548-1553. G) 1553-1556. H) 1551-1552. Test tasks (127-152) (Topic 3.7): 127. The process of removing moisture from various materials and products of chemical technology is called: A) Absorption. B) Rectification. C) Drying. D) Heating. E) Distillation. F) Condensation. 128. The drying process, in which the transfer of heat to the dried material is carried out directly from the heat carriers, is called: A) Drying by evaporation. B) Contact drying.

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C) Convective drying. D) Drying by heating. E) By freeze-drying. F) Vacuum drying. 129. Drying, in which the transfer of heat to the dried material is carried out by thermal conductivity through the wall, is called: A) Drying by evaporation. B) Contact drying. C) Convective drying. D) Drying by heating. E) Freeze-drying. F) Vacuum drying. 130. What should be the vapor pressure of moisture at the surface of the dried material (Pm), depending on the partial pressure of water vapor in the air (Pv) for drying? A) Pm < Pv. B) Pm > Pv. C) Pm  Pv. D) Pm  Pv. E) Pm = Pv. F) Pm  Pv. 131. What should be the moisture vapor pressure at the surface of the dried material (Pm), depending on the partial pressure of water vapor in the air (Pv) to stop the drying process? A) Pm < Pv. B) Pm > Pv. C) Pm  Pv. D) Pm  Pv. E) Pm = Pv. F) Pm  Pv. 132. What type of moisture associated with the material is not removed during the drying process? A) Physico-mechanical. B) Physico-chemical. C) Chemical. D) Mechanical. E) Adsorption. F) Desorption. 133. The dependence of the absolute humidity of the dried material on time, is called: A) Kinetics of drying.

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B) Curve of drying. C) Isotherm of drying. D) Isobar of drying. E) Statics of drying. F) Isostere of drying. 134. What drying materials are used for vacuum drying? A) Resistant to low temperatures. B) Resistant to high temperatures. C) Unstable to low temperatures. D) Unstable to high temperatures. E) Independent of temperature. F) Unstable to average temperatures. 135. The method of drying gases, based on the absorption of moisture from gases by liquid substances, whose aqueous solutions have a low water vapor pressure, is called: A) Adsorption. B) Absorption. C) Physical. D) Chemical. E) Physico-chemical. F) Physico-mechanical. 136. The method of drying gases, based on the absorption of moisture from gases by solids, is called: A) Adsorption. B) Absorption. C) Physical. D) Chemical. E) Physico-chemical. F) Physico-mechanical. 137. The vacuum drying process is accompanied by: A) Molecular diffusion. B) Molecular condensation. C) Diffusion in the direction of the temperature gradient. D) Absorption. E) Adsorption. F) Temperature diffusion. 138. The drying method based on cooling the drying gas with water or a coolant is called: A) Adsorption. B) Absorption. C) Physical.

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D) Chemical. E) Physico-chemical. F) Еhe release of moisture in the form of ice. 139. Special types of drying are: A) Drying by evaporation. B) Radiation drying. C) Convective drying. D) Drying by heating. E) Freeze-drying. F) Artificial drying. 140. Special types of drying are: A) Drying by evaporation. B) Radiation drying. C) Convective drying. D) Drying by heating. E) Artificial drying. F) Dielectric drying. 141. Special types of drying are: A) Drying by evaporation. B) Convective drying. C) Drying by heating. D) Freeze-drying. E) Artificial drying. F) Dielectric drying. 142. Academician P.A. Rebinder proposed the following forms of connection of moisture with the material: A) Chemical. B) Convective. C) Physico-chemical. D) Sublimation. E) Radiation. F) Dielectric. 143. Academician P.A. Rebinder proposed the following forms of connection of moisture with the material: A) Convective. B) Physico-chemical. C) Physical. D) Sublimation. E) Physico-mechanical. F) Dielectric.

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144. The material balance of the drying process is determined by the equation: A) . B) 1 1 . ⁄ . .. C) D) 0,622 . ./ . .. 2493 ∙ 10 . E) 1000 1,97 ∙ 10 F) F . 145. The main parameters of humid air are: A) Moisture content. B) Pressure. C) Density. D) Relative humidity. E) The volume. F) Enthalpy. G) Temperature H) Entropy. 146. The drying curve of the material consists of the following main sections: A) The stage of material heating. B) The stage of cooling the material. C) Drying stage with increasing rate. D) Drying stage with constant rate. E) Period of increasing drying rate. F) The period of the falling drying rate. G) Stage of complete removal of moisture. H) Stage of unchanged temperature of the material. 147. The main parameters of humid air are described by the equations: A) . 1 1 . B) ⁄ . .. C) D) 0,622 . ./ . .. E) 1000 1,97 ∙ 10 2493 ∙ 10 . F) . H) F . 148. The partial pressure of water vapor is 59.8 mm Hg.col. The total pressure is 380 mm Hg.col. Relative humidity of air 0.75. The moisture content (in kg of steam/kg of dry air) of the steam-air mixture will be in the range: A) 0.160-0.167. B) 0.085-0.087. C) 0.159-0.169. D) 0.086-0.088.

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E) 0.163-0.173. F) 0.075-0.078. G) 0.075-0.076. H) 0.074-0.077. 149. The heat input to the dryer is 142500 Watts. The specific heat of condensation of the heating steam was 2122 kJ/kg, and the humidity was 6%. The consumption (in kg/s) of the heating steam will be in the range: A) 0.0713-0.0716. B) 0.0716-0.0719. C) 0.0712-0.0715. D) 0.0716-0.0719. E) 0.0717-0.0718. F) 0.0711-0.0712. G) 0.0711-0.0717. H) 0.0715-0.0718. 150. The moisture content of the air was 0.021 kg/kg of dry air. The enthalpy (in J/kg) of air at 30 °C is in the range: A) 83980-84100. B) 83880-83910. C) 83950-83980. D) 83850-83920. E) 83960-83990. F) 83890-83930. G) 84100-84200. H) 84200-84300. 151. For the theoretical dryer, t1 = 111 °С, t2 = 50 °С, tm = 37 °С are known. The driving force (in °C) of the drying process will be within: A) 32-36. B) 37-38. C) 33-37. D) 36-38. E) 38-40. F) 31-33. G) 31-38. H) 30-34. 152. The dry air consumption for drying was 2560 kg/h. The enthalpies of air at the entrance to the air heater and at the outlet from it were 33.5103 and 111103 J/kg of dry air, respectively. The heat consumption (in W) by the air transferred to the air heater will be in the range: A) 55108-55115. B) 55010-55080. C) 55070-55090. D) 55090-55120.

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E) 55060-55070. F) 55080-55100. G) 55080-55130. H) 55120-55130. Test tasks (153-176) (Topic 3.8): 153. The process of separation of a solid from a solution or a melt is called: A) Evaporation. B) Drying. C) Crystallization. D) Centrifugation. E) Precipitation. F) Filtration. 154. At what stage of the process are the crystallization processes carried out? A) Initial. B) Intermediate. C) Medium. D) Serial. E) Final. F) Parallel. 155. The most important characteristic of crystalline hydrates is: A) The elasticity of water vapor. B) The saturated vapor pressure. C) The partial water vapor pressure. D) The vapor pressure of moisture. E) The pressure of the gas mixture. F) The partial vapor pressure of volatile components. 156. A solution that contains the maximum possible amount of a substance for a given temperature is called: A) The true solution. B) The saturated solution. C) The supersaturated solution. D) A colloidal solution. E) A mixed solution. F) A standard solution. 157. A solution containing an excess of dissolved substance with respect to the saturation state at a given temperature is called: A) The true solution. B) The saturated solution. C) The supersaturated solution.

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D) A colloidal solution. E) A mixed solution. F) A standard solution. 158. The main factor determining the crystallization process is the ability of the crystallized salt to form: A) Supersaturated solutions. B) Saturated solutions. C) True solutions. D) Colloidal solutions. E) Mixed solutions. F) Standard solutions. 159. The crystallization method used for substances whose solubility insignificantly depends on temperature is accompanied by: A) Cooling of the solvent. B) Evaporation of part of the liquid. C) Cooling of the solution. D) Heating of the solvent. E) Addition of the impurity to the solvent. F) Staining of the solution. 160. The crystallization method used for substances in which the solubility falls with decreasing temperature is accompanied by: A) Cooling of the solvent. B) Evaporation of part of the liquid. C) Cooling of the solution. D) Heating of the solvent. E) Addition of the impurity to the solvent. F) Staining of the solution. 161. The crystallization process is carried out for: A) Preparation of saturated solutions. B) Preparation of unsaturated solutions. C) The release of substances from solutions. D) Production of supersaturated solutions. E) Drying of substances. F) Preparation of single crystals. 162. With the help of crystallization, the following tasks are solved: A) Preparation of saturated solutions. B) Separation of various mixtures into fractions. C) Preparation of unsaturated solutions. D) Preparation of supersaturated solutions. E) Preparation of substances with certain physico-chemical properties. F) Drying of substances.

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163. With the help of crystallization, the following tasks are solved: A) Preparation of saturated solutions. B) Preparation of unsaturated solutions. C) Preparation of supersaturated solutions. D) Preparation of substances with certain physico-chemical properties. E) Concentration of diluted solutions. F) Distillation of mixtures. 164. To disturb the equilibrium and form a supersaturated solution, we can use: A) Heating of a part of the liquid. B) Evaporation of part of the liquid. C) Heating of the solution. D) Boiling of the solution. E) Cooling of the solution. F) First cooling of the solution and then its boiling. 165. To disturb the equilibrium and form a supersaturated solution, we can use: A) Heating of a part of the liquid. B) Boiling of the solution. C) Cooling of the solution. D) First cooling of the solution, and then boiling it. E) First heating of the solution, and then boiling it. F) Simultaneous cooling and evaporation of part of the solution. 166. The main factors determining the rate of crystallization are: A) Degree of supersaturation of solution. B) Gravity. C) Frictional forces. D) Forces of inertia. E) Formation of crystallization centers. F) The volume. 167. According to the principle of operation, the following types of industrial crystallizers are used: A) Crystallizers with removal of a part of the solvent. B) Crystallizers with heating of a part of the solvent. C) Crystallizers with heating of the solvent. D) Crystallizers with solvent cooling. E) Crystallizers with solution cooling. F) Crystallizers with heating and boiling of the solution. 168. According to the principle of operation, the following types of industrial crystallizers are used: A) Crystallizers with heating of a part of the solvent.

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B) Crystallizers with heating of the solvent. C) Crystallizers with solvent cooling. D) Crystallizers with solution cooling. E) Crystallizers with heating and boiling of the solution. F) Vacuum crystallizers. 169. The material balance of crystallization for the whole amount of the substance consists of: A) The averaged amount of solution. B) The minimum amount of solution. C) The amount of initial solution. D) The maximum amount of solution. E) The initial amount of mother liquor. F) The amount of mother liquid. G) The minimum amount of mother liquor. H) The number of crystals. 170. In the heat balance equation of the crystallization process, the heat input is composed of: A) The heat of the initial solution. B) The heat of the mother liquor. C) The heat of crystallization. D) The heat of solvent vapors. E) The heat of dehydration. F) The heat of the cooling agent. G) The loss of the environment. H) The heat of crystals. 171. In the heat balance equation of the crystallization process, the heat consumption is composed of: A) The heat of the initial solution. B) The heat of the mother liquid. C) The heat of crystallization. D) The heat of solvent vapors. E) The heat of dehydration. F) The heat of the cooling agent. G) The heat received from the heat carrier. H) The heat expended in dissolving the substance. 172. A 300 kg solution with a mass fraction of a solute of 0.0768 was evaporated. The mass fraction of the dissolved substance in the evaporated solution was 0.56. The quantity (in kg) of evaporated water will be in the range: А) 255-257. В) 251-254. С) 256-260. D) 251-255.

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Е) 258-261. F) 257-263. G) 260-263. H) 261-264. 173. A 250 kg solution with a solid content of 0.0675 was evaporated. The mass fraction of the dissolved substance in the evaporated solution was 0.58. The quantity (in kg) of the final solution was in the range: А) 29.5-29.7. В) 28.5-29.3. С) 28.7-29.5. D) 29.6-29.8. Е) 28.6-29.6. F) 28.4-28.8 G) 28.3-28.7. H) 28.1-28.5. 174. A 20 t solution with a solute concentration of 5% was evaporated. The concentration of the dissolved substance in the evaporated solution was 50%. The amount (in kg) of evaporated water was in the range: А) 17000-17500. В) 17500-18100. С) 17500-17800. D) 17600-17900. Е) 17900-18200. F) 18200-18400. G) 18100-18300. H) 17700-18150. 175. After evaporation, a solution with a mass of 30 kg was obtained with a mass fraction of the solute in the evaporated solution 0.6. The mass fraction of the dissolved substance was 0.068. The amount (in kg) of the initial solution was in the range: A) 255-275. B) 270-275. C) 261-271. D) 245-255. E) 275-285. F) 271-281. G) 245-270. H) 241-251. 176. The amount of heat removed was 130 kW. The coefficient of heat transfer is assumed equal to 100 W/(m2K). The average temperature difference is 36.2 °C. In the crystallizer, the surface area (in m2) of cooling was in the range: A) 33-37.

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B) 32-34. C) 35-38. D) 31-35. E) 30-33. F) 38-39. G) 34-39. H) 31-34.

387 

 

ANSWERS TO THE TEST TASKS Hydrodynamic processes: Number Correct of answer question (Topic 1.2) Tests 1-30 1 А 2 А 3 D 4 B 5 D 6 A 7 D 8 B 9 A 10 D 11 B 12 A 13 A, D 14 C, F 15 C, E 16 F, G 17 A, C 18 B, D 19 B, F 20 C, F 21 A, D 22 C, F, H 23 A, C, G 24 A, D, G 25 B, D, F 26 B, E, G 27 A, D, G 28 B, D, H 29 A, C, F 30 B, E, G (Topic 1.6) Tests 121-150 121 B 122 C 123 D

Number Correct of answer question (Topic1.3) Tests 31-60 31 A 32 B 33 B 34 A 35 B 36 A 37 D 38 D 39 A 40 E 41 B, F 42 A, G 43 F, G 44 A, G 45 A, F 46 D, F 47 D, E 48 E, F 49 B, F, H 50 B, D, F 51 B, D, G 52 A, E, H 53 B, D, F 54 A, C, E 55 A, D, F 56 C, E, G 57 B, E, H 58 B, E, H 59 B, E, H 60 B, E, H (Topic 1.7) Tests 151-180 151 B 152 A 153 A

Number Correct of answer question (Topic 1.4) Tests 61-90 61 B 62 D 63 D 64 B 65 A 66 A 67 A 68 B 69 D 70 B 71 D, F 72 B, E 73 D, G 74 A, C 75 A, F 76 C, E 77 C, F 78 A, C, E 79 A, C, E 80 A, E, F 81 A, D, G 82 B, D, F 83 B, D, F 84 A, C, F 85 B, D, F 86 A, G, H 87 B, D, F 88 A, F, G 89 A, C, H 90 B, C, H (Topic 1.8) Tests 181-210 181 A 182 A 183 A

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Number Correct of answer question (Topic 1.5) Tests 91-120 91 D 92 A 93 B 94 A 95 A 96 A 97 D 98 A 99 A 100 B 101 D 102 C 103 F 104 C 105 A, D 106 A, D 107 A, C 108 A, E 109 A, C 110 A, C 111 B, C 112 A, D, E 113 A, D, F 114 A, C, E 115 B, D, H 116 A, C, H 117 B, E, G 118 B, D, H 119 A, C, G 120 B, D, E (Topic 1.9) Tests 211-242 211 A 212 A 213 C

124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150

B B A B A E D D E B, G A, C A, C C, E A, B A, D, G A, C, E C, E, F A, C, E C, E, H A, C, G C, E, G A, C, E A, D, G B, D, F A, F, H B, D, H B, D, H

(Topic 1.10) Tests 243-272 243 B 244 A 245 A 246 B 247 B 248 E 249 D 250 A 251 C 252 E 253 C, D 254 B, F 255 A, D

154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180

C D A C E A, B A, B A, B A, C A, C A, B A, C B, D B, D A, C A, C, E C, F, H A, C, G B, D, H B, F, G B, D, G B, D, G A, D, H A, C, E B, D, F A, C, E D, F, H

(Topic 1.10) Tests 243-272 258 C, E 259 A, D 260 A, F 261 B, F 262 D, G 263 A, C, E 264 B, D, F 265 A, C, F 266 B, D, G 267 A, D, G 268 A, D, E 269 A, D, F 270 B, E, H

389 

 

184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210

B C B B A B A D A, D A, C B, C A, E B, D, G A, C, E B, C, E A, E, H B, E, G A, C, F A, D, F C, E, H B, F, G C, E, G A, F, H B, D, G B, E, H C, E, G A, D, G

(Topic 1.11) Tests 273-305 273 E 274 A 275 D 276 E 277 D 278 A 279 D 280 A 281 E 282 D 283 A 284 B 285 A, F

214 E 215 A 216 E 217 A 218 A 219 A 220 A 221 A 222 B 223 C 224 A, G 225 A, D 226 A, D 227 A, B, C 228 A, C, F 229 B, D, F 230 A, D, H 231 A, C, H 232 A, C, E 233 B, D, F 234 F, G, H 235 A, C, E 236 A, C, H 237 E, G, H 238 A, D, H 239 B, E, G 240 A, D, F 241 A, C, E 242 B, D, G (Topic 1.11) Tests 273-305 290 A, F 291 A, D, G 292 A, C, F 293 B, D, E 294 F, G, H 295 A, F, G 296 A, F, H 297 A, E, G 298 A, F, G 299 B, E, H 300 A, C, G 301 C, E, F 302 A, C, H

256 257

C, F A, C

271 272

C, E, H B, D, G

286 287 288 289

C, E C, F C, E B, C

303 304 305

E, F, G A, F, G B, F, G

  Thermal processes: Number Correct of answer question (Topic 2.1) Tests 1-25 1 B 2 B 3 A 4 A 5 E 6 D 7 B 8 A 9 B 10 B, C 11 C, F 12 A, E 13 B, E 14 A, D 15 B, C 16 A, D 17 D, F 18 A, C, F 19 A, C, E 20 A, D, F 21 A, C, F 22 A, D, H 23 A, B, G 24 B, D, F 25 A, C, G (Topic 2.8) Tests 101-125 101 A 102 A 103 B 104 A 105 B

Number Correct of answer question (Topics 2.2-2.4) Tests 26-50 26 A 27 E 28 A 29 A 30 C 31 A 32 D 33 C 34 C 35 A, C 36 B, E 37 A, F 38 A, F 39 A, B 40 B, C 41 A, C 42 B, F 43 A, D, F 44 A, C, F 45 A, E, F 46 A, C, G 47 A, C, G 48 A, D, H 49 A, E, G 50 A, F, H (Topic 2.8) Tests 101-125 107 E 108 D 109 A 110 B, D 111 A, B

Number Correct of answer question (Topic 2.5) Тесты 51-75 51 C 52 C 53 C 54 C 55 A 56 B 57 D 58 E 59 B 60 E, F 61 C, F 62 E, F 63 A, F 64 A, B 65 C, F 66 A, B 67 A, C 68 A, D, F 69 A, D, G 70 A, D, G 71 A, C, G 72 A, D, G 73 A, C, G 74 A, E, G 75 A, C, G (Topic 2.8) Tests 101-125 113 A, B 114 C, D 115 A, B 116 A, B 117 A, B

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Number Correct of answer question (Topics 2.6, 2.7) Тесты 76-100 76 A 77 A 78 B 79 C 80 D 81 E 82 A 83 E 84 B 85 A, B 86 C, E 87 B, C 88 C, D 89 E, F 90 B, C 91 C, D 92 A, B 93 A, B, C 94 A, B, C 95 A, D, E 96 A, D H 97 B, D, G 98 A, C, F 99 A, G, H 100 A, C, G (Topic 2.8) Tests 101-125 119 B, D, E 120 A, B, F 121 A, C, G 122 A, B, G 123 A, C, G

106

A

112

C, D

118

B, C, D

124 125

A, C, E A, C, E

Mass exchange processes: Number of question

Correct answer

(Topic 3.1) Tests 1-25 1 E 2 E 3 B 4 C 5 A 6 C 7 A 8 A 9 A 10 D, F 11 B, D 12 B, D 13 A, C 14 E, F 15 B, D 16 A, C 17 A, C 18 A, B, F 19 A, B, C 20 A, B, C 21 A, C, G 22 A, C, G 23 A, C, G 24 A, C, G 25 A, D, H (Topic 3.6) Tests 102-126 102 C 103 B 104 C 105 C 106 C

Numbe r of Correct questio answer n (Topic 3.2) Tests 26-51 26 A 27 B 28 A 29 A 30 E 31 D 32 B 33 B 34 C 35 B, C 36 B, C 37 A, D 38 E, F 39 E, F 40 A, F 41 A, B 42 C, D 43 E, F 44 B, C, G 45 F, G, H 46 B, E, G 47 A, C, G 48 A, E, F 49 A, C, D 50 B, D, F 51 A, C, H (Topic 3.7) Tests 127-152 127 C 128 C 129 B 130 B 131 E

Number of question

391 

 

Correct answer

(Topic 3.3, 3.4) Tests 52-76 52 B 53 C 54 A 55 D 56 A 57 C 58 A 59 B 60 E 61 A, C 62 A, B 63 C, D 64 E, F 65 E, F 66 A, B 67 A, B 68 A, B 69 A, B, C 70 A, B, C 71 A, B, C 72 A, C, G 73 A, C, G 74 A, C, G 75 A, C, G 76 A, C, G (Topic 3.8) Tests 153-176 153 C 154 E 155 A 156 B 157 C

Number of question

Correct answer

(Topic 3.5) Tests 77-101 77 D 78 E 79 D 80 B 81 C 82 D 83 D 84 D 85 C 86 A, C 87 A, B 88 D, E 89 B, C 90 A, F 91 A, B 92 A, B 93 A, B 94 A, B, C 95 D, E, F 96 D, E, F 97 C, E, G 98 B, D, F 99 A, C, G 100 A, C, G 101 A, C, G

107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126

C B C C A, D A, E C, D B, E B, F A, C C, F D, F A, D, H A, B, C A, B, C B, C, D A, B, D C, E, G A, C, G A, D, F

132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152

C B D B A C, F C, F B, E B, F D, F A, C B, E A, B A, D, F A, D, F C, D, E A, C, E A, C, G B, D, F A, C, G A, D, G

392 

 

158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176

A B C C, F B, E D, E B, E C, F A, E A, E D, F C, F, H A, C, E B, D, F C, E, F B, C, E B, E, H A, C, G A, C, G

CONTENT INTRODUCTION ................................................................................3 1. THEORETICAL BASICS OF PROCESSES OF CHEMICAL TECHNOLOGY .....................................................4 1.1. Laws of conservation .....................................................................6 1.1.1. The law of conservation of mass ..................................................6 1.1.2. The law of conservation of energy................................................9 1.1.3. The law of conservation of impulse ..............................................10 1.2. Hydromechanical processes ..........................................................11 1.2.1. The equation of continuity of a flow.............................................11 1.2.2. Determination of liquid and gas consumption ..............................13 1.2.3. Calculation of pipe and apparatus diameters ................................13 Questions for self-control .......................................................................14 1.3. The basic equation of hydrostatics ...............................................15 1.3.1. The Bernoulli equation .................................................................18 1.3.2. Forces acting in a real liquid .........................................................22 Questions for self-control .......................................................................26 1.4. Real liquid motion modes ..............................................................26 1.4.1. Speed distribution and liquid flow with the laminar flow streaming .............................................................28 1.4.2. Turbulent movement of the liquid ................................................32 1.4.3. Film current of liquids ..................................................................34 Questions for self-control .......................................................................36 1.5. Modeling of chemical-technological processes ............................36 1.5.1. The method of generalized variables ............................................37 1.5.2. Invariants of similarity and criteria of similarity ..........................40 1.5.3. Hydrodynamic similarity ..............................................................42 Questions for self-control .......................................................................47 1.6. Resistance of flow ...........................................................................48 1.6.1. Local resistance of flow ................................................................49 1.6.2. Losses of pressure for motion of liquid in apparatus ....................50 Questions for self-control .......................................................................53

393 

 

1.7. Mixing in liquid environments......................................................54 1.7.1. Mechanical mixing .......................................................................55 1.7.2. Energy consumption for mixing ...................................................59 1.7.3. Constructions of mixers ................................................................61 Questions for self-control .......................................................................64 1.8. Basics of the principle of fluidization ...........................................65 1.8.1. Technological parameters of the process of fluidization ..............66 1.8.2. Application of pseudofluidized layer in industrial practice ...................................................................................................69 Questions for self-control .......................................................................70 1.9. Transportation of liquids ..............................................................70 1.9.1. Pumps. Basic parameters ..............................................................71 1.9.2. Piston pumps.................................................................................73 1.9.3. Piston pump productivity ..............................................................77 1.9.4. Pump pressure. Suction height......................................................78 1.9.5. Centrifugal pumps ........................................................................83 Questions for self-control .......................................................................87 1.10. Сompression and transportation of gases..................................87 1.10.1. Thermodynamics of the compressor process ..............................89 1.10.2. Piston compressors .....................................................................93 1.10.3. Vacuum pumps ...........................................................................101 Questions for self-control .......................................................................103 1.11. Hydromechanic separation of heterogeneous systems..............104 1.11.1. Material balance of the separation process .................................105 1.11.2. Upholding ...................................................................................106 1.11.3. Filtration .....................................................................................108 1.11.4. Theory of filtering.......................................................................109 1.11.5. Construction of filters .................................................................113 1.11.6. Centrifugation .............................................................................114 Questions for self-control .......................................................................116 2. THERMAL PROCESSES ...............................................................118 2.1. General information ......................................................................118 2.1.1. Thermal balances ..........................................................................119 2.1.2. Temperature field and temperature gradient .................................121 2.1.3. Transfer of heat by heat conductivity ...........................................123

394 

 

2.1.4. The equation of heat conductivity of a flat wall ...........................125 2.1.5. Equation of heat conductivity of a cylindrical wall ......................127 Questions for self-control .......................................................................128 2.2. Convective heat exchange .............................................................129 2.2.1. Equation of convective-conductive transfer of heat......................132 2.2.2. Criteria for thermal similarities.....................................................132 2.3. Thermal radiation.............................................................................137

2.4. Heat emission at boiling and condensation ......................................141 Questions for self-control .......................................................................145 2.5. Heat transfer in heat exchanging devices ....................................146 2.5.1. Heat transfer through a flat wall ...................................................147 2.5.2. Heat transfer through the cylindrical wall.....................................149 2.5.3. Average temperature head ............................................................150 2.5.4. Thermal insulation ........................................................................155 Questions for self-control .......................................................................156 2.6. Evaporation ....................................................................................156 2.6.1. Ways of evaporation .....................................................................157 2.6.2. Evaporating devices ......................................................................158 2.6.3. Material balance of the evaporation device ..................................160 2.6.4. Thermal balance of the evaporation device ..................................161 2.7. Heat exchanging devices................................................................164 2.7.1. Surface heat exchangers................................................................164 2.7.2. Mixing heat exchangers ................................................................167 Questions for self-control .......................................................................168 2.8. Heating processes ...........................................................................169 2.8.1. Heating with water vapor ..............................................................169 2.8.2. Heating with flue gases .................................................................171 2.8.3. Heating with high-temperature heat carriers .................................171 2.8.4. Heating with electricity .................................................................173 Questions for self-control .......................................................................174 3. MASS EXCHANGE PROCESSES .................................................175 3.1. Basiсs of mass transfer ..................................................................175 3.1.1. Phase equilibrium .........................................................................175

395 

 

3.1.2. Material balance of mass-exchange processes ..............................176 3.1.3. Basic equation of mass transfer ....................................................178 3.1.4. Average moving force of the process of mass transfer .................180 Questions for self-control .......................................................................183 3.2. Modified equation of mass transfer..............................................183 3.2.1. Mass transfer between phases .......................................................185 3.2.2. Convective diffusion .....................................................................186 3.2.3. Criteria of diffusional similarity ...................................................188 Questions for self-control .......................................................................192 3.3. Absorption ......................................................................................192 3.3.1. Physical bases of the process of absorption ..................................193 3.3.2. Influence of temperature and pressure on the process of absorption ...........................................................................................196 3.3.3. Material balance and kinetic laws of absorption ...........................197 3.3.4. Absorption devices .......................................................................198 3.4. Adsorption ......................................................................................204 3.4.1. Equilibrium between phases .........................................................206 3.4.2. Material balance of adsorption process.........................................209 3.4.3. Kinetics of adsorption ...................................................................209 Questions for self-control .......................................................................210 3.5. Distillation and rectification .........................................................211 3.5.1. General information ......................................................................211 3.5.2. Physico-chemical basics of the distillation processes ...................212 3.5.3. Material balance of simple distillation ..........................................220 3.5.4. Distillation with water vapor ........................................................222 3.5.5. Rectification..................................................................................223 3.5.6. Calculation of the number of plates of the rectification column of continuous action for separation of binary liquid mixtures .......................................................................................225 3.5.7. Rectification under different pressures .........................................228 Questions for self-control .......................................................................229 3.6. Extraction .......................................................................................229 3.6.1. Physical basics of the extraction process ......................................231 3.6.2. Triple systems ...............................................................................233 Questions for self-control .......................................................................237

396 

 

3.7. Drying .............................................................................................238 3.7.1. General information ......................................................................238 3.7.2. Main parameters of wet air ...........................................................239 3.7.3. Statics of drying ............................................................................240 3.7.4. Material balance of drying ............................................................241 3.7.5. Kinetics of drying .........................................................................242 3.7.6. Vacuum drying .............................................................................245 3.7.7. Drying of gases .............................................................................245 Questions for self-control .......................................................................246 3.8. Crystallization ................................................................................246 3.8.1. Physical basics of the crystallization process ...............................247 3.8.2. Methods of crystallization and crystallizers..................................248 3.8.3. Material balance of crystallization ................................................249 3.8.4. Thermal balance of the crystallization process .............................250 Questions for self-control .......................................................................251 BIBLIOGRAPHIC LIST .....................................................................252 THE TEST TASKS ..............................................................................253 ANSWERS OF TEST TASKS .............................................................388

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Еducational issue

Akbayeva Dina Nauryzbaevna Yeshova Zhaniya Turlukhanovna LECTURES ON THE COURSE: FUNDAMENTAL PROCESSES AND DEVICES OF CHEMICAL TECHNOLOGY Stereotypical pyblication Editor B. Popova Typesetting K. Umirbekova Cover design Ya. Gorbunov Cover design used photos from sites www.MyTravelBook.org

IB №13309

Signed for publishing 25.02.2020. Format 60x84 1/16. Offset paper. Digital printing. Volume 25 printer’s sheet. 100 copies. Order №388. Publishing house «Qazaq University» Al-Farabi Kazakh National University KazNU, 71 Al-Farabi, 050040, Almaty Printed in the printing office of the «Qazaq University» publishing house.