Chemical Reaction Engineering—Boston 9780841207325, 9780841209206, 0-8412-0732-1

Table of contents :
Title Page......Page 1
Copyright......Page 2
ACS Symposium Series......Page 3
FOREWORD......Page 4
PdftkEmptyString......Page 0
PREFACE......Page 5
1 Catalytic Air Oxidation of Propylene to Acrolein: Modeling Based on Data from an Industrial Fixed-Bed Reactor......Page 6
Modeling......Page 7
Discussion......Page 13
Literature Cited......Page 16
2 Simultaneous Uncorrelated Changes of Process Variables in a Fixed-Bed Reactor......Page 18
Mathematical Evaluation of the Dynamic Experiments - Simulation of Reactor Behaviour......Page 19
Conclusions......Page 27
Legend of Symbols......Page 29
Literature Cited......Page 30
Mathematical Formulation......Page 31
Literature Cited......Page 40
4 A Simulation of Coke Burning in a Fixed-Bed Reactor......Page 41
Mathematical Model......Page 42
Results......Page 44
Legend of Symbols......Page 48
Literature Cited......Page 50
5 Impact of Porosity and Velocity Distribution on the Theoretical Prediction of Fixed-Bed Chemical Reactor Performance Comparison with Experimental Data......Page 51
Creeping Zones In An Adiabatic Fixed Bed Reactor......Page 54
Steady State Axial Temperature Profiles In Wall Cooled Fixed Bed Reactors......Page 57
Legend of Symbols......Page 61
Literature Cited......Page 62
6 A Novel Method for Determining the Multiplicity Features of Multi-Reaction Systems......Page 64
Heuristic Description of the Theory......Page 65
Ν Parallel Reactions in a CSTR......Page 66
Adiabatic case (α = 0) and γ » θ......Page 68
Non-Adiabatic Case (α ≠ 0) and γ » θ......Page 71
Concluding Remarks......Page 72
Literature Cited......Page 74
7 Reaction Rate Oscillations During the Carbon Monoxide Oxidation Reaction Over Pt/γ-Al2O3 Catalysts: An IR-Transmission Spectroscopy Study......Page 75
Experimental Considerations......Page 76
Experimental Results & Discussion......Page 80
Conclusions......Page 83
Acknowledgement......Page 85
Literature Cited......Page 86
8 Multiplicity and Propagating Fronts in Adiabatic and Nonadiabatic Fixed-Bed Reactors......Page 87
Model Equations and Numerical Solution......Page 88
Adiabatic Case......Page 89
Nonadiabatic case......Page 90
Literature Cited......Page 94
9 Forced Composition Cycling Experiments in a Fixed-Bed Ammonia Synthesis Reactor......Page 95
Forced Composition Cycling Results......Page 99
Interpretation......Page 102
Industrial Application......Page 103
Literature Cited......Page 105
10 Dynamic Behavior of an Industrial Scale Fixed-Bed Catalytic Reactor......Page 106
Theoretical Developments......Page 107
Results and Discussion......Page 110
Conclusions......Page 113
Literature Cited......Page 116
11 Modeling Complex Reaction Systems in Fluidized-Bed Reactors......Page 118
The two-phase model for complex reaction systems......Page 119
Synthesis of maleic anhydride on benzene feedstock......Page 121
Synthesis of maleic anhydride on C4-feedstock......Page 122
Summary and conclusions......Page 126
Literature Cited......Page 128
12 Runaway in an Industrial Hydrogenation Reactor......Page 129
Literature Cited......Page 139
13 Transitions Between Periodic and Chaotic States in a Continuous Stirred Reactor......Page 140
Results......Page 141
Effect of External Disturbances......Page 146
Literature Cited......Page 148
14 On-Line Estimation of the State of Biochemical Reactors......Page 150
The Estimation Problem......Page 151
State Estimation Algorithms for Biochemical Reactors......Page 153
Results - Discussion......Page 157
Literature Cited......Page 159
15 Rate Oscillations During Propylene Oxide Oxidation on Silver Films in a Continuous Stirred Reactor......Page 160
Summary of Experimental Results......Page 161
Development of the Dynamic Model......Page 162
Summary......Page 170
Legend of Symbols......Page 172
Literature Cited......Page 173
16 Steam Reforming of Natural Gas: Intrinsic Kinetics, Diffusional Influences, and Reactor Design......Page 174
Intrinsic kinetics of methane steam reforming......Page 175
Internal mass transfer limitations in industrial operation......Page 177
Reactor simulation and design......Page 183
Legend of Symbols......Page 188
Literature cited......Page 190
17 Transient Kinetics of the Fischer-Tropsch Synthesis......Page 191
Kinetic model for pulse simulation......Page 192
Experimental......Page 199
Results and discussion......Page 201
Legend of Symbols......Page 203
Literature Cited......Page 204
Experimental Procedure......Page 205
Steady State Analysis......Page 206
Transient State Analysis......Page 207
Literature Cited......Page 215
Experimental......Page 216
Intrinsic Kinetics......Page 217
Mass Transfer......Page 219
Product Selectivity......Page 222
Conclusions......Page 224
Subscripts......Page 226
Literature Cited......Page 227
20 The Fischer-Tropsch Synthesis by Amorphous Fe20Ni60P20 and Fe90Zr10 Catalysts......Page 228
Experiments......Page 229
Experimental Results.......Page 230
Analysis and Discussion......Page 234
Conclusion......Page 238
Literature Cited......Page 239
21Modeling Zeolite Catalyst Deactivation by Coking and Nitrogen Compound Poisoning......Page 240
Results and Discussion......Page 241
Comparison With Other Models......Page 246
Conclusions......Page 248
Legend of Symbols......Page 249
Literature Cited......Page 250
22 Rate of Oxidation of Ammonia on Platinum Wires, Ribbons, and Gauzes......Page 251
CONVERSION ON SINGLE WIRES AND RIBBONS......Page 252
THE SURFACE REACTION RATE......Page 254
PREDICTION OF THE REACTION RATE AT ATMOSPHERIC PRESSURE......Page 256
Literature Cited......Page 260
Experimental......Page 261
Steady State Kinetics......Page 263
Transient Kinetics......Page 265
A Possible Reaction Mechanism......Page 270
Literature Cited......Page 272
Experimental......Page 273
Results and Discussion......Page 275
Literature Cited......Page 285
Experimental Section......Page 286
Experimental Results......Page 288
Reactor Simulation......Page 292
Discussion......Page 293
Acknowledgment......Page 294
Appendix......Page 295
26 Catalyst Decay During Hydrotreatment of a Heavy Coal Oil......Page 296
Experimental......Page 297
Experimental Results......Page 298
Discussion......Page 303
Conclusion......Page 305
Subscripts......Page 306
Literature Cited......Page 307
27 The Steady-State Permeation Model for Underground Coal Gasification......Page 308
Model Equations......Page 309
Computational Results......Page 313
Conclusions......Page 317
Subscripts......Page 319
Literature Cited......Page 320
28 A Pore Diffusion Model of Char Gasification with Simultaneous Sulfur Capture......Page 321
The Model......Page 322
Modeling Equations......Page 324
Sulfur Capture During the Initial Stages of Char Gasification......Page 326
Sulfur Capture During Complete Burnout......Page 327
Acknowledgment......Page 331
Literature Cited......Page 332
29 Nitric Oxide Reduction by Hydrogen and Carbon Monoxide over Char Surface Fundamental Kinetics for Nitric Oxide Emission Control from Fluidized-Bed Combustor of Coal......Page 333
Experimental Apparatus and Procedure......Page 334
Experimental Results and Discussion......Page 335
Concluding Remarks......Page 341
Literature Cited......Page 343
30 Transient Simulation of Moving-Bed Coal Gasifiers......Page 344
Legend of Symbols......Page 357
Literature Cited......Page 358
31 Simultaneous Mass Transfer of Hydrogen Sulfide and Carbon Dioxide with Complex Chemical Reaction in an Aqueous Diisopropanolamine Solution......Page 359
Theory......Page 360
Experimental procedures and results.......Page 366
Conclusions......Page 371
Literature Cited......Page 374
32 Hydrodynamics and Mass Transfer in Pulsing Trickle-Bed Columns......Page 375
Transition from gas-continuous to pulsing flow......Page 376
Mass transfer between stagnant and dynamic holdup......Page 378
Mass transfer from gas to liquid in the pulsing flow regime......Page 382
Conclusion......Page 387
Literature Cited......Page 388
33 The Percolation Theory: A Powerful Tool for a Novel Approach to the Design of Trickle-Bed Reactors and Columns......Page 389
The percolation process......Page 391
Modelling of the transport processes......Page 393
Concluding remarks......Page 398
Literature Cited......Page 400
34 Trickle-Bed Reactors: Dynamic Tracer Tests, Reaction Studies, and Modeling of Reactor Performance......Page 402
Reaction Kinetics......Page 403
Trickle-Bed Reactor Model Development......Page 407
Evaluation of Liquid-Solid Contacting Efficiency......Page 412
Discussion of Reaction Studies in a Trickle-Bed Reactor......Page 414
Conclusions......Page 416
Legend of Symbols......Page 420
Literature Cited......Page 421
35 Exothermic Gas Absorption with ComplexReaction: Sulfonation and Discoloration in the Absorption of Sulfur Trioxide in Dodecylbenzene......Page 422
Stirred Cell Experiments......Page 423
Exothermic Absorption with Two Parallel Reactions......Page 427
Literature Cited......Page 437
36 Analysis of Chemical and Physical Processes During Devolatilization of a Single, Large Particle of Wood......Page 438
Brief Description of Mathematical Model......Page 439
Results and Discussion......Page 440
Literature Cited......Page 449
37 Characterization of Nonisobaric Diffusion Due to Nonequimolar Fluxes in Catalyst Particles......Page 451
Model of Diffusion in a Porous Solid......Page 452
Experimental Equipment......Page 454
Results......Page 456
Discussion......Page 459
Conclusion......Page 463
Literature Cited......Page 466
38 Coke Deposition on a Commercial Nickel Oxide Catalyst During the Steam Reforming of Methane......Page 467
Reaction Equations......Page 468
Experimental......Page 469
Discussion......Page 471
Literature Cited......Page 475
39 Physical Aspects in Organic Liquid-Phase Oxidations......Page 476
Cyclohexane Oxidation—Previous Studies......Page 477
Mass Transfer Effects......Page 479
Mass Transfer Coefficients......Page 480
Experimental Techniques......Page 483
Results and Discussion......Page 484
Conclusions......Page 489
Literature Cited......Page 490
40 Structural Variations as a Tool to Analyze the Mechanism of Noncatalytic Solid-Gas Reactions......Page 492
Experimental......Page 493
Zone Reaction Model......Page 497
Results......Page 499
Legend of Symbols......Page 500
Literature Cited......Page 502
41 Heat Transfer in Packed Reactor Tubes Suitable for Selective Oxidation......Page 503
Experimental......Page 504
Empirical Data Correlation......Page 508
Particle Shape......Page 509
Prediction of Heat Transfer Parameters......Page 512
Comparison of Model Predictions......Page 515
Legend of Symbols......Page 517
Literature Cited......Page 518
42 A New Chemical Method for the Study of Local Micromixing Conditions in Industrial Stirred Tanks......Page 519
Reaction system......Page 520
Principle of the measurement......Page 522
Example of experimental results......Page 523
Interpretation and discussion......Page 525
Legend of symbols......Page 527
Literature cited......Page 528
43 Considerations of Macromixing and Micromixing in Semi-Batch Stirred Bioreactors......Page 529
Two Environment Recirculation Model......Page 530
Results......Page 532
Discussion and Conclusions......Page 533
Literature Cited......Page 538
44 Mixing, Diffusion, and Chemical Reaction in a Single Screw Extruder......Page 540
Physical and Mathematical Model......Page 541
Results and Discussion......Page 546
Legend of Symbols......Page 548
Literature Cited......Page 550
45 Mathematical Model of Low Density Polyethylene Tubular Reactor......Page 552
Fluiddynamic study......Page 555
Kinetic assumptions......Page 556
Mathematical model......Page 557
Results......Page 558
Acknowledgments......Page 562
Literature Cited......Page 563
46 The Effect of Mixing on Steady-State and Stability Characteristics of Low Density Polyethylene Vessel Reactors......Page 564
The Perfectly Mixed Model......Page 565
The Imperfectly Mixed Model......Page 570
Results and Conclusions......Page 572
Literature Cited......Page 574
B......Page 576
C......Page 577
F......Page 579
H......Page 580
I......Page 581
M......Page 582
O......Page 583
P......Page 584
S......Page 585
T......Page 586
Z......Page 587

Citation preview

Chemical Reaction Engineering—Boston James Wei, EDITOR Massachusetts Institute of Technology Christo Massachusetts Institute of Technology

Developed i n advance of the 7th International Symposium on Chemical Reaction Engineering in Boston, Massachusetts October 4-6, 1982

ACS SYMPOSIUM SERIES

AMERICAN CHEMICAL SOCIETY WASHINGTON, D. C. 1981

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

196

Library of Congress Cataloging in Publication Data International Symposium on Chemical Reaction Engi­ neering (7th: 1982: Boston, Mass.) Chemical reaction engineering, (ACS symposium series, ISSN 0097-6156; 196) Includes bibliographies and index. 1. Chemical engineering—Congresses. 2. Chemical reactors—Congresses. I. Wei, James, 1930. II. Georgakis, Christos, 1947. III. Title. IV. Series. TP5.I67 1982 660.2'99 82-11629 ACSMC8 196 1-614 ISBN 0-8412-0732-1 1982

Copyright © 1982 American Chemical Society All Rights Reserved. The appearance of the code at the bottom of the first page of each article in this volume indicates the copyright owner's consent that reprographic copies of the article may be made for personal or internal use or for the personal or internal use of specific clients. This consent is given on the condition, however, that the copier pay the stated per copy fee through the Copyright Clearance Center, Inc. for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law. This consent does not extend to copying or transmission by any means—graphic or electronic—for any other purpose, such as for general distribution, for advertising or promotional purposes, for creating new collective work, for resale, or for information storage and retrieval systems. The copying fee for each chapter is indicated in the code at the bottom of the first page of the chapter. The citation of trade names and lot names of manufacturers in this publication is not to be construed as an endorsement or as approval by ACS of the commercial products or services referenced herein; nor should the mere reference herein to any drawing, specification, chemical process, or other data be regarded as a license or as a conveyance of any right or permission, to the holder, reader, or any other person or corporation, to manufacture, repro­ duce, use, or sell any patented invention or copyrighted work that may in any way be related thereto. PRINTED IN THE UNITED STATES OF AMERICA

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

ACS Symposium Series M . Joa

Advisory Board David L. Allara

Marvin Margoshes

Robert Baker

Robert Ory

Donald D. Dollberg

Leon Petrakis

Robert E. Feeney

Theodore Provder

Brian M. Harney

Charles N. Satterfield

W. Jeffrey Howe

Dennis Schuetzle

James D. Idol, Jr.

Davis L. Temple, Jr.

Herbert D. Kaesz

Gunter Zweig

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

FOREWORD The ACS SYMPOSIUM SERIES was founded in 1974 to provide a medium for publishing symposia quickly in book form. The format of the SERIES parallels that of the continuing ADVANCES I N CHEMISTRY SERIES except that in order to save time the papers are not typeset but are reproduced as they are sub­ mitted by the authors in camera-ready form. As a further means of saving time, the papers are not edited or reviewed except by the symposium chairman, who becomes editor of the book. Papers published in the ACS S Y M P O S I U M SERIES are original contributions not published elsewhere in whole or major part and include reports of research as well as reviews since symposia may embrace both types of presentation.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

PREFACE T H E 7th INTERNATIONAL S Y M P O S I U M on Chemical Reaction Engineer­ ing represents another milestone in the advancement of the art and science of the chemical reactor. Forty-six contributed papers are presented here: nineteen from Western Europe, five from Asia and Australia, one from Canada, and twenty-one from the United States. The Symposium con­ tinues to be dominated by university professors—only six papers have one or more coauthors from serve industry, strong message bridge cannot give good service if there is a massive pier on one shore and a flimsy one on the other. After many years, chemical reaction engineering has developed a paradigm: classic papers that are universally admired, basic assumptions and analysis, successful applications of principles to particular problems, and standard textbooks and curricula that are generally accepted. Chemi­ cal reaction engineering is not yet completely matured and thus has not been reduced to restatements of old results and remeasurements with greater accuracy. The innovation processes continue to develop. New needs of society, such as synthetic fuels, and new technical opportunities, such as recombinant D N A , will keep this subject vigorous for many years to come. James Wei Massachusetts Institute of Technology Cambridge, Massachusetts 02139 Christos Georgakis Massachusetts Institute of Technology Cambridge, Massachusetts 02139 October 1982

ix In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

1 Catalytic Air Oxidation of Propylene to Acrolein: Modeling Based on Data from an Industrial Fixed-Bed Reactor D. ARNTZ, Κ. ΚΝΑΡΡ, and G. PRESCHER Degussa AG, Hanau, Federal Republic of Germany G. EMIG and H . H O F M A N N Inst. f. Techn. Chemie I, Universität Erlangen-Nürnberg, Federal Republic of Germany

From a few w e l l chosen experiments in an i n t e g r a l r e a c t o r o f t e c h n i c a l dimensions with side-stream a n a l y s i s both r e a c t i o n schemes and the e f f e c t i v e heat t r a n s f e r and k i n e t i c parameters o f a r e a c t i o n model f o r propylene o x i d a t i o n could be deduced, from which v a l u a b l e information f o r both c a t a l y s t development and o p t i m i z a t i o n o f the r e a c t i o n c o n d i t i o n s could be obtained. The economic s i g n i f i c a n c e (1,2,3) o f the c a t a l y t i c p r o p y l e ne o x i d a t i o n n e c e s s i t a t e s a c o n t i n u i n g refinement o f the c a t a l y s t . This i n t u r n r e q u i r e s c o n t i n u i n g o p t i m i z a t i o n o f the r e a c t i o n c o n d i t i o n s , as these depend upon the c a t a l y s t . The goal o f t h i s i n v e s t i g a t i o n was the development o f a s u i t a b l e r e a c t o r model f o r propylene o x i d a t i o n i n an i n d u s t r i a l s i z e packed-bed r e a c t o r operated under i n d u s t r i a l l y r e l e v a n t conditions (4). From the l i t e r a t u r e i t i s not p o s s i b l e t o deduce a k i n e t i c scheme s u i t a b l e f o r modeling the r e a c t i o n , s i n c e the majority of p u b l i c a t i o n s (10-39) do not present an unequivocal p i c t u r e . Also the fundamental d i f f i c u l t i e s o f e s t i m a t i n g from independent measurements heat t r a n s f e r parameters f o r a packed-bed r e a c t o r are w e l l known (5,6,7). Therefore, an attempt was made t o determine the k i n e t i c r e a c t i o n scheme and e f f e c t i v e heat t r a n s f e r as w e l l as k i n e t i c parameters from a l i m i t e d number o f experimental r e s u l t s i n a s i n g l e - t u b e r e a c t o r o f i n d u s t r i a l dimensions with side-stream a n a l y s i s . The data e v a l u a t i o n was performed with a pseudohomogeneous two-dimensional continuum model without a x i a l d i s p e r s i o n . The model was t e s t e d f o r i t s s u i t a b i l i t y f o r p r e d i c t i o n .

0097-6156/82/0196-0003$06.00/0 © 1982 American Chemical Society

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

4

CHEMICAL REACTION ENGINEERING

E x p e r i m e n t a l Set-Up

and R e s u l t s

The r e s u l t s w e r e o b t a i n e d i n a c o n t i n u o u s l y o p e r a t e d p o l y t r o p i c p i l o t p l a n t r e a c t o r w i t h a f e e d o f a p p r o x i m a t e l y 2-5 m o l e s p r o p y l e n e p e r h o u r . The r e ­ a c t o r was a s i n g l e t u b e h a v i n g a c a t a l y t i c b e d l e n g t h o f 2.70 m a n d a n i n n e r d i a m e t e r o f 0 . 0 2 0 5 m. T e m p e r a t u r e was c o n t r o l l e d b y a c i r c u l a t i n g m o l t e n s a l t b a t h . T h e t e m p e r a t u r e p r o f i l e w i t h i n t h e r e a c t o r was m o n i t o r e d w i t h s i d e - e n t r y t h e r m o c o u p l e s : e l e v e n i n t h e c e n t e r o f t h e t u b e , t w o i n a n 1/2 r a d i u s p o s i t i o n , and t h r e e a t t h e w a l l . F e e d s o f p r o p y l e n e , a i r , i n e r t g a s a n d w a t e r w e r e m o n i t o ­ red by r o t a m e t e r s and preheated t o s a l t bath temperature. O v e r a l l a c r o l e i n y i e l d s a v e r a g e d o v e r 48 h o u r s p e r i o d s , were e v a l u a t e d by i s o l a t i n g c r u d e a c r o l e i n by a b s o r p t i o n with water and subsequent d e s o r p t i o n . Unreacted p r o p y l e n e , c a r b o n o x i d e s a n d o x y g e n w e r e m e a s u r e d i n t h e e f f l u e n t g a s ( G . C . ) a n d a c r y l i c a c i d was a n a l y s e d (G.C.) i n t h e a c r o l e i n - f r e e bottoms. To measure t h e a x i a l c o n c e n t r a t i o n p r o f i l e o f t h e r e a c t o r gaseous samples ( 5 p r o b e s a l o n g t h e r e a c t o r ) were a n a l y s e d (water scrubber and e f f l u e n t and f o r m a l d e h y d e ( G . C , a n a l y s e analysed b e s i d e s a c r y l i c a c i d ) and p o l y a c r o l e i n ( r e s i d u e o f e v a p o r a t i o n ) always t o t a l e d l e s s t h a n 4 %, b a s e d o n t h e p r o p y l e n e f e d i n ; t h e c o r r e s p o n d i n g s i d e - r e ­ a c t i o n s were n e g l e c t e d f o r m o d e l i n g . The s p h e r i c a l c a t a l y s t , b a s e d o n a m u l t i c o m p o n e n t b i s m u t h m o l y b d a t e was p r e p a r e d a c c o r d i n g t o ( 8 ) w i t h d = 5.3 . 1 0 " m , λ = 0.8 . 1 0 - K J / m . s . ° K a n d P = 1145 kg/m f o r t h e c a t a l y t i c b e d . The range o f v a r i a b l e s s t u d i e d i n t h e packed-bed experiments i s given i n Table I . T y p i c a l d e t a i l e d r e s u l t s f o r an ex­ perimental run are given i n Table I I . 3

p

3

ρ

3

g

Modeling R e a c t o r Model. The d e s i g n o f an i n d u s t r i a l packed-bed r e a c t o r r e q u i r e s a r e a c t o r m o d e l a s w e l l a s t h e c h e m i c a l a n d t h e h e a t a n d mass t r a n s f e r p a r a m e t e r s of the c a t a l y s t bed - gas stream system. Since these parameters are model-speci­ f i c , i t seemed a d v i s a b l e t o employ a continuum model f o r t h e r e a c t o r c a l c u l a t i o n . T h i s i s t h e o n l y model t o date f o r which t h e l i t e r a t u r e c o n t a i n s c o n s i s t e n t d a t a f o r c a l c u l a t i n g h e a t a n d mass t r a n s f e r p a r a m e t e r s ( 5 , 6 , 7 ) . T h i s m o d e l i n i t s

Table I

Experiments Run No.

Τ

1 2 3 4 5

296 320 311 334 377

- Range o f V a r i a b l e s

Τ

w

max C o m p o s i t i o n o f R e a c t o r F e e d ( M o l e F r a c t i o n ) O v e r a l l propene propene propane N 0 H 0 c o n v e r s i o n {%) 301 0.047i 0.0022 0.595 0.158 0.198 45 335 0.047 0 . 0 0 2 4 0 . 5 9 9 0.159 0.192 72 325 0.088 0.0041 0 . 5 7 0 0.151 0.187 42 358 0.089! 67 0 . 0 0 3 8 0.569 0.151 0.187 415 0.089 0 . 0 0 4 3 0.567 0.150 0.190 85 2

2

2

6

2

5

T =T(salt bath); G - 1.16 ± 0.02 ( k g / m * . s ) ; ρ = 1.63 ± 0.01 ( b a r ) a t r e a c t o r i n l e t ; p r e s s u r e d r o p : A P = 0 . 0 4 9 g - 0 . 0 0 2 , * = remains unreacted under a l l o p e r a t i n g c o n d i t i o n s . (bar/m) w

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

1.

ARNTZ ET A L .

Table I I

Catalytic Propylene Oxidation

Run No. 5 - D e t a i l e d I n f o r m a t i o n

bed l e n g t h (•) 0 0.15 0.30 0.45 0.60 0.80 1.00 1.20 1.40 1.70 2.00 2.30 2.60 2.70

m o l e f r a c t i o n x\ p r o p e n e I C 0 , CO a c r o l e i n a c r y l i c

temperatureQ)

] acid;

2

°C 377 415 413 387® 407 406 385© 397 391 390 388 387 386

0.089

5

0.071

6

0.003J

0.056

3

0.005

0

4

0

0

.

0.0162

0.00054

:

0.030

0.0010

8

] 1 1

2

; 0.035

2

0.008g

0.049

0

0.00218

0.021

4

0.013

0

0.059

8

0.0036

0.013

6

0.016

2

0.065

3

6

j t (

0.0050 J 15 i n c e n t e r o f t u b e , (^ 2 iΓ n 1/2 r p o s i t i o n G = 1.178 ( k g / m * . s ) Δ ρ = 0.051 ( b a r / m ) ρ = 1.633 ( ° ) 0

a r

two-dimensional form, i n which t h e a x i a l heat c o n d u c t i o n and a x i a l d i s p e r s i o n a r e n e g l e c t e d , y i e l d s f o r t h e mass b a l a n c e o f t h e c o m p o n e n t s :

3 y

3z

j

1 3 , 3j r~ 3Γ" r (Γ 1

»'

M ] Γ : i=l

r

V

a

2

i

e

f

;

j=l

Ν

(1)

with t h e boundary

and f o r t h e e n e r g y b a l a n c e : 3Θ S-^f

f

conditions:

z=0:yj=yj ; 9=0 (r), 0

k

Σ 1=1

(-

Û H

0*r*l

0

r

i

) i,eff 3 y

3 y

^

i

3Θ

i =

3Θ 3 T »

0 ;

O^z^l

B

i

(

e

- V

0^z="l

The t r a n s p o r t p a r a m e t e r s i n a j , b j a n d B i a r e e f f e c t i v e p a r a m e t e r s w i t h w h i c h , j u s t a s w i t h t h e e f f e c t i v e r a t e r f f , s e v e r a l d i f f e r e n t p h y s i c a l phenomena a r e lumped. The t w o - d i m e n s i o n a l p s e u d o h o m o g e n o u s r e a c t o r m o d e l ( E q . l ) i s t h e b a s i s f o r t h e s t a n d a r d i z e d c o m p u t e r p r o g r a m F I B S A S ( 9 ) , w h i c h was u s e d f o r t h e e v a l u a t i o n and s i m u l a t i o n r e p o r t e d h e r e . e

Reaction Schemes and Networks. Within the l a s t few years a s e r i e s o f review a r t i c l e s have appeared concerning the o x i d a ­ t i o n o f propylene t o a c r o l e i n (10-16). I t i s g e n e r a l l y assumed that the f i r s t r e a c t i o n step, the formation o f an adsorbed a l l y l i c s p e c i e s , i s rate-determining f o r the formation o f aero-

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

6

CHEMICAL REACTION ENGINEERING

l e i n . Side r e a c t i o n s o f t h i s intermediate s p e c i e s as w e l l as d i r e c t p a r a l l e l r e a c t i o n s are p o s s i b l e . However, previous mechanistic i n v e s t i g a t i o n s l e a d n e i t h e r to unequivocal c o n c l u s i o n s over the r e a c t i o n scheme nor over the r e a c t i o n k i n e t i c s . A l a r g e number o f i n v e s t i g a t i o n s do not even consider the formation o f the i n d u s t r i a l l y important a c r y l i c a c i d (Models I I I I ) . The most d e t a i l e d Model V, on the other hand, i s too complex f o r a p r a c t i c a l a p p l i c a t i o n . I n v e s t i g a t i o n s o f model s i m p l i f i c a t i o n s f o r i n d u s t r i a l l y r e l e v a n t c a t a l y s t s are e i t h e r nonexistent or lead to d i f f e r i n g r e s u l t s (Models I-IV). A p o i n t common to a l l the models i s that they are based upon a redox-type mechanism, i n which the r e o x i d a t i o n o f the c a t a l y s t i s not a l i m i t i n g f a c t o r . Corresponding, none o f them employ the model expression o f Mars and van Krevelen (37). On c o n t r a s t newer works by Keulks (38,39 l i m i t i n g e f f e c t from th on oxygen p a r t i a l pressure f o r the a c r o l e i n formation and to a two to t h r e e - f o l d higher a c t i v a t i o n energy compared with the r e a c t i o n at higher temperatures. Thus a c o n s i d e r a t i o n o f the l i t e r a t u r e data n e c e s s i t a t e s e s t a b l i s h i n g a network before determining the e f f e c t i v e k i n e t i c parameters. D e r i v a t i o n o f Reaction Schemes Based on Experimental R e s u l t s . Although numerous methods f o r e v a l u a t i n g r e a c t i o n s schemes have been developed (40-44), most o f them (40-42) s t a r t with a hypothet i c a l mechanism which i s , by means o f experiments, e i t h e r c o n f i r med or r e j e c t e d . A newly developed method f o r the systematic e l u c i d a t i o n o f r e a c t i o n schemes o f complex systems r e q u i r e s no chemic a l c o n s i d e r a t i o n s , but concentration-time measurements and sys t e m - a n a l y t i c a l c o n s i d e r a t i o n s (45). The method i s based on the i n i t i a l slope o f the concentration-time p r o f i l e s and when necessary the higher d e r i v a t i v e s o f these curves a t t = 0. Reaction steps i n which products are formed d i r e c t l y from r e a c t a n t s can be i d e n t i f i e d i n a concentration-time p l o t by a p o s i t i v e g r a d i e n t dc- a t t = 0 (zero order d e l a y ) . dt I t can be seen from a t y p i c a l , p r a c t i c a l l y isothermal conc e n t r a t i o n p r o f i l e (Figure 1) t h a t a t t = 0 a l l products e x h i b i t a non-zero s l o p e . This i m p l i e s that a l l o f them must be formed d i r e c t l y from the r e a c t a n t s propylene and oxygen, which e l i m i n a tes the r e a c t i o n schemes I and IV (Table I I I ). Therefore the f o l l o w i n g s t o i c h i o m e t r i c equations were used i n the a n a l y s i s ; f o r equation (4) the approximately constant r a t i o o f CO and CO^ which was a c t u a l l y measured was a p p l i e d . J

k

Pe

+

0

Pe

+

1.5 0

Pe

+

4 1/6

2

i * > Ac + H 0

(2)

^> As + H 0

(3)

2

2

2

0

2

*3

y

2/3

CO + 2 1/3

C0 + 3 H 0 2

2

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

(4)

1.

ARNTZ ET A L .

Catalytic Propylene Oxidation

Table III

7

R e a c t i o n Models

I

(17-20)

P e — » Ac —> C 0 , C 0 ;

III

(26-30)

Pe

2

vC0,C0 ;

I I (21-25)

I V (31) Pe — >

o

co,co

2

Fo,Ad V

(32-36)

Pe - M s \

C0,C0 y

2

9

Fo.Ad

acrolein acetaldehyde acrylic acid formaldehyde propylene

Ac Ad As Fo Pe

Further systematic a p p l i c a t i o c l u s i o n that the r e a c t i o such r i g o r o u s model b u i l d i n g demands independent v a r i a t i o n s o f a l l r e a c t a n t c o n c e n t r a t i o n s , which was beyond the scope o f t h i s investigation.

(5) The r e a c t i o n scheme was t h e r e f o r e completed using a d d i t i o n a l i n ­ formation from the concentration-time-diagram. In experiments with a high degree o f conversion (Table I I ) the y i e l d o f a c r o l e i n i s obviously l i m i t e d with i n c r e a s i n g residence time. At the same time the a c r y l i c a c i d c o n c e n t r a t i o n i s s t i l l i n c r e a s i n g a t the end o f the r e a c t o r , suggesting a concecutive o x i d a t i o n o f a c r o l e i n to a c r y l i c a c i d as an a d d i t i o n a l r e a c t i o n . Heat T r a n s f e r Parameters. Attempts i n t h i s i n v e s t i g a t i o n t o use heat t r a n s f e r parameters ( λ ^ h ) c a l c u l a t e d from c o r r e l a ­ t i o n s based on data without r e a c t i o n Τβ,7) l e d t o the r e s u l t t h a t the energy balance o f the r e a c t o r a t the measured temperatures was not s a t i s f i e d . On the other hand, the simultaneous e s t i m a t i o n o f heat t r a n s f e r and k i n e t i c parameters by r e g r e s s i o n a n a l y s i s o f p o l y t r o p i c measurements allows these parameters t o i n f l u e n c e each other. I t was observed that the parameters c a l c u l a t e d by these two methods were q u i t e d i f f e r e n t (5,46). Therefore i n t h i s r e p o r t the heat t r a n s f e r parameters were determined from experimental r e ­ s u l t s by a t h i r d method with a minimum o f a d d i t i o n a l assumptions: The e n e r g y b a l a n c e e q u a t i o n was s o l v e d f o r t h e m o s t e x o t h e r m i c c a s e ( R u n 5 ) , ( T a b l e s I and I I ) t o g e t h e r w i t h t h e mass b a l a n c e e q u a t i o n ( 1 ) . T h u s , t h e r ^ were d e d u c e d f r o m a w e l l - f i t t e d b u t w i t h r e s p e c t t o t h e k i n e t i c e x p r e s s i o n ' s t i l l a r b i t r a r y d e s c r i p t i o n of the experimental c o n c e n t r a t i o n p r o f i l e along the r e a c t o r . S i n c e t h e Δ Η ^ a r e known, i t r e m a i n s t o c h o o s e h and X f f s o t h a t t h e e x p e r i m e n t a l l y measured temperature g r a d i e n t § | i s c o r r e c t l y d e s c r i b e d . For t h i s , w

e

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

CHEMICAL REACTION ENGINEERING

8

mole nj 100 mole Pe

Figure 1.

Experimental results from Run 3, Table 1.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

1.

9

Catalytic Propylene Oxidation

ARNTZ ET A L .

two a s s u m p t i o n s w e r e made: 1. t h e m o d e l e x p r e s s i o n g i v e n i n ( 7 ) ( w i t h o u t t h e l o n ­ g i t u d i n a l c o r r e c t i o n ( 9 ) i s c o r r e c t ) ; 2 . B i o t i s c o n s t a n t ( t h e same c o r r e c t i o n f a c t o r f o r h and * f f ) · These heat t r a n s f e r parameters were used f o r a l l experiments (Table IV); they are d i s t i n c t l y higher than those which can be c a l c u l a t e d from ( 7 ) f o r the case without r e a c t i o n . T h i s agrees with i n v e s t i g a t i o n s o f the o x i d a t i o n o f CO ( 5 ) . w

e

Table IV λ „ (KJ/m.s.K) err, r h (KJ/m w

i

2

R e f e r e n c e (2) 0.82 χ 10-

experimentally determined 1.25 χ 1 ( H

.s . K)

0.27

0.412

E f f e c t i v e K i n e t i c Parameters t h r e a c t i o n the p o t e n t i a

r. = A. exp(-Ei/RT)T

0

F o r the r a t e

Pj

o f the

(6)

ij

was chosen. An i n i t i a l s e t o f parameters ( Α χ , E n j ) was de­ termined f o r each t r i a l s e p a r a t e l y (Runs 1 - 5 ) , (Table I ) by simultaneous f i t t i n g o f measured c o n c e n t r a t i o n and temperature p r o f i l e s along the r e a c t o r . I n i t i a l gross f i t t i n g was accompli­ shed by o p t i c a l o p t i m i z a t i o n ( 4 7 ) t h r o u g h v a r i a t i o n o f A E i , n i j . I t p r o v e d e f f e c t u a l t o s e t s m a l l v a l u e s f o r i{ ( 4 0 - 7 0 x l 0 J / k m o l e ) and n i j ( 0 . 3 - 0 . 5 ) a n d a c h i e v e t h e f i r s t f i t b y v a r y i n g A j . A b e t t e r f i t was a c h i e v e d b y v a r i a t i o n o f E j a n d n j : , w h e r e b y A j was r e c a l c u l a t e d f o r e a c h s u b s e q u e n t com­ putation according to ( 7 ) . l f

x

l f

6

The k i n e t i c parameters obtained from t h i s o p t i c a l o p t i m i z a ­ t i o n are used as s t a r t i n g values f o r the FIBSAS o p t i m i z a t i o n sub­ r o u t i n e SIMPLEX. The procedure d e s c r i b e d above was a p p l i e d t o a l l t r i a l s (Runs 1 - 5 ) , whereby some o f the parameters obtained f o r the d i f f e r e n t t r i a l runs s t i l l showed s i g n i f i c a n t v a r i a t i o n . A set o f parameters v a l i d f o r a l l runs was obtained from the l i n e a r regression ( 8 ) : I n r . = I n A. - ( E . / R T ) Σ η . . I n p . ι ι ι j 1J j

( 8 )

Τ and p. i n ( 8 ) a r e experimental values; the other parameters a r i s e from the former f i t t i n g s f o r Runs 1 - 5 . In each step o f approximation the best f i t i s f i r s t achieved f o r i = l and then, one a f t e r another, f o r i = 2 - 4 . The r e s u l t o f t h i s e s t i m a t i o n o f k i n e t i c parameters i s shown i n Table V and F i g u r e s 2 - 4 .

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

10

CHEMICAL RE ACTION

Table V

Results for Effective Kinetic

/ r- / χ i , e f f " i * *P · P A

e

A.

E.

1

1

RT

[Z n..) K m o l e / n r . s . P a s c a l J i j J/Kmole

i 1 2 3 4

16.7 χ 1.3 χ 1.28x 77.1 χ

ΙΟ-* 10~ 10" 10~

5

47.4 42.8 52.8 93.2

6

3

3

χ χ χ χ

106 10 10 10 6

6

6

Parameters

π., η. _ η. _ i l ι2 ι3 · \ ·P c

Λ Τ

r

ENGINEERING

P e

A

"il

n

i2

η. i3

0.44 0.54 0.66 0

0.93 0.54 0 0

0 0 0 1

0

Discussion The model d e s c r i b e s , w i t h i n the l i m i t s o f measuring e r r o r , the experimental temperature and c o n c e n t r a t i o n p r o f i l e s q u i t e w e l l over a wide temperature range (more than 100 C) and propy­ lene conversion range (Table I ) , (Figures 2 - 4 ) . But the r e ­ a c t i o n orders f o r propylene and oxygen have only a l i m i t e d r e ­ l i a b i l i t y s i n c e e s p e c i a l l y the oxygen c o n c e n t r a t i o n along the r e a c t o r v a r i e d only w i t h i n narrow l i m i t s . A d d i t i o n a l l y , pressure and flow r a t e were, f o r the most p a r t , h e l d constant (Table I ) . The model was then used to p r e d i c t measured r e s u l t s f o r a wide range o f experimental c o n d i t i o n s (T = 343-360 , ( x ) = 0.07-0.09, ( x ) = 0.13-0.15 , ( x ) = 0 . I 8 5 " 0-003, p

β

W

Q

5

H 2 0

1

G = 1.17 - 1.70 kg.m^s" ) as w e l l as f o r a c a t a l y s t d i f f e r e n t from t h a t used i n Runs 1-5 . The new c a t a l y s t was based upon the same chemical system but contained more a c t i v e m a t e r i a l ( 8 ) . It was s u r p r i s i n g t h a t only the pre-exponential f a c t o r s A^ had to be newly estimated (Table VI) whereby the conversion f a c t o r s f o r A f o r the three p a r a l l e l r e a c t i o n s s t a r t i n g from propylene ( i = l - 3 , Table VI) proved to be about the same. From these r e l a t i o n s h i p s u s e f u l i n f o r m a t i o n f o r f u t u r e c a t a l y s t p r e ­ p a r a t i o n may be drawn ("learning model"). x

Table

VI

A . f o r new r u n s

1

A.

1

1 j 2 3! 4 ·

3

(Kmole/m s . P a s c a l 30.4 2.26 2.03 272.5

χ χ χ χ

ΙΟ" 10~ 10" 10"

6

J

(different

catalyst)

i n . . A. (5 new r u n s ) ) A* ( r u n 1 - 5 ) 1 J

1

1.8 1.7 1.5g 3.5 2

6

4

3

3

3

The agreement o f the p r e d i c t i v e c a l c u l a t i o n s with the measu­ red r e s u l t s i s q u i t e good f o r those new runs ( " p r e d i c t i v e model")

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

1.

ARNTZ ET AL.

11

Catalytic Propylene Oxidation

Figure 2. Experimental results from Run 2, Table L Key: X , temperature mea­ sured; •> propylene; · , acrolein; A * acrylic acid; and ψ , CO and C0 . Z

Figure 3. Experimental results from Run 4, Table I. Symbols are the same as in Figure 2.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

1 2

CHEMICAL REACTION ENGINEERING

Figure 4.

Experimental results from Run 5, Table I. Symbols are the same as in Figure 2.

Figure 5.

Data plotted of a predicted run. Symbols are the same as in Figure 2.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

1.

ARNTZ ET A L .

13

Catalytic Propylene Oxidation

as i l l u s t r a t e d i n Figure 5 ( d i f f e r e n t c a t a l y s t ; reduced bed length; (XQ ) = 0.127; ( X H O ) = °·004; G = 1.67 k g . m ^ s " ) . The p r e d i c t i o n o f the new runs succeeded, even though, be­ s i d e s the c a t a l y s t , the r e a c t o r feed and flow r a t e were s i g n i f i ­ c a n t l y d i f f e r e n t from those o f the experimental r e s u l t s (Tables I and II) from which the model was d e r i v e d . C l e a r l y , the s i m p l i f i c a t i o n o f the r e a c t i o n scheme t o the four r e a c t i o n s found i n network (5) i s only v a l i d f o r the tempe­ r a t u r e and c o n c e n t r a t i o n range which was i n v e s t i g a t e d . E s p e c i a l l y at higher temperatures, a d d i t i o n a l secondary r e a c t i o n s , p a r t i c u ­ l a r l y the o x i d a t i o n o f a c r o l e i n t o CO and CO2, must be e x p l i c i t l y considered. 1

2

2

0

Legend of Symbols 4.(q /P ).(L/d ).(d /d L · M /G P*m = u . d p / D f f , P e e l e t No. ( m a s s , r a d i a l ) P e - G . C p . d p A f f , P e c l e t No.(heat,radial) preexponential factor 4.(L/d ).(d /d ).(Pe )r 2r'/d^, reduced r a d i a l coordinate L/(G.c .T ) b r' = radial coordinate m Bi df h /2V,eff B i ° t number r i f f = e f f . rate of i th reaction Cp = mass s p e c i f i c h e a t a t c o n s t a n t time s pressure K J k g " Κ"* temperature CJ = molar c o n c e n t r a t i o n kmole linear velocity ms dp,d|.= d i a m e t e r ( p a r t i c l e , t u b e ) mole f r a c t i o n ^r,eff effective radial dispersion pseudo-mole f r a c t i o n y j = n j / 5 n j coefficient mV z'/L reduced a x i a l coordinate E = a c t i v a t i o n energy J mole""* ζ· = a x i a l c o o r d i n a t e m G = mass s p e c i f i c f l o w r a t e k g n r ^ s " * V , e f f e f f e c t i v e r a d i a l t h e r m a l c o n d u c t i ­ = reaction enthalpy J mole"* ΔΗ v i t y o f t h e c a t a l . b e d K J . n r V .K" = wall heat t r a n s f e r stoichiometric coefficient w coefficient KJ.nrV ^| v o l u m e t r i c mass kg m • reaction rate constant o f i th θ : reduced temperature T / T ki reaction superscript: L = lenght of reactor b

0

t

p

0

0

r? e

h

r f e

1

t

p

2

p

t

h

0

w

f e

1

- 1

0

1

1

h

1

Y i j

- 3

0

M

= mean m o l a r mass = amount o f s u b s t a n c e = reaction order

subscripts: g = gasphase i = f o r t h e it h r e a c t i o n j = f o r t h e jt h s p e c i e s ρ = particle

kg k m o l e - 1 mole

i , (i+1) step o f i t e r a t i o n

s t w 0

= s o l i d phase = tube = wall = conditions at reactor inlet

Literature Cited

1. 2.

Kirk-Othmer "Encyclopedia of Chemical Technology"; Wiley, J., New York, 1978; Vol. 1, p. 288. Weigert,W. "Ullmanns Encyklopädie d. technischen Chemie"; Verlag Chemie, Weinheim, 1974; Vol. 7, p. 74.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

14

CHEMICAL REACTION ENGINEERING

3. Weigert, W.M; Maschke, H. Chew. Zeitung, 1974, 98 ( 2 ) , 61 4. Shinnar, R. "ACS-Symposium Series 72", American Chemical Society, Washington D.C., 1978; p. 1-36 5. Hofmann, H. Chem. Ing. Techn., 1979, 51, 257 6. Schlünder, E.U., "ACS-Symposium Series 72", Chem. React. Eng. Rev.-Houston, 1978, p. 110 - 161 7. "VDI-Wärmeatlas"; VDI-Verlag, Düsseldorf, 1977; p. Gg 8. Degussa, DE-PS 20 49 583, 1970, Degussa, DOS 31 25 061, 1981 9. Hofmann, U., Fortschr.-Ber., VDI-Zeitung. 1977, 3, 49 10. Haber. J., Kin. K a t a l . , 1980. 21, 123 - 135 11. Hucknall, D.J., " S e l e c t i v e Oxidation o f Hydrocarbons", Academic Press, London 1974 12. V.D.Wiele. K., v.d.Berg, P.J., "Comprehensive Chemical K i n e t i c s " , E l s e v i e r , Amsterdam, 1978, V o l . 20, p. 123 13. Krenzke, L.D., Keulks, G.W., Sklyarov, A.V., Firsova,A.A., Kutirev,M., Margolis,L.Y., Krylov,O.V,J.Catal.,1978,52, 418 14. Burlington, J.D., G r a s s e l l i 15. G r a s s e l l i , R.K., Burrington 72-72/12 16. Aso, J., Furukawa, S., Yamazone, N., Seiyama, T. J. Catal., 1980, 64, 29 17. Serban, S. Revue Chim. (Bucharest) 1967, 18, 65 18. C a r t l i d g e , J . , Mc Grath, L., Wilson, S.H., Trans. Inst. Chem. Eng., 1975, 53, 117 19. Köppner, D i s s e r t a t i o n U n i v e r s i t ä t Erlangen-Nürnberg, 1975 20. Varadarajan, T.K., Visvanathan, Β., S a s t r i , M.V.C., Indian J. Chem., 1977, 15, 452 21. Adams, C.R., Voge, J . J . C a t a l . 1961, 3, 379 22. Peacock, J.M., Parker, A.J., Ashmore,P.G., Hockey, J.A. J. C a t a l . , 1968, 15, 308 23. Wragg, R.P., Ashmore, P.G., Hockey, J.A., J. C a t a l . , 1973, 31, 293 24. S h i p a i l o , V.Y., Fedevich, E.V., Krivko, V.R., Zhurnal F i z i c h e s k o i Khimii, 1977, 51, 538 25. Lemberanskij, R.A., Azerb. Khim. Zh., 1968, 6, 19 26. Lapidus, V.L., Neftek., 1968, 9, 400 27. Gorshkov, A.P.,Gargarin. S.G., Kolchin, K., Neftek.,1970, 10, 59 28. Crozat, M., Germain, J.E., B u l l . Soc. Chim. F., 1973, 2498 29. Daniel, Ch., Keulks, G., J. Catal., 1973, 29, 475 30. Seinalow, R.J., Rustamow, M.I., Aliew, W.S., Model Khim. Reactorov T r . Vsos. Konf. Khim. Reactoram, 1968, 3, 41 31. Berty, J.M., Vortrag, U n i v e r s i t ä t Erlangen-Nürnberg, 1978 32. Moro-Oka, Y., Tan. S., Ozaki, Α., J. Catal., 1968, 12, 291 33. T j u r i n , J.N. Andruskewitsch, TW., Neftek., 1977, 17, 744 34. Bednorova, S., Habersberger, K., Chem. Prum., 1978, 28, 182 35. Vinogradova, O.M., Vytnov, G.F., Luiksaar, I.V., K i n . K a t a l . , 1975, 16, 576 36. Sheplew. W.S., Andruskewitsch, T.W., K a t a l l z . i. K a t a l i t . Processy, 1977, 171 37. Mars, P., v.Krevelen, D.W., Spec. Supp. Chem. Eng. S c i . , 1954, 3, 41 38. Krenzke, L.D., Keulks, G.W., J . C a t a l . , 1980, 64, 295 39. Monnier, J.R., Keulks, G.W., J . C a t a l . , 1981, 68, 51 40. Frost, Α.Α., Pearson, R.G., " K i n e t i c s and Mechanism.", John Wiley and Sons, New York, 1961 41. Petersen, E.E., "Chemical Reaction A n a l y s i s " , P r e n t i c e - H a l l , Inc. Engelwood Cliffs, 1964 42. Wei, J . , Prater, C.D., Adv. Cat., 1962, 13, 203 43. Lee, H.H., AIChE Journal, 1977, 23, 116 44. Akella, L.M., Lee, H.H., Chem. Eng. Jl., 1981, 22, 25 - 41 45. Probst, K., D i s s e r t a t i o n . U n i v e r s i t ä t Erlangen-Nürnberg, 1981 46. Emig, G., Hofmann. H., F r i e d r i c h , H., Proc. 5 th Europ. 2nd Int. Symp. Chem. React. Eng., 1972. Β 5 - 23 47. Gans, P. Comp. Chem., 1977, 1, 291

RECEIVED April 27, 1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

2 Simultaneous Uncorrelated Changes of Process Variables in a Fixed-Bed Reactor 1

A. BAIKER, M . BERGOUGNAN, and W. RICHARZ Swiss Federal Institute of Technology (ΕΤΗ), Department of Industrial and Engineering Chemistry, CH-8092 Zurich, Switzerland

A dynamic experimental method f o th i n v e s t i g a t i o of the behaviou f i x e d bed r e a c t o r is presented. The method is based on the a n a l y s i s of the a x i a l and r a d i a l temperature and c o n c e n t r a t i o n p r o f i l e s measured under the in­ fluence of f o r c e d u n c o r r e l a t e d s i n u s o i d a l changes of the process v a r i a b l e s . A two-dimensional r e a c t o r model is employed f o r the d e s c r i p t i o n of the r e a c t o r behaviour. The model parameters are estimated by statistical a n a l y s i s of the measured profiles. The e f f i c i e n c y of the dynamic method is shown f o r the i n v e s t i g a t i o n of a pilot p l a n t f i x e d bed r e a c t o r using the hydrogenation of toluene with a commercial n i c k e l c a t a l y s t as a t e s t r e a c t i o n . For proper c o n t r o l of i n d u s t r i a l f i x e d bed r e a c t o r s i t i s necessary t o know t h e i r dynamic behaviour. This behaviour may be i n v e s t i g a t e d by a s e r i e s of experiments where a s i n g l e process v a r i a b l e i s changed a t a time (1-6). In general such experiments allow f o r the development of a r e a c t o r model which d e s c r i b e s the dynamic r e a c t o r behaviour. However, very o f t e n a l a r g e number of experiments i s r e q u i r e d . In the present work a method i s described to e x t r a c t the i n ­ formation necessary f o r modelling from only a few dynamic e x p e r i ­ mental runs. The method i s based on the measurement of the changes of the temperature and c o n c e n t r a t i o n p r o f i l e s i n the r e a c t o r under the i n f l u e n c e of forced simultaneous s i n u s o i d a l v a ­ r i a t i o n s of the process v a r i a b l e s . The c h a r a c t e r i s t i c features of the dynamic method are demonstrated using the behaviour of a non­ isothermal-nonadiabatic p i l o t p l a n t f i x e d bed r e a c t o r as an example. The t e s t r e a c t i o n a p p l i e d was the hydrogénation of toluene to methylcyclohexane on a commercial n i c k e l c a t a l y s t . 1

Current address: Produits Chimiques Ugine Kuhlmann, F-69310 Pierre-Bénite, France. 0097-6156/82/0196-0015$06.00/0 © 1982 American Chemical Society In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

16

CHEMICAL REACTION

ENGINEERING

Experimental Equipment and Procedure. The f i x e d bed r e a c t o r p i l o t p l a n t i s shown s c h e m a t i c a l l y i n F i g u r e 1. The r e a c t o r was operated as a continuous f i x e d bed r e a c t o r , w i t h r e c y c l e of the hydrogen. The j a c k e t e d r e a c t o r tube of 2 m l e n g t h and 0.05 m inner diameter was equipped f o r the measurement of a x i a l and r a d i a l temperature and c o n c e n t r a t i o n p r o f i l e s . The r e a c t o r jacked temperature was c o n t r o l l e d by a c i r c u l a t i n g p r e s s u r i z e d water system. F i g u r e 2 i n d i c a t e s s c h e m a t i c a l l y the l o c a t i o n s of the a x i a l and r a d i a l measuring devices w i t h i n the f i x e d bed. The c o n c e n t r a t i o n and temperature measuring devices c o n s i s t e d of c a p i l l a r y tubes w i t h the NiCr/Ni thermocouple j u n c t i o n i n the center of the tube entrance. The c a p i l l a r i e gas sampling p o s i t i o n e gas analyzer (URAS) was u t i l i z e d f o r the automatic a n a l y s i s of the toluene c o n c e n t r a t i o n at the d i f f e r e n t l o c a t i o n s i n the r e a c t o r . In a d d i t i o n , the composition of the gas mixture was measured by gas chromatography at the r e a c t o r i n l e t and o u t l e t . A process computer (PDP 11/10) was used f o r the p l a n t c o n t r o l and the data p r o c e s s i n g . The f o l l o w i n g process v a r i a b l e s were changed simultaneously: the toluene c o n c e n t r a t i o n a t the r e a c t o r i n l e t , the r e a c t o r bath temperature and the t o t a l gas flow r a t e . R e s u l t s . The r e s u l t s of a t y p i c a l experiment w i t h uncorre­ l a t e d changes of the process v a r i a b l e s are presented i n the F i g u r e s 3.a)-c). F i g u r e 3.a) shows the u n c o r r e l a t e d s i n u s o i d a l changes of the process v a r i a b l e s . The r e s u l t i n g temperature and concentrations measured at d i f f e r e n t a x i a l and r a d i a l p o s i t i o n s are presented i n F i g u r e 3.b) and c ) , r e s p e c t i v e l y . Mathematical E v a l u a t i o n of the Dynamic Experiments Simulation of Reactor Behaviour A dynamic pseudo-homogeneous two-dimensional model i s employed f o r the d e s c r i p t i o n of the r e a c t o r behaviour. heat

balance:

8T at

r

9r

ΔΗ -

RG

(C, T)

PK

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

(1)

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982. PRODUCT

Figure 1. Fixed bed reactor pilot plant. Key: 1, fixed bed reactor; 2, metering pump; 3, compressor; 4, circulating pump; 5, flow sensor; 6, evaporator; 7, level control; 8, separator; 9, buffer volumes; 10, cooler; 11,flowcontrol valve; and 12, heat exchanger.

C L : C O O L I N G LIQUID ( - 2 0 ° C )

18

CHEMICAL REACTION ENGINEERING

5.2

19-23

m '/ζλ

Figure 2. Locations of axial and radial measuring devices in reactor. Key: @, catalyst bed; ®, inert packing; 1-23, thermocouples and sampling to gas an­ alyzer; and 30, 31, sampling to gas chromatograph.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

2.

BAIKER ET

AL.

Process Variables in

19

Fixed-Bed Reactor

% 100

TEMPERATURES

PRESSURE

UJ ω

TOLUENE CONCENTRATION AT 1,2,3 AND 4

GAS FLOW RATE REACTOR BATH TEMPERATUR 200

Ί3θ

TIME (minutes)

Figure 3a. Time profiles of the uncor­ related changes of process variables. Ranges of variables: temperature of re­ actor bath, 0-250°C; toluene concentra­ tion at reactor inlet, 0-5 Vol%; total gas flow rate, 0-1200 mol/h; and total pres­ sure 0-2.5 bar.

100 TIME ( m i n u t e s )

Figure 3b. Resulting profiles of uncor­ related changes of process variables for axial measuring points.

Figure 3c. Resulting profiles of uncor­ related changes of process variables for radial measuring points.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

20

CHEMICAL REACTION ENGINEERING

mass balance:

ae

ac

Λ

= - u — + D 3t 3z e

a c

ι ac

.2 3r

r 3r

(1-ε)ρ

ι;

RG (C, T)

(2)

boundary c o n d i t i o n s : Τ (ζ = ο, r , t ) = Τ

χ

C (z - o, r , t ) = C

x

(r, t)

(3)

(r, t)

(4)

3T 3r (z, r = o, t ) = o 3T Έ

(ζ, r = R, t ) = -

^

( z , r = R, t ) = o

f

(6)

(T - T ) w

(7)

i n i t i a l conditions: T ( z , r , t = o) = T

2

(z, r)

(8)

C ( z , r , t = o) = C

2

(z, r)

(9)

D i s c r e t i z a t i o n o f the p a r t i a l d i f f e r e n t i a l equation system i n a x i a l (z) and r a d i a l ( r ) d i r e c t i o n by means of the orthogonal c o l l o c a t i o n method (7) leads to the f o l l o w i n g system of o r d i n a r y d i f f e r e n t i a l equations. dT. . =

NZ NR Α1.^[νΐΖ. .Τ^.] Α2.^[[ ..ν2Κ. Λ

+A3-RG(C.

dC. dt

NZ BI- Σ [VIZ

+

7

> 1 ς +

νΐ . Κ

) 1 ς

].Τ. ] Λ

T. .)

C

(10)

NR ] Β2·Σ [[y.-V2R +

,+VlR

]-C

]

+B3*RG(C. ., T. .)

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

(11)

2.

BAIKER ET A L .

21

Process Variables in Fixed-Bed Reactor

with: ζ

,r.2

χ -τ

A

1

;

. .

' ( 1

U

-

P

-

f P

£ ) p

k A2

φ

y -

F

BI - - ?

C

k pk

L

4

D

S ( 1

-

G ) p

B2 C

k pk

R 2

R

ΔΗ A3 =

4

e

2

(Ι-ε)ρ B

c . pk

ε

_ h D l - - * -= 2 k e boundary c o n d i t i o n s : T. . ( t ) = TAj. t) (12) C. . ( t ) - C-iy.pt) »J J >1 J NR 2*i*NZ Σ V1R. , T. = D1«(T. — Τ ) rïR,k i , k i,NR w 9

A

1

Α

TD

2*i«NZ

NR Σ V k=l

i

y C

(13)

1

-o

(14)

(15)

i n i t i a l conditions: Τ

(t-0) - T

(x.,y.)

(16)

C

J caJ.c employing Eqs. 10) and 11), r e s p e c t i v e l y . A

are c a l c u l a t e d by

By i n s e r t i o n o f Eqs. 12)-15) i n t o Eqs. 10) and 11) a system of ordinary d i f f e r e n t i a l equations i s obtained i n which only T. . and C. . a t the ten c o l l o c a t i o n p o i n t s (2*i*NZ; l^j^NR-1) remain as independent v a r i a b l e s . A nonlinear multiresponse r e g r e s s i o n program (9) was used to search f o r the parameters which y i e l d s t a t i s t i c a l l y the best accordance (maximum l i k e l i h o o d (10)) between the twenty i n t e r ­ polated and c a l c u l a t e d responses. For the s i m u l a t i o n o f the r e a c t o r behaviour the system of ordinary d i f f e r e n t i a l equations was i n t e g r a t e d by means of a Runge-Kutta-Merson method w i t h v a r i a b l e step length, whereas the nonlinear a l g e b r a i c equations were solved by a Newton-Raphson iteration. K i n e t i c Rate Equation and Heat T r a n s f e r C o e f f i c i e n t s . K i n e t i c r a t e equations of d i f f e r e n t complexity w i t h 2 to 8 parameters were t e s t e d f o r the s i m u l a t i o n o f the r e a c t o r behaviour. F i n a l l y , the semi-empirical three parameter r a t e equation 20) was chosen f o r the s i m u l a t i o n because r a t e expressions of higher complexity y i e l d e d no b e t t e r s i m u l a t i o n o f the r e a c t o r behaviour and showed l a r g e r c o r r e l a t i o n s between the estimated parameters i n the given ranges of the process v a r i a b l e s .

3

Α ·10~ (Ρ /Ρ ) RG(T,P ) = i i — i — 1 + (Ρ /Ρ ) exp [A -10 (1/T- 1/A -10^)]

(20)

J

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

CHEMICAL REACTION ENGINEERING

24

The heat t r a n s f e r c o e f f i c i e n t h

and k used i n the twow e dimensional model were estimated simultaneously w i t h the k i n e t i c parameters and were checked by an independent e s t i m a t i o n from experiments without r e a c t i o n i n which methylcyclohexane was s u b s t i t u t e d f o r toluene. Within the confidence l i m i t s both type of experiments l e d to s i m i l a r heat t r a n s f e r c o e f f i c i e n t s . Comparison of Measured and C a l c u l a t e d P r o f i l e s . In order to compare the measured time p r o f i l e s shown i n F i g u r e 3 w i t h the c a l c u l a t e d time p r o f i l e s , the former were a x i a l l y and r a d i a l l y i n t e r p o l a t e d to o b t a i n the corresponding p r o f i l e s at the c o l l o ­ c a t i o n p o i n t s . F i g u r e s 5.a) and b) show the measured (I) and c a l c u l a t e d (II) time p r o f i l e s f o r the a x i a l and r a d i a l c o l l o ­ cation points, respectively The parameters estimate used f o r the s i m u l a t i o n were A^ = 5.0 mol/kg s (46); A^ = 6.0 Κ (68); A

2

= 4.23 Κ (426); h = 158 J/m s Κ (27); k = 0.87 J/m s Κ J w e (26). The values given i n parentheses are the t-values of the estimated parameters. The comparative r e s u l t s shown i n F i g u r e 5 i n d i c a t e that the r e a c t o r behaviour c o u l d be simulated e x c e l l e n t l y w i t h the presented model. 0

Conclusions The presented dynamic i n v e s t i g a t i o n method employing f o r c e d u n c o r r e l a t e d changes of the process v a r i a b l e s allows a more e f f i c i e n t modelling of the dynamic behaviour of a f i x e d bed r e a c t o r p i l o t p l a n t than r e s u l t s when only one process v a r i a b l e i s changed at a time. Models f o r the r e a c t o r s i m u l a t i o n can be developed w i t h data c o l l e c t e d from only one or a few experimental runs w i t h simultaneous u n c o r r e l a t e d changes of the process v a r i ­ a b l e s . A necessary requirement f o r the a p p l i c a t i o n of the presented method i s , however, that the temperature and concen­ t r a t i o n p r o f i l e s can be measured i n the r e a c t o r . The method d e s c r i b e d may be p a r t i c u l a r l y u s e f u l f o r the i n v e s t i g a t i o n of i n d u s t r i a l p i l o t p l a n t r e a c t o r s s i n c e many problems l i n k e d w i t h r e a c t o r design and c o n t r o l can be s t u d i e d more e f f i c i e n t l y .

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

2.

BAIKER ET A L .

Ο

1

Ï5Ô

Process Variables in Fixed-Bed Reactor

2ÔO

1

2feO

Ο

1

TIME (minutes )

°

'

Ï3Ô

'

TIME (minutes)

ϊδδ

25

'

2ÔO

250

TIME (minutes)

2ÔO

2èO

Ο

' Ï5Ô ' TIME (minutes)

2ÔO

250

Figure 5. Comparison of measured profiles interpolated at the collocation points (left) and calculated profiles (right). Ranges of variables are the same as in Figure 3. Key: a, time profiles for temperature and concentration at axial collocation points; and b, time profiles for radial collocation points.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

26

CHEMICAL REACTION ENGINEERING

Legend of Symbols A^

k i n e t i c parameter, mol/kg s

A^

k i n e t i c parameter, Κ

A~

k i n e t i c parameter, Κ 3 toluene c o n c e n t r a t i o n , mol/m s p e c i f i c heat of c a t a l y s t , J/kg Κ

C c ρκ. c

s p e c i f i c heat of f l u i d , J/kg Κ . 2 r a d i a l e f f e c t i v e d i f f u s i v i t y , m /s

P

h

coefficient 2

W

wall,

f o r heat t r a n s f e r

through r e a c t o r

j/m s Κ

ΔΗ^

r e a c t i o n enthalpy, J/mol

k^

r a d i a l heat c o n d u c t i v i t y i n c a t a l y s t bed, J/m s Κ

L

a x i a l d i s t a n c e between the two r a d i a l p r o f i l e measuring d e v i c e s , m

P

T

P

T

toluene p a r t i a l pressure, bar mean toluene p a r t i a l pressure, bar

r

r a d i a l coordinate, m

R

radius of r e a c t o r tube, m

RG

r e a c t i o n r a t e , mol/kg s

t

time coordinate, s

Τ

temperature, Κ

u

s u p e r f i c i a l gas v e l o c i t y ,

ζ

a x i a l coordinate, m

VIZ,

V1R, V2R

m/s

d i f f e r e n t i a t i o n weighting f a c t o r s (7)

ε

bed p o r o s i t y

p„

d e n s i t y of f l u i d , kg/m

3 F

p^

3 apparent d e n s i t y of c a t a l y s t ,

kg/m

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

2.

BAIKER ET A L .

Literature

Process Variables in Fixed-Bed Reactor

Cited

1. Hansen, K.W.; Jörgensen, S.B. Chem. Eng. S c i . 1976, 31, 579. 2. Hoiberg, J.A.; Lyche, B . C . ; Foss, A.S. Α . I . C h . E . J . 1971, 17, 1434. 3. Lee, R . S . H . ; Agnew, J . B . Ind. Eng. Chem., Proc. Des. Dev. 1977, 16, 490. 4. Sharma, C . S . ; Hughes, R. Chem. Eng. S c i . 1979, 34, 613. 5. Sörensen, J . P . Chem. Eng. S c i . 1976, 31, 719. 6. Baiker, Α . ; Casanova, R.; Richarz, W. Germ. Chem. Eng. 1980, 3, 112. 7. Villadsen, J.V.; Michelsen, M.L. "Solution of Differential Equation Models by Polynomial Approximation", Prentice H a l l , New Jersey, 1978. 8. Van den Bosch, B . ; Hellinckx 9. Klaus, R.; Rippin, D.W.T. Proc. 12th Symp.on Comp. Appl. in Chem. Enging., Montreux 1979, p.155. 10. Bard, Y. "Nonlinear Parameter Estimation"; Academic Press, Now York, 1974; p.61. RECEIVED April 27, 1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

27

3 Direct Reduction of Iron Ore in a Moving-Bed Reactor: Analyzed by Using the Water Gas Shift Reaction R. HUGHES and Ε . Κ. T. K A M University of Salford, Department of Chemical Engineering, Salford M5 4WT, England A model f o r th d i r e c t r e d u c t i o f iro in a moving bed has f o r the water ga equilibriu u c t i o n by the species H and CO. I n c l u s i o n o f t h i s e q u i l i b r i u m has been shown t o enhance r e d u c t i o n e s p e c i a l l y a t the h i g h conversions required.Increase of o p e r a t i n g temperature can g i v e decreased conver­ sions. 2

One of the more important a l t e r n a t i v e s t o the b l a s t furnace f o r the production o f i r o n i s d i r e c t r e d u c t i o n of p e l l e t i s e d o r e i n a s h a f t r e a c t o r . The reducing gas mixture i s u s u a l l y obtained by steam reforming of n a t u r a l gas and flows upward,countercurrent to the downward flow of s o l i d s . Sponge i r o n obtained by d i r e c t r e d u c t i o n may be used d i r e c t l y i n a r c furnaces f o r s t e e l prod­ uction. Previous s t u d i e s of d i r e c t r e d u c t i o n on i r o n ore p e l l e t s have been reviewed by T h e m e l i s ( l ) , Bogdandy(2) and Huebler(3). Work on r e d ­ u c t i o n by mixtures has been reported by Szekely(4) and Hughes e t a l ( 5 ) . Modelling s t u d i e s on countercurrent moving bed systems have been reported by S p i t z e r ( 6 ) f o r isothermal r e d u c t i o n i n hydrogen, by M i l 1 e r ( 7 ) f o r non-isothermal r e d u c t i o n i n carbon monoxide and more r e c e n t l y by Tsay e t a l ( 8 ) and Kam and Hughes(9) f o r C0/H2 mixtures. However, s i n c e i r o n i s known t o be a c a t a l y s t f o r the water gas s h i f t r e a c t i o n , t h i s r e a c t i o n w i l l i n f l u e n c e the gas composition and t h e r e f o r e the extent of r e d u c t i o n . None of the previous analyses have considered t h i s aspect and the o b j e c t i v e of the present paper i s t o account f o r the o v e r a l l r e d u c t i o n by i n c l u s i o n of t h i s r e a c t i o n . Mathematical

Formulation

The water gas s h i f t r e a c t i o n occurs on or w i t h i n the i r o n oxide p a r t i c l e and t h e r e f o r e a heterogeneous model i s employed u s i n g separate balances f o r the p e l l e t s and the r e a c t o r . 0097-6156/82/0196-0029$06.00/0 © 1982 American Chemical Society In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

30

CHEMICAL REACTION ENGINEERING

S i n g l e p e l l e t r e d u c t i o n . The r e d u c t i o n occurs at high temp­ eratures and a s h r i n k i n g core model i s appropriate as confirmed experimentally(5). Removal of oxygen occurs a t the advancing i n t e r f a c e while the water gas s h i f t r e a c t i o n occurs i n the outer l a y e r of reduced i r o n . The mechanism of the water gas s h i f t r e ­ a c t i o n i s thought t o be (10,11) between adsorbed oxygen and CO on the a c t i v e surface of the product i r o n , i . e :

K

U

f C0

0(ads)

(1)

'co„

or i n terms of the e q u i l i b r i u m constant, Κ "CO R

H 0

'CO.

2

= k

w

(2) C

H

with the r a t e constant k given by k=5.6xl0

Τ exp

The o v e r a l l r e d u c t i o n scheme can be s i m p l i f i e d to the three reactions:3C0 + F e 0 2

3H

2

CO

Fe 0

+

2

2Fe + 3C0

3

3

At the i n t e r f a c e

H

In the i r o n l a y e r

2

+ H 0

^

2

2

2Fe + 3H 0 0

2

+ C0

' ~

n

2

Since the reducing gas flow i s very high ( t y p i c a l l y 1800 m / tonne of product), i t i s assumed that the bulk of the mass t r a n s ­ f e r r e s i s t a n c e i s w i t h i n the p e l l e t . Under these c o n d i t i o n s , the dimensionless m a t e r i a l balance f o r hydrogen i n the p e l l e t i s 2

v y

=

V

H 2




2

2

The multi-component d i f f u s i v i t i e s i n the gas mixture can be approximated by the m o d i f i e d Stefan-Maxwell equations(8,90 i . e :

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

3.

HUGHES AND K A M

De. i-m

Direct Reduction of Iron Ore

ι—, £ Q _ + τ D.„ £iK

31

(5)

η (y.N.-y.N.)-r y * J J I Η D.. J=l lj J y

1

Λ

At the r e a c t i o n i n t e r f a c e 6* between the ore and i r o n l a y e r s , using the pseudo steady s t a t e assumption the dimensionless m a t e r i a l balances may be represented by y

H 0 ••- w. Η -Η 0

~3δ~ δ=δ*

2

= Da^ δ=δ* 2 \

3δ

2

H 0 2

2

H

(6) K e

H

2

^co = - w.

co-co„

δ=δ*

CO 'CO

δ=δ*

K, «C0

The D i r i c h l e t boundary c o n d i t i o n s apply t o eqns (6) and (7) since e x t e r n a l mass t r a n s f e r i s n e g l e c t e d . F i n a l l y , the dimensionl e s s e x p r e s s i o n f o r the r a t e of advance o f the i n t e r f a c e i s : 3y, 36* CO 36 δ = δ * 3τ 36 δ = δ * H -CO 2

yH o

y

2

= Da„

y

-

H

+

D a

W

C 0 H -CO 2

'2-1

r

co

C0

2

(8) C e

C0

Counter-cur rent moving bed I n t h i s r e a c t o r s o l i d s flow i s down­ ward w i t h the oxide c o n c e n t r a t i o n Cg | a t the top of the reactor. The gaseous s p e c i e s flow upwards w i t h a bottom ( i n l e t ) concent­ r a t i o n o f Cg Other assumptions a r e : £=0 £=0 1)

Steady s t a t e isothermal o p e r a t i o n ( t h i s may be assumed because of the balance between exothermic CO r e d u c t i o n and endothermic H r e d u c t i o n ) . Plug flow f o r both gas and s o l i d streams. Uniform motion of the s o l i d p e l l e t s w i t h constant voidage. P e l l e t s a r e s p h e r i c a l i n shape and a s h r i n k i n g core,sharp i n t e r f a c e model i s assumed f o r the p e l l e t reduction(8y 9 ) . For the gas s p e c i e s , the dimensionless c o n t i n u i t y eqtns a r e : 2

2) 3) 4)

3y° 9

= σ (δ*)'

yH

2

3ξ

ay,CO 3ξ

(9) δ=δ*

=

σ

_ ,r*>2 H -CO *> W

(6

2

CO 36 δ = δ *

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

(ΙΟ)

32

CHEMICAL REACTION ENGINEERING

and f o r the s o l i d phase

ay,CO

Ή.

Br* = Ω I F

+ w H -CO

do

2

"6=6*

(11) 6=6*

where 3(1-ε') D, eH -m 2

2

(r ) U ο g and C

D

TO

e

H 2

-m

L

Ω = 2

(Ρ x b ) ( r ) U o o I t should be noted the dependent on D „ 2""^ Method o f s o l u t i o n . A t r i a l and e r r o r method was used t o s o l v e the mass c o n t i n u i t y equations f o r one o f t h e s p e c i e s (e.g. CO) i n the s i n g l e p e l l e t b a l a n c e s . To do t h i s , expressions f o r other s p e c i e s i n terms o f y c o are d e r i v e d through the water gass h i f t r e a c t i o n and the r e a c t i o n s a t t h e i n t e r f a c e , i . e : e

Y

Y

H 0 2

co„

y E

2

( y

H -H 0 2

2

H

ο y

Y 2

)

H 2

w 2

co-co

+ w (y CO-H *C0 X

2

.

Y 2

(12)

H

.ο

co

= y *E

J

W

2

_ r

0

° H 0

y

co ~ co y

(13)

) + δ*(δ*-ΐ)

2

86

6=6* CO-H„ +w

CO 36 6=6*

(14)

In order t o s i m p l i f y the procedures f o r s o l v i n g the water gass h i f t r e a c t i o n i n the s i n g l e p e l l e t , an average value o f the con­ c e n t r a t i o n f o r each o f t h e reducing gases i s employed, i . e : Y

H 2

=

H

*bo"

°-

5

(

Y

+

H 2

Y

H

0 . 5 2

(15)

H

0

+y

c o

)

(16)

Further s i m p l i f i c a t i o n can be achieved by l i n e a r i s i n g the water g a s - s h i f t r e a c t i o n r a t e , and u s i n g T a y l o r ' s s e r i e s expansion the flowing expression f o r the s h i f t r e a c t i o n can be obtained \

y

= *1 *C0 - *2 H

+ 2

*3

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

(17)

3.

33

Direct Reduction of Iron Ore

HUGHES AND K A M

where t h e l i n e a r i s a t i o n constants a r e

y ο

»coco

H

(18)

2 r

CO

(19) y~ 2 H

y

1

W

co (20)

+

y

* i co

Hence, the l i n e a r i s e d form o f eqtn.(4)

V

y

C0

=

ν

Η ^0

i n terms o f CO becomes

Φ

2

An a n a l y t i c a l s o l u t i o n o f t h e above equation can be obtained as

y

C0

a ^ i n h i i ^ 6*)+a cosh(^a^ δ*) 2

δ*

Ύο-Ι —

Y, ±

Ύ

(22)

1

where *1

CO-Η,

+

W

H -

C 0

*

2

2

y

γ

CO-Η,

2

φ

{ψ (δ*)(δ*-1)

H2

9

δ=δ*

+ wH„-C0

*y,CO 36

δ=δ*

and W

CC-H

and 0 ^ and a

2

2

*

W Î ,

+

W

H 2

C

0

^

0

)

are i n t e g r a t i o n constants which can be d e r i v e d from

the boundary c o n d i t i o n s a t the i n t e r f a c e . The procedure f o r the s o l u t i o n o f the above s e t o f equations i s as f o l l o w s : (1) (2)

v a l u e s o f δ* a r e s e l e c t e d a value o f y a t δ* i s assumed

(3)

y„ » y . and y a r e c a l c u l a t e d from eqtns.(12-14) 2 2° °2 the multi-component d i f f u s i v i t i e s i n the bulk, a t the i n t e r ­ f a c e and the mean v a l u e s are c a l c u l a t e d y i s c a l c u l a t e d from eqtn.(22) and compared w i t h the assumed value o f y i n step (1). Steps (2) t o (5) a r e repeated u n t i l agreement i s a t t a i n e d the time r e q u i r e d f o r the i n t e r f a c e advancement v i a eqtn. (8) i s obtained, and steps (1-6) a r e repeated u n t i l t h e process i s completed.

C

n

H

(4) (5)

(6) (7)

Q

H

c

C

o

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

34

CHEMICAL REACTION ENGINEERING

The s o l u t i o n procedure f o r the moving bed has been d e s c r i b e d i n d e t a i l elsewhere(9). The two p o i n t boundary v a l u e problem i s s o l v e d by a p r e d i c t o r - c o r r e c t o r procedure on the m i s s i n g boundary a t the top o f the r e a c t o r u n t i l agreement with the i n l e t gas composition a t the base o f t h e r e a c t o r i s achieved. R e s u l t s and D i s c u s s i o n . Some experimental r e s u l t s on H2/CO mixtures with no added CO2 o r H2O, were a v a i l a b l e from p r e v i o u s work (12) u s i n g a h i g h p u r i t y p e l l e t i s e d ore (Carol Lake). A comparison o f t h e experimental and p r e d i c t e d r e s u l t s u s i n g t h e water gas s h i f t r e a c t i o n a t a s o l i d conversion o f 50% i s g i v e n i n Table I below. "Table I "

V

100

80

50

C0% E x p t l (min) 12 21 31 P r e d i c t e d (min) 14 19 25 Experimental r e s u l t s were not a v a i l a b l e f o r CO r i c h mixtures, but the agreement i s seen t o be adequate. B e t t e r agreement might have been obtained i f t h e experimental gas mixture had contained both CO2 and H2O, i n s t e a d o f j u s t CO and H 2 . Because i n s i n g l e p e l l e t s experiments, there i s l i t t l e o p p o r t u n i t y f o r an e q u i l i b r i u m i n the gas mixture t o be a t t a i n e d , s i n g l e p e l l e t r e s u l t s are not g e n e r a l l y i n d i c a t i v e o f o v e r a l l r e a c t o r behaviour. A parametric study o f moving bed behaviour has been undertaken. The s o l i d p e l l e t s a r e assumed t o be preheated t o the appr o p r i a t e r e d u c t i o n temperatures b e f o r e e n t e r i n g t h e r e a c t i o n zone of the r e a c t o r . Although t h i s n e g l e c t s the s o l i d s preheat zone, t h i s can e a s i l y be i n c l u d e d i n the model i f r e q u i r e d . The present study t h e r e f o r e i s focussed on the r e a c t i o n zone i t s e l f where the important parameters o f gas and s o l i d flow r a t e s , gas i n l e t tempe r a t u r e and gas mixture composition a r e c o n s i d e r e d . Reactor l e n g t h i s a l s o o f major importance but i n the present paper t h i s has been f i x e d a t lm i n order t o o b t a i n comparative d a t a . Modelling s t u d i e s f o r the moving bed were made a t two gas compositions, a hydrogen r i c h composition c o n t a i n i n g 50% H2 and 20% CO with 10% H2O and 5% C02# and a CO r i c h gas mixture cont a i n i n g 50% CO and 20% H2 w i t h 5% H2O and 20% C02. Most r e s u l t s were obtained w i t h the l a t t e r mixture, which i s r e p r e s e n t a t i v e o f gas produced from c o a l g a s i f i c a t i o n , which i s l i k e l y t o have a major a p p l i c a t i o n f o r r e d u c t i o n processes i n the f u t u r e . P e l l e t s of 8mm diameter were modelled u n l e s s otherwise indicated.Temperatures were v a r i e d from 873 t o 1273K while gas flows and s o l i d flow rates are t y p i c a l o f those used commercially. F i g u r e 1 shows the e f f e c t o f gas flow r a t e p r e d i c t e d by the model on the s o l i d c o n v e r s i o n f o r a CO r i c h gas mixture. Three gas flow r a t e s o f 9,7 and 5 m/s a r e shown. A l s o i l l u s t r a t e d i s the p r e d i c t e d conversion f o r the model which does n o t i n c l u d e the

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

3.

HUGHES AND K A M

Direct Reduction of Iron Ore

35

water gas s h i f t r e a c t i o n ( f o r a gas flow r a t e o f 7 m/s) , The f i n a l conversion i s seen t o be 58.5% when the water gas s h i f t r e a c t i o n i s n e g l e c t e d but 70% when t h i s i s included.Furthermore, the shape o f the curve i s d i f f e r e n t ; the curve i n which the water gas s h i f t r e a c t i o n i s n e g l e c t e d being convex towards the conversion a x i s , whereas when the water gas s h i f t r e a c t i o n i s i n c l u d e d t h i s does not happen and indeed a t higher flow r a t e s the curve becomes con­ cave t o the conversion a x i s . T h i s i s e s p e c i a l l y pronounced f o r the 5 m/s flow r a t e and demonstrates the e f f i c i e n c y o f the water gas s h i f t r e a c t i o n i n promoting c o n v e r s i o n . An i n c r e a s e i n gas flow r a t e g i v e s a g r e a t e r f r a c t i o n a l con­ v e r s i o n o f the i r o n o r e . T h i s e f f e c t i s not due t o i n c r e a s e d mass t r a n s p o r t with i n c r e a s i n g flow as the c a l c u l a t e d Sherwood number i s 500, j u s t i f y i n g n e g l e c t o f t h i s i n the model. The most probable reason f o r i n c r e a s e d conversio as the gas flow i n c r e a s e s higher r e l a t i v e c o n c e n t r a t i o n c o n t a c t i n g the ore i s i n c r e a s e d . Hence, a f a s t e r r a t e o f r e d u c t i o n ensues. The e f f e c t o f s o l i d flow r a t e i s i l l u s t r a t e d i n Figure 2 f o r 3 s o l i d flow r a t e s o f 1.5, 2.0 and 2.5xlO~ m/s r e s p e c t i v e l y . A l s o shown by the broken curves are r e s u l t s when the water gas s h i f t r e a c t i o n i s not i n c l u d e d . I t can be seen t h a t when the s o l i d con­ v e r s i o n i s l a r g e ( s o l i d s flow 1.5xlO~ m/s) the enhancement o f conversion by the water gas s h i f t r e a c t i o n i s c o n s i d e r a b l e g i v i n g 99% conversion o f s o l i d under these c o n d i t i o n s , compared t o o n l y 75% i f the water gas s h i f t process i s n e g l e c t e d . A t l a r g e r flow r a t e s , where the conversion i s l e s s , the e f f e c t o f the water gas s h i f t r e a c t i o n becomes l e s s important. Again, i t can be noted t h a t f o r the water gas s h i f t , the X vs ξ curves, a f t e r , an i n i t i a l convex behaviour (up t o ξ= .1) become concave t o the X a x i s whereas when t h i s r e a c t i o n i s not i n c l u d e d the X vs ξ curves a r e convex t o the X a x i s throughout. For both models, i n c r e a s e i n s o l i d s flow r a t e r e s u l t s i n a decreased s o l i d s conversion as would be expected. The i n f l u e n c e o f gas i n l e t temperature on the r e d u c t i o n was a l s o s t u d i e d . I n s t u d i e s o f s i n g l e p e l l e t r e d u c t i o n by e i t h e r pure gases o f gas mixtures an i n c r e a s e i n r e a c t i o n temperature w i l l normally r e s u l t i n an i n c r e a s e d oxide conversion.However, i n the present study, i n a moving bed with e i t h e r a H2 r i c h o r CO r i c h r e a c t i o n mixture the r e v e r s e e f f e c t was observed. That f o r a CO r i c h mixture i s shown i n F i g u r e 3 where the broken curves a l s o show the p r e d i c t e d curves when the water gas s h i f t r e a c t i o n i s ignored. The l a t t e r r e s u l t s confirm the c o n c l u s i o n s a l r e a d y made,that when conversions are h i g h the water gas s h i f t r e a c t i o n enhances the reduction.However,for both cases, a more g e n e r a l c o n c l u s i o n i s a l s o obtained i . e . , the conversion decreases with i n c r e a s i n g op­ e r a t i n g temperature. The extent o f the decrease i n conversion with temperature was found t o be l e s s f o r the H2 r i c h mixture, as shown i n Fig.4 where a comparison i s made with the CO-rich mixture f o r 10mm diameter p e l l e t s . I f a H2 r i c h mixture had no CO2 p r e s e n t and 4

4

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

36

CHEMICAL REACTION ENGINEERING

Figure 2. Effect of solids velocity, U , on conversion in α CO rich mixture. Num­ bers on curves are solid velocities (ΧίΟ' m/s). Key: , water gas shift reaction included; and , water gas shift reaction excluded. a

4

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

HUGHES AND KAM

Direct Reduction of Iron Ore

Figure 3. Effect of T on conversion in a CO rich mixture. Key: , water gas shift reaction included; and , water gas shift reaction excluded. 0

Figure 4. Effect of gas composition and T on conversion. Key: mixtures; and , H rich mixtures. 0

x

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

, CO rich

38

CHEMICAL REACTION ENGINEERING

the water gas s h i f t r e a c t i o n was neglected,then an i n c r e a s e d c o n v e r s i o n w i t h i n c r e a s i n g temperature was predicted.The deccreased c o n v e r s i o n a t h i g h e r temperatures observed i n F i g s . 3 and 4 i s due t o the i n f l u e n c e of temperature on the e q u i l i b r i u m con­ s t a n t f o r the CO r e d u c t i o n . T h i s decreases w i t h temperature (CO r e d u c t i o n i s exothermic) while the H2 r e d u c t i o n e q u i l i b r i u m constant i n c r e a s e s w i t h temperature (reduction i s endothermic). Thus, a t h i g h e r temperatures, the r e a c t i o n o f any C02 p r e s e n t with the reduced i r o n t o produce oxide i s favoured and t h i s r e s t r i c t s the o v e r a l l r e d u c t i o n by both H2 and CO i n the mixture and hence the f r a c t i o n a l conversion i s reduced. Legend of Symbols b Ci

stoichiometric coefficient concentration of species i

DaH2/Daco Damkohler number,define De^ effective diffusivit iK Knudsen d i f f u s i v i t y o f s p e c i e s i i - m molecular d i f f u s i v i t y , s p e c i e s i i n mixture m k r a t e constant K water gas s h i f t e q u i l i b r i u m constant KecO'^Ho e q u i l i b r i u m constant f o r CO or H2 r e d u c t i o n r , r * p e l l e t radius, radius of r e a c t i o n i n t e r f a c e i n p e l l e t W' H2' C0 © of water gas s h i f t r e a c t i o n , H 2 reduction,CO reduction,respectively 5 surface a r e a o f p e l l e t g^ s 9 solids velocity, respectively y dimensionless c o n c e n t r a t i o n X s o l i d s conversion i n bed ξ dimensionless bed length δ,δ* dimensionless p e l l e t r a d i u s , r e a c t i o n r a d i u s r e s p e c t i v e l y ρ p e l l e t density ε' bed voidage Literature Cited 1. Themelis,N.J. and Gauvin,W.H.,AIChE Jl.8, 437 (1962). 2. Von Bogdandy,L. and Engell,H.J.'The Reduction o f I r o n Ores' Springer V e r l a g , B e r l i n , 1 9 7 1 . 3. Huebler,J.,Iron Ore Reduction Proc.Symp.Chicago,Pergamon Press,Oxford (1962). 4. S z e k e l y , J . and E l - T a w i l , Y . Met.Trans.7B, 490 (1976). 5. Hughes,R., Mogadamzadeh,H. and Kam,Ε.Κ.Τ., 2nd European Symposium on Thermal A n a l y s i s , Aberdeen (1981)-(in p r e s s ) . 6. S p i t z e r , R.H.,Manning,F.S. and Philbrook,W.O., TMS-AIME, 236, 726 (1966). 7. M i l l e r , R . L . , Ph.D.Thesis,Mellon U n i v e r s i t y , P i t t s b u r g h (1972). 8. Tsay,Q.T.,Ray,W.H. and Szekelv,J.,AIChE Jl,22,1072 (1976). 9. Kam,Ε.Κ.Τ. and Hughes,R.,Trans.Inst.Chem.Engrs.59,196 (1981). 10. Kaneko,Y. and Oki,S.,J.Res.Inst.Catalysis,Hokkaido Univ., 13, N o . l , 55 (1965). 11. Meschter,P.J. and Grabke,H.J.,Met.Trans.,10B, 323 (1979). D

D

w

0

R

R

u

12.

u

R

r a t

a s

Mogadamzadeh,Η.,

RECEIVED May

11,

Ph.D.Thesis,Salford U n i v e r s i t y

(1977).

1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

4 A Simulation of Coke Burning in a Fixed-Bed Reactor W.-K. LIAW, J. VILLADSEN, and R. JACKSON University of Houston, Department of Chemical Engineering, Houston, TX 77004

In many c a t a l y t i tures coke is deposite sequently be removed. This paper describes a mathem a t i c a l model and a s s o c i a t e d computer s i m u l a t i o n o f the o x i d a t i o n of coke from a f i x e d bed o f c a t a l y s t , using n i t r o g e n c o n t a i n i n g a s m a l l p r o p o r t i o n of oxygen. A r e l i a b l e s i m u l a t i o n is important, f o r example, i n planning coke burning from c a t a l y t i c reformers, where e x c e s s i v e l y high temperatures can cause s i n t e r i n g o f metal crystallites. We consider the s i t u a t i o n i n which coke i s o x i d i z e d from a f i x e d c a t a l y s t bed by oxygen i n low concentration i n a n i t r o g e n stream, as i n c a t a l y t i c reforming. I t i s important to be able to p r e d i c t temperatures a t t a i n e d during burning i n order t o achieve a quick burn without s i n t e r i n g metal c r y s t a l l i t e s on the c a t a l y s t . This problem was addressed by Van Deemter [1], who assumed a constant burning r a t e t o o b t a i n a s o l u t i o n i n c l o s e d form. L a t e r , Johnson e t . a l . [2] and Olson e t a l . [3] t r e a t e d h i g h temperature, d i f f u s i o n c o n t r o l l e d burning, where the r e a c t i o n r a t e depends only weakly on temperature. Both p r e d i c t e d the propagation of a sharply defined burn f r o n t , but n e i t h e r gave any i n d i c a t i o n o f what might happen a t lower temperatures, where chemical r e a c t i o n r a t e c o n t r o l s . This case was discussed by Ozawa [ 4 ] , who showed that o x i d a t i o n i s slow and there i s no c l e a r burn f r o n t . In p r a c t i c e i t i s important t o simulate the whole range of behavior between these extremes, s i n c e the disappearance o f a sharp burn f r o n t places a lower bound on o p e r a t i n g temperatures. One should a l s o be able to simulate the e f f e c t o f switching i n l e t c o n d i t i o n s during the burn, which i s necessary i n p r a c t i c e to obtain c l e a n c a t a l y s t i n a short time.

0097-6156/82/0196-0039$06.00/0 © 1982 American Chemical Society In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

40

CHEMICAL REACTION ENGINEERING

This paper presents a s i m u l a t i o n of coke burning v a l i d f o r a l l i n l e t c o n d i t i o n s , and capable of h a n d l i n g any sequence of switches i n these c o n d i t i o n s . Sample r e s u l t s are presented f o r c o n d i t i o n s of i n t e r e s t i n c a t a l y t i c reforming. Mathematical Model T y p i c a l reforming c a t a l y s t c o n s i s t s of porous spheres 1.5 mm i n diameter i n a packed bed about 1 m deep. Regeneration i s c a r r i e d out at about 400 C and 10 atm u s i n g n i t r o g e n c o n t a i n i n g 0.5-2.0% oxygen. At the s t a r t of regeneration the c a t a l y s t t y p i c a l l y bears 2% coke by weight. For the present purpose the coke i s t r e a t e d as carbon and the C0 /C0 r a t i o i n the combustion products i s r e l a t e d to temperature as suggested by Arthur [5] and Rossberg [6]. Then the f o l l o w i n 2

1)

The accumulation term i s neglected i n the oxygen balance w i t h i n a p e l l e t . 2) The accumulation term i s n e g l e c t e d i n the oxygen balance f o r the f l o w i n g gas. 3) Temperature v a r i a t i o n w i t h i n a p e l l e t i s n e g l e c t e d . 4) Energy accumulation terms a s s o c i a t e d with the gas are neglected compared with those a s s o c i a t e d with the s o l i d . 5) L a t e r a l composition and temperature v a r i a t i o n s vanish and a x i a l d i s p e r s i o n of heat and matter i s n e g l e c t e d . 6). P h y s i c a l p r o p e r t i e s are a l l evaluated at gas i n l e t c o n d i t i o n s , s i n c e percentage v a r i a t i o n s i n gas com­ p o s i t i o n and absolute temperature are s m a l l . Adopting these approximations, and assuming that the r a t e of coke burning i s given by R

c

- K(T )c c - A exp(-E/RT )c S OS c s o s r

c c

(1)

equations d e s c r i b i n g the behavior of a c a t a l y s t p e l l e t can be w r i t t e n i n the f o l l o w i n g dimensionless form. t γ-

3f 3ΪΤ - -

f

f c

s g e x p [ X ( l - l / 0 ) ] , with f f

s

Q

= 1 at τ = 0

(2)

s

7

h

[*

2

ττ)

-

a

/

f

c

f s

« ρ ΐ λ α - ι / β . ) ] = ο.

with 3f /3s - 0 at s = 0 and 3f /3s = B i (1-f ) at s - 1 s s m s and t, 3Θ ~~~ -ς-β- « H (θ - θ ) + 3, Danf , w i t h θ = θ at τ=0 t 3τ p g s' h g* s so v

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

Ο)

(4)

4.

LIAW ET A L .

41

Coke Burning in a Fixed-Bed Reactor

These represent a coke balance, an oxygen balance and an energy balance, r e s p e c t i v e l y . The p e l l e t equations a r e coupled t o the f o l l o w i n g m a t e r i a l and energy balances f o r the f l o w i n g gas 3f - S - - = -Danf , with f = 1 a t χ = 0 3x g g

(5)

8Θ - τ - = Η (θ - θ ) , w i t h θ = 1 a t χ = 0 3x Ρ s g ' g

(6)

2

4

7

Equations (2)-(6) are the working equations of the model, but a f u r t h e r s i m p l i f i c a t i o n was a l s o i n v e s t i g a t e d , i n which the temperature d i f f e r e n c n e g l e c t e d . Then (4) an ΛΛ

Vt S

ΟΌ

3 7

+

—

vt

ΟΌ

9x

=

S ~L~

Q

_

g

η

/ (

7

7

x

)

w h i l e the other equations remain unchanged. The model d e s c r i b e d by equns. (2)-(6) w i l l be c a l l e d the heterogeneous model, w h i l e that i n which equns. (4) and (6) a r e r e p l a c e d by (7) w i l l be c a l l e d the pseudo-homogeneous model. D e t a i l s of the numerical s o l u t i o n procedure are given e l s e ­ where [7] but we mention that equn. (3) i s s o l v e d f o r f by orthogonal c o l l o c a t i o n and the r e s u l t i n g p r o f i l e i s u s e l i n c a l ­ c u l a t i n g the e f f e c t i v e n e s s f a c t o r η. The remaining equations are then i n t e g r a t e d by f i n i t e d i f f e r e n c e methods. At h i g h tem­ p e r a t u r e s , where the burning i s d i f f u s i o n c o n t r o l l e d , the coke p r o f i l e w i t h i n a p e l l e t has the " s h r i n k i n g c o r e " form, and orthogonal c o l l o c a t i o n does not reproduce t h i s very a c c u r a t e l y . Nevertheless, experience suggests i t s t i l l gives a good estimate of the e f f e c t i v e n e s s f a c t o r . In the pseudo-homogeneous model equn. (7) i s w r i t t e n i n c h a r a c t e r i s t i c normal form .

Z

h s

u

d9

A

h

g

h s

When i n t e g r a t i n g , the increments i n τ and χ a r e r e l a t e d as above so as t o f o l l o w the development o f θ along the c h a r a c t e r i s t i c s . Though the pseudo-homogeneous model gives s h o r t e r s o l u t i o n times we s h a l l see that i t introduces s i g n i f i c a n t e r r o r i n θ i n c e r ­ t a i n circumstances.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

42

CHEMICAL REACTION ENGINEERING

Results The f o l l o w i n g r e s u l t s r e f e r to a bed 0.91 m deep c o n t a i n i n g s p h e r i c a l c a t a l y s t p e l l e t s of diameter 1.52 mm, w i t h p o r o s i t y 0.4 due to pores of diameter 75 A and t o r t u o s i t y f a c t o r 3.5. The gas pressure i s 10 atm. Before regeneration the c a t a l y s t c a r r i e s 2% wt. coke d i s t r i b u t e d uniformly throughout the p e l l e t s , and the whole bed i s at the i n l e t gas temperature. F i g s . 1 and 2 show coke c o n c e n t r a t i o n and temperature prof i l e s f o r burns with a gas flow of 780 kg/m h c o n t a i n i n g 0.5 mole % oxygen. Results are presented f o r i n l e t temperatures of 316C, 343C, 371C and 399C. The continuous l i n e s correspond to the pseudo-homogeneous model and the broken l i n e s to the h e t e r o geneous model where th At an i n l e t temperatur c o n t r o l l e d and a sharp f r o n t s e p a r a t i n g burnt and unburnt regions r a p i d l y forms, then moves along the bed at constant v e l o c i t y without change of form. Correspondingly, there i s a sharp oxygen breakthrough as the burn f r o n t leaves the bed. E a r l y i n the burn a w e l l - d e f i n e d temperature wave forms, whose l e a d i n g edge, moving with the v e l o c i t y of thermal d i s t u r b a n c e s , q u i c k l y passes out of the bed, w h i l e the t r a i l i n g edge moves through the bed with the burn f r o n t . At 316C i n l e t temperature, r e a c t i o n r a t e c o n t r o l s , and the coke o x i d i z e s slowly everywhere i n the bed. There i s no d i s cernable temperature wave and a s i g n i f i c a n t c o n c e n t r a t i o n of oxygen leaves the bed throughout the burn. Behavior intermediate between these extremes i s found at 343C i n l e t temperature. The coke concentration p r o f i l e s pass through minima w i t h i n the bed because of the competing i n f l u ences of r i s i n g temperature and decreasing oxygen c o n c e n t r a t i o n . C l e a r l y , burning should be performed at a temperature h i g h enough to give a sharp burn f r o n t , but alone t h i s i s s t i l l not s u f f i c i e n t to reduce the coke to an acceptable l e v e l i n a short time, f o r two reasons. F i r s t , the r a t e of coke burning decreases markedly when the center of the burn f r o n t passes out of the bed and, second, coke c o n s i s t s of a mixture, some of whose components burn much more slowly than the others. Consequently, i t i s common to switch to more severe c o n d i t i o n s f o r a p e r i o d of secondary burn f o l l o w i n g the primary burn. This s i t u a t i o n can be modeled simply by regarding a s m a l l p r o p o r t i o n of the t o t a l coke as " r e f r a c t o r y coke", with a much s m a l l e r burning r a t e constant. Then the consequences of s w i t c h ing to secondary burn c o n d i t i o n s are i l l u s t r a t e d by F i g s . 3 and 4. Curve 0 i n F i g . 3 shows the average coke c o n c e n t r a t i o n i n the bed, as a f u n c t i o n of time, f o r a primary burn with a gas flow of 1173 kg/m h at 399C and c o n t a i n i n g 0.5% oxygen. A f r a c t i o n 0.05 of the t o t a l coke i n i t i a l l y present i s assumed

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

4.

LIAW ET AL.

Coke Burning in a Fixed-Bed Reactor

TIME (hr) = 0.25

TIME (hr) * I

TIME (hr) = 5

TIME (hr) = 9

43

UJ Ο

DIMENSIONLESS

DISTANCE, χ

Figure 1. Coke concentration profiles in a primary burn. Curves 1, 2, 3, and 4 correspond to inlet temperatures of 316,343,371, and 399°C, respectively.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

44

CHEMICAL REACTION ENGINEERING

TIME (hr)*0.25

DIMENSIONLESS

TIME (hr) = I

DISTANCE, χ

Figure 2. Temperature profiles in a primary burn. Curves 1, 2, 3, and 4 corre­ spond to inlet temperatures of 316, 343,371, and 399°C, respectively.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

LIAW ET AL.

Coke Burning in a Fixed-Bed Reactor

TIME (hr),t Figure 4. Maximum temperature in bed, with a switch to secondary burn conditions.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

46

CHEMICAL REACTION ENGINEERING

to be r e f r a c t o r y coke, w i t h a r a t e constant one t e n t h that of the remainder. Curve 1 shows the e f f e c t of s w i t c h i n g the i n l e t oxygen c o n c e n t r a t i o n to 2% at 5.8 hours, while curve 2 c o r r e s ­ ponds t o a change i n both oxygen c o n c e n t r a t i o n and i n l e t tempera­ ture at t h i s time, to 2 mole % and 427C, r e s p e c t i v e l y . In t h i s case the burn i s v i r t u a l l y complete w i t h i n seven hours. The max­ imum temperature i n the bed i s shown i n F i g . 4, and the maximum temperature reached a f t e r the switch never exceeds the h i g h e s t temperature i n the primary burn. When both temperature and oxygen c o n c e n t r a t i o n are switched there i s a double peak i n the maximum temperature curve. The f i r s t corresponds t o coke burn­ ing due to the i n c r e a s e d oxygen c o n c e n t r a t i o n , w h i l e the second i s a s s o c i a t e d with the temperature wave generated by the switch i n i n l e t temperature. Acknowledgement Acknowledgement i s made t o the Donors of the Petroleum Research Fund, administered by the ACS, f o r support of the work. Legend of Symbols A

frequency f a c t o r f o r r a t e constant

Bi c

m

b i o t number f o r mass t r a n s f e r : coke c o n c e n t r a t i o n i n c a t a l y s t

c

c C

K r /D m ρ e (mole/vol)

i n i t i a l coke c o n c e n t r a t i o n i n c a t a l y s t

co og

oxygen c o n c e n t r a t i o n i n f l o w i n g gas

(mole/vol)

c ^ Q

i n l e t gas oxygen c o n c e n t r a t i o n (mole/vol)

C

Q S

oxygen c o n c e n t r a t i o n i n gas w i t h i n p e l l e t

Cg

s p e c i f i c heat of gas

C

s p e c i f i c heat of s o l i d

g

Da D Ε f

g

c

f g

f

Η

g

(mole/vol)

Damkohler number: α ( l - e ) L K ( T . )c /V c b g i co ο e f f e c t i v e d i f f u s i o n c o e f f i c i e n t of oxygen i n p e l l e t a c t i v a t i o n energy f o r r a t e constant v

dimensionless coke c o n c e n t r a t i o n : c /e c co dimensionless oxygen c o n c e n t r a t i o n i n f l o w i n g gas: c /c . Og O l dimensionless oxygen c o n c e n t r a t i o n i n p e l l e t : c /c os og dimensionless heat t r a n s f e r f a c t o r : 3

1

e

< - b

) L K

h

/ V

P

C

r

o 8 g p

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

4.

LIAW ET A L .

Coke Burning in a Fixed-Bed Reactor

(-AH )

heat of combustion per mole coke burned

K(T )

r a t e constant f o r coke burning

c

g

K

m

heat t r a n s f e r c o e f f i c i e n t

from p e l l e t to flowing gas

mass t r a n s f e r c o e f f i c i e n t

from p e l l e t to flowing gas

L

t o t a l depth of bed

r

r a d i a l d i s t a n c e from center of p e l l e t

r

pellet

R

molar gas constant

R

c

s

radius

r a t e of o x i d a t i o n of coke (moles/vol. time) dimensionless r a d i a l d i s t a n c e :

t

time

t, h t m t r t

thermal residence time:

v

r/r

(l-ε, )Lp C /V ρ C b s s o"g g

gas residence time: ε, L/V b o c h a r a c t e r i s t i c r e a c t i o n time:

1/K(T ,)c . gi' oi v

a r b i t r a r i l y chosen time u n i t flowing gas temperature

T

g i

i n l e t gas temperature

T

g

pellet

T

g o

i n i t i a l p e l l e t temperatui

ν

thermal pulse v e l o c i t y :

V

q

gas s u p e r f i c i a l v e l o c i t y

temperature

L/t

h at i n l e t c o n d i t i o n s

χ

dimensionless d i s t a n c e down bed:

ζ

d i s t a n c e down bed

z/L

moles oxygen consumed per mole coke burned 3, h ε,

dimensionless heat of combustion: v o i d f r a c t i o n of packed bed

η

effectiveness factor:

(-ΔΗ

c

)c ./α ρ C Τ . oi c g g gi

f 3 exp [λ(1-1/θ )] f f ds" Jo ° s

θ

common value of

9g

dimensionless gas temperature:

6

dimensionless s o l i d temperature:

g

and 0

g

i n pseudo-homogeneous model

λ

dimensionless a c t i v a t i o n energy:

ρ^

gas d e n s i t y

p

s o l i d density

e

Τ / T

^ T

g

/ gi

E/RT^

American Chemical Society Library 1155 16th St. N. W.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Washington, DC, 1982. Washington, D. C. Society: 20038

CHEMICAL REACTION ENGINEERING

48

τ

dimensionless time: t / t

φ

T h i e l e modulus:

γ

s r K(T ,)c /D ρ g i co e

Literature Cited 1. 2. 3. 4. 5. 6. 7.

Van Deemter, J . J . Ind. Eng. Chem. 1953, 45, 1227; 1954, 45, 2300. Johnson, B. M.; Froment, G. F.; Watson, C. C. Chem. Eng. S c i . 1962, 17, 835. Olson, Κ. E.; Luss, D.; Amundson, Ν. R. Ind. Eng. Chem. (Pro. Des. Dev.) 1968, 7, 96. Ozawa, Y. Ind. Eng. Chem. (Pro. Des. Dev.) 1969, 8, 3. Arthur, J . R. Trans, Farad. Soc., 1951, 47, 164. Rossberg, M. Z. Electrochem Liaw, W-K, MS T h e s i s U n i v e r s i t y of Houston, 1981.

RECEIVED April 27, 1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

5 Impact of Porosity and Velocity Distribution on the Theoretical Prediction of Fixed-Bed Chemical Reactor Performance Comparison with Experimental Data D. V O R T M E Y E R and R. P. WINTER Fakultät für Maschinenwesen, Technische Universität München, Arcisstrasse 21, 8000 München 2, Federal Republic of Germany

Due to porosit change d th nonsli condition at th r o s i t y p r o f i l e s in packed beds exhibit steep maxima close to the w a l l . The govern­ ing equations of energy and mass conserva­ tion were solved for fixed bed chemical reactors including these p r o f i l e s . Under the assumption of non uniform flow the problems become two-dimensional also under adiabatic conditions. In all cases the agreement between available experimental data and t h e o r e t i c a l predictions based on realistic flow conditions is improved. In p a r t i c u l a r measured and calculated moving speeds of migrating reaction zones fit to­ gether very well for adiabatic fixed bed reactors. Also considerable improvements concerning multiple steady s t a t e s , temper­ ature p r o f i l e s and conversion rates were obtained in situations when the reactor was wall cooled. I n f i x e d b e d c h e m i c a l r e a c t o r a n a l y s i s i t i s common to assume u n i f o r m f l o w d i s t r i b u t i o n w i t h i n t h e b e d . The r e a l i t y h o w e v e r i s d i f f e r e n t . Due t o a c h a n g e o f t h e average p o r o s i t y near the w a l l [ 1 , 2 , 3 ] , ( F i g u r e 1.) ε=1 a t t h e w a l l - t h e f l o w v e l o c i t y i n c r e a s e s u n t i l c l o s e t o t h e w a l l and i s r e d u c e d a g a i n b e c a u s e o f t h e non s l i p c o n d i t i o n ( F i g u r e 2.) The a r t i f i c i a l f l o w p r o ­ f i l e i s d e s c r i b e d by t h e B r i n k m a n e q u a t i o n I àz

B.C.

=-150^ a

e

3

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0

d p

2

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; Γ = 0 :

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£

d

p

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0097-6156/82/0196-0049$06.00/0 © 1982 American Chemical Society In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

(

1

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50

CHEMICAL REACTION ENGINEERING

w h i c h c o n t a i n s t h e w a l l f r i c t i o n and t h e E r g u n p r e s s u r e l o s s term. Although E q u a t i o n (1) i s a simple d i f f e r e n ­ t i a l e q u a t i o n so f a r o u r e f f o r t s had f a i l e d t o s o l v e t h i s e q u a t i o n i n c l u d i n g ε=1 a t t h e w a l l b e c a u s e o f n u ­ m e r i c a l i n s t a b i l i t i e s . We do n o t know a b o u t t h e s u c c e s s o f o t h e r g r o u p s w o r k i n g i n t h i s f i e l d h o w e v e r , so f a r in l i t e r a t u r e s o l u t i o n s are p u b l i s h e d f o r c o n d i t i o n s o n l y s e t t i n g the p o r o s i t y a t the w a l l to a v a l u e say of ε = 0 . 5 o r 0.6. T h e r e f o r e , S c h u s t e r and V o r t m e y e r [4] r e ­ c e n t l y f o r m u l a t e d t h e e q u i v a l e n t v a r i a t i o n a l p r o b l e m by m i n i m i z i n g the energy d i s s i p a t i o n w i t h i n the bed. For d e t a i l s we r e f e r t o [ 4 ] . The s o l u t i o n o f t h e v a r i a t i o n ­ a l p r o b l e m was o b t a i n e d w i t h o u t d i f f i c u l t i e s and F i g u r e 2 shows a t y p i c a l c a l c u l a t e d f l o w p r o f i l e . To o u r s u r ­ p r i s e the c a l c u l a t e d i f f e r e n t from the mai ( F i g u r e 2 ) , [ 5 , 6 ] w h i c h w e r e t a k e n some m i l l i m e t e r s above the e x i t c r o s s e c t i o n of the f i x e d bed w i t h i n t h e empty t u b e . C o m p a r i n g a m e a s u r e d and c a l u c u l a t e d p r o ­ f i l e i n F i g u r e 2 we f i n d t h a t t h e c a l c u l a t e d maximum f l o w v e l o c i t y i s much h i g h e r t h a n t h e m e a s u r e d one and t h a t a l s o t h e c a l c u l a t e d maximum l i e s c l o s e r t o t h e w a l l . O b v i o u s l y the f l o w p r o f i l e changes r a p i d l y once i t h a s l e f t t h e f i x e d b e d . T h a t t h i s i s i n d e e d t r u e was d e m o n s t r a t e d by s o l v i n g t h e t w o d i m e n s i o n a l NavierS t o k e s - E q u a t i o n s f o r t h e empty t u b e t a k i n g t h e c a l c u ­ l a t e d f i x e d bed f l o w p r o f i l e as t h e e n t r a n c e profile [4]. I t i s i n t e r e s t i n g to note t h a t the measurements of P r i c e [7] now a p p e a r i n a new l i g h t . P r i c e d e v i d e d t h e e x i t c r o s s e c t i o n o f the p a c k e d bed i n t o c o n c e n t r i c c i r c l e s and m e a s u r e d f l o w v e l o c i t i e s w i t h i n t h e r a d i a l ­ l y s h i e l d e d s e g m e n t s . By t h i s m e t h o d he s u p p r e s s e d the r a d i a l f l o w c o m p o n e n t s a b o v e t h e b e d and o b t a i n e d p r o ­ f i l e s s i m i l a r to the c a l c u l a t e d ones ( F i g u r e 3 ) . In p a r t i c u l a r P r i c e a l s o f o u n d t h e maximum v e r y c l o s e t o the w a l l . Comparing the t r u e f l o w d i s t r i b u t i o n i n s i d e the bed w i t h t h e u s u a l l y assumed c o n s t a n t f l o w d i s t r i b u ­ t i o n we f e e l t h a t r e a l and a s s u m e d f l o w a r e v e r y f a r a p a r t i n p a r t i c u l a r f o r s m a l l r a t i o s of tube to p a r t i ­ c l e diameter. For l a r g e v a l u e s of t h i s r a t i o c e r t a i n l y the assumption o f c o n s t a n t f l o w i s more r e a l i s t i c . A s u r v e y o f l i t e r a t u r e e x h i b i t s t h e f a c t t h a t up t o now n o t much a t t e n t i o n h a s b e e n p a i d t o t h e impact o f p o r o s i t y and v e l o c i t y d i s t r i b u t i o n on t h e a n a l y s i s of f i x e d bed c h e m i c a l r e a c t o r s . Under n o n - u n i f o r m flow c o n d i t i o n s C h a u d h a r y e t a l . [8] c o m p a r e d m e a s u r e d and c a l c u l a t e d c o n c e n t r a t i o n p r o f i l e s f o r an i s o m e r i z a t i o n r e a c t i o n i n an i s o t h e r m a l f i x e d b e d c h e m i c a l r e a c t o r

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

Fixed-Bed Chemical Reactor Performance

VORTMEYER AND WINTER

Î

1.0

0,8

J nnnno^ Τ

ω Γ 0,4

τ — I — Γ " 2

3

r l i n dp ]

4

5

Figure 1. Porosity distribution in packed bed. Key: • , measured by Réf. 1; and; , average porosity junction after Ref. 4.

Figure 2. Flow profiles Re = 600. Key: , measured 25 mm above the bed (5); and , calculated inside the bed after Ref. 4. p

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

52

CHEMICAL REACTION ENGINEERING

h a v i n g u n i f o r m and d e l i b e r a t e n o n - u n i f o r m p a c k i n g s . B u c h l i n e t a l [9] c o r r e l a t e d t h e p o s i t i o n o f h o t s p o t s w i t h t h e p o r o s i t y minimum ( F i g u r e 1) n e a r t h e w a l l . L e r o u and F r o m e n t [10] f o u n d by c a l c u l a t i o n s t h a t a r e a c t o r may i g n i t e u n d e r non c o n s t a n t f l o w c o n d i t i o n s w h i l e i t i s s t i l l s t a b l e i f c o n s t a n t f l o w i s assumed. K a l t h o f f and V o r t m e y e r [ 1 1 ] , ( F i g u r e 4) f o u n d an imp r o v e d a g r e e m e n t b e t w e e n m e a s u r e d and c a l c u l a t e d r a n g e s o f m u l t i p l e s o l u t i o n s f o r non - u n i f o r m f l o w . F r o m t h e p r e v i o u s w o r k t h e r e f o r e c a n be c o n c l u d e d t h a t non-unif o r m p o r o s i t y and f l o w d i s t r i b u t i o n s e f f e c t t h e c h e m i c a l r e a c t o r p e r f o r m a n c e . The q u e s t i o n h o w e v e r , w h e t h e r r e a l i m p r o v e m e n t s a r e o b t a i n e d has t o be s u b j e c t t o a c o m p a r i s o n of e x p e r i m e n t a l r e s u l t s w i t h c a l c u l a t i o n s . On t h e n e x t p a g e s w f a r have o b t a i n e d . Creeping

Zones

I n An

Adiabatic Fixed

Bed

Reactor

One o f t h e p h e n o m e n a most s e n s i t i v e t o n o n - u n i f o r m f l o w d i s t r i b u t i o n s h o u l d be m o v i n g o r c r e e p i n g r e a c t i o n z o n e s w h i c h h a v e f o u n d much a t t e n t i o n d u r i n g t h e p a s t t w e n t y y e a r s [ 1 2 - 1 9 ] . F o r t u n a t e l y a number o f v e r y a c c u r a t e m e a s u r e m e n t s made by S i m o n [19] i s a v a i l a b l e . S i n c e a l s o the o v e r a l l k i n e t i c d a t a of the i r r e v e r s i b l e e t h a n e o x i d a t i o n on s p h e r i c a l Pd - A ^ O ^ c a t a l y s t part i c l e s w e r e p u b l i s h e d i n [19] a q u a n t i t a t i v e c o m p a r i s o n o f m e a s u r e m e n t s and c o m p u t a t i o n s c a n be c a r r i e d o u t . The t h e o r e t i c a l a n a l y s i s o f c r e e p i n g z o n e s h a s a l ways b e e n p e r f o r m e d by a s s u m i n g c o n s t a n t f l o w c o n d i t i o n s i n the packed bed. C o n s e q u e n t l y i n model c a l c u l a t i o n s a f l a t r e a c t i o n z o n e w i l l move t h r o u g h t h e a d i a b a t i c r e a c t o r . However, a f l a t moving t e m p e r a t u r e p r o f i l e i s n o t i n a g r e e m e n t w i t h e x p e r i m e n t a l f a c t s as obs e r v e d by S i m o n [ 1 9 ] . He f o u n d - i f we c o n s i d e r one i s o t h e r m - t h a t i n a r e a c t i o n zone moving a g a i n s t f l o w i n the c e n t r e o f the bed the i s o t h e r m s were a h e a d . S i n c e the e x p e r i m e n t a l c o n d i t i o n s were c l o s e t o a d i a b a t i c o n e s , t h e r e i s h a r d l y any i n t e r p r e t a t i o n f o r t h i s obs e r v a t i o n on t h e g r o u n d o f c o n s t a n t f l o w d i s t r i b u t i o n . I f however, the r a d i a l d i s t r i b u t i o n of f l o w i s i n t r o duced the bent shape of the r e a c t i o n zone f i n d s a n a t u r a l e x p l a n a t i o n . S i n c e m o v i n g s p e e d and m o v i n g d i r e c t i o n of the r e a c t i o n zone a r e v e r y s e n s i t i v e to the f l o w r a t e , t h e r e a r e s i t u a t i o n s where the c e n t r a l f l u i d f l o w v e l o c i t i e s a r e such t h a t the r e a c t i o n zone wants to m i g r a t e a g a i n s t the incoming f l o w w h i l e at h i g h e r v e l o c i t i e s n e a r t h e w a l l , t h e z o n e i n t e n d s t o move o u t o f t h e r e a c t o r . What r e a l l y h a p p e n s d e p e n d s on w h e t h e r t h e c o n d i t i o n s i n the c e n t r a l or i n the w a l l r e g i o n are

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

VORTMEYER AND WINTER

Fixed-Bed Chemical Reactor Performance

1 0

Γ

50

100

r Imm]

150 ^

Figure 3. Flow profiles. Key: -, measured by Ref. 7; and inside the bed after Ref. 4.

, calculated

590

580 h

0.04

0.06 U

NTP

I

m

,

s

'

Figure 4. Range of multiplicity in a wall cooled reactor. Key: $, ignition (measurement); $ » extinction (measurement); , calculated with uniform flow; and , calculated with nonuniform flow. (Reproduced, with permission, from Ref. 11. Copyright 1979, Pergamon Press, Ltd.)

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

CHEMICAL REACTION ENGINEERING

54

g a i n i n g more w e i g h t a n d on t h e m a g n i t u d e o f r a d i a l e x change p r o c e s s e s . In p e r f o r m i n g c a l c u l a t i o n s we a r e c o n f r o n t e d w i t h t h e s i t u a t i o n t h a t a l t h o u g h we h a v e no h e a t l o s s e s t o t h e w a l l t h e a d i a b a t i c r e a c t o r h a s t o be d e s c r i b e d by two d i m e n s i o n a l d i f f e r e n t i a l e q u a t i o n s : The n u m e r i c a l s o l u t i o n s w e r e o b t a i n e d on a C y b e r 175 w i t h t h e m e t h o d of f i n i t e d i f f e r e n c e s .

b

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.

* m - . « 02

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I.C.

t=0:

T = T

0

b.c.Z=o=

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g

z L:

f

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| L ôr

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C

2

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6

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)

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.

^

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C

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6

= yc H .o;y 2

6

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T h i s s e t o f e q u a t i o n s was s o l v e d i n o r d e r t o s i m u l a t e o n c e more t h e e x p e r i m e n t a l c o n d i t i o n s a n d r e s u l t s o f S i m o n and V o r t m e y e r [18] s i n c e t h e s e a u t h o r s w e r e unable to f i n d a s a t i s f a c t o r y q u a n t i t a t i v e e x p l a n a t i o n f o r t h e d e v i a t i o n s between o b s e r v e d and c a l c u l a t e d m i g r a t i o n s p e e d s . We h a v e r e p e a t e d t h e c a l c u l a t i o n s w i t h t h e same k i n e t i c a n d t r a n s p o r t p a r a m e t e r s a s i n [18] however, w i t h non-uniform f l o w d i s t r i b u t i o n . The e f f e c t i v e r a d i a l h e a t c o n d u c t i v i t y w h i c h i n a d d i t i o n had t o be i n t r o d u c e d was e v a l u a t e d f r o m t h e r e l a t i o n ( 5 ) w h i c h i s q u i t e o f t e n quoted i n l i t e r a t u r e . C d

= *f-0.1.Re .Pr.X p

5

g

Figure 5 contains c a l c u l a t e d isotherms of a react i o n z o n e w h i c h moves a g a i n s t t h e i n c o m i n g f l o w . I t i s seen t h a t the shape o f t h e i s o t h e r m s i s i n agreement w i t h p r e v i o u s e x p e r i m e n t a l o b s e r v a t i o n s . The f i r s t isotherm a t the temperature T=605 Κ i n F i g u r e 5 i s m o v i n g from r i g h t to l e f t a g a i n s t the incoming f l o w . I f the temperature i s m e a s u r e d by a m o v a b l e t h e r m o c o u p l e i n t h e a x i s o f t h e b e d we f i n d a l r e a d y a t e m p e r a t u r e rise in the a x i s w h i l e the temperature i n t h e same p l a n e n e a r the

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

5.

Fixed-Bed Chemical Reactor Performance

VORTMEYER AND WINTER

55

w a l l a r e lower.Most i n t e r e s t i n g however i s t h e f o r ­ mation o f hot spots near the w a l l . Because o f the h i g h e r mass f l o w r a t e s more h e a t i s r e l e a s e d i n t h e s e a r e a s . The c a l c u l a t e d h o t s p o t s a r e i n a g r e e m e n t w i t h experimental observation of Buchlin et a l [ 9 ] . The t h r e e F i g u r e s 6,7,8 p r e s e n t m e a s u r e d a n d c a l ­ c u l a t e d m i g r a t i o n s p e e d s . One o f t h e t h e o r e t i c a l c u r v e s was c a l c u l a t e d by S i m o n [ 1 8 ] u n d e r t h e a s s u m p t i o n o f constant flow d i s t r i b u t i o n . Quite b i g d i f f e r e n c e s to the e x p e r i m e n t a l p o i n t s a r e o b s e r v e d . I n c l u d i n g t h e r a d i a l f l o w d i s t r i b u t i o n and s o l v i n g t h e e x t e n d e d equs* ( 2 , 3 , 4 ) o f t h i s p a p e r we f i n d e x c e l l e n t a g r e e m e n t . Steady S t a t e A x i a l Temperature F i x e d Bed R e a c t o r s

Profiles

In Wall

Cooled

T h i s t i m e i n s t e a d o f h a v i n g o n e t h e r m o c o u p l e mov­ a b l e i n s i d e an a x i a l c e r a m i c tube as i n [11,18] t h e t h e r m o c o u p l e s were f i x e d i n s i d e o f c a t a l y s t p e l l e t s . The t h e r m o c o u p l e w i r e s l e f t t h e r e a c t o r r a d i a l l y t h r o u g h t h e w a l l . S i x such p e l l e t s were s i t u a t e d a l o n g the a x i s e q u i d i s t a n t l y i n a r e a c t o r w i t h p a r t i c l e s o f 2.3 mm a n d 5.2 mm ( c o r r e s p o n d i n g D / d = 10.4 a n d 4 . 6 ) . The c a l c u l a t e d f l o w p r o f i l e s f o r b o t n p a c k i n g s a r e p r e s e n t e d i n F i g u r e 9, t y p i c a l m e a s u r e d p r o f i l e s a r e p l o t t e d i n F i g u r e s l O a n d 11 f o r t e m p e r a t u r e s . F o r a c o m p a r i s o n w i t h m o d e l c a l c u l a t i o n s we s o l v e equs. (2) t o (4) s u b j e c t t o t h e boundary c o n d i t i o n s : p

B.C.

r = R : α

(T-T ) = X 0

e

f f r

. -g-

6

The w a l l h e a t t r a n s f e r c o e f f i c i e n t s w e r e e v a l u a t e d f r o m a r e l a t i o n by H e n n e c k e a n d S c h l i i n d e r [20] . I n o u r p a r t i c u l a r c a s e we o b t a i n e d a v a l u e o f α = 62 Wm~ K~1 f o r t h e r e a c t o r i n F i g u r e 10 a n d α = 42 Wm" K~l for t h e one i n F i g u r e 1 1 . Under u n i f o r m f l o w c o n d i t i o n s t h e c o m p a r i s o n b e t ­ ween m e a s u r e m e n t s a n d c a l c u l a t i o n s t u r n e d o u t t o be q u i t e u n s a t i s f a c t o r y as t h e p l o t s i n F i g u r e s 10 a n d 11 show a l t h o u g h i n t h e c a s e o f t h e r e a c t o r w i t h a s m a l l D / d p - r a t i o measured and c a l c u l a t e d p r o f i l e s l i e c l o s e r t o g e t h e r t h a n i n F i g u r e 10 d e m o n s t r a t i n g t h e s i t u a t i o n f o r the l a r g e r D / d - r a t i o . There i s a q u a l i ­ t a t i v e e x p l a n a t i o n f o r t h i s o b s e r v a t i o n i f we c o n c e n ­ t r a t e f o r a moment on F i g u r e 9 c o n t a i n i n g t h e c a l c u l a t ­ ed f l o w p r o f i l e s f o r b o t h r e a c t o r s . I t i s s e e n from t h i s Figure that the flow p r o f i l e s f o r the r e a c t o r with D/dp = 4.6 t u r n s o u t t o be more h o m o g e n e o u s t h a n t h a t o f t h e r e a c t o r w i t h D / d = 1 0 . 4 . T h i s i s r e f l e c t e d by 2

2

p

D

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

56

CHEMICAL REACTION ENGINEERING

creeping

U

y

direction

NTP r C

μ 2 6

=0,0038

H

Figure 5.

Isotherms of moving reaction zones calculated with nonuniform flow.

- V. -1 10 w 5

[m Is]

,

T

= 571 Κ

0

*C H 2

%0 2

=

0

6

=

0

0

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3

3

3

2

4

9

6

10 u z

N T p

8

10

[m/s]

Figure 6. Migration speeds as a function of the average gas flow. Key: · , mea­ sured points (IS); , calculation with uniformflow(IS); and , calculation with nonuniform flow.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

VORTMEYER AND WINTER

Fixed-Bed Chemical Reactor Performance

Figure 8. Migration speeds as a function of the average gasflow.Key is the same as in Figure 6.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

58

CHEMICAL REACTION ENGINEERING

u(r)

û

Figure 9. Calculatedflowprofiles inside packed beds after Ref. 4. Key: Re = 20; , D/d = 10.4; and , D/d = 4.6. p

p

800

Figure 10. Axial temperature profiles in a wall cooled reactor. Conditions: yC H = 0.005; T = 613 K; and Re = 20. Key: Φ, measured points; , calcu­ lated with uniformflow;and , calcu­ lated with nonuniform flow. t

0

s

p

Figure 11. Axial temperature profiles in a wall cooled reactor. Conditions and key are the same as in Figure 10.

15

20

ζ [cm]

»

z[cm]

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

5.

VORTMEYER AND WINTER

Fixed-Bed Chemical Reactor Performance

59

the b e t t e r agreement between u n i f o r m f l o w c a l c u l a t i o n and m e a s u r e m e n t i n F i g u r e 1 1 · f o r t h e s m a l l t u b e t o p a r ­ t i c l e diameter r a t i o . The s i t u a t i o n c h a n g e s d r a m a t i c a l l y i f t h e c a l c u ­ l a t i o n s are performed f o r non-uniform flow d i s t r i b u t i o n w h i c h means t h a t t h e f l o w p r o f i l e s o f F i g u r e s 9 a r e a p p l i e d . While n e a r l y p e r f e c t agreement i s then o b t a i n ­ ed i n F i g u r e 11. s l i g h t d e v i a t i o n s s t i l l a r e o b s e r v e d i n F i g u r e 10. f o r w h i c h p r e s e n t l y we h a v e no e x p l a n a t i o n . A s i m i l a r r e s u l t was p r e v i o u s l y o b s e r v e d b y K a l t h o f f and V o r t m e y e r [ 1 1 ] . The p h y s i c a l c h e m i c a l b a c k g r o u n d f o r t h e i m p r o v e m e n t s i s due t o t h e f a c t t h a t u n d e r r e ­ a l i s t i c flow c o n d i t i o n s the flow rates near the w a l l a r e h i g h e r t h a n i n t h e b e d c e n t r e . T h i s means h i g h e r heat r e l e a s e r a t e s nea t u r e s and t h e r e f o r e with c a l c u l a t i o n s with uniform flow. These e f f e c t s a r e n o t expected i f t h e r e a c t o r w o r k s u n d e r a d i a b a t i c c o n d i t i o n s . D i e t r i c h [21] h a s always obtained good a g r e e m e n t between m e a s u r e d and c a l c u l a t e d steady s t a t e p r o f i l e s . In t h i s case the heat l o s s e s t o t h e w a l l a r e z e r o and t h e d e f i c i e n c y o f heat r e l e a s e i n t h e c e n t r e o f t h e bed i s c o m p e n s a t e d by r a d i a l e x c h a n g e p r o c e s s e s w h i c h - b e c a u s e o f no w a l l heat l o s s e s - t r a n s p o r t heat to the i n s i d e of thebed. Conclusions The i m p a c t o f r e a l i s t i c f l o w p r o f i l e s o n m o d e l c a l ­ c u l a t i o n s f o r t h e p r e d i c t i o n o f f i x e d bed r e a c t o r p e r ­ f o r m a n c e i s q u i t e l a r g e f o r D/d r a t i o s a c t u a l l y used. In a l l i n v e s t i g a t e d c a s e s l a r g e i m p r o v e m e n t s between p r e d i c t i o n s and measurements were o b s e r v e d i n p a r t i c u ­ lar f o r s i t u a t i o n s which are very s e n s i t i v e to flow d i s t r i b u t i o n as moving r e a c t i o n zones i n a d i a b a t i c r e ­ a c t o r s and s t e a d y s t a t e t e m p e r a t u r e p r o f i l e s i n w a l l cooled reactors. P

Legend of Symbols specific

heat

capacity

o f t h e gas

[j/kgK]

specific

heat

capacity

of the p a r t i c l e s

Pg c s tot D d Ρ ΔΗ Ρ Pr C

concentration

o f t h e gas m i x t u r e

t u b e d i a m e t e r [m] p a r t i c l e diameter reaction enthalpie pressure [bar] P r a n d t l number

[J/kgK] 3

[ m o l /m ]

[m] [j/mol]

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

CHEMICAL REACTION ENGINEERING

60

r a d i a l c o o r d i n a t e [m] r a t e of r e a c t i o n [mol/m s]

r

i

3

ν Re

= Ρ

Τ t u w y C2H6 y

udpPg/^g p a r t i c l e

axial Greek α ε Xg X

number

temperature fK] time [s] b u l k f l o w v e l o c i t y b a s e d on t h e a r e a o f empty t u b e [m/s] m i g r a t i o n s p e e d [m/s] mole f r a c t i o n o f ethane [mol/mol] mole

H20

Reynolds

fraction

of water

coordinate

vapour

[mol/mol]

[m]

Letters w a l l heat t r a n s f e void fraction thermal

conductivity

o f t h e gas [W/mK]

eff

effective

axial

\eff

effective

radial

T)g

dynamic

therm,

cond.

[W/mK]

therm.cond.

[W/mK]

a χ viscosity

o f t h e gas

[kg/ms]

3

pg d e n s i t y o f t h e gas [kg/m ] A c k n o w l e d g e m e n t - We a p p r e c i a t e Mr. D. S t e i n l e i t n e r s a s s i s t a n c e f o r p r o g r a m m i n g ; t h i s w o r k was s u p p o r t e d b y t h e D e u t s c h e F o r s c h u n g s g e m e i n s c h a f t ( D F G ) , G r a n t SFB 1 5 3 . 1

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Benenati,R.F.; Brosilow,C.Β.: AIChE J o u r n a l , 1962, 8, 359-361. Korolev,V.N.; Syromyatnikov,Ν.I.; Tolmachev,Ε.M.: I n z h e n e r n o - F i z i k e s k i i Z h u r n a l , 1971, 6, 973-978. Roblee,L.H.; Baird,R.M.; T i e r n e y , J . W . : AIChE J o u r n . 1958, 4, 460-464. S c h u s t e r , J . ; Vortmeyer,D.: Chem.-Ing.-Technik, 1981, 53, 806-807. Schertz,W.W.; Bischoff,K.B.: AIChE J o u r n a l , 1969, 15, 597-604. S c h w a r t z , C . E . ; S m i t h , J . M . : I n d . Engng. Chem., 1953, 45, 1209-1218. P r i c e , S . : Mech.Chem.Engng.Transact i o n s , 1968, 7-14. Choudhary,M.; Szekely,J.; W e l l e r , S . W . : AIChE J o u r n . 1976, 22, 1021-1032. B u c h l i n , S . M . ; L a p t h o r n , S. C.; G i m o u x , S . S . : Vt " V e r f a h r e n s t e c h n i k " , 1977, 11, 620-624. Lerou,S.S.; F r o m e n t , G . F . : C h e m . E n g n g . S c i . , 1977, 32 853-861.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

5.

11. 12. 13. 14. 15. 16. 17. Vysoké 18. 19. 20. 21.

VORTMEYER AND WINTER

Fixed-Bed Chemical Reactor Performance

61

Kalthoff,O.: P h . D . T h e s i s , T e c h n . U n i v . München,1978 -; V o r t m e y e r , D . : C h e m . E n g n g . S c i . , 1 9 7 9 , 3 5 , 1 6 3 7 - 1 6 4 3 . W i c k e , E . ; Vor tmeyer, D.: Zeitschrift für Elektrochemie, 1959, 63, 145-152. Vortmeyer,D.: Zeitschrift für Elektrochemie, 1961 65, 282-289. V o r t m e y e r , D . ; J a h n e l , W . : C h e m . E n g n g . S c i . , 1972, 27 1485-1496. Ree,H.K.; Foley,D.; Amundson,N.R.: C h e m . E n g n g . S c i . , 1973, 28, 607-615. Ree,H.K.; Lewis,R.P.; Amundson,N.R.: I n d . E n g n g . Fundi., 1974, 13, 31 7-323. Gilles,E.: 5th Symp. Computers i n C h e m . E n g n g . , 1977, Tatry, Czechoslovakia Simon,B.; Vortmeyer,D. 109-114. S i m o n , B . : P h . D . T h e s i s , T e c h n . U n i v . München, 1976, Hennecke, F.W.; S c h l ü n d e r , Ε.U.: C h e m . - I n g . - T e c h n . , 1973, 45, 277-284. Dietrich,K.: P h . D . T h e s i s , T e c h n . U n i v . München,1974.

R E C E I V E D April 27,

1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

6 A Novel Method for Determining the Multiplicity Features of Multi-Reaction Systems VEMURI B A L A K O T A I A H

and D A N LUSS

University of Houston, Department of Chemical Engineering, Houston, TX 77004

The q u a l i t a t i v e multiplicity f e a t u r e s o f a lumped­ -parameter system i n which s e v e r a l r e a c t i o n s occur sim­ u l t a n e o u s l y can be determined i n a systematic f a s h i o n by f i n d i n g the o r g a n i z i n g s i n g u l a r i t i e s o f the steady­ - s t a t e equation and its u n i v e r s a l u n f o l d i n g . To illus­ trate the technique we determine the maximal number o f s o l u t i o n s of a CSTR in which Ν parallel, first-order r e a c t i o n s with equal and h i g h a c t i v a t i o n energies occur as w e l l as the i n f l u e n c e of changes in the resi­ dence time on the number and type o f s o l u t i o n s . We d e s c r i b e here a new technique based on the s i n g u l a r i t y and b i f u r c a t i o n t h e o r i e s f o r p r e d i c t i n g the m u l t i p l i c i t y f e a ­ tures of lumped-parameter systems i n which s e v e r a l r e a c t i o n s occur simultaneously. Our purpose i s mainly t o i l l u s t r a t e the power of the technique and present some n o v e l r e s u l t s . A more d e t a i l e d a n a l y s i s i s presented elsewhere [1 2 J . We use the technique to answer the f o l l o w i n g questions: 9

(a)

What i s the maximum number of s t e a d y - s t a t e s o l u t i o n s f o r a lumped-parameter system i n which s e v e r a l chemical r e a c ­ t i o n s occur simultaneously, and f o r what values of the parameters w i l l t h i s occur?

(b)

What are a l l the q u a l i t a t i v e l y d i f f e r e n t types o f b i f u r ­ c a t i o n diagrams which d e s c r i b e the dependence o f a s t a t e v a r i a b l e (such as the temperature) on a design o r operat­ ing v a r i a b l e (such as the feed temperature o r flow r a t e ) and f o r what parameter values w i l l a t r a n s i t i o n from one type t o the other occur?

0097-6156/82/0196-0065$06.00/0 © 1982 American Chemical Society In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

CHEMICAL REACTION

66

ENGINEERING

H e u r i s t i c D e s c r i p t i o n of the Theory Consider a n o n l i n e a r s t e a d y - s t a t e equation o f the form F(x,X, ) - 0

(1)

2

where χ i s a s t a t e v a r i a b l e , λ i s a b i f u r c a t i o n v a r i a b l e and £ i s a v e c t o r of parameters. F i s assumed to be smooth with respect to a l l the v a r i a b l e s . The graph of χ versus λ which s a t i s f i e s Eq. (1) f o r a f i x e d £ i s d e f i n e d as a b i f u r c a t i o n d i a ­ gram. A l o c a l b i f u r c a t i o n diagram d e s c r i b e s t h i s dependence i n a s m a l l neighborhood of some p o i n t , w h i l e a g l o b a l b i f u r c a t i o n diagram d e s c r i b e s i t f o r a l l χ and λ w i t h i n the domain of i n t e r ­ est. The parameter space £ c o n s i s t s o f regions with d i f f e r e n t types of b i f u r c a t i o n diagrams erate points (singula regions coalesce so that i n t h e i r neighborhood s e v e r a l d i f f e r e n t types of l o c a l b i f u r c a t i o n diagrams e x i s t . These p o i n t s a r e c h a r a c t e r i z e d by the v a n i s h i n g of a f i n i t e number o f d e r i v a t i v e s of F with respect to χ and λ. I t i s u s u a l l y p o s s i b l e t o f i n d a smooth, n o n l i n e a r and i n v e r t i b l e change of coordinates (χ,λ,£) •> (y,y,a) that t r a n s ­ forms the s t e a d y - s t a t e equation (1) i n t o a polynomial f u n c t i o n G(y,y,a) = 0, having a l l the q u a l i t a t i v e features o f equation (1) i n the neighborhood of these s i n g u l a r p o i n t s . A polynomial G, which can represent a l l the l o c a l b i f u r c a t i o n diagrams e x i s t ­ ing next to a s i n g u l a r p o i n t of Eq. (1) and which contains the minimal number of parameters a . i s c a l l e d the u n i v e r s a l u n f o l d i n g of the s i n g u l a r i t y . Our a n a l y s i s i s based on the f o l l o w i n g theorem [3]. Suppose that the steady-state equation (1) has a s i n g u l a r p o i n t at which 1

0

F(x°,X , °) = 0 £

•^J 9X

0

2)

(2)

1

then i n the neighborhood o f (χ°,λ°,£°), the u n i v e r s a l u n f o l d i n g of F ( x , X , ) i s : £

(i)

1

G(y,p,a) â y**

- a^y*

1

1

Γ

2

- ct^^ " -

£

G(y,y a) = y*"*" - α ^

provided

1

(χ°,λ°, °) |f

provided

(ii)

-

....-c^y - μ - 0 (3)

(χ°,λ°, ) < 0. £

- ....-a y 2

2

- α

χ

+ \iy = 0

-55- (χ°,λ°, °) = 0 £

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

(4)

(5)

(6)

6.

BALAKOTAIAH

and

AND LUSS

— ^ 9x

Multiplicity of Multi-Reaction Systems

(χ ,λ ,£ )

(χ ,λ ,£ ) > 0.

67

(7)

The maximum number o f s o l u t i o n s o f equation (1) i s r+1 next t o such a s i n g u l a r p o i n t . Moreover, a l l the l o c a l b i f u r c a t i o n d i a ­ grams of the f u n c t i o n F can be determined by the a n a l y s i s o f the simpler polynomial f u n c t i o n G. The values o f λ (within the domain o f i n t e r e s t ) at which the number of s o l u t i o n s o f Eq. (1) changes are c a l l e d b i f u r c a t i o n points. At these p o i n t s F = 3F/8x = 0. Using b i f u r c a t i o n theory i t can be shown that the nature o f a b i f u r c a t i o n diagram can change only i f the parameter values cross one o f three hypers u r f a c e s [3]. The f i r s the s e t o f a l l p o i n t s i

F(x,A,£) = g

(Χ,λ,£) = ^ | (Χ,λ,£) = 0. 3x

(8)

E l i m i n a t i o n of χ and λ from these three equations gives a s i n g l e a l g e b r a i c equation i n £ , d e f i n i n g a hypersurface. When £ values cross the Η v a r i e t y two b i f u r c a t i o n p o i n t s appear o r disappear and the nature o f the b i f u r c a t i o n diagram changes as shown i n Figure l . a . The I s o l a v a r i e t y ( I ) i s the s e t o f a l l p o i n t s £ s a t i s f y i n g F

( χ

λ

(x>*,£) - f " > > £ >

=

χ

λ

| f < > >£>

9

- °·

When £ crosses t h i s v a r i e t y two b i f u r c a t i o n p o i n t s appear o r d i s ­ appear so that e i t h e r the b i f u r c a t i o n diagram i s separated l o c a l ­ l y i n t o two i s o l a t e d graphs (Figure l . c ) or one i s o l a t e d curve appears o r disappears (Figure l . b ) . The Double L i m i t v a r i e t y (DL) i s the s e t o f £ values s a t i s ­ fying F(

X;L

, X , £ ) - F(x ,X,£) - 0 2

3F 3F -g^ (χ ,λ,£) - -gj (χ ,λ,£) = 0 x φ x . (10) The number o f b i f u r c a t i o n p o i n t s does not change as £ crosses t h i s hypersurface, but the r e l a t i v e p o s i t i o n o f the b i f u r c a t i o n p o i n t s changes as i l l u s t r a t e d by F i g u r e s l . d and I.e. These three hypersurfaces d i v i d e the g l o b a l parameter space £ i n t o d i f f e r e n t regions i n each o f which a d i f f e r e n t type o f b i f u r c a ­ t i o n diagram e x i s t s . 1

2

±

2

Ν P a r a l l e l Reactions i n a CSTR The

s i n g u l a r i t y and b i f u r c a t i o n t h e o r i e s

can be used t o

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

68

CHEMICAL REACTION ENGINEERING

s.

/ r \

s

/

b X

Χ

:3d ι

2> m

z>

c

i Ρ λ

Figure 1. Possible forms of transformation of an unstable bifurcation diagram (middle column) into either one of two possible stable forms (left or right column) at the Hysteresis (a), Isola (b, c) and Double Limit varieties (d, e).

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

6.

BALAKOTAIAH AND LUSS

Multiplicity of Multi-Reaction Systems

p r e d i c t the q u a l i t a t i v e m u l t i p l i c i t y features o f lumped para­ meter chemically r e a c t i n g systems. We consider as an example a non-adiabatic CSTR i n which Ν p a r a l l e l , f i r s t - o r d e r r e a c t i o n s k. A ^ ~ ^ i i = 1,2, ,N p

±

occur. To s i m p l i f y the a l g e b r a i c manipulations we assume that the a c t i v a t i o n energies of a l l the r e a c t i o n s are equal. The species and energy balances can be combined to give a s i n g l e equation f o r the dimensionless steady-state temperature Θ: Λ

F(0,Da,£) = (l-KxDa)0 - aDa0 where

Ε Ύ

=

-

c

D

τ-τ

B

Ύ (

ο

ο

Δ Η

/pC

ο

Da = Vk.. (Τ )/q I ο T

V

i • - Λ, p o io

(11)

' Τ -Τ

_

α = Ua/Vk-(T )pc l o p

X

"

ο

ο

a

,

Χ

ρRT τ"

Ν Β V DaX Σ ^ - 0 i=l i

=

k

(T

)/k

(

i i o lV

v

The dimensionless v a r i a b l e s a r e defined so that changes i n the flow r a t e (residence time) a f f e c t only Da which i s s e l e c t e d to be the b i f u r c a t i o n parameter. We s h a l l determine the maximum number o f steady-state so­ l u t i o n s and a l l the b i f u r c a t i o n diagrams (Θ vs. Da) o f Eq. (11). We consider s e p a r a t e l y two cases; A d i a b a t i c case (a = 0) and γ » Here Eq.

θ

(11) s i m p l i f i e s to

fl

Ν B.V.Dae V ) = θ - Σ g- - 0 i = l 1+VjDae Λ

F(0,Da,B

(13)

I t can be shown [1] that the set o f equations

* « U 3Θ has a s o l u t i o n Λ θ = θ° - 2

= -^i 2Ν

=

0

(

1

4

)

9 Θ

N

Σ 1/i i=l

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

(15)

70

CHEMICAL REACTION ENGINEERING

v

i

D

a

v

D a

• ±°

=

°

(

1

z

)

" i

β χ

θ

ρ(- °)/

ζ

16

±

where z^ are the zeros of the Legendre polynomial of order Ν d e f i n e d over the u n i t i n t e r v a l (0,1) and w.^ are the correspond­ i n g Gauss-Legendre quadrature weights. Moreover, at any s i n g u ­ l a r point defined by Eqs. (14) 9

2N+1

3 Θ

. — 9Da

2Ν+1

< 0 ' U

u

(17} ' /

The q u a l i t a t i v e features of the l o c a l b i f u r c a t i o n diagrams (Θ vs. Da) of Eq. (13) i d e f i n e d by (14) are sam G(x,X

a) = x

2 N + 1

- a

2 0 X T

l

ZN-1

W

- . . . .-OLX - λ = 0 1

X

(18)

Assume that (6°,B?,v?,Da°) i s a s o l u t i o n of (14). Because of the symmetry of the^problem any permutation of the (B°,V^,Da ) i s also a solution. Therefore, there e x i s t N! separate para­ meter regions i n each of which the steady-state Eq. (13) has (2N+1) s o l u t i o n s . Eq. (18) can have f o r any N, e i t h e r zero, two, four, . . . or 2N b i f u r c a t i o n p o i n t s . A l l the p o s s i b l e l o c a l b i f u r c a t i o n diagrams can be constructed by a method described i n [1]. Moreover, i t can be proven [1] that any g l o b a l b i f u r c a t i o n d i a ­ gram of Eq. (13) must be s i m i l a r to one of the l o c a l b i f u r c a ­ t i o n diagrams of Eq. (18). For N=l, Eq. (18) describes the cusp s i n g u l a r i t y Q

Οίχ,λ,αρ = χ

3

- α χ χ

- λ - 0.

(19)

The I s o l a and Double L i m i t v a r i e t i e s do not e x i s t i n t h i s case. The H y s t e r e s i s v a r i e t y (a =0) d i v i d e s the space i n t o two regions (a^ > 0 and < 0) corresponding to the two b i f u r c a ­ t i o n diagrams shown i n F i g u r e s 2.a and 2.b. These two are a l s o the only p o s s i b l e g l o b a l b i f u r c a t i o n diagrams (Θ vs. Da) f o r Eq. (13) as the H y s t e r e s i s v a r i e t y (B =4) d i v i d e s the B^ space i n t o two r e g i o n s . For N=2, F(x,X

Eq.

α) = χ

(18) 5

defines the b u t t e r f l y s i n g u l a r i t y

- a x 3

3

- a x 2

2

- αχ χ

- λ = 0.

(20)

The H y s t e r e s i s and the Double L i m i t V a r i t i e s d i v i d e i n t h i s case the (α.,ο^,οΟ space i n t o seven regions corresponding to the seven b i f u r c a t i o n diagrams shown i n Figures 2.a-g.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

BALAKOTAIAH AND LUSS

Figure 2.

Multiplicity of Multi-Reaction Systems

Classification of the bifurcation diagrams of Equation 18 for Ν (a,b)forN = 2(a-g).

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

72

CHEMICAL REACTION ENGINEERING

S i m i l a r l y , the H y s t e r e s i s and Double L i m i t v a r i e t i e s d i v i d e the g l o b a l parameter space of ( i > 2 » 9 ^ regions having the b i f u r c a t i o n diagrams shown i n F i g u r e s 2.a-g. Because of the e x i s t e n c e of two s i n g u l a r p o i n t s there e x i s t two i s o l a t e d parameter regions corresponding to each of the f i v e b i f u r c a t i o n diagrams shown i n Figures 2.c-g. B

B

V

i

Non-Adiabatic Case (α φ 0) and γ »

n

t

0

s

e

v

e

n

θ

We consider f i r s t the s p e c i a l case o f equal coolant and feed temperature (Τ = Τ ). I t i s proven i n [2] that Eq. (11) has N! s i n g u l a r p o i n t s c R a r a c t e r i z e d by

_Λ-9Σ

= i l - i?I -

F

9 6

3Θ

2

«i)

"

and 3 9 Θ

2 N + 1

2

F 2Ν+1

9F > 363Da

where θ° and ν °

Da° are d e f i n e d by Eq.

±

a° D a

0

0.

(16)

and

= θ°-1

B.° = ι

1

,. z^l-zj

,

θ

— ( θ

(22)

ο_

1 }

The q u a l i t a t i v e features of the steady-state Eq. (11) i n the neighborhood of these s i n g u l a r p o i n t s are the same as those of the u n i v e r s a l u n f o l d i n g x

G(x,A,a) = χ -α

χ

- O&2N

"

2n-l

X

" · · ·

a

" 2

x

+ λ χ = 0

(23)

Eq. (23> has at most 2Ν+1 s o l u t i o n s and up to (2Ν+1) b i f u r c a ­ t i o n p o i n t s . An I s o l a v a r i e t y e x i s t s i n t h i s case so that the b i f u r c a t i o n diagrams are more i n t r i c a t e and c o n t a i n i s o l a s ( i s o l a t e d branches) i n a d d i t i o n to the h y s t e r e s i s loops. In the case of a s i n g l e r e a c t i o n Eq. (23) d e s c r i b e s the pitchfork singularity δ(χ,λ,α) = χ

3

- α χ 2

2

+ λ χ - α

= 0

(24)

3 The H y s t e r e s i s v a r i e t y of Eq. (24) i s ou = 27α- while the Isola variety is = 0. The two v a r i e t i e s d i v i d e the (α^,α ) 2

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

6.

BALAKOTAIAH

AND LUSS

73

Multiplicity of Multi-Reaction Systems

plane i n t o four regions w i t h d i f f e r e n t b i f u r c a t i o n diagrams. The H y s t e r e s i s and I s o l a v a r i e t i e s o f the steady s t a t e Eq. (11) were constructed i n [4] and a r e shown i n F i g u r e 3. Four d i f ­ f e r e n t types of b i f u r c a t i o n diagrams denoted as b,c,d and f i n F i g u r e 4, e x i s t next to the p i t c h f o r k s i n g u l a r i t y , which i s l o c a t e d a t α = exp(2) and = 8. An a d d i t i o n a l b i f u r c a t i o n diagram, shown as case a i n F i g u r e 4, e x i s t s i n the g l o b a l (α,Β^) plane. Z e l d o v i c h and Z y s i n p r e d i c t e d a l r e a d y i n 1941 [5] that f i v e d i f f e r e n t types o f b i f u r c a t i o n diagrams e x i s t i n t h i s case. When 9 ^ 0 and γ i s f i n i t e , Eq. (11) has h i g h e r order singularities. The coordinates o f the s i n g u l a r p o i n t s are cumbersome expressions reported i n [2]. For Ν-1 Eq. (11) has a unique s i n g u l a r p o i n t , the u n i v e r s a l u n f o l d i n g o f which i s the winged cusp s i n g u l a r i t (25) I t was shown i n [6] that the H y s t e r e s i s and I s o l a v a r i e t i e s d i v i d e the (α-,ο^,οΟ space i n t o seven regions w i t h d i f f e r e n t b i f u r c a t i o n diagrams. A c o n s t r u c t i o n o f the H y s t e r e s i s and I s o l a v a r i e t i e s of the s t e a d y - s t a t e Eq. (11) has shown that the seven b i f u r c a t i o n diagrams shown i n F i g u r e 4 are the only ones that e x i s t i n the g l o b a l parameter space (α,Β,θ ,γ) [ 4 J . I t i s important to note that w h i l e the s e l e c t i o n of the b i f u r c a t i o n v a r i a b l e does not a f f e c t the maximal number o f s t e a d y - s t a t e s o l u t i o n s , i t a f f e c t s the number and type o f b i ­ f u r c a t i o n diagrams. For example, i f we s e l e c t e d the coolant or feed temperature as the b i f u r c a t i o n v a r i a b l e then Eq. (18) would be the u n i v e r s a l u n f o l d i n g f o r both the a d i a b a t i c and the cooled case and no i s o l a s would e x i s t [ 1^,2]. Concluding Remarks The s t e a d y - s t a t e equations d e s c r i b i n g lumped parameter systems i n which s e v e r a l r e a c t i o n s occur simultaneously c o n t a i n a very l a r g e number o f parameters. Thus, i t i s i m p r a c t i c a l t o conduct an exhaustive parametric study t o determine t h e i r features. The new technique presented here p r e d i c t s q u a l i t a ­ t i v e features of these systems such as the maximum number o f s o l u t i o n s , parameter values f o r which these s o l u t i o n s e x i s t and a l l the l o c a l b i f u r c a t i o n diagrams. C o n s t r u c t i o n o f the three v a r i e t i e s enables the d i v i s i o n o f the g l o b a l parameter space i n t o regions with d i f f e r e n t b i f u r c a t i o n diagrams. We have used t h i s technique t o determine the q u a l i t a t i v e f e a t u r e s of s e v e r a l m u l t i - r e a c t i o n systems and the r e s u l t s w i l l be reported elsewhere [1,2]. I t i s expected that t h i s method w i l l become the standard t o o l f o r p r e d i c t i n g the q u a l i t a t i v e m u l t i p l i c i t y features o f these systems.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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CHEMICAL REACTION ENGINEERING

Figure 3.

A schematic of the Hysteresis and Isola varieties of Equation 11 for Ν = 1, θ = 0, and γ -> oo. ΰ

D = H(T)V/q Q

Figure 4.

0

Bifurcation diagrams describing the dependence of the dimensionless temperature θ on the flow rate (D ) for the single reaction case. a

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

6.

BALAKOTAIAH AND LUSS

Multiplicity of Multi-Reaction Systems

Acknowledgement We are t h a n k f u l to the N a t i o n a l Science Foundation f o r support o f t h i s research. Legend o f Symbols a Β c DI Ε ΔΗ k £ q Τ V x,y α γ θ λ, y ρ

heat t r a n s f e r area dimensionless heat of r e a c t i o n concentration heat c a p a c i t y Damkohler number a c t i v a t i o n energy heat of r e a c t i o n r a t e constant v e c t o r of parameter flow r a t e temperature volume state variables parameters v e c t o r dimensionless a c t i v a t i o n energy dimensionless temperature bifurcation variables density r a t i o o f r a t e constants defined by Eq.

(12)

Subscripts ο i c

i n l e t conditions i - t h r e a c t i o n o r i - t h element coolant

Superscripts ο

singular point

coordinate

Literature Cited [1] [2] [3] [4] [5] [6]

Balakotaiah, V.; Luss, D. Chem. Eng. S c i . accepted f o r publication. Balakotaiah, V.; Luss, D. Chem. Eng. Sci. submitted for publication. G o l u b i t s k y , M.; Schaeffer, D. Comm. on Pure and Appl. Math. 1979, 32, 21-98. Balakotaiah, V.; Luss, D. Chem. Eng. Comm. accepted f o r publication. Z e l d o v i c h Ya. B.; Z y s i n , Y. A. J. T e c h n i c a l P h y s i c s . 1941, 11, 502. G o l u b i t s k y , M.; K e y f i t z , B. L. SIAM J . Math. A n a l . 1980, 11, 316-339.

RECEIVED April 27, 1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

7 Reaction Rate Oscillations During the Carbon Monoxide Oxidation Reaction Over Pt/γ-Al O Catalysts: An IR-Transmission Spectroscopy Study 2

3

A. E. ELHADERI and T. T. TSOTSIS University of Southern California Los Angeles, CA 90007

Reaction rate oscillations have been observed during the o x i ­ dation reaction of CO over P t / γ - A l O catalysts. The technique of IR transmission spectroscopy has been u t i l i z e d to monitor the sur­ face state of the catalyst under both steady-state and oscillatory conditions. The effect of hydrocarbon impurities and catalyst deactivation on the dynamic behavior of the system has also been investigated. 2

3

Self-sustained reaction rate oscillations have been shown to occur in many heterogeneous catalytic systems [1-8]. By now, sev­ eral comprehensive review papers have been published which deal with different aspects of the problem [3, 9, 10]. An impressive volume of theoretical work has also been accumulated [3, 9, 11], which tries to discover, understand, and model the underlying principles and causative factors behind the phenomenon of o s c i l l a ­ tions. Most of the people working in this area seem to believe that i n t r i n s i c surface processes and rates rather than the inter­ action between physical and chemical processes are responsible for this unexpected and interesting behavior. However, the majority of the available experimental literature (with a few exceptions [7, 13]) does not contain any surface data and information which could help us to c r i t i c a l l y test and further improve the hypothec ses and ideas set forth in the literature to explain this type of behavior. For the CO oxidation reaction on Pt, in particular, several fundamental questions s t i l l remain unanswered. Quite recently doubts and questions have been raised even about the existence of an oscillatory regime for this reaction system. Cutlip and Kenney [l2] have been unable to observe any oscillations during the o x i ­ dation of CO over a 0.5% Pt/y-Al203 catalyst in a recycle reactor. Their study, however, u t i l i z e d low feed compositions of CO (0.5-33) 0097-6156/82/0196-0077$06.00/0 © 1982 American Chemical Society In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

78

CHEMICAL REACTION ENGINEERING

and O2 ( 2 - 4 % ) i n Ar and a c a t a l y s t bed which was v u l n e r a b l e to i n t e r n a l d i f f u s i o n l i m i t a t i o n s . The authors were a b l e to observe very r e p r o d u c i b l e o s c i l l a t i o n s with a r e a c t i o n mixture of 2% CO, 3% O2 and 1% 1-butene i n A r . Due, however, to the h i g h concentrat i o n o f 1-butene i n t h e i r system and i n view of the f a c t t h a t o x i d a t i o n r e a c t i o n s of hydrocarbons have been shown to o s c i l l a t e [ 7 , 8 ] , t h e i r experimental r e s u l t s a r e very d i f f i c u l t to i n t e r p r e t and analyze. Carberry et a l . [ 2 ] have observed a s t a r t l i n g e f f e c t of hydrocarbon i m p u r i t i e s on the o s c i l l a t o r y behavior i n t h e i r system· O s c i l l a t i o n s were observed when an "Impure" O2 was used and d i s appeared when the "Impure" O2 was r e p l a c e d by an " u l t r a p u r e " O 2 . The only apparent d i f f e r e n c e between the " u l t r a p u r e " and the "impure" O2 i s a 30 ppm impurity of hydrocarbons. F i n a l l y , Schmitz an alumina paint,which was the r e a c t o r w a l l seemed to be the prime reason f o r the o s c i l l a t i o n s they observed. When the alumina p a i n t was removed, the o s c i l l a t i o n s seemed a l s o to disappear. I t i s almost Impossible f o r a s i n g l e study alone t o answer a l l the questions r a i s e d so f a r i n the l i t e r a t u r e about the steady s t a t e and the dynamic behavior of the CO o x i d a t i o n r e a c t i o n s y s tem and, i n p a r t i c u l a r , quest ions about system i m p u r i t i e s , when the Impurity l e v e l s i n v o l v e d a r e below the d e t e c t i o n l i m i t s of any known i n s i t u s u r f a c e techniques. We, however, hope that our study w i l l be considered as a f i r s t p o s i t i v e step towards t h i s d i r e c t i o n . We have i n v e s t i g a t e d the o x i d a t i o n r e a c t i o n of CO over Pt/y-Al203 type c a t a l y s t s in.an a l l Pyrex g l a s s flow r e a c t o r . We have c a r e f u l l y t r i e d to e l i m i n a t e a l l r e a c t a n t i m p u r i t i e s or p o s s i b l e i n t e r f e r e n c e s caused by the presence of temperature and f l o w c o n t r o l l e r s or h i g h volume r e c y ^ c l e streams. Furthermore, during our study, s u r f a c e intermediates have been c l a s s i f i e d and monitored by the technique of IR t r a n s m i s s i o n spectroscopy (IRTS) both under s t e a d y - s t a t e and o s c i l l a t o r y c o n d i t i o n s . Our study i s c u r r e n t l y i n progress. A few of our i n i t i a l experimental observations a r e presented i n t h i s paper. F u r t h e r d e t a i l s w i l l be presented elsewhere [16]. 9

Experimental C o n s i d e r a t i o n s Experimental Apparatus. Our experimental apparatus i s shown i n F i g . l a . Constant composition gas streams o f CO, N 2 and O2 were obtained by three separate s o n i c o r i f i c e meters. The flow through the s o n i c o r i f i c e meters i s a f f e c t e d only by the upstream pressure and i s independent of the f l u c t u a t i o n s downstream as long as the r a t i o between t h e upstream and downstream p r e s s u r e s i s g r e a t e r than 2 . Exposure of the r e a c t a n t streams to s t a i n l e s s s t e e l was minimized by u s i n g o n l y T e f l o n tubing a f t e r the s w i t c h ing v a l v e j u n c t i o n . The switching v a l v e d i r e c t e d a d e s i r e d gas mixture f l o w to the r e a c t o r while another gas mixture f l o w was

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

Figure la.

Schematic diagram of the experimental system.

SECTION RECORDING 8 REACTOR SECTION METERING GAS

Gas treatment

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

80

CHEMICAL REACTION ENGINEERING

p r e c i s e l y measured by the sonic o r i f i c e meters. A s w i t c h i n t e r ­ changed t h e r e a c t o r and f l o w meter streams e l i m i n a t i n g , t h e r e f o r e , the need f o r r e a c t o r shut-down o r unnecessary long t r a n s i e n t p e r i ­ ods during the step changes o f flow and/or composition. Reactor C e l l . The flow r e a c t o r employed i n t h i s study i s shown i n F i g . l b . The r e a c t o r was made from Pyrex g l a s s and f i t s i n the sample compartment o f the Perkin-Elmer 681 IR R a t i o Rec­ ording Spectrophotometer. Residence time d i s t r i b u t i o n s t u d i e s by u t i l i z i n g a CO2 Beckman 864 IR a n a l y z e r have shown that the c e l l behaves as a CSTR f o r the range o f flow r a t e s employed i n t h i s study ^ f o r f u r t h e r d e t a i l s see [ l 6 ] ) . The r e a c t o r volume was 150 cm . The o p t i c a l path l e n g t h was 0.7 cm. We have u t i l i z e d C a F 2 windows which were sealed to the c e l l body by a s i l i c o n - r u b ­ ber s e a l a n t (Dow Corning C o r p o r a t i o n MI 48640) The sample holder was made from Pyrex an an i n t e g r a l p a r t o f th thermocouples which were shown to be u n r e a c t i v e f o r the range o f c o n d i t i o n s i n v e s t i g a t e d i n t h i s study. The two p a r t s o f t h e r e ­ a c t o r were clamped together and a V i t o n 0-ring was used t o provide l e a k - f r e e o p e r a t i o n . A r e p l i c a o f the lower p a r t o f the c e l l was a l s o constructed,without any windows,in order t o t e s t the e f f e c t of the s i l i c o n - r u b b e r s e a l a n t and f o r h i g h temperature investiga-* tions. Heating was provided by two h e a t i n g tapes; one f o r t h e p r e heater and the o t h e r f o r the r e a c t o r to compensate f o r thermal l o s s e s from the windows. The gas phase temperature was c o n t r o l l e d by manual adjustment o f t h e input v o l t a g e to the h e a t i n g tapes. Thermal i n s u l a t i o n was p r o v i d e d by l " - t h i c k l a y e r o f F i b e r f r a x (The Carborundum Co.). C a t a l y s t . The c a t a l y s t was prepared by impregnation o f t h e alumina (Degussa-Type C, BET surface area o f 100 m^/g, average p a r t i c l e s i z e o f 200 Â) w i t h H2PtCl6'6H20 s o l u t i o n (Ventron Corp., A l f a D i v i s i o n , MA 01923) [14, 15]. The c a t a l y t i c wafer was made by p u l v e r i z i n g the sample i n an e l e c t r i c m i l l f o r 1 min. and then p r e s s i n g i t i n a d i e under 1 t o n / i n f o r about 2 min. The wafer was then c a l c i n e d i n a i r f o r 2 h r s a t 400°C and reduced i n flowing H2 (1 cc/s) f o r 2 h r s a t 400°C. Wafers o f two d i f f e r e n t P t cont e n t s were u t i l i z e d i n t h i s study, i . e . . 1% P t and 3.2% P t on γ-Αΐ2θ3· A l l wafers made were 30 mg/cm t h i c k (^0.3 mm t h i c k n e s s and o f 1 i n diameter). H 2 chemisorption measurements (at Chevron Research Center, Richmond, CA) showed t h a t by i n c r e a s i n g the Pt content from 1 t o 3.2%, the Pt s u r f a c e area increased from 4.8% to 10.9% o f t h e sup­ port a r e a . Pt c r y s t a l l i t e s i z e measurements were conducted by TEM ( H i t a c h i E l e c t r o n Microscope type HU-125). C r y s t a l l i t e s were found i n the range o f 10 to 100A. F u r t h e r d e t a i l s o f sample p r e p a r a t i o n techniques can be found elsewhere [16]. 2

2

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

Figure lb. Reactor and catalyst support. Key: B, gas inlet; C, CaF windows; D, Silicon-rubber sealant; E gas outlet; F, catalyst holder; G, Pyrex rods; and H, thermocouples. t

t

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

82

CHEMICAL REACTION ENGINEERING

Experimental R e s u l t s & D i s c u s s i o n CO Surface S t a t e s . We have conducted a s e r i e s of experiments i n our flow r e a c t o r t o determine the a d s o r p t i o n bands of CO on Pt/y-Al2()3 and on pure γ-Αΐ2θ3 wafers. No bands of CO were found on pure A I 2 O 3 f o r 0.4% CO i n N2 up t o pure CO and f o r a temperature range o f 25°C to 250°C. Three bands o f adsorbed CO (0.4% CO i n N2 up to pure CO; 25°C to 250°C; on 1% and 3.2% Pt c a t a l y s t s ) were found on Pt/y-Al203 wafers. The f i r s t band, a r a t h e r broad band around 1800 cm"* (see F i g . 2) corresponds to a b r i d g e adsorbed s t a t e o f CO [17]· The second band, a sharp band observed a t 2060 cm" , has been assigned i n the l i t e r a t u r e to a l i n e a r l y adsorbed CO [17, 1 8 ] . The t h i r d band a t 2120 cm" , which has a l s o been observed by many other authors [ l 7 , 18], has been assigned t o a twin-type adsorbed CO molecules volving C O 2 , or f i n a l l adsorbed on adjacent Pt atoms. When the CO i n N2 stream i s r e ­ placed by pure N 2 both the bands a t 2060 cm" and 1800 cm" grad­ u a l l y decrease i n s i z e (the band a t 1800 cm" s h i f t s a l s o to lower frequencies) u n t i l they f i n a l l y disappear (see F i g . 2 ) . However, the band a t 2120 cm" decreases very s l o w l y . U s u a l l y a treatment of over 4 h r s a t 200°C i n flowing N 2 i s used i n order to remove the band a t 2120 cm" . When a CO i n a i r stream i s introduced i n the r e a c t i o n c e l l , f o r the range of c o n d i t i o n s we have examined i n t h i s study (CO i n a i r 0.4-3%, temperatures between 25-250°C), the behavior o f the sys­ tem i s a f u n c t i o n of i t s p r i o r h i s t o r y . I f the c a t a l y s t had been p r e v i o u s l y t r e a t e d i n a CO i n N 2 mixture,then the band a t 1800 cm" g r a d u a l l y disappears, t h e band a t 2060 cm" decreases i n s i z e (a broadening o f t h e 2060 cm" band i s a l s o observed) w h i l e the band at 2120 cm" i n c r e a s e s i n s i z e a p p a r e n t l y i n expense o f the bands at 2060 cm" and 1800 cm" . However, i f a f r e s h c a t a l y s t (or a c a t a l y s t t r e a t e d i n N 2 ) was used,then o n l y the bands a t 2120 cm" and 2060 cm" appear. I t i s c o n c e i v a b l e , however, that f o r lower O2 c o n c e n t r a t i o n s s i m i l a r to the ones used by C u t l i p and Kenney [12], the band a t 1800 cm" might be present. T h i s i s c u r r e n t l y under i n v e s t i g a t i o n . 1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

The O s c i l l a t o r y Behavior. We have so f a r focused our a t t e n ­ t i o n on three questions: (a) Does an o s c i l l a t o r y regime e x i s t f o r t h i s r e a c t i o n system? (b) What i s the e f f e c t o f hydrocarbon impu­ r i t i e s ? and (c) What i s the e f f e c t of c a t a l y s t d e a c t i v a t i o n on the dynamic behavior? To i n v e s t i g a t e the e x i s t e n c e o f a r e g i o n o f o s c i l l a t o r y be­ h a v i o r we have employed the f o l l o w i n g experimental procedure. The c a t a l y s t i s l e f t i n a p o s i t i v e atmosphere of N 2 f o r a minimum of 24 h r s and then t r e a t e d i n flowing N 2 a t 200°C f o r 4 h r s (or u n t i l the 2120 cm" band has disappeared). The c a t a l y s t i s subsequently t r e a t e d i n flowing a i r f o r 1 hr a t 200°C and 33 c c / s . At the end of the a i r treatment the c a t a l y s t i s switched t o 1

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

ELHADERI AND TSOTSIS

Carbon Monoxide Oxidation Reaction

Figure 2. CO bands on 3.2% Pt/y-Al O . Key: a, pure CO at room temperature; b, 3% CO in N at 170°C, c, after 5 min of step b inflowingN ; and d, after 15 min of step b inflowingN . t

s

t

B

t

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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0.4% CO i n a i r and t h e s t e a d y - s t a t e behavior i s s t u d i e d . The c a t a l y s t i s then subjected to step changes i n CO c o n c e n t r a t i o n up to 3% and the s t e a d y - s t a t e and/or o s c i l l a t o r y behavior i s s t u d i e d . A f t e r t h e end of t h i s r u n t h e above procedure i s repeated ( t r e a t ment i n N 2 , treatment i n a i r , step changes o f CO) but a t a flow r a t e of 25.6 c c / s , and subsequently a t a flow r a t e o f 16.7 c c / s . The above whole procedure i s then repeated f o r g r a d u l l a y lower gas phase temperatures. We have thus examined s i x d i f f e r e n t temperatures (200°C, 185°C, 170°C, 150°C, 130°C and 115°C), three d i f f e r ent flow r a t e s (33 c c / s , 25.6 c c / s , 16.7 c c / s ) , and a s e r i e s o f c o n c e n t r a t i o n s between 0.4% CO t o 3% CO i n a i r . A t t h e end o f t h i s run the lower p a r t o f our c e l l was replaced by i t s r e p l i c a c e l l ; the c a t a l y s t was again t r e a t e d i n N 2 and a i r a t 200°C and 33 c c / s , cooled i n the flowing N 2 a t 185°C and t h e steady s t a t e and dynamic behavior wer above study f o r the 3.2 as f o l l o w s ( d e t a i l s o f our experimental observations f o r t h e 1% Pt/y-Al203 system w i l l be presented elsewhere [ 1 6 ] ) . (a) During our experimental runs, while temperature and flow r a t e remain constant, the c a t a l y s t does not d e a c t i v a t e t o any app r e c i a b l e degree. T h i s was v e r i f i e d under steady-state and o s c i l l a t o r y c o n d i t i o n s f o r v a r y i n g time spans o f up to four days. Under steady-state c o n d i t i o n s the conversion does not change to any a p p r e c i a b l e degree, while under o s c i l l a t o r y c o n d i t i o n s both t h e maximum and minimum conversions o f the c y c l e as w e l l as the mean conversion remain constant w i t h i n 1-2%. This o b s e r v a t i o n , o f course,does not agree with p r i o r observations by Schmitz and c o workers f o r the same r e a c t i o n [ l 9 ] . We cannot e x p l a i n a t t h i s p o i n t the apparent r e s i s t a n c e o f our c a t a l y s t system t o d e a c t i v a t i o n . P o s s i b l e reasons, we c o u l d t h i n k o f , a r e the much higher r a t i o o f s u r f a c e area to geometric area o f our c a t a l y s t , the use of a Pyrex-glass r e a c t o r and our lower experimental temperatures. (b) We have found no q u a l i t a t i v e d i f f e r e n c e between the experimental observations i n the IR c e l l and i n t h e r e p l i c a c e l l . There a r e s l i g h t d i f f e r e n c e s i n steady s t a t e conversions but there are no apparent trends. O s c i l l a t i o n s have been observed f o r both systems i n the same r e g i o n o f CO c o n c e n t r a t i o n s . And while the f i n e f e a t u r e s o f the o s c i l l a t i o n s a r e sometimes d i f f e r e n t , t h e mean c y c l e conversions are i n the worst o f cases only a few percentage p o i n t s o f f . T h i s we b e l i e v e e l i m i n a t e s the p o s s i b i l i t y that the s i l i c o n - r u b b e r sealant i s the prime cause o f o s c i l l a t i o n s i n our r e a c t o r system. (c) During our runs a t 150°C and 130°C and a flow r a t e o f 33 c c / s we have replaced t h e "impure 0 2 " and "impure CO" used during our run by an " u l t r a pure" type O2 and CO s i m i l a r to t h e ones used by Carberry et a l . [ 2 j ( s e e Table I ) . We have been unable t o observe any apparent changes both during steady-state as w e l l as during the o s c i l l a t i o n s . We cannot e x p l a i n a t t h i s p o i n t the apparent d i f f e r e n c e s . Some o f the reasons that might be causing the d i f f e r e n c e s i n behavior are: ( i ) t h e much higher r a t i o o f s u r f a c e

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

7.

ELHADERI AND TSOTSIS

Carbon Monoxide Oxidation Reaction

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area t o geometric area o f our c a t a l y s t ; ( i i ) the low Pt l o a d i n g o f the c a t a l y s t i n study [ 2 ] ( 0 . 0 3 5 % Pt/y-Al203) which could r e s u l t i n nonuniform metal d i s t r i b u t i o n s a c r o s s the p e l l e t r a d i u s ; ( i i i ) the N2 o f the a i r mixture we a r e u s i n g (Carberry was u s i n g pure O 2 ) might be d i l u t i n g the impurity e f f e c t . (d) We have observed o s c i l l a t i o n s f o r a c l o s e d r e g i o n o f CO c o n c e n t r a t i o n s on the ascending p o r t i o n o f the s t e a d y - s t a t e curve f o r the m a j o r i t y o f c o n d i t i o n s we have examined. For temperatures higher than 185°C the o s c i l l a t o r y r e g i o n l i e s t o t a l l y i n s i d e the r e g i o n o f CO c o n c e n t r a t i o n o f 0.4 to 3.0%. Soft b i f u r c a t i o n s o c cur on both s i d e s o f t h e r e g i o n . However, f o r temperatures lower than 170°C t h e lower b i f u r c a t i o n p o i n t i s apparently s m a l l e r than 0.4% CO (0.3% CO i s the lower l i m i t o f CO c o n c e n t r a t i o n s we can e s t a b l i s h i n our experimental system f o r the above range o f f l o w r a t e s without v i o l a t i n c e n t r a t i o n i n c r e a s e s , th a maximum. We have not observed any o s c i l l a t i o n s that we c o u l d s a t i s f a c t o r i l y c h a r a c t e r i z e as o f a smooth s i n g l e peak type. A l though we have observed s i n g l e peak type o s c i l l a t i o n s a t low temperatures and flow r a t e s (see F i g . 3a), the m a j o r i t y o f t h e o s c i l l a t i o n s a r e e i t h e r o f the multi-peak type ( F i g . 3b) or spikes or o f completely a p e r i o d i c type ( F i g 4a, 4 b ) . During the o s c i l l a t i o n s we have monitored the IR absorption of the 2060 cm" and 2120 cm" bands. As can be seen from F i g s . 3 and 4,the band a t 2060 cm" o s c i l l a t e s a p p a r e n t l y a t 180° out o f phase w i t h the gas phase c o n c e n t r a t i o n . The c a t a l y s t o s c i l l a t e s between a s t a t e r i c h i n l i n e a r l y adsorbed CO and v i r t u a l l y f r e e of CO. However, r e p e t i t i v e scans d u r i n g o s c i l l a t i o n s o f l a r g e r p e r i o d s , have shown that t h e band a t 2060 cm"l i s a r a t h e r broad and extends between 2060 cm" and 2090 cm" . What i s i n t e r e s t i n g , however, i s that the band a t 2120 cm" , which remains q u i t e sharp, does not seem to o s c i l l a t e a t a l l . Only a t low temperatures (the 115 C run), f o r the v e r y l a r g e peak o s c i l l a t i o n s , d i d the band a t 2120 cm" e x h i b i t any o s c i l l a t o r y behavior. However, t h e peak t o peak amplitude was small and we tend t o b e l i e v e t h a t the o s c i l l a t i o n s might' be the r e s u l t o f the s u p e r p o s i t i o n o f t h e o s c i l l a t i n g 2060 cm" broad band. 1

1

1

1

1

1

1

1

Conclusions Reaction r a t e o s c i l l a t i o n s have been observed d u r i n g t h e CO o x i d a t i o n r e a c t i o n over Pt/Y-Al203 i n an a l l Pyrex g l a s s f l o w r e a c t o r . During our experimental study we have c a r e f u l l y t r i e d t o e l i m i n a t e a l l known sources o f i m p u r i t i e s and o t h e r p o s s i b l e extraneous i n t e r f e r e n c e s caused by temperature and f l o w c o n t r o l l e r s and by h i g h volume r e c y c l e streams. The s u r f a c e s t a t e o f t h e c a t a l y s t has been monitored by the technique o f IR t r a n s m i s s i o n spectroscopy. During o s c i l l a t i o n s o n l y t h e band a t 2060 cm" has been found to o s c i l l a t e . 1

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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ywww 0.1% C 0

2

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TIME — > ·

—

, (α)

52 % T

65% Τ

t

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TIME ·

2

87% Τ

(b)

1

Figure 3. CO concentration and adsorbed CO (2060 cm' ) oscillations during the oxidation of CO on 32% Pt/y-Al O catalyst. Key: a, T 115°C, flow rate 33 cc/s, and 0.4% CO in air; and b, T 150°C, flow rate 33 mL/s, and 2.6% CO in air. t

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s

e

0

.

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3

I

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O . l f and low or moderate values o f Pe. The r e a c t i o n mixture i s able t o r e a c t , i g n i t i o n occurs a t the r e a c t o r e x i t and a r e a c t i o n f r o n t moves toward r e a c t o r i n l e t . The r e s u l t i n g steady s t a t e i s a t the r e a c t o r i n l e t and a strong pre­ h e a t i n g o f the i n l e t gas occurs. The t r a n s i e n t o p e r a t i o n i s r e f e r r e d t o as "creeping p r o f i l e s " and was e x t e n s i v e l y s t u d i e d by Amundson [4-6]. Experimentally observed i n [1, 1 5 ] . (4) unique steady s t a t e (τ < τ, ω « ν ) . C h a r a c t e r i s t i c f o r high v a l u e s o f Da (Da > O . l f and high values o f Pe. Similar to (3) however, the steady s t a t e stays i n the middle o f the bed. Common i n o p e r a t i o n o f i n d u s t r i a l packed a d i a b a t i c r e a c t o r s .

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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(5) unique steady s t a t e (τ > τ, ω < ν ) . Q u a s i i so thermal opera­ t i o n . A l l the above mentioned operations of the bed were e x p e r i ­ mentally observed and the experiments are i n q u a l i t a t i v e agreement w i t h theory 114]. The "creeping p r o f i l e s " are represented by a propagating f r o n t moving w i t h constant v e l o c i t y and without a change of i t s geome­ t r i c a l form [4-6]. Frank-Kameneckii [16] i n d i c a t e d that i n an i n f i n i t e r e a c t o r the propagating r e a c t i o n zone can be stopped a t an a r b i t r a r y p o s i t i o n f o r c e r t a i n v a l u e s of i n l e t c o n d i t i o n s . However, s i n c e the bed i s of i n f i n i t e l e n g t h a simple t r a n s l a ­ t i o n of the coordinate i n d i c a t e s that a l l these p r o f i l e s are identical. For an a d i a b a t i c bed having a f i n i t e l e n g t h t h i s phenomenon does not e x i s t , i . e . , f o r a given v a l u e of i n l e t c o n d i t i o n s only one s i n g l e p r o f i l e occurs. P u s z y n s k i [15] obser­ ved experimentally that v a l u e s of i n l e t c o n d i t i o n and i t behaves almost l i k e a "standing wave". However, a f t e r a long time, the r e a c t i o n zone s t a r t s moving. Nonadiabatic case The c l a s s i f i c a t i o n of a d i a b a t i c o p e r a t i o n presented above may be a l s o used f o r nonadiabatic r e a c t o r s , however, new pheno­ mena were observed. Numerical c a l c u l a t i o n and experimental observations r e v e a l e d t h a t the "constant p a t t e r n p r o f i l e s " do not e x i s t , the shape of a propagating f r o n t changes. In problems a s s o c i a t e d w i t h a steep temperature f r o n t , r e g a r d l e s s of the r e a c t o r l e n g t h , the a x i a l d i s p e r s i o n e f f e c t s must not be n e g l e c t e d . Experiments as w e l l as numerical s i m u l a t i o n pointed out t h a t m u l t i p l i c i t y can e x i s t f o r v e r y long bed (Pe > 1000) [11]. For c e r t a i n o p e r a t i o n a l c o n d i t i o n s and p h y s i c a l p r o p e r t i e s of the r e a c t i n g system ( a c t i v a t i o n energy and heat of r e a c t i o n ) a number of d i f f e r e n t m u l t i p l i c i t y regimes may e x i s t . Three s t a b l e steady s t a t e s i n the bed were t h e o r e t i c a l l y p r e d i c t e d [18] and experimentally observed [13]. For a h i g h l y a c t i v e c a t a l y s t , the t h e o r e t i c a l l y p r e d i c t e d t h i r d steady s t a t e occurs near the r e a c t o r e x i t . A systematic experimental search d i d not f i n d i t [20]. A c a l c u l a t i o n w i t h more r e a l i s t i c boundary c o n d i t i o n s [19] r e s u l t e d i n i t s e l i m i n a t i o n . However, f o r a c a t a l y s t of lower a c t i v i t y the t h i r d steady s t a t e was experimentally l o c a t e d [13]. For a s h o r t nonadiabatic bed ( e q u i v a l e n t to case (1)) m u l t i p l i c i t y was experimentally found and t r a n s i e n t o p e r a t i o n i n v e s t i g a t e d [20]. T r a n s i t i o n from the q u a s i i s o t h e r m a l to the d i f f u s i o n regime r e s u l t e d i n an i g n i t i o n process at the r e a c t o r o u t l e t . The r e a c t i o n f r o n t was i g n i t e d at the r e a c t o r o u t l e t and moved upstream. The hot spot temperature increased toward the r e a c t o r inlet. Decreasing the i n l e t temperature the r e a c t i o n f r o n t moves downstream and disappears i n the middle p a r t of the r e a c t o r . Experiments and numerical s i m u l a t i o n i n d i c a t e d that i n long non­ a d i a b a t i c r e a c t o r the i g n i t i o n process does not s t a r t a t the r e a c t o r o u t l e t but i n s i d e the bed [21].

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

8.

HLAVACEK E T A L .

Adiabatic & Nonadiabatic Fixed-Bed Reactors

93

I n v e s t i g a t i o n o f the propagating f r o n t s f o r nonadiabatic c o n d i t i o n s shown that the f r o n t v e l o c i t y i s not constant and depends on the p o s i t i o n of the f r o n t i n the r e a c t o r 115]. For a downstream propagating f r o n t , the v e l o c i t y , hot spot temperature and e x i t conversion e x h i b i t e d an o s c i l l a t o r y character 17]· For a nonadiabatic operation of a packed bed m u l t i p l i c i t y of propagating f r o n t s has been observed [ 7 ] . F i g s . 1 and 2 d i s p l a y m u l t i p l e f r o n t s . The s t r a t e g y of a d j u s t i n g a p a r t i c u l a r f r o n t i s reported i n these f i g u r e s i n the upper right-hand p o r t i o n o f the drawings. Obviously, f o r the i d e n t i c a l i n l e t c o n d i t i o n s a downstream or an upstream propagating f r o n t may e x i s t . A d e t a i l e d experimental study of o p e r a t i n g c o n d i t i o n s i n a nonadiabatic f i x e d bed r e a c t o r revealed that f o r c e r t a i n i n l e t cond i t i o n s o s c i l l a t o r y or e r r a t i c behavior o f temperature p r o f i l e s can be observed [23]. T couple temperature readin monitored. The r e s u l t s o f measurements are reported i n F i g . 3. From the r e s u l t s measured, i t i s obvious that a temperature f r o n t a r i s e s i n the i n l e t p a r t o f the r e a c t o r , moves downstream and disappears i n the middle p a r t of the r e a c t o r . The l o c a l temperat u r e readings i n d i c a t e t h a t a very complicated dynamic process occurs. For a case that one s t a b l e steady s t a t e e x i s t s t r a n s i e n t temperature p r o f i l e s c a l c u l a t e d agree s a t i s f a c t o r i l y with the measurements. For a case o f three steady s t a t e s the s i t u a t i o n i s q u i t e complicated. The model used d e s c r i b e s propagation o f the f r o n t s however, apparently cannot d e s c r i b e f r o n t m u l t i p l i c i t y . A d e t a i l e d c a l c u l a t i o n o f the two-dimensional steady s t a t e equations i n c l u d i n g a l s o the r a d i a l d i s p e r s i o n terms i n d i c a t e s that the onedimensional model i s a very rough approximation f o r the " d i f f u s i o n " regime. We expect that dynamic c a l c u l a t i o n s w i t h the one-phase two-dimensional model could e x p l a i n m u l t i p l i c i t y of the f r o n t s . The s i t u a t i o n e x h i b i t i n g f i v e steady s t a t e s i s s i m i l a r t o t h a t f o r three steady s t a t e s . R e s u l t s of the steady s t a t e s i m u l a t i o n revealed that the t h i r d s t a b l e steady s t a t e i s l o c a t e d a t the r e a c t o r o u t l e t [22]. C a l c u l a t i o n o f the r e a c t o r with an a f t e r s e c t i o n packed by i n e r t m a t e r i a l i n d i c a t e d that f i v e steady s t a t e s are e l i m i n a t e d . [15]. For the same type o f c a t a l y s t we have observed i n a r e c i r c u l a t i o n l a b o r a t o r y r e a c t o r m u l t i p l i c i t y , p e r i o d i c and c h a o t i c behavior. Unfortunately, so f a r we are not able t o suggest such a r e a c t i o n r a t e expression which would be capable o f p r e d i c t i n g a l l three regimes [ 8 ] . However, there i s a number o f complex k i n e t i c expressions which can d e s c r i b e p e r i o d i c a c t i v i t y . One can expect that such k i n e t i c expressions combined with heat and mass balances of a tubular nonadiabatic r e a c t o r may g i v e r i s e t o o s c i l l a t o r y behavior. D e t a i l e d c a l c u l a t i o n s o f o s c i l l a t o r y behavior of s i n g u l a r l y perturbed p a r a b o l i c systems d e s c r i b i n g heat and mass t r a n s f e r and exothermic r e a c t i o n are apparently beyond, the c a p a b i l i t y o f both standard current computers and mathematical sof tware·

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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x(mH0 Figure 1.

2

Temperature profiles for an upstream moving wave. Conditions: G 9.26 χ 10*kg/m s;T = 90°C;and Y° = 3.15% CO.

0

=

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0

Li

1 0

1

1 iO

1

co

1

.

20

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30

40

,

\ 50

•

x(mH0 Figure 2.

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60 2

Temperature profiles for a downstream moving wave. Conditions: G 9.26 χ W* kg/mh; T = 90°C; and Y° = 3.15%.

0

0

co

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

=

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982. 1

2

10

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.

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14

16

0

18

20

_L

0

22 T(h)

Figure 3. Recording of oscillations of local temperature. Conditions: T = 145°C; 1 % CO; G = 1.852 X 1Ô kg/m S; and position of the thermocouple at I — 0.2 m.

140

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200-

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Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.

Padberg G., Wicke Ε., Chem. Engng. S c i . 1967, 22, 1035. F i e g u t h P., Wicke Ε., Chem. Engng. Techn. 1971, 43, 604. Vortmeyer D., J a h n e l W., Chem. Engng. S c i . 1972, 27, 1485. Chem. Engng. Techn. 1971, 43, 461. Rhee H. K., Amundson N. R., Ind. Engng. Chem. Fund,1974, 13,1. Rhee Η. Κ., Lewis R. P. Amundson, N. R. Ind. Engng. Chem. Fund. 1973, 28, 607. Rhee H. K., Foley D., Amundson N. R., Chem. Engng. S c i . 1973, 28, 607. Puszynski J . , Hlavacek V., Chem. Engng. Sci. 1980, 35, 1769. Rathousky J . , Hlavacek V., Jour. Chem. Phys. 1981, 75, 749. Hlavacek V., Rathousky J . , Chem. Engng. Sci. 1982, 37, 375. Eigenberger G. and Lubeck B., Chem. Eng Carey G. F. and F i n l a y s o n Β. Α., Chem. Eng. Sci., 1975, 30, 587. Hlavacek V. and Votruba J . , Adv. Chem. Ser. No. 133, 1974, pg. 545. Votruba J . , Ph.D. T h e s i s (Prague, 1973). P u s z y n s k i , J., Ph.D. Thesis (Prague, 1981). Franck-Kameneckij D. Α., D i f f u s i o n and Heat T r a n s f e r in Chemi­ cal K i n e t i c s , 2nd Ed. Plenum P r e s s , New York, 1969. Puszynski J . , S n i t a D., Hlavacek V. and Hofmann Η., Chem. Eng. S c i . 1981, 36, 1605. Hlavacek F., Hofman Η., Chem. Eng. Sci., 1971, 26, 1629. Hlavacek V., Holodniok Μ., Sinkule J . and Kubicek Μ., Chem. Eng. Commun., 1979, 3, 451. Puszynski J . , Hlavacek F., Chem. Eng. Sci., in p r e s s . Puszynski J . , S n i t a D., Hlavacek V., Chem. Eng. Sci., i n p r e s s . K a l t h o f f O., Vortmeyer D., Chem. Eng. Sci. 1980, 35, 1637. Rathousky J . , Puszynski J., Hlavacek J . , Z e i t . N a t u r f o r s c h . 1980, 35a, 1238.

R E C E I V E D April 27, 1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

9 Forced Composition Cycling Experiments in a Fixed-Bed Ammonia Synthesis Reactor 1

A. K. JAIN , P. L . SILVESTON, and R. R. HUDGINS University of Waterloo, Department of Chemical Engineering, Waterloo, Ontario, Canada

The e f f e c t o time-average rat plored i n the region o f i n t e g r a l conversion i n a l a b o r a t o r y f i x e d bed ammonia synthesis r e a c t o r . Experiments were c a r r i e d out at 400°C and 2.38 MPa over 40/50 US mesh c a t a l y s t p a r t i c l e s . The e f f e c t of v a r i o u s c y c l i n g parameters, such as c y c l e p e r i o d , c y c l e - s p l i t , and the mean composition, on the improvement i n time-average rate over the steady state were i n v e s t i g a t e d . Improvement by c y c l i n g was in the range o f 30 to 50%. T h i s was almost i d e n t i c a l to the improvement achieved i n experiments performed i n a l a b oratory recycle reactor. This f i n d i n g shows that measurements made by our research group and others on d i f f e r e n t i a l o r Berty-type r e a c t o r s are a r e l i a b l e guide to the performance o f full-scale equipment. Maximum improvement occurred when the feed mixture was d e f i c i e n t i n n i t r o g e n . Average bed temperature increased during c y c l i n g , although there was no s i g n i f i c a n t change i n the maximum temperature. The temperature d i s t r i b u t i o n was much more uniform i n p e r i o d i c than i n steadystate o p e r a t i o n . Consequently, c y c l i n g appears t o be a technique f o r avoiding hot-spot problems i n fixed-bed exothermic r e a c t o r s .

1

Current address: Process Research Laboratories, Petrocanada, Calgary, Alberta, Canada.

0097-6156/82/0196-0097$06.00/0 © 1982 American Chemical Society In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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The possibility of improving selectivity or polymer molecular weight d i s t r i b u t i o n by p e r i o d i c a l l y changing the comp o s i t i o n of the r e a c t o r feed was pointed out by B a i l e y and Horn and co-workers on one hand U,2,2) and by Douglas and Rippen (4,5) and others (6) i n the l a t e I960 s and e a r l y 1970's. Experimental investigations i n the following years 0»8) confirmed the p r e d i c t i o n s of these t h e o r e t i c a l s t u d i e s . In a series of c o n t r i b u t i o n s beginning i n 1973 (9,10,11), our research group demonstrated e x p e r i m e n t a l l y that periodic switching of feed composition also can s u b s t a n t i a l l y increase catalyst activity. C u t l i p (12) has reported s i m i l a r r e s u l t s . Reactor performance under p e r i o d i c o p e r a t i o n was found to depend on c y c l i n g frequency and amplitude as well as upon the usual v a r i a b l e s such as feed composition, pressure and temperature. The frequency dependenc a c t i v i t y rose markedly frequency band suggesting a resonance phenomenon. The Waterloo work was performed with o x i d a t i o n r e a c t i o n s and with c a t a l y s t s which operated on redox mechanisms. Laboratory r e a c t o r s were d i f f e r e n t i a l and uniform square waves i n feed composition were used to force p e r i o d i c o p e r a t i o n . 1

Research d i s c u s s e d i n t h i s paper continues our concern with the use of p e r i o d i c o p e r a t i o n to increase catalyst a c t i v i t y . Questions addressed are 1) can p e r i o d i c o p e r a t i o n improve a c t i v i t y i n a "hydrogénation" r e a c t i o n which does not appear to proceed v i a a redox mechanism? 2) w i l l "resonance" e f f e c t s be observed? 3) w i l l non-uniform, but s t i l l p e r i o d i c , c o n c e n t r a t i o n square waves be more e f f e c t i v e than uniform square waves? and 4) w i l l the behavior under p e r i o d i c o p e r a t i o n of a f i x e d bed r e a c t o r with r e l a t i v e l y large conversion d i f f e r s i g n i f i c a n t l y from the behavior i n a d i f f e r e n t i a l r e a c t o r ? Because hot spot l o c a t i o n and magnitude depend on feed conditions, p e r i o d i c o p e r a t i o n should cause the hot spot to wander and should d i m i n i s h i t s magnitude. T h i s s u p p o s i t i o n was examined e x p e r i m e n t a l l y i n our study. Synthesis of ammonia over a commercial i r o n c a t a l y s t was chosen as the t e s t system because of i t s i n d u s t r i a l importance and because of the thorough experimental study i t has r e c e i v e d . I t was thought that the knowledge accumulated f o r t h i s r e a c t i o n could be u s e f u l f o r i n t e r p r e t i n g r e s u l t s o b t a i n e d . Figure I shows a schematic of the experimental system used. Research grade Ife and H 2 , supplied from cylinders pressured to 41 MPa, were p u r i f i e d f u r t h e r by d r y i n g over 14-X sieves and lowering oxygen to less than 1 ppm through a Matheson Deox Unit followed by D r i e r i t e tubes. Flows were metered by mass flow meters and p o s i t i v e l y c o n t r o l l e d as shown i n F i g u r e 2. Composition cycling was accomplished by timer-driven, solenoid three-way valves which switched the flow between e i t h e r of two branches, each one set at d i f f e r e n t flow r e s i s t a n c e s through micrometering v a l v e s (Figure 2 ) . Timers were ganged to permit the two parts of the cycle to have d i f f e r e n t l e n g t h s .

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

9.

JAIN E T A L .

Forced Composition Cycling Experiments

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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Non-uniform square waves were generated i n t h i s way. Nonu n i f o r m i t y i s measured by a c y c l e s p l i t r a t i o defined as the r a t i o of the r i c h p o r t i o n of the c y c l e to the c y c l e p e r i o d . Flow r e s i s t a n c e s were set corresponding to the c y c l e s p l i t r a t i o so that the average tfe and c o n c e n t r a t i o n i n a c y c l e remained the same even though the c y c l e s p l i t r a t i o changed. In the experiments discussed i n the paper, the c y c l e s p l i t r a t i o ranged between 0.2 and 0.85; the c y c l e period v a r i e d from 1 to 60 minutes. The complexity of the flow system i n Figure 2 r e f l e c t s the d i f f i c u l t y i n handling the d i s s i m i l a r v i s c o s i t i e s o f the Ifc and N/ . However, the f i n a l design d i d provide almost p e r f e c t c o n c e n t r a t i o n square-waves ( 1 3 ) . Although two r e a c t o r s are shown i n Figure 1, they were not used s i m u l t a n e o u s l y . The r e a c t o r shown i n the center was the fixed bed r e a c t o r whic contribution. It consiste s t e e l tube packed with 40/50 mesh c a t a l y s t (0.3 ram average p a r t i c l e d i a m e t e r ) . The r e a c t o r was heated by a nichrome wire c o i l and was well i n s u l a t e d . The c o i l spacing was adjusted and was packed i n i n s u l a t i o n with the intent o f making the r e a c t o r crudely adiabatic. A v a r i a c c o n t r o l l e d heater on the r e a c t o r i n l e t and a thermocouple sensor kept the feed to the reactor at the nominal r e a c t i o n (or feed i n l e t ) temperature of 400°C. The tube of the fixed-bed, r e a c t o r was f i t t e d with 12 thermocouples to record the a x i a l temperature p r o f i l e i n the bed (Figure 1). The second reactor o f the Berty, r e c y c l e type i s shown i n the upper l e f t center of Figure 1. I t was also used to explore the e f f e c t of p e r i o d i c operation. Ammonia c o n c e n t r a t i o n l e a v i n g e i t h e r reactor was measured by a Beckman i a f r a - r e d spectrometer at a 1030 cm"" wave number. The c a t a l y s t used i n t h i s study was triply-promoted K^O, CaO and A1 0^ , i r o n supplied by United C a t a l y s t Inc. L o u i s v i l l e , Kentucky, U.S.A. under the trade number "C 73-1-01". P o r o s i t y i s about 0.45 and average pore radius about 24 nm. To a c t i v a t e the c a t a l y s t , a 60-h r e d u c t i o n at 440°C i n pure hydrogen at a space v e l o c i t y of 1500 1/h was employed. By the end o f t h i s p e r i o d , the a c t i v i t y had become constant. Long-term c a t a l y s t a c t i v i t y was checked f r e q u e n t l y and, over the course o f the study, remained constant. The percentage v a r i a t i o n among runs made under i d e n t i c a l c o n d i t i o n s was w i t h i n 4%. Equipment l i m i t a t i o n s d i c t a t e d operating both reactors at 2.38 MPa, more than an order o f magnitude below pressures encountered i n commercial u n i t s . A few experiments performed at a t o t a l pressure 50% greater confirmed the r e s u l t s which now w i l l be reported. These experiments suggest composition c y c l i n g w i l l improve performance at pressures found i n commercial u n i t s . 1

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Forced Composition C y c l i n g R e s u l t s P e r i o d i c composition changes can s u b s t a n t i a l l y increase the activity o f the triply-promoted iron catalyst i n NH3 synthesis at 400°C and 2.38 MPa. This i s evident from Figure 3 In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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which p l o t s the experimentally measured space-mean, time-average rate of NH3 synthesis f o r a c y c l e s p l i t of 0.4 and a H mole f r a c t i o n i n the feed of 0.75. Proper choice of the period can provide about a 25% increase i n e f f e c t i v e c a t a l y s t a c t i v i t y over what can be achieved at steady state f o r a 0.75 H2 mole fraction. Figure 3 suggests the existence of a rate of r e a c t i o n "resonance". Time average rate goes through a maximum as the period decrease and f i n a l l y drops sharply. Although a s i m i l a r behavior was seen with SO o x i d a t i o n over a vanadia c a t a l y s t (9) and with CO o x i d a t i o n over both vanadia (10,11) and n i c k e l oxide (14), i t i s not c e r t a i n that the same phenomena are involved i n NH3 synthesis over i r o n . The measurement showing a decrease i n rate was made at a 1 minute c y c l e period where c a l c u l a t i o n s (13) suggest the amplitude o by mixing upstream o chemical phenomena, may be the source of the rate maximum. With SOz and CO o x i d a t i o n , the rate maxima occurred at such periods that mixing could not be important. Even i f mixing i s not the explanation of the maximum i n Figure 3, as period i s reduced f u r t h e r below one minute, mixing w i l l e v e n t u a l l y damp out the input concentration square wave so that the time-average rate must f a l l back i n t o the steady state. The steady state rate i s experimentally measured even though data points are not shown i n Figure 3. Since the r e a c t o r is i n t e g r a l , the rate shown i s a l s o a space-mean v a l u e . As the period i n c r e a s e s , the time-average synthesis rate falls towards the space-mean, quasi steady state value as expected. At large periods, the steady state i s approached i n each p o r t i o n of the c y c l e . The quasi-steady s t a t e line in Figure 3 was calculated from steady-state measurements. Curvature of the rate vs composition r e l a t i o n causes the quasi steady-state rate to be well below the steady-state r e a c t o r performance. This emphasizes the very large e f f e c t of c y c l i n g frequency on the time average synthesis r a t e . Improvement over steady-state c a t a l y s t a c t i v i t y was found i n a l l of the 64 f i x e d bed experiments performed. I f maxima i n the rate vs period curves (such as Figure 3) are considered i n each experiment and p l o t t e d against composition as the % mole f r a c t i o n i n the feed, the upper boundary of the double hatched area i n Figure 4 i s obtained. The c i r c l e s represent these maxima. They do not represent the same c y c l e s p l i t r a t i o s or periods, but they do d e f i n e an upper bound f o r space-mean, time-average rates obtainable by forced composition c y c l i n g f o r the experimental c o n d i t i o n s employed. The open c i r c l e s i n the bottom curve show the space average steady s t a t e synthesis rates. These points define the upper bound of space-mean rates obtainable through steady state o p e r a t i o n . What i s so s t r i k i n g about Figure 3 i s that i t demonstrates that p e r i o d i c operation can achieve c a t a l y s t a c t i v i t y or r e a c t o r performances which cannot be obtained by even optimal steady-state o p e r a t i o n . Of course, c y c l e s p l i t and period must be properly chosen. z

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In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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Forced Composition Cycling Experiments

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Figure 4. Steady-state and time-average cycling rate envelopes vs. feed com­ position. Conditions: Τ = 400°C; Ρ = 2.38 MPa; and particle diam = 0.3 mm. Key: -Ο-, steady-state; and —·—, cycling.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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The r e s u l t s i l l u s t r a t e d by Figures 3 and 4 resemble those obtained i n the Berty r e c y c l e r e a c t o r under s i m i l a r c o n d i t i o n s . The space-mean, time average r a t e s f o r the fixed-bed reactor were only about 50% of those measured i n the Berty reactor, because, of course the former r e a c t o r achieved conversions high enough for the back reaction to become important. The significance of these observations i s that 1) CSTR and d i f f e r e n t i a l r e a c t o r s , widely used f o r l a b o r a t o r y s t u d i e s , seem to r e f l e c t performance improvements obtainable with fixed-bed, integral reactor which resemble commercial units, and 2) improvement from p e r i o d i c o p e r a t i o n are s t i l l observed even when reverse r e a c t i o n s become important. Influence

of C y c l i n g

Variables

Besides the very evident i n Figure 3, the Ife mole f r a c t i o n i n the r e a c t o r feed and the c y c l e s p l i t r a t i o are a l s o important. T h i s i s evident from the curvature of the upper bound i n Figure 4. This figure i n d i c a t e s the improvement p o s s i b l e at the s t o i c h i o m e t r i c H2 mole f r a c t i o n i s about 30%, but r i s e s to 40% when the mole f r a c t i o n i s 0.5 and as high as 46% when i t i s 0.9. The maximum i n the steady-state rate at the s t o i c h i o m e t r i c H2 mole f r a c t i o n (0.75) i n d i c a t e s that synthesis rate is c o n t r o l l e d by a surface rate process, not H2 or Nfc chemisorption (13). Greater increase i n c a t a l y s t a c t i v i t y at higher H2 mole fractions suggests that hydrogen i s involved i n the rate c o n t r o l l i n g step. The improvement over the steady state rate is also s e n s i t i v e to the c y c l e s p l i t . When c y c l i n g with a period of 8 min. between pure and a lfe-N2 mixture, such that the mean Ife mole f r a c t i o n was always 0.5, a c y c l e s p l i t of 0.2 gave a time-average rate about 20% higher than steady s t a t e . At a c y c l e s p l i t of 0.4, t h i s maximum f e l l to about 15%. Also, as the c y c l e period increased, the time-average r a t e f e l l more r a p i d l y for the higher c y c l e s p l i t v a l u e s . The c y c l e s p l i t r e s u l t s a l s o suggests Ife i s involved i n the rate c o n t r o l l i n g step. Interpretation We have speculated i n other i n v e s t i g a t i o n s of c y c l i n g (14) that p e r i o d i c changes i n gas phase composition cause changes i n c o - o r d i n a t i o n of the a c t i v e c a t i o n s i n the c a t a l y s t at the g a s - s o l i d i n t e r f a c e which propagate inward towards the c a t a l y s t support i n t e r f a c e . Thus, we have a t t r i b u t e d improvement due to p e r i o d i c operation to storage of a r e a c t a n t , oxygen, i n the catalyst resulting i n more of the catalyst (by weight) participating i n the r e a c t i o n . This seems to be what i s happening i n NH3 synthesis over i r o n . Transient experiments point to the formation of i r o n n i t r i d e when the i r o n c a t a l y s t i s exposed to n i t r o g e n (13). The existence of n i t r i d e s i n the Nlfc

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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synthesis system i s claimed, indeed, by many i n v e s t i g a t o r s (15-19). The ammonia precursors must form then from Ife r e d u c t i o n of the n i t r i d e . N i t r i d e formation must be quite r a p i d i f the highest improvement due to p e r i o d i c o p e r a t i o n i s found i n the N z - d e f i c i e n t r e g i o n . P o s s i b l y Hz r e d u c t i o n o f the n i t r i d e i s rate l i m i t i n g . Hot Spot and Bed Temperature

Profile

The s u b s t a n t i a l change i n the temperature p r o f i l e that accompanies forced c o n c e n t r a t i o n c y c l i n g i s shown i n Figure 5. The dark c i r c l e s represent the steady state temperature p r o f i l e i n the f i x e d bed. The open c i r c l e s represent mean behavior f o r a c y c l e - p e r i o d of 20 minutes. The hatched region i n d i c a t e s the temperature f l u c t u a t i o n temperature i s increase operation and i s s h i f t e d downstream slightly. This i s remarkable because the time-average rate of r e a c t i o n i s about 25% g r e a t e r . The temperature p r o f i l e i n p e r i o d i c o p e r a t i o n i s almost i d e n t i c a l to the steady-state p r o f i l e upstream from the maximum, but downstream i t i s more uniform than the l a t t e r . The case shown i n Figure 5 i s a "woest case" v a l u e , since the length of the period causes l o c a l temperatures to f l u c t u a t e w i t h i n the region shown i n the f i g u r e . At shorter c y c l e - p e r i o d s ( f o r example, at 6 minutes), the temperature profile does not f l u c t u a t e with time because o f the thermal i n e r t i a o f the bed r e l a t i v e to the speed o f change o f c o n c e n t r a t i o n i n the bed. Furthermore, as the c y c l e - p e r i o d i s reduced to 6 minutes, the temperature p r o f i l e downstream from the maximum increases and the bed temperature becomes more uniform. Equating the maximum temperature i n Figure 5 with a hot spot, i t seems reasonable that under c e r t a i n c o n d i t i o n s , p e r i o d i c o p e r a t i o n o f f e r s a method o f avoiding or reducing hot-spot problems i n fixed-bed, exothermic r e a c t o r s . Our expectations at the outset o f t h i s study seem confirmed. Industrial Application A s e r i e s o f runs was done at a t o t a l pressure of 3.76 MPa (58% increase i n pressure). In general, substantial improvements were found, p a r t i c u l a r l y at the longer periods (16-20 min). For reasons that are not understood, an increase i n t o t a l pressure appears to improve the time-average r a t e . Thus, for periodic o p e r a t i o n at 20-30 MPa, the range o f i n d u s t r i a l o p e r a t i o n , might also improve the r a t e . Our demonstration that forced composition c y c l i n g o f Nt% synthesis over an i r o n c a t a l y s t d r a m a t i c a l l y increases c a t a l y s t a c t i v i t y and smooths the temperature p r o f i l e i n f i x e d c a t a l y s t beds seems to c a l l f o r an examination o f the a p p l i c a t i o n o f the approach to f u l l - s c a l e r e a c t o r s . There i s a major process design h u r d l e which must be overcome, however. Industrial r e a c t o r s give r e l a t i v e l y low conversions o f NH3 per pass, so In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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4301

Ο

BED LENGTH , 4 / L Figure 5. Temperature profiles in thefixed-bedreactor. Conditions: time-average H mol jr. = 0.5; and cycle split = 0.2. Key: · , steady-state; and Ο, τ = 20 (exp. no. 405). t

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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that the reactant gases must be r e c y c l e d a f t e r NH3 i s s t r i p p e d out. I f a synthesis reactor i s to be operated p e r i o d i c a l l y , the phase lags i n the r e c y c l e streams must equal or be an even m u l t i p l e of lags or hold-up i n the r e a c t o r . This may be d i f f i c u l t to achieve i n p r a c t i c e . Acknowledgement s The authors are g r a t e f u l f o r support i n the form o f an equipment grant f o r the Berty reactor from the N a t i o n a l Science and Engineering Research C o u n c i l o f Canada, as w e l l as f o r operating funds from the same source. Mr. J a i n was supported by the U n i v e r s i t y o f Waterloo through a Dean o f Engineering Scholarship. C a t a l y s t was k i n d l y provided by United C a t a l y s t Inc., L o u i s v i l l e , Kentucky Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

15. 16) 17) 18) 19)

Horn, F.J.M. & L i n , R.C., I&EC Proc. Pes. Dev. 1967, j>, 21. B a i l e y , J.E. and Horn, F.J.M., AIChEJ 1971, 17, 550. B a i l e y , J.E. and Horn, F.J.M. & L i n , R.C., AIChEJ 1971, Π_, 818. Douglas, J.M., & Rippen, D.W.T., Chem. Eng. S c i . 1966, 21, 305. Douglas, J.M., I&EC Proc. Pes. Dev. 1967, 6^, 43. C o d e l l , R.B. & Engel, A.J., AIChEJ 1971, JL7, 220. Renken, Α., Helmrich, H. & Schuegerl, Κ., Chem. Ingr., Techn. 1974, 46, 647. B i l i m o r i a , M.R. and B a i l e y , J.E., Proc. 5th I n t e r n . Symp. Chem. Reac. Eng., Houston, Texas, 1977, p.526,. Unni, M.P., Hudgins, R.R. & S i l v e s t o n , P.L., Can. J . Chem. Eng. 1973, 51, 623. Abdul-Kareem, H.K., S i l v e s t o n , P.L. & Hudgins, R.R., Chem. Eng. S c i . 1980, j[5, 273. Jain, A.K., Abdul-Kareem, H.K, Hudgins, R.R. and S i l v e s t o n , P.L., Chem. Eng. S c i . 1980, 35, 273. C u t l i p , M.B., AIChEJ 1979, 25, 502. Jain, A.K., Ph.D. T h e s i s , University o f Waterloo, Waterloo, O n t a r i o , Canada, 1981. Abdul-Kareem, H.K., S i l v e s t o n , P.L. and Hudgins, R.R. Proc. 2nd World Cong. Chem. Eng., Montreal, 1981, Paper 11.9.2 H o r i u t i , J . & K i t a , H., J . Res. I n s t . C a t a l . , Hokkaido Univ. 1956, 4, 132. Dûmesic, J.Α., Topsoe, H., Kharamouma, S. & Boudart, Μ., J. Catal. 1975, 37, 503. Duesic, J.Α., Topsoe, H. & Boudart, M., J . C a t a l . 1975, 37, 513 (1975). Bozso, F., E r t l , G. & Weiss, M., J . C a t a l . 1977, 50, 519. Grabke, H.J., Mat. S c i . Eng. 1980, 42, 91.

R E C E I V E D April 27, 1982. In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

10 Dynamic Behavior of an Industrial Scale FixedBed Catalytic Reactor L . S. KERSHENBAUM and F. LOPEZ-ISUNZA

1

Imperial College of Science and Technology, Department of Chemical Engineering and Chemical Technology, London SW7, England

T r a n s i e n t and stead ature measurement air o x i d a t i o n o f o-xylene t o p h t h a l i c anhydride over a V 2 O 5 / T i O 2 c a t a l y s t in an i n d u s t r i a l s c a l e fixed-bed r e a c t o r , t o determine the e f f e c t s o f v a r i a t i o n s o f j a c k e t temperature and feed composit i o n and temperature on the dynamic behaviour o f the r e a c t o r . F o r small p e r t u r b a t i o n s , the e x p e r i mental r e s u l t s are c o n s i s t e n t with the p r e d i c t i o n s from a heterogeneous two-dimensional model o f the r e a c t o r and give i n s i g h t i n t o the behaviour o f r e a c t o r s with small t u b e - t o - p a r t i c l e diameter r a t i o s . However, somewhat l a r g e r p e r t u r b a t i o n s lead t o a s l i g h t , partially reversible deactivat i o n o f the c a t a l y s t which makes a comparison with model p r e d i c t i o n s difficult. A dynamic model f o r o n - l i n e e s t i m a t i o n and c o n t r o l o f a f i x e d bed c a t a l y t i c r e a c t o r must be based on a thorough experimental program. I t must be able t o p r e d i c t the measured experimental e f f e c t s o f the v a r i a t i o n of key v a r i a b l e s such as j a c k e t temperat u r e , feed flow r a t e , composition and temperature on the dynamic behaviour o f the r e a c t o r ; t h i s , i n t u r n , r e q u i r e s the knowledge of the k i n e t i c and " e f f e c t i v e " t r a n s p o r t parameters i n v o l v e d i n the model. Due t o the strong i n t e r a c t i o n between the p h y s i c a l and chemical mechanisms, p a r t i c u l a r l y when c a t a l y s t d e a c t i v a t i o n i s present, the parameter e s t i m a t i o n becomes very d i f f i c u l t . The k i n e t i c parameters are normally obtained from l a b o r a t o r y s c a l e r e a c t o r s and when used i n p i l o t p l a n t s t u d i e s , have t o be tuned (1, 2) o r even re-evaluated (3, 4) to o b t a i n reasonable p r e d i c t i o n s . The t r a n s p o r t parameters are estimated 1

Current address: Universidad Autonoma Metropolitana-Iztapalapa, Depto. de Ingenieria, Apdo. Postal 55-534, Mexico 09340. 0097-6156/82/0196-0109$06.00/0 © 1982 American Chemical Society In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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e i t h e r from steady s t a t e or dynamic experiments without r e a c t i o n , to o b t a i n approximate v a l u e s under r e a c t i o n c o n d i t i o n s . To i n v e s t i g a t e the behaviour of the present r e a c t o r , a s e r i e s of steady s t a t e and dynamic experiments were performed, c o n s i s t i n g of r e a c t o r s t a r t - u p , step changes i n feed composition and ramp changes i n feed and j a c k e t temperature. Heat t r a n s f e r experiments without r e a c t i o n were a l s o performed. Some of the r e s u l t s are compared w i t h model s i m u l a t i o n s , u s i n g , whenever p o s s i b l e , £ p r i o r i v a l u e s of model parameters. Experimental System The schematic flow diagram of the p i l o t p l a n t i s shown i n F i g u r e 1. The r e a c t o r i s a s i n g l e tube of 25 mm i n t e r n a l diameter, 2.5 mm w a l l thickness and 3 length packed with 2.6 colum f V2O5/T1O2 c a t a l y s t p e l l e t s of molten s a l t . The c a t a l y s develope y F a b r i k von Heyden, and c o n s i s t e d of an i n e r t s p h e r i c a l c a r r i e r of 8.2 mm diameter, covered w i t h a t h i n a c t i v e c o a t i n g which contained V2O5 and T1O2 ( 5 ) . There are 26 a x i a l sampling p o i n t s of which 5 were used to measure composition by o n - l i n e chromatography, and the r e s t to measure temperature u s i n g 3 mm OD p l a t inum r e s i s t a n c e thermometers. For measurement of r a d i a l temperat u r e - p r o f i l e s around the hot spot, the platinum r e s i s t a n c e thermometers could be r e p l a c e d by 1.5 mm OD Chrome 1-Alumel sheathed thermocouples which were f r e e to move r a d i a l l y w i t h i n the r e a c t o r . The r e a c t a n t mixture, c o n s i s t i n g of 1 mole % o-xylene i n a i r was r a i s e d to a temperature of 105-110°C by a v a p o r i z e r l o c a t e d up-stream of the r e a c t o r , before e n t e r i n g the top of the bed. The gas stream l e a v i n g the r e a c t o r passed to a condenser where the p h t h a l i c anhydride sublimated. The r e s i d u a l gas was conveyed to a s t r i p p e r where the organic m a t e r i a l was washed out b e f o r e being vented to atmosphere. Theoretical

Developments

K i n e t i c Scheme The k i n e t i c s used i n t h i s study are based on the work of Calderbank and co-workers CI) s i n c e t h e i r r e s u l t s have been found to apply to a v a r i e t y of commercial c a t a l y s t s . At low r e a c t a n t c o n c e n t r a t i o n , the proposed r e a c t i o n scheme can be summarised as comprising s i x major r e a c t i o n s : 2

OX OT PT PA

O-xylene O-tolualdehyde Phthalide P h t h a l i c Anhydride

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

Figure I.

Schematic diagram of o-xylene oxidation pilot plant

•—Α

I

to

δ.

s:

ι

§

Γ*

ο w

α

>

»

w

ρ

S3

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

112

CHEMICAL REACTION

ENGINEERING

A 'redox' type o f k i n e t i c model was developed i n which the r a t e of r e a c t i o n f o r any o f the Ν s p e c i e s , i s expressed i n the form

6

R

= k

ρ

° 2 2s

n

6

Σ j

ν .R. n

=

1

J

=

y

J

Σ j

ν . R. n

=

1

J

J

~N Σ k.p. . , i*is 1=1 with u common f o r a l l r e a c t i o n s and species and Rj f i r s t order i n reactant p a r t i a l pressure. F o r t h i s work, i t was assumed that CO2 and CO were formed i n the r a t i o o f 3:1. Dynamic Model A two-dimensiona was developed, which d e s c r i b e s the mass and energy balances i n both phases. In dimensionless form, f o r the vfi component and the temperature i n the gas phase, 1

3x

. +

η

3x η

1 3^x 1 , η

-

+

1 3x 1 η.

*

= a (χ

\ - χ )

/1 \ (1)

m

(2) 3t

3z

P, lîlF n

and f o r the coated s o l i d c a t a l y s t

r 3r

pellets,

3x

c •ne

—

^

;

ν a

(x

x

" m n - ns>

+

= a (y - y ) + 6 s

s

6

m "

h

y ^ , y,) ^

V

R

nj j

β.

R

j

(

(

V

V V

(3

y ) g

>

(4)

These can be solved n u m e r i c a l l y given the usual i n i t i a l and boundary c o n d i t i o n s , i n c l u d i n g the thermal boundary c o n d i t i o n at the r e a c t o r w a l l , r = l : - 3y/3r

=

B i (y - y ) w

w

(5)

E a r l i e r s i m u l a t i o n s t u d i e s (6, 7) assessed the importance o f a r a d i a l v e l o c i t y p r o f i l e f o r t h i s system and showed that the increased v e l o c i t y near the w a l l d i d not have a s i g n i f i c a n t e f f e c t on the p r e d i c t i o n of the r e a c t o r ' s behaviour. Subsequent work has assumed a uniform r a d i a l v e l o c i t y p r o f i l e .

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

10.

K E R S H E N B A U M A N D LOPEZ-isuNZA

Industrial Fixed-Bed Reactor

113

In order to reduce the complexity o f the model two a d d i t i o n a l s i m p l i f y i n g assumptions were made, (a) With t y p i c a l r e s i d e n c e times o f 1 second, p a r t i c l e Reynolds numbers o f 800 and tube-top a r t i c l e diameter r a t i o s o f 3, one would expect small v a l u e s o f the w a l l B i o t number; thus, a small number o f r a d i a l f i n i t e d i f f e r e n c e (or c o l l o c a t i o n ) p o i n t s should be adequate f o r the numerical s o l u t i o n o f the equations ( 8 ) . (b) I t was assumed that the dynamic term f o r the accumulation o f mass a t the c a t a l y s t p e l l e t s (eqn. 3) could be n e g l e c t e d (9^, 10). Numerical S o l u t i o n Numerical s o l u t i o n s of eqns. (1) - (5) based on the above assumptions a r e r e p o r t e d elsewhere ( 7 ) . Using orthogonal c o l l o c a t i o n i n the r a d i a l d i r e c t i o n (one i n t e r i o r c o l l o c a t i o n p o i n t ) equations (1) and (2) were reduced from p a r a ­ b o l i c t o h y p e r b o l i c form further reduction to a t i o n s and n o n - l i n e a r a l g e b r a i c equations. T h i s system of equations was solved u s i n g orthogonal c o l l o c a t i o n on f i n i t e elements (11) ( a l s o c a l l e d g l o b a l s p l i n e c o l l o c a t i o n (12)) i n the a x i a l d i r e c ­ tion. The e n t i r e domain 0 < ζ 4 1 i s d i v i d e d i n t o s e v e r a l subi n t e r v a l s and orthogonal c o l l o c a t i o n i s a p p l i e d a t i n t e r i o r p o i n t s w i t h i n these s u b - i n t e r v a l s . The s i z e and number o f s u b - i n t e r v a l s , and the number o f i n t e r i o r c o l l o c a t i o n p o i n t s a t each s u b - i n t e r v a l , were chosen to s u i t the steepness of the temperature p r o f i l e obtained. G e n e r a l l y , four o r f i v e s u b - i n t e r v a l s , with 4 i n t e r i o r p o i n t s f o r each one, were used f o r the whole r e a c t o r l e n g t h . F i n a l l y , the r e s u l t i n g equations - coupled o r d i n a r y d i f f e r e n t i a l equations (one f o r each c o l l o c a t i o n p o i n t ) p l u s s e t s o f coupled l i n e a r and n o n - l i n e a r a l g e b r a i c equations - were solved by a f o u r t h - o r d e r Runge-Kutta method together with Gaussian e l i m i n a t i o n techniques and an implementation o f Broyden's method (13).

R e s u l t s and D i s c u s s i o n D e t a i l s o f the r e a c t o r o p e r a t i n g c o n d i t i o n s which correspond to t y p i c a l i n d u s t r i a l o p e r a t i o n are given i n Table I . A l l the experiments reported here were performed a f t e r f o u r weeks o f con­ tinuous running o f the p l a n t under steady c o n d i t i o n s i n order t o allow the c a t a l y s t a c t i v i t y t o s t a b i l i z e . Steady-State Behaviour The dashed l i n e i n F i g u r e 2 shows a t y p i c a l experimental a x i a l temperature p r o f i l e f o r c o n d i t i o n s l i s t e d i n Table I . The banded r e g i o n i n the v i c i n i t y o f the hot spot i n c l u d e s those p o i n t s ( l a b e l l e d a, b and c) i n which r a d i a l temperature p r o f i l e s were a l s o measured u s i n g moving thermocouples. There, the upper and lower l i n e s represent the h i g h e s t measured temperature and the w a l l temperature, r e s p e c t i v e l y , a t those a x i a l points. The measured r a d i a l p r o f i l e s a r e i l l u s t r a t e d i n F i g u r e 3 and show a remarkable r e p r o d u c i b i l i t y d e s p i t e the low t u b e / p a r t i c l e diameter r a t i o . The magnitude of the r a d i a l gradient (up t o 40 C o

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

114

CHEMICAL REACTION ENGINEERING

Table Reactor Operating 3

A i r flow r a t e : 4 m /hr (STP) O-xylene flow r a t e : 176 g/hr Feed temperature: 370°C I n l e t Pressure: 1.4 bar

I Conditions Bath Temperature: 380°C Bed Voidage: 0.5 C a t a l y s t Bulk D e n s i t y : 1300 kg/m 3

i n a J " r a d i a l d i s t a n c e ) g i v e s v a l u a b l e i n f o r m a t i o n about the heat t r a n s f e r p r o p e r t i e s of beds i n t h i s important, but p o o r l y charact e r i z e d regime. The r e s u l t s w i l l be presented i n more d e t a i l at a l a t e r date (7, 14). The asymmetry i n the r a d i a l p r o f i l e i s caused by the conductive heat l o s s e s along the sampling tube which i s welded to the r e a c t o r tube and through which the thermocouple enters the r e a c t o r . Onl p r o f i l e s i n F i g u r e 3 ar The r e s u l t s of the steady-state model f o r the r e a c t o r under the same o p e r a t i n g c o n d i t i o n s are d i s p l a y e d as the s o l i d l i n e s i n F i g u r e 2. The p r e d i c t e d c a t a l y s t and gas temperatures are shown at each of the a x i a l c o l l o c a t i o n p o i n t s . As d i s c u s s e d e a r l i e r , a p r i o r i values of k i n e t i c parameters were used (1, 2); s i m i l a r l y , heat and mass t r a n s f e r parameters (which are l i s t e d i n Table I I ) were taken from standard c o r r e l a t i o n s (15, 16, 17) or from e x p e r i mental temperature measurements i n the r e a c t o r under non-reactive c o n d i t i o n s . The agreement with experimental data i s encouraging, c o n s i d e r i n g the u n c e r t a i n t y which e x i s t s i n the c a t a l y s t a c t i v i t y and i n the heat t r a n s f e r parameters f o r beds w i t h such l a r g e particles. Dynamic Behaviour Reactor behaviour d u r i n g s t a r t - u p i s i l l u s t r a t e d i n F i g u r e 4. The r e a c t o r was o p e r a t i n g i n i t i a l l y at normal c o n d i t i o n s but without o-xylene i n the f e e d , when the o-xylene flow r a t e was r a i s e d to 152 g/hr. The hot spot developed q u i c k l y ( w i t h i n 3 minutes) at the r e a c t o r e x i t and propagated upstream as heat t r a n s f e r and chemical r e a c t i o n e f f e c t s l e d to the h e a t i n g of the c a t a l y s t p e l l e t s to t h e i r steady-state temperatures . F i g u r e 5 shows the l e s s d r a s t i c response to a step i n c r e a s e i n feed composition, and subsequently, a step decrease of the same magnitude. P e r t u r b a t i o n s i n the form of step changes up to 10%, caused r e v e r s i b l e i n c r e a s e s or decreases i n the magnitude of the hot spot but no change i n i t s p o s i t i o n . F i g u r e 5 a l s o shows the t r a n s i e n t response p r e d i c t e d by the s i m u l a t i o n . Larger i n c r e a s e s i n the feed c o n c e n t r a t i o n , however, l e d to a p a r t i a l d e a c t i v a t i o n of the c a t a l y s t near the r e a c t o r i n l e t . T h i s was r e f l e c t e d by the movement of the hot spot down towards the middle of the r e a c t o r ; i t was not p o s s i b l e to p r e d i c t t h i s behaviour without the a r b i t r a r y i n c o r p o r a t i o n of c a t a l y s t a c t i v i t y p r o f i l e s i n the bed.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

10.

K E R S H E N B A U M A N D LOPEZ-isuNZA

Industrial Fixed-Bed Reactor

560

AXIAL POSITION

(CM)

Figure 2. Typical steady-state axial temperature profiles. Key: - Λ - Δ - , simu­ lated catalyst surface temperature; - V - V - , simulated gas temperature; and - - 0 - - 0 - - , experimental results.

Figure 3.

Steady-state radial temperature profiles corresponding to Figure 2.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

116

CHEMICAL REACTION

ENGINEERING

Table I I Transport Parameters f o r Reactor

Simulation

E f f e c t i v e Wall B i o t Number, B i =0.84 E f f e c t i v e R a d i a l P e c l e t Numbers: P^ = 0.083 ; P = 0.075 E f f e c t i v e G a s / S o l i d Heat and Mass T r a n s f e r c o e f f i c i e n t s : h = 264. W/m °C ; k = 0.161 m/s Dimensionless G a s / S o l i d Transport Parameters: a^ = 34.6 ; w

m

2

g

am = 17.1 ; a

g

s

= 0.00945

The s e n s i t i v i t y o f the a x i a l temperature p r o f i l e t o the feed and s a l t bath temperature t i v e l y . F i g u r e 6 show feed temperature by 2 C over a p e r i o d of 10 minutes. F o r small p e r t u r b a t i o n s (up to 5°C), the hot spot t r a v e l s downstream and passes through a maximum value before reaching i t s new steadys t a t e . When the disturbance i s r e v e r s e d , the hot spot moves upstream i n a s i m i l a r manner and r e t u r n s t o the former steadystate. F i g u r e 7 shows the e f f e c t of a 1°C increase i n the s a l t bath temperature. As b e f o r e , the hot spot t r a v e l s upstream; however, i n t h i s case", i t passes through a maximum temperature which could be h i g h enough t o d e a c t i v a t e that r e g i o n of the bed, e s p e c i a l l y when a newly charged, h i g h l y a c t i v e c a t a l y s t i s being used. Conclusions Dynamic experiments have shown that f o r t h i s r e a c t o r system, feed composition and flow r a t e can be used to a l t e r the p o s i t i o n and magnitude of the hot spot w i t h i n f a i r l y t i g h t l i m i t s . When feed and s a l t bath temperature disturbances are of a somewhat l a r g e r s c a l e , s i g n i f i c a n t departures from the o r i g i n a l steady-state are observed, some o f which can lead to c a t a l y s t d e a c t i v a t i o n . Model c a l c u l a t i o n s based upon some experimentally determined heat t r a n s f e r parameters p l u s k i n e t i c schemes and other parameters taken from the l i t e r a t u r e give reasonably good p r e d i c t i o n s o f the steady-state and dynamic behaviour o f the r e a c t o r when p e r t u r b a t i o n s are s m a l l . Serious l i m i t a t i o n s e x i s t f o r the p r e d i c t i o n of the response t o l a r g e p e r t u r b a t i o n s s i n c e the observed v a r i a t i o n s i n c a t a l y s t a c t i v i t y are not contained i n the k i n e t i c scheme and parameter e s t i m a t i o n becomes very u n c e r t a i n .

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

10.

K E R S H E N B A U M A N D LOPEZ-isuNZA

Industrial Fixed-Bed Reactor

117

475

4

ι\

450

i.25f




Αι» - 1.09·10~

5

T/Y

p r Q

Legend of Symbols a

1/2

=

ο Al Αί

-

Oxygen a c t i v i t y , b a r Ki S/F

=

KiS/F.Y

p r o

p r o

A

2

=

K S/F.Y

A

3

=

V ^ P r o

Αι»

=

A

=

2

S

C

/ V c

Y

c

=

- s T- Pro K S - Y /FY 0 Pro Propylene oxide c o n c e n t r a t i o n , môle/cm

c°

=

Feed Propylene oxide c o n c e n t r a t i o n , mole/cm

c

=

Surface c o n c e n t r a t i o n of monomer a t f u l l coverage, mole/cm

5

03

0

2

s

3

2

C

T o t a l gas c o n c e n t r a t i o n , mole/cm

β

T F k

3

3

T o t a l molar f l o w r a t e , mole/s K 'S,

-

2

r a t e c o e f f i c i e n t of r e a c t i o n [3,3],mole/s

2

Κι,Κχ,Κ ,Κ3,Κ ,Κρ 2

ρ

-

S p e c i f i c r a t e constants, mole/cm

Q

T o t a l volumetric f l o w r a t e , cnrSTP/min

S

C a t a l y s t s u r f a c e area, cm

t

Real time, s

V -

x

2

2

Reactor volume c c° c°/c T

y

y

Pro

o

=

= 2

°o T / q oxygen c o n c e n t r a t i o n , mole/cnr /

C

2

C o

c

2

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

178

CHEMICAL

REACTION

α

=

Heaviside f u n c t i o n Η ζ θ ^ - θ χ )

θχ

=

monomer coverage

=

monomer coverage corresponding t o the c e i l i n g temperature

=

f r a c t i o n of s u r f a c e s i t e s covered by i-mer η Σ θ i=2 i

6^

9

c

i

θ„

ENGINEERING

dimensionless time, F-t/Vc, t

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

Wagner, C., Adv. C a t a l . , 1970, 21, 323. K a l i b e r d o , LM. e t al., K i n e t . K a t a l . , 1967, 8, ( 1 ) , 105. Cant, N.W. and Hall, W.K. J . C a t a l . , 1978, 52, 81. Stoukides, M. and Vayenas, C.G., J. C a t a l . , 1982, in p r e s s . Stoukides, Μ., and Vayenas, C.G., J. C a t a l . , 1981, 69, 18. Vayenas, C.G., Lee, B. and Michaels, J., J. C a t a l . , 1980, 66, 18. Kurtanjek, Z., Sheintuch, M. and Luss, D., J . C a t a l . , 1980, 66, 11. Sheintuch, Μ., and Schmitz, R., C a t a l . Rev. Sci. Eng., 1977, 15, ( 2 ) . Vayenas, C.G., Georgakis, C., Michaels, J. and Tormo, J., J . C a t a l . , 1981, 67, 348. Stoukides, Μ., and Vayenas, C., J. C a t a l . , 1980, 64, 18. F r e r i k s , I.C., Bouwman, R., and Greenen, P.V., J. C a t a l . , 1980, 65, 311. Davydov, Α.Α., e t al. J. C a t a l . , 1978, 55, 299. Kobayashi, Μ., Can. J. of Chem. Eng., 1980, 58, 588. A l l e n , P.E.M. and P a t r i c k , C.R., " K i n e t i c s and Mechanism of P o l y m e r i z a t i o n Reactions", J . Wiley, 1974.

RECEIVED

April 27, 1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

16 Steam Reforming of Natural Gas: Intrinsic Kinetics, Diffusional Influences, and Reactor Design J. C. D E DEKEN, E . F. DEVOS, and G . F. FROMENT Laboratorium voor Petrochemische Techniek, Rijksuniversiteit, Gent, Belgium The intrinsic kinetic f th catalytic stea refor ming o f n a t u r a l in a tubular reacto temperatur rang 8 2 3 - 9 5 3 ° K and in the pressure range o f 5-15 b a r . With c a t a l y s t r i n g s o f the s i z e used in i n d u s t r i a l o p e r a t i o n , pronounced c o n c e n t r a t i o n g r a d i e n t s occur i n s i d e the c a t a l y s t . The e f f e c t i v e diffusivity re­ q u i r e d i n the s i m u l a t i o n o f these g r a d i e n t s was obtained from the molecular and Knudsen diffusivi­ ties, the i n t e r n a l v o i d f r a c t i o n and the t o r t u o s i t y f a c t o r . The latter was determined by the dynamic gas chromatographic method, u s i n g the Van Deemter equa­ tion. The t o r t u o s i t y f a c t o r was found t o v a r y between 4.39 and 4.99 and to be independent o f temperature. The reformer tube o p e r a t i o n was simulated on the b a s i s o f a set o f c o n t i n u i t y - , energy- and momentum equations u s i n g one and two dimensional heterogeneous models. I n t r a p a r t i c l e g r a d i e n t s in the r i n g s were accounted f o r by the use o f the g e n e r a l i z e d modulus concept. The steam reforming o f n a t u r a l gas, the main process f o r hydrogen- o r synthesis-gas p r o d u c t i o n i s c a r r i e d out on supported N i c a t a l y s t s i n m u l t i t u b u l a r r e a c t o r s operated a t temperatures v a r y i n g from 500 t o 800°C, pressures ranging from 20 t o 40 bar and molar steam-to-carbon r a t i o s i n the feed between 2.0 and 4.0. Despite the i n d u s t r i a l importance o f the process, t h e design o f the furnace and r e a c t o r tube i s s t i l l c a r r i e d out along very empir i c a l l i n e s . The present work r e p o r t s on the r e s u l t s o f an i n v e s t i g a t i o n o f the k i n e t i c s , i n c l u d i n g the i n f l u e n c e o f i n t r a p a r t i c l e c o n c e n t r a t i o n gradients,and combines t h i s i n f o r m a t i o n with fundamental models f o r the s i m u l a t i o n and design o f reformer tubes i n s e r t e d i n t o g a s - f i r e d furnaces.

0097-6156/82/0196-0181$06.00/0 © 1982 American Chemical Society In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

182

CHEMICAL REACTION ENGINEERING

I n t r i n s i c k i n e t i c s o f methane steam

reforming

The commercial c a t a l y s t used i n t h i s work c o n t a i n s 12 wt% N i and 83 wt% (1-AI2O3. I t has a BET t o t a l surface area o f 3.4m /g and a unimodal pore s i z e d i s t r i b u t i o n with volume 0.155 cc/g, mean pore r a d i u s 1600 Â and v o i d f r a c t i o n 0.362. I t s a c t i v a t i o n r e q u i r e d a r e d u c t i o n which was c a r r i e d out under atmospheric pressure i n s i t u , f o r 72 hrs a t 850°C by means o f a pure d r i e d hydrogen flow o f 100 Nl/hr. These severe r e d u c t i o n c o n d i t i o n s were r e q u i r e d because 20 wt% of the Ni was present as N1AI2O4-spinel phase, which c o u l d o n l y be reduced above 770°C. I t l e d t o a very a c t i v e c a t a l y s t , with a s p e c i f i c N i - s u r f a c e area o f 0.68 m Ni/g.cat. The k i n e t i c study was conducted i n a bench s c a l e u n i t b u i l t around a t u b u l a r r e a c t o r (HK40;I.D.35mm), operated i n the i n t e g r a l mode i n the ranges 550-675°C steam-to-methane r a t i o preheated and mixed p r i o r to e n t e r i n g the r e a c t o r , c o n s i s t i n g o f preheat-, r e a c t i o n - and a f t e r - z o n e s and e l e c t r i c a l l y heated by 5 independently c o n t r o l l e d s e c t i o n s . The r e a c t i o n s e c t i o n contained 6 grams o f c a t a l y s t , crushed t o 350 Mm t o e l i m i n a t e i n t e r n a l mass t r a n s f e r l i m i t a t i o n s and d i l u t e d with i n e r t r e f r a c t o r y m a t e r i a l s to ensure i s o t h e r m i c i t y . A f t e r condensation o f the steam, the dry e x i t gas was analyzed by two gas chromatographs c o n t a i n i n g Porapack Q and Ν columns and connected with a PDP-8A process computer. Heated l i n e s a l s o permit bypassing the r e a c t o r t o prevent a l t e r i n g the c a t a l y s t d u r i n g s t a r t - u p and shut-down o p e r a t i o n s . Molar H^/CH^ feed r a t i o s between 1.0 and 3.25 were maintained d u r i n g the expe­ r i m e n t a t i o n (1_) , t o prevent any carbon b u i l d up and r e o x i d a t i o n o f the c a t a l y s t and t h e r e f o r e d e a c t i v a t i o n . By way of example a small p o r t i o n of the experimental r e s u l t s i s shown i n F i g u r e 1. These r e s u l t s l e d t o the f o l l o w i n g r e a c t i o n mechanism : CH +S ^z±S-C+2H (1) H 0+S* ^ ± S - 0 + H (2) S-C+S-0 ^ ± S - C 0 + S : r.d.s. (3) S-CO ^±C0+S (4) S-C+2S-0^z±S-C0 +2S* : r . d . s . (5) s-co ^±co +s* (6) Since the gas phase c o n t a i n s f i v e components which should s a t i s f y three elementary mass balances, two a r b i t r a r i l y chosen, but inde­ pendent, conversions are r e q u i r e d to d e f i n e i t s composition, e.g. the t o t a l methane conversion, X^H-r and the conversion o f methane i n t o C0 , Xco p r e d i c t i o n o f these conversions i n any p o i n t o f the r e a c t o r t h e r e f o r e n e c e s s i t a t e s two r a t e equations, each d e r i v e d under the assumption o f a t l e a s t one r a t e determining step ( r . d . s . ) . A number o f authors have used one r a t e equation only, thereby assuming the watergas s h i f t r e a c t i o n ( C 0 + H 0 ^ ± C 0 2 + H ) t o be a t e q u i l i b r i u m a t any p o i n t i n the r e a c t o r (2/3,4) , but others have c o n t r a d i c t e d t h i s assumption (5/6) . From t h i s mechanism and a f t e r d i s c r i m i n a t i o n between more than 150 r i v a l models (1_) , the 2

2

X

4

2

2

2

X

X

2

2

2

T

2

h

e

2

2

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

2

DE DEKEN ET AL.

Steam Reforming of Natural Gas

183

Figure 1. Total methane conversion versus W/F° H at 5 BAR, steam-to-carbon ratio of 5.0, and different temperatures. Key: · , experimental; and , model prediction. C

k

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

184

CHEMICAL REACTION ENGINEERING

following

Langmuir-Hinshelwood type r a t e equations were obtained : P

P

W CH H,O r

=

CO

/P

H i

= — ί

W

( p

cH

p H

n

/ p

2

H 2

R

(7)

—

;*CO'\) 2

2

(8)

3

( t

Vco'

with the p a r t i a l p r e s s u r e s g i v e n by t h e r e l a t i o n s : P

p

P

CH,

= (i-'W/N

co

= < CH- CO,

C0

X

H

=
not separated), as w e l l as carbon monoxide, carbon d i o x i d e and water. A l c o h o l s and aldehydes could be detected by the gas chromotography but were not found to be produced i n s i z a b l e amounts. An X-ray d i f f r a c t i o n a n a l y s i s was made to determine the s o l i d s t r u c t u r e of the c a t a l y s t s b e f o r e and a f t e r the r e a c t i o n . The s p e c i f i c surface area of the c a t a l y s t s was determined by the BET method u s i n g n i t r o g e n at i t s b o i l i n g p o i n t . The s u r f a c e area of the v i r g i n c a t a l y s t ribbons ranged 0.2 to 0.3 m /g, which was about one order of magnitude greater than the g e o m e t r i c a l s u r f a c e area of the r i b b o n s . 2

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

20.

YOKOYAMA ET A L .

Catalysts in Fischer-Tropsch Synthesis

239

Experimental R e s u l t s . A c t i v i t y . The c a t a l y t i c a c t i v i t y o f the Fe2oNi6oP2 0 a l l o y s f o r the F i s c h e r - T r o p s c h s y n t h e s i s was analyzed and i t was found that the amorphous a l l o y has the c a t a l y t i c a c t i v i t y about three hundred times higher than the c r y s t a l l i n e a l l o y (5. 6). For Fe9 0 Z r i o a l l o y , the c a t a l y t i c a c t i v i t y o f the amorphous and c r y s t a l l i n e phases was analyzed f o r the same r e a c t i o n a t 248 and 255°C. As i s shown i n F i g u r e 1, the production r a t e s of the major hydrocarbons were kept constant f o r the amorphous c a t a l y s t . However, the c r y s t a l l i n e Fe9oZrio c a t a l y s t which was prepared by h e a t i n g the amorphous c a t a l y s t a t 560°C f o r 20 h r s d i d n ' t approach any steady a c t i v i t y , as i s shown i n F i g u r e 2. The BET s u r f a c e areas o f both the amorphous and the c r y s t a l l i n e Fe2oNÎ6oP2 0 c a t a l y s t s were n e a r l y the same and constant during the r e a c t i o n , but th s u r f a c c h a r a c t e r f th amorphou and the c r y s t a l l i n e phase with each other. For th c r y s t a l l i n c a t a l y s t , area was kept constant during the r e a c t i o n a t about 0.25 m /g. On the other hand, the amorphous c a t a l y s t ribbons broke i n t o f i n e chips o f d i f f e r e n t s i z e s and the BET s u r f a c e area a f t e r the r e a c t i o n went up t o 0.9 m /g. Since the pretreatment w i t h a stream o f hydrogen d i d not produce any breakage of the a l l o y r i b b o n , and a l s o because the c a t a l y t i c a c i t v i t y had been kept constant s h o r t l y a f t e r the s t a r t o f the r e a c t i o n , the i n c r e a s e o f the s u r f a c e area of the amorphous c a t a l y s t i s considered t o take p l a c e a t the i n i t i a l p e r i o d of the r e a c t i o n by carbon monoxide and hydrogen. Product D i s t r i b u t i o n . F i g u r e s 3 and 4 show the d i s t r i b u t i o n s of the carbon number o f hydrocarbon products by weight, measured under the d i f f e r e n t i a l r e a c t o r c o n d i t i o n s f o r the amorphous c a t a l y s t s , Fe9oZrio and Fe2oNi6oP20> r e s p e c t i v e l y . As the p a r t i a l pressure of carbon monoxide i n c r e a s e d , the product d i s t r i b u t i o n s of these c a t a l y s t s tended toward higher hydrocarbons. I t may be g e n e r a l l y agreed t h a t , i n the F-T s y n t h e s i s , the product d i s t r i b u t i o n tends toward higher hydrocarbons by the i n c r e a s e o f the p a r t i a l pressure of carbon monoxide (9,10), but the d i s c u s s i o n on such tendency has been l i m i t e d t o the F-T s y n t h e s i s f o r o b t a i n i n g high hydrocarbons as l i q u i d f u e l s . Recently, the e f f e c t o f t h e p a r t i a l pressure o f carbon monoxide on the product d i s t r i b u t i o n was s t u d i e d f o r the F-T s y n t h e s i s f o r o b t a i n i n g lower hydrocarbons using Ru, Rh, Co, Fe, and N i as c a t a l y s t s (11). The e f f e c t s f o r the amorphous c a t a l y s t s used i n t h i s study a r e much more s i g n i f i cant than those f o r the c a t a l y s t s o f the previous study (11). Furthermore, i t i s i n t e r e s t i n g that the amorphous F e 2 û N i e o P 2 0 c a t a l y s t e x h i b i t e d the high s e l e c t i v i t y t o C 2 t o C 5 hydrocarbons. F i g u r e 5 and 6 show the contact time dependence o f the conc e n t r a t i o n o f each hydrocarbon represented by carbon monoxide conv e r s i o n base f o r these c a t a l y s t s . I t i s reasonable t o d e r i v e the e x i s t e n c e o f the s u c c e s s i v e r e a c t i o n step o f o l e f i n s from the conf

2

2

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

240

CHEMICAL REACTION ENGINEERING

ϋ)_φ_ φ Q—Ο-Ο-Ο-

-ο-

C Ο

$1C? c ο ο •ΠΦ Total A C

2

AQ

3

ac

5V=2.0xlO (hr) A

10 20 30 Reaction Time(hr) Figure 1. The activity of amorphous Fe Zr catalyst at 248°C, P o = 0.17 atm, and P = 0.83 atm. Key: O, C , ; Δ , CJ; Δ , C ; • , C ; CJ; and Φ, total. 90

10

Ht

C

t

s

20 30 AO Reaction Time(hr) Figure 2.

The activity of crystalline Fe Zr catalyst at 255°C, with P atm, and P = 0.83 atm. 90

î0

Ht

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

co

=

0.17

20.

241

Catalysts in Fischer-Tropsch Synthesis

YOKOYAMA ET A L .

Carbon Number Figure 3. Effect of partial pressure of carbon monoxide for amorphous Fe Zr catalyst at 248°C with P = 0.5 atm. Key to P : O, 0.1 atm; Δ , 0.2 atm; and • , 0.5 atm. 9ù

H%

10

c

Carbon Number Figure 4. Effect of partial pressure of carbon monoxide for amorphous Fe Ni oPto catalyst at 230°C, and P — 0.5 atm. Key to P o is the same as in Figure 3. to

Hi

C

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

e

242

CHEMICAL REACTION ENGINEERING

-1

2

3

Ax,0"3

Sv'ihr) Figure 5. Concentrations of hydrocarbon products as a function of contact time with amorphous Fe Zr at 296°C, P = 0.17 atm, and P , = 0.83 atm. Key: O, C ; A , C,'; Δ , C ; (J, q u i n o l i n e > a n i l i n e . The oc values f o r a given dosage o f poison followed the same trend as the order o f b a s i c i t y , so the degree of p o l y m e r i z a t i o n o f coke decreas­ ed with the i n c r e a s e o f b a s i c i t y o f n i t r o g e n compounds. The ot values increase more r a p i d l ings o f q u i n o l i n e and a n i l i n e The r a t e c o e f f i c i e n t o f c r a c k i n g r e a c t i o n , k ^ K ^ L ^ was found to be p r o p o r t i o n a l t o the number o f a v a i l a b l e a c t i v e s i t e s . can be expressed as f o l l o w s : k K L x

A

c

= (k K L ) 1

where (k^K^L^o

A

c

(1 - o-Cps)

c

It

(20)

i s the r a t e constant o f c r a c k i n g r e a c t i o n i n

absence o f poison compound, β" i s a s o r p t i o n d i s t r i b u t i o n c o e f f i ­ c i e n t . P l o t s o f k^K L^ versus the l o a d i n g o f poison a r e shown i n A

F i g u r e 4. The l i n e a r r e l a t i o n s h i p o f p o i s o n i n g might be due t o uniform poisoning, i . e . , s i t e s o f equal a c t i v i t y were d e a c t i v a t e d at zero coke content. Figure 4 shows that p y r i d i n e and q u i n o l i n e are more poisonous than a n i l i n e . I t shows that the higher b a s i c ­ i t y compounds have greater e f f e c t i v e n e s s as poisons. Quinoline which has a higher molecular weight and lower b a s i c i t y than p y r i ­ dine showed a s l i g h t l y lower e f f e c t i v e n e s s than p y r i d i n e . On the b a s i s o f the p o i s o n i n g s t u d i e s , the number of a c t i v e s i t e s o f the c a t a l y s t were 1.63 χ 1 0 ^ r gram obtained from p y r i d i n e poisoning and cumene c r a c k i n g r e a c t i o n a t 300°C. T h i s number i s c l o s e to the number reported by Jacobs and Heylen (13) i n the study o f poisoning with 2,6-methylpyridine o f cumene crack­ i n g a c t i v i t y o f the HY z e o l i t e s . p

e

Comparison With Other Models I f equation

φ =

(14) i s s u b s t i t u t e d i n t o equation

-

l

(10), then (21)

1 + «ck ,K L P t cl A c A A

A

T h i s form o f the d e a c t i v a t i o n f u n c t i o n i s very s i m i l a r t o forms used i n the time-on-stream approach t o c r a c k i n g c a t a l y s t a c t i v i t y

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

256

CHEMICAL REACTION ENGINEERING

Figure 3. Poison compound loading vs. a. Key: O, 300°C; Δ, 250°C; and • , 200°C in pyridine; V , 300°C in quinoline; and 0,300°C in aniline.

P o i s o n , Eq/g χ 10* Figure 4. Poison compound loading vs. ktK L . Key: O, 300°C; Δ, 250°C; and • , 200°C in pyridine; - V - , 300°C in quinoline; and 0, 300°C in aniline. A

c

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

21.

257

Zeolite Catalyst Deactivation

LIN AND HATCHER

decay. F o r example, i n bench s c a l e s t u d i e s o f c r a c k i n g commercial feedstocks, Jacob e t a l (14) reported that the f o l l o w i n g e m p i r i c a l d e a c t i v a t i o n f u n c t i o n represented t h e i r data.

ψ =

a P

m

(22) C

(1 + b t )

In equation (22) ρ i s the i n l e t p a r t i a l pressure o f o i l and a,b,c, and m are constants that depend on the feedstock. The e f f e c t o f n i t r o g e n compound p o i s o n i n g found i n the p r e s ­ ent study i s two-fold as shown by equations (19) and (20). These e f f e c t s are p o s s i b l y due to the c o n t r i b u t i o n to pore blockage and to chemisorption on a c t i v e s i t e s r e s p e c t i v e l y . P u t t i n g the two n i t r o g e n p o i s o n i n g e f f e c t s together r e s u l t s i n the f o l l o w i n g expression. φ

1

-

Ν

(1 + oi k

- q~cps c l

K L P A

c

A

t) Ρ

C

p

s

/

*

(23)

N i t r o g e n d e a c t i v a t i o n e f f e c t s o f commercial feedstocks as reported by Jacob e t a l (14) was represented by an equation o f the f o l ­ lowing form.

Φ

Ν

-

I 1 + K

1

(2*> Cps t

By u s i n g the parameter v a l u e s obtained i n the present study and assuming values o f i n equation (24), d e a c t i v a t i o n e f f e c t s o f n i t r o g e n as p r e d i c t e d by equations (23) and (24) can be q u i t e s i m i l a r . A b a s i c d i f f e r e n c e i n the method o f n i t r o g e n p o i s o n i n g i n the two s t u d i e s i s that i n the present study the c a t a l y s t was poisoned with the n i t r o g e n compound and then the c r a c k i n g a c t i v i t y was determined w h i l e i n the study by Jacobs e t a l (14), n i t r o g e n p o i s o n i n g and c r a c k i n g occurred simultaneously. Conclusions The e f f e c t s o f coking and n i t r o g e n compound p o i s o n i n g on a z e o l i t e c a t a l y s t a c t i v i t y can be modeled w i t h a separable r a t e expression. The e f f e c t o f coking on c a t a l y s t a c t i v i t y was accounted f o r by a d e a c t i v a t i o n f u n c t i o n i n an e x p o n e n t i a l form. The c r a c k i n g r e a c t i o n and the coking r e a c t i o n were s i m i l a r l y dependent on the c a t a l y s t coke content. The mechanism o f d e a c t i ­ v a t i o n by n i t r o g e n compound p o i s o n i n g appeared t o be uniform p o i s o n i n g i n the absence o f coke e f f e c t . The value o f the deac­ t i v a t i o n c o e f f i c i e n t increased w i t h i n c r e a s i n g poison l o a d i n g on the z e o l i t e .

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

258

CHEMICAL REACTION

ENGINEERING

Legend of Symbols a,b,c Cc Cps *Ao Κ Kl K k i A

c

k 2 c

k 3 c

k 4 c

KR kl L m ρ PA PR Pg R r r c

c

r r i c

c

r 2 c

r 3 c

t Τ W oc Q v

$

^

m

decay constants i n equation (22) coke content on the c a t a l y s t , g/g poison c o n c e n t r a t i o n i n the gas phase i n s i d e the c a t a l y s t , mole/g ° l - r a t e of cumene vapor i n the feed, mole/s e

e q u i l i b r i u m constant f o r cumene c r a c k i n g , atm constant i n equation (24) a d s o r p t i o n c o e f f i c i e n t f o r cumene, atm~l i n i t i a l r a t e constant o f coke formation f o r p a r a l l e l step, 8-1 i n i t i a l r a t e constant o f coke formation f o r consecutive step, s""* i n i t i a l r a t e constan for reactant, s " i n i t i a l r a t e constant of coke formation f o r combined step from product, s ~ l a d s o r p t i o n c o e f f i c i e n t f o r propylene, atm~l s u r f a c e r e a c t i o n r a t e constant, s*"l c o n c e n t r a t i o n o f t o t a l a c t i v e s i t e s , mole/g constant i n equation (22) i n l e t p a r t i a l pressure of o i l , atm p a r t i a l pressure o f cumene, atm p a r t i a l pressure o f propylene, atm p a r t i a l pressure o f benzene, atm gas law constant r a t e o f cumene c r a c k i n g , mole/g - s r a t e o f coke formation, g/g - s i n i t i a l r a t e o f coke formation, g/g - s r a t e of conversion of r e a c t a n t i n t o coke, p a r a l l e l model, g/g - s r a t e o f conversion o f product i n t o coke, consecutive model, g/g - s r a t e of conversion o f reactant and product i n t o coke, com­ bined model, g/g - s time, s r e a c t i o n temperature, Κ i n i t i a l weight o f c a t a l y s t , g f r a c t i o n a l conversion o f cumene c o e f f i c i e n t of d e a c t i v a t i o n f u n c t i o n , g/g constant i n equation (23) s o r p t i o n d i s t r i b u t i o n c o e f f i c i e n t of the poison compound, g/mole d e a c t i v a t i o n f u n c t i o n by coking d e a c t i v a t i o n by n i t r o g e n p o i s o n i n g

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

21.

L I N AND HATCHER

Zeolite Catalyst Deactivation

259

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

V o o r h i e s , A. Ind. & Eng. Chem., 1945, 37, 318 Wojciechowski, Β. W. Can. J. Chem. Eng., 1968, 46, 48 Froment, G. F. and B i s c h o f f , Κ. Β. Chem. Eng.Sci.,1961, 16, 189 DePauw, R. P. and Froment, G. F. Chem. Eng. Sci., 1975, 30, 789 Dumez, F. J. and Froment, G. F. Ind. Eng. Chem. Process Design Develop., 1976, 15, 291 M i l l s , G. Α.; Boedeker, E. R. and Oblad, A. G. J . Amer. Chem. Soc., 1950, 72, 1554 G o l d s t e i n , M.S. and Morgan, T. R. J . C a t a l . , 1970, 16, 232 C o r r i g a n , T. E.; Graver, J. C.; Rase, H. F. and K i r k , R. S. Chem. Eng. Progress P r a t e r , C. D. and 8, 293 Hatcher, W. J . ; Park, S. W. and Lin, C. C., April 1979, 86th N a t i o n a l Meeting o f AIChE, Houston, Paper 72a Beeckman, J. W. and Froment, G. F. Ind. Eng. Chem. Fund., 1979, 18, 245 L i n , C. C.; Park, S. W. and Hatcher, W. J . , June 1982, N a t i o n a l Meeting o f AIChE, Anaheim, C a l i f o r n i a Jacobs, P. A. and Heylen, C. F. J . C a t a l . , 1974, 34, 267 Jacob, S. M.; Gross, B,; V o l t z , S. E. and Weekman, V. W. AIChE J . , 1976, 22, 701

RECEIVED April 27, 1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

22 Rate of Oxidation of Ammonia on Platinum Wires, Ribbons, and Gauzes C. W. NUTT, S. KAPUR, and A . M A J E E D Heriot-Watt University, Department of Chemical and Process Engineering, Edinburgh, England

The r a t e o pressure on s i n g l e wires and ribbons has been d e t e r mined as a f u n c t i o n o f a gas flow r a t e and c a t a l y s t s i z e . In agreement with boundary l a y e r d i f f u s i o n theory the f u n c t i o n rx , where r is the average r a t e o f r e a c t i o n / u n i t area, and x is the l e n g t h o f the surface measured in the d i r e c t i o n o f gas flow, is directly p r o p o r t i o n a l to gas v e l o c i t y . Surface r e a c t i o n r a t e data were determined i n independent s t u d i e s in which the d i f f u s i o n constraint was removed by molecular beam techniques. P r e d i c t e d values f o r the o v e r a l l r e a c t i o n r a t e , computed by c o u p l i n g t h i s data with d i f f u s i o n r a t e s from boundary l a y e r theory, a r e in e x c e l l e n t agreement w i t h e x p e r i mental values f o r ribbons and w i r e s . A p p l i c a t i o n o f the computational techniques to p r e d i c t conversions on pads o f i n d u s t r i a l gauzes give r e s u l t s which are r a t h e r lower than p r a c t i c a l e x p e r i ence suggests, due probably to i n t e r r u p t i o n s o f the boundary l a y e r and the l a r g e r s u r f a c e area associated with the roughness o f the a c t i v e commercial gauzes. Extension o f the computations to take account of n i t r o g e n formation by p y r o l y s i s o f ammonia and its r e a c t i o n with nitric oxide on the c a t a l y s t s u r f a c e should permit b e t t e r p r e d i c t i o n o f the performance of i n d u s t r i a l converters. 1/2

The manufacture o f n i t r i c a c i d by the o x i d a t i o n o f ammonia on platinum-type metal gauzes uses a technology which has change l i t t l e s i n c e i t s f i r s t i n t r o d u c t i o n i n 1902. Although the convers i o n proceeds w i t h an e f f i c i e n c y i n excess o f 90%, the l o s s o f

0097-6156/82/0196-0261$06.00/0 © 1982 American Chemical Society In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

CHEMICAL REACTION ENGINEERING

262

ammonia i s of c o n s i d e r a b l e economic importance when the s c a l e of the o p e r a t i o n i s taken i n t o account. U n f o r t u n a t e l y , l a c k o f a d e t a i l e d q u a n t i t a t i v e understanding o f the o v e r a l l k i n e t i c s o f the process precludes a proper understanding o f the cause o f the i n e f f i c i e n c y and i n h i b i t s attempts to minimise i t . This paper i s concerned w i t h an attempt to provide t h i s fundamental understanding and i n d i c a t e s the manner i n which f u r t h e r refinement i s desirable. CONVERSION ON SINGLE WIRES AND

RIBBONS

Experimental. The r a t e s o f conversion o f ammonia to n i t r i c oxide on two wires of platinum/10% rhodium (0.0002 and 0.0005 m diameter) and a ribbon of platinum (2 thou t h i c k and 0.00325 mwide) edgeon to the gas stream, wer v a r i o u s feed composition c a l l y i n s e c t i o n i n F i g u r e 1. (1) Oxygen, n i t r o g e n and ammonia could be f e d a t c o n t r o l l e d and measured r a t e s to a r e a c t o r v i a a pre-mixing v e s s e l and a pre-heater, c o n s t r u c t e d from blocks of aluminium a l l o y BSHP15, r e s i s t a n t to ammonia, lagged and f i t t e d with e l e c t r i c a l h e a t i n g elements. Temperatures were monitored by thermocouples l o c a t e d w i t h i n the b l o c k s . As i l l u s t r a t e d i n Figure 1 a stream of r e a c t a n t gas passed v e r t i c a l l y upwards through a channel having a c r o s s - s e c t i o n 0.001m x0.0508m past the c a t a l y s t wire or ribbon mounted j u s t above the e x i t of the duct. Preheated, i n e r t gas passed through the two outer ducts, minimised c o o l i n g of the product stream by contact with the w a l l s and e l i m i n a t e d c a t a l y t i c r e a c t i o n t h e r e . The c a t a l y s t was r i g i d l y attached to an i n s u l a t e d e l e c t r i c a l connector on the o u t s i d e of one s i d e o f the r e a c t o r chamber, and a f t e r e n t e r i n g and c r o s s i n g the chamber emerged through a hole on the other s i d e and passed over a p u l l e y , and was then l i g h t l y s p r i n g - l o a d e d to take up thermal expansion to ensure that i t remained taut and s t r a i g h t even when hot. Other apertures through the w a l l of the r e a c t o r , sealed w i t h s i l i c a windows, permitted o b s e r v a t i o n of the c a t a l y s t and enabled the temperature d i s t r i b u t i o n to be determined by o p t i c a l pyrometry. The c a t a l y s t c o u l d be heated by p a s s i n g an e l e c t r i c c u r r e n t through the wire or r i b b o n , to a c t i v a t e i t and to enable s t a r t - u p of the o x i d a t i o n to proceed. A c u r r e n t o f 1 - 2 amps s u f f i c e d to pre-heat an a c t i v e c a t a l y s t to about 850°K whereupon a r e a c t a n t stream pre-heated to 500°K c o u l d r e a c t i n a thermally s e l f s u s t a i n i n g manner. A probe p o s i t i o n e d j u s t over the c e n t r e - p o i n t of the c a t a l y s t permitted continuous sampling o f the product gas f o r a n a l y s i s by mass spectrometry. R e s u l t s . F i g u r e 2 compares the observed r a t e s o f r e a c t i o n (gram moles of n i t r i c oxide produced per second per cm of c a t a l y s t ) as a f u n c t i o n of the l i n e a r v e l o c i t y of the gas f o r three d i f f e r e n t c a t a l y s t s and two d i f f e r e n t gas compositions. For a given gas flow r a t e the r a t e o f r e a c t i o n i s c r i t i c a l l y dependent upon the 2

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

22.

Figure 1.

263

Ammonia Oxidation on Platinum

NUTT ET AL.

Vertical section of reactor. Key: A, normal to catalyst wire; B, reactant gas stream; and C, argon stream.

0

I

Ο

1

ι

ι

10

ι

ι

20

Ι­ 30

V cm s~

1

Figure 2. Reaction rate/unit area vs. gas velocity. Key: · , 0.02 cm wire NH /0 = 0.3; • , 0.05 cm wire NH /0* = 0.3; O, 0.02 cm wire NH /O = 0.45; Δ , Ribbon wire NH /O = 0.45. s

2

s

s

s

t

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

t

264

CHEMICAL REACTION ENGINEERING

p h y s i c a l dimensions o f the c a t a l y s t but almost independent o f the gas composition. T h i s i s because f o r the bigger c a t a l y s t s the boundary l a y e r s a r e longer and t h e i r average thickness i s greater so that the average r a t e o f d i f f u s i o n through the boundary l a y e r i s l e s s . Since the thickness o f the boundary l a y e r v a r i e s as x5 where χ i s the d i s t a n c e along the boundary l a y e r from the l e a d i n g edge, p l o t s o f rx* where r i s the average r a t e o f r e a c t i o n on the surface versus the l i n e a r v e l o c i t y , are independent o f the s i z e o f the c a t a l y s t , as i l l u s t r a t e d i n F i g u r e 3, even though f o r a given c a t a l y s t and gas composition the e q u i l i b r i u m temperature increased somewhat w i t h gas f l o w - r a t e . THE SURFACE REACTION RATE Experimental. The surfac were determined by i n v e s t i g a t i o n was removed by use o f molecular beam mass spectrometric which have been d e s c r i b e d elsewhere. (2,3)

techniques

R e s u l t s . The r e s u l t s demonstrated i n an unambiguous manner that over the temperature range 500-1100°Κ the s u r f a c e r e a c t i o n proceeded through a dual s i t e mechanism by r e a c t i o n between adsorbed molecules of oxygen and ammonia i n accordance w i t h the r a t e equation: k NO

( 1

+ k

o

0 χ

2

k 2

ο

NH +

T

0

3

I 2

k

2

NH

NH

3

(1)

hm^*

3

when l£ denotes the i o n beam c u r r e n t ( i n the a r b i t r a r y u n i t s used) i n the mass spectrum o f the species sampled from the c a t a l y s t s u r ­ face, and the r a t e constants, k , Κ φ and k j ^ take the smoothed numerical values s e t out i n Table I . TABLE I . s

Temp

k

900° 1000 1100 1200

s

x 10"

3

2

k x 10 02 0.89525 0.77296 0.68544 0.62012

3

n

0.58129 0.70719 0.83023 0.94897

*ΝΗ

X

1

0

2

3

0.71553 0.48602 0.35418 0.27208

By c o n s i d e r a t i o n o f the r e l a t i o n s h i p between the i o n beam c u r r e n t s and the e q u i v a l e n t p a r t i a l pressures, p ^ o f the species a t the c a t a l y s t s u r f a c e , e s t i m a t i n g the l a t t e r from the geometry and e f f u s i o n c h a r a c t e r i s t i c s o f the molecular beam i n l e t and sampling system, i t followed that the r a t e o f production o f n i t r i c oxide a t the c a t a l y s t s u r f a c e , r , was given by: f

n

2753 x 1 0 " k

s 0 ^ 3 ( 1 + 0 . 5 * 1 0 k, Ό 0 k

P

2

0

P 2

NH

3

1

n

p

2

+

2

1 0 1 1

* Ν ΗL

3 3

NH3

1

molecule cm"" s e c " (2)

when the s e n s i t i v i t y exponent η - 5

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

NUTT ET AL.

Ammonia Oxidation on Platinum

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

266

CHEMICAL REACTION

PREDICTION OF THE

ENGINEERING

REACTION RATE AT ATMOSPHERIC PRESSURE

The r a t e of r e a c t i o n a t atmospheric pressure can be estimated by equating the r a t e of the s u r f a c e r e a c t i o n given by 2 to the r a t e of d i f f u s i o n through the mass t r a n s f e r boundary l a y e r a t the catalyst surface. P r e d i c t i o n s f o r Ribbons. The s i m p l e s t s i t u a t i o n to c o n s i d e r i s that when the c a t a l y s t i s a f l a t ribbon o r i e n t a t e d p a r a l l e l to the d i r e c t i o n o f flow of gas. Then a t a d i s t a n c e x downstream from the l e a d i n g edge the l o c a l mass t r a n s f e r c o e f f i c i e n t , h, i s given by: hx

1

1

—

=

given by:

0.323 Re * S c

5

and

x

thus the r a t e of d i f f u s i o n r , i s

r = hAc wher

r = 14.42V Sc~* Re"^ (P - p) (3) where V i s the gas v e l o c i t y (m/s), Ρ the b u l k p a r t i a l pressure (atm), and ρ the s u r f a c e p a r t i a l pressure (atm) o f the substance under c o n s i d e r a t i o n . Equations such as (3) apply to each r e a c t a n t and product i n the mixture with the a d d i t i o n a l c o n s t r a i n t : ΪΡ - 1 (4) Σρ = 1 (5) together with 4 ^

- Sr^

= 4r

N Q

(6)

= ôr^.

from the s t o i c h i o m e t r y o f the r e a c t i o n : 4NH + 50z - 4N0 + 6 H 2 O . S t r i c t l y the mathematical e x p r e s s i o n to be used f o r the d i f f u s i o n process should take account o f these c o n s t r a i n t s ; however, t h i s k i n d of c o u n t e r - d i f f u s i o n i n v o l v i n g two r e a c t a n t s and two products i n p r o p o r t i o n s determined by the s t o i c h i o m e t r y of the process i s of a complexity which has not y e t been considered theoretically. In the absence of such a t h e o r e t i c a l treatment, Equation (3) was a p p l i e d u s i n g d i f f u s i o n c o e f f i c i e n t s r e p o r t e d i n the l i t e r a t u r e f o r each o f the components f o r d i f f u s i o n a t room temperature. A small c o r r e c t i o n f o r the e f f e c t of the temperature g r a d i e n t i n the boundary l a y e r on the d i f f u s i o n c o e f f i c i e n t was made i n a manner d i s c u s s e d l a t e r . To e f f e c t a s o l u t i o n , the boundary l a y e r was c o n s i d e r e d to be d i v i d e d i n t o a l a r g e number of increments and f o r the element m, the l o c a l r a t e of d i f f u s i o n o f ammonia can be expressed: r

m

= 14.42 V S c NH3

Re ~^ m

x n j

fp. , , - p 1 [ NH3,(m-l) *rJH ,mJ n

1 N

(7)

x n j

3

and f o r oxygen: r

= 14.42V S c -§ " O2

NH ,m 3

=

5

n

Equating P

» Re. "-1 ί ρ

5

m

(7) and P

m

(8) we

, - p„ Ϊ0.8 [ 02,(m-l) 0z,m) Λ

have:-

N H , ( D H L ) " ( 0 ,(m-1) " P

3

y

2

Sc P

0 ,J°* 2

NH

1

1

3

8 S C

0

(8)

2

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

(9)

22.

267

Ammonia Oxidation on Platinum

NUTT ET AL.

which f o r s i m p l i c i t y i s expressed as (C > i n l a t e r equations Since, i n the steady s t a t e , the r a t e o f d i f f u s i o n o f ammonia i s equal to the r a t e o f r e a c t i o n , we may equate (2) and (8) and e l i m i n a t e p.„ by Equation (9) to g i v e : Nti3,m m

m

T

5S05.6 x 0.5 x 10* k [l

k^ k

g

n

+

0.5 x 1 0 k 1

Q 2

+

g

p ^ C J

>

10° k ^ P f c , , ,

J

-14.42 V S c . " R e ~ (P. , - p. ) 0.C Φ = 0 (10) U2 m U2»(lB-"l) 02,ul In Equation (10), Φ c o r r e c t s f o r the temperature o f the boundary l a t e r as d i s c u s s e d elsewhere. F o r a given c a t a l y s t temperature knowing n, k , , k ^ , k ^ , S c ^ , R e , V, * _ P ,(„_!)· a

m

0

i

t

i

m

i

y

n

d

œ

Φ, Equation (10) could b From t h i s the surface p a r t i a l pressures o f the other components were c a l c u l a t e d , b u t because t h i s procedure d i d n o t p r o p e r l y take account o f the counter-current nature o f the process, the values so p r e d i c t e d f a i l e d to conform to Equation ( 5 ) . G e n e r a l l y the d e v i a t i o n was l e s s than 10% but to prevent accumulation o f e r r o r s , the simple procedure o f n o r m a l i s i n g the p a r t i a l pressures was adopted. A f t e r c a l c u l a t i n g the l o c a l r a t e o f r e a c t i o n u s i n g Equation (2) and knowing the v o l u m e t r i c f l o w - r a t e o f gas past the s u r f a c e (from the v e l o c i t y and the width o f the duct) the b u l k p a r t i a l pressure o f r e a c t a n t s and products l e a v i n g the element m could be estimated, so p e r m i t t i n g the c a l c u l a t i o n o f the composi­ t i o n e n t e r i n g the (m+1) th element. To explore the e f f e c t s o f p o s s i b l e e r r o r s i n the value o f n, and a l s o to i l l u s t r a t e the e f f e c t o f the absolute r a t e o f s u r f a c e r e a c t i o n r e l a t i v e to the r a t e o f d i f f u s i o n , the c a l c u l a t i o n s were c a r r i e d through f o r a r i b b o n under c o n d i t i o n s s e t out i n P a r t 1, f o r values o f η » 4,5,6 and 7. The p r e d i c t i o n s i l l u s t r a t e d by the f u l l curves i n F i g u r e 4 c l e a r l y demonstrate how, when the chemical r e a c t i o n r a t e i s l a r g e ( n 4 , 5 ) the o v e r a l l r a t e i s c o n t r o l l e d by the r a t e o f d i f f u s i o n through the boundary l a y e r and i s independ­ ent o f chemical r e a c t i o n r a t e , but s t r o n g l y dependent on gas v e l o c i t y . These c o n c l u s i o n s were confirmed by examination o f the p r e d i c t e d values o f the l o c a l r e a c t i o n r a t e , and l o c a l concentra­ t i o n gradients along the r i b b o n over the range o f c o n d i t i o n s examined · The c a l c u l a t i o n s s e t out above were based on the assumption that the c a t a l y s t surface was always a t a temperature o f 900°K, however, p r a c t i c a l experience during the i n v e s t i g a t i o n s e t out i n Part 1, r e v e a l e d that the c a t a l y s t temperature always increased with i n c r e a s e i n gas f l o w - r a t e . The dotted curves i n F i g u r e 4 i l l u s t r a t e the e f f e c t o f such a v a r i a t i o n from 900°K to 1200°K a t the h i g h e s t v e l o c i t y , f o r the d i f f e r e n t values o f n. When d i f f u ­ s i o n c o n t r o l s , the s u r f a c e temperature has no e f f e c t , but when the chemical r e a c t i o n r a t e c o n t r o l s ( n = 7 ) the o v e r a l l r a t e i n c r e a s e s e

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

268

CHEMICAL REACTION ENGINEERING

w i t h i n c r e a s i n g v e l o c i t y through the a s s o c i a t e d temperature change. P r e d i c t e d values o f the r a t e of r e a c t i o n with η = 5 , 6 , tended to be s i g n i f i c a n t l y higher than experimental r e s u l t s . However, i n the experimental s t u d i e s i t was observed that e x c e s s i v e amounts o f n i t r o g e n appeared i n the products due probably to r e a c t i o n during sampling. When c o r r e c t i o n f o r t h i s was made, agreement between theory and experiment was s a t i s f a c t o r y , as shown i n the f i g u r e .

P r e d i c t i o n s f o r Round Wires. S i m i l a r computations were c a r r i e d out f o r d i f f u s i o n through the boundary l a y e r around a round wire, assuming that the gas v e l o c i t y j u s t o u t s i d e the boundary l a y e r (U) was given by p o t e n t i a l flow theory; U=2V s i n Θ, where V i s the v e l o c i t y i n the undisturbe angle r e l a t i v e to the forwar P r e d i c t i o n s were completely analogous to those f o r the ribbon and are shown i n F i g u r e 5. Analogous p r e d i c t i o n s r e s u l t e d f o r other gas compositions and wire s i z e s . As w i t h the r i b b o n , p r e ­ d i c t i o n f o r n = 5 agreed w e l l with experimental o b s e r v a t i o n when c o r r e c t i o n was made f o r l o s s by N formation during sampling. 2

Conversion on Gauze Pads. The computational technique was a l s o a p p l i e d to p r e d i c t conversions on an i n d u s t r i a l pad o f gauze, assumed to have 1024 apertures/cm constructed of wire 0.06cm diameter, o p e r a t i n g a t atmospheric pressure and 1100°K with a gas (11% NH3 i n a i r ) v e l o c i t y o f 0.45ft/sec. The computations were c a r r i e d out f o r a s t r a i g h t wire immersed i n a duct having a h a l f width equal to the mean h y d r a u l i c r a d i u s (0.0244cm) of the gauze system. The conversion so p r e d i c t e d tended to be somewhat lower than p r a c t i c a l experience suggests, as i l l u s t r a t e d i n F i g u r e 6. Since the p r e d i c t i o n s are based on theory and data f o r smooth, round w i r e s , w h i l s t i n d u s t r i a l gauzes always present a very g r a n u l a r sur­ face which i s l i k e l y to break-up the boundary l a y e r and to present a much l a r g e r e f f e c t i v e s u r f a c e area, the present agreement between p r e d i c t i o n and experience must be considered to be s a t i s f a c t o r y . F u r t h e r study i s d e s i r a b l e to r e f i n e the experimental and computational techniques, and i n p a r t i c u l a r to take i n t o account c a t a l y s t surface side r e a c t i o n s such as the p y r o l y s i s o f ammonia to n i t r o g e n which are observed i n the molecular beam i n v e s t i g a t i o n s . 2

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

22.

269

Ammonia Oxidation on Platinum

NUTT ET AL.

¥ c m »" Figure 4. Predicted value of rx* vs. V for flat ribbon. Key: , isothermal surface; , where catalyst surface temperature increases from 900° to 1200° over range of velocities shown; and X, experimental conversion (corrected for loss to Ng during sampling). τ

1—ι—ι ι ι ι 11

1—ι—ι ι ι I I

F

χ*

I

I

I

I

»ι ι »

/

¥ Figure 5.

•I

I

I

I

I I I M

I

too

10

cms-

1

Predicted value of rx* vs. V for round wire of 0.0005 m dia., when NH O = 0.3. Key is the same as in Figure 4. s

t

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

270

CHEMICAL REACTION ENGINEERING

0

4 NUMBER

Figure 6.

OF

GAUZES

Percent conversion of feed NH vs. number of gauzes in pad. S

Literature Cited 1. Majeed,A: PhD T h e s i s , Heriot-Watt Univ. 1976. "The Mechanisat i o n of the O x i d a t i o n o f Ammonia on a S i n g l e Wire C a t a l y s t " . 2. Nutt,C.W. & Kapur,S: Nature. 224, 160, 1969. " O x i d a t i o n o f Ammonia on Platinum". A l s o Nature. 220, 697, 1968. "Mechanism of O x i d a t i o n o f Ammonia on Platinum". 3. Kapur,S: PhD T h e s i s , Univ. o f Birmingham 1969. " O x i d a t i o n of Ammonia on Platinum". RECEIVED April 27,

1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

23 Dynamic Discernment of Catalytic Kinetics DEEPAK PERTI

1

and ROBERT L . K A B E L

Pennsylvania State University, Department of Chemical Engineering, University Park, PA 16802

Steady s t a t s u b s t a n t i a l thoug i n t e r p r e t a t i o n s are combined in an attempt t o de­ f i n e and understand the c a t a l y t i c k i n e t i c s f o r crrbon monoxide o x i d a t i o n over c o b a l t oxide (Co O ) supported on alumina. The r e s u l t is a r a t h e r c o ­ herent p i c t u r e o f o x i d a t i o n - r e d u c t i o n c a t a l y s i s by a metal oxide. I t is shown that the dynamic methods yield v a s t l y more i n f o r m a t i o n than steady s t a t e s t u d i e s with significantly l e s s experimental e f f o r t . 3

4

Dynamic r e a c t o r s t u d i e s a r e not new, but they have not been widely used i n s p i t e of the f a c t that they can provide a wealth of i n f o r m a t i o n r e g a r d i n g r e a c t i o n mechanisms. In t h i s r e s e a r c h , o x i d a t i o n o f carbon monoxide over supported c o b a l t oxide ( C 0 3 O 4 ) was s t u d i e d by both dynamic and conventional steady s t a t e methods. Among metal oxides, c o b a l t oxide i s known to be one o f the most a c t i v e c a t a l y s t s f o r CO and hydrocarbon o x i d a t i o n , i t s a c t i v i t y being comparable to that o f noble metals such as p a l l a d i u m o r platinum. Experimental C a t a l y s t . Supported c o b a l t oxide c a t a l y s t was prepared by impregnating c y l i n d r i c a l γ - Α ^ Ο β p e l l e t s (1.6 mm χ 1.6 mm) with c o b a l t n i t r a t e s o l u t i o n and c a l c i n i n g a t 773 Κ f o r 4 h. Cobalt oxide l o a d i n g was 6.851 g C03O4/IOO g γ - Α ^ Ο β . The Β.Ε.T. area of the support and the supported c a t a l y s t was 250 m^/g. X-ray d i f f r a c t i o n patterns showed only C 0 3 O 4 and γ-Αΐ2θ3 phases i n the c a t a l y s t . E l e c t r o n microprobe and S.E.M. x-ray mapping techniques revealed a w e l l d i s p e r s e d C 0 3 O 4 phase w i t h i n the p e l l e t s . 1

Current address: Ε. I. duPont de Nemours and Company, Photo Products Department, Rochester, NY 14603. 0097-6156/82/0196-0271$06.00/0 © 1982 American Chemical Society In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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ENGINEERING

Equipment. A v e r t i c a l fixed-bed r e a c t o r , made o f a 0.168 m I.D. and 0.5 m long 316 s t a i n l e s s s t e e l tube with an a x i a l thermowell, was used. The amounts o f c a t a l y s t used f o r the steady s t a t e and dynamic experiments were 6.35 and 18.69 g, r e s p e c t i v e l y . The r e a c t o r tube was heated by a f l u i d i z e d bed sand bath. The r e a c t i o n gases, 0£ and CO, and the d i l u e n t , He, were metered through rotameters and mixed p r i o r to t h e i r entry to the r e a c t o r . The mixing j u n c t i o n was designed such that e i t h e r o f the r e a c t i o n gases o r CO2 could be introduced o r removed from the stream to simulate a step i n c r e a s e o r decrease o f the component i n question. The e f f l u e n t from the r e a c t o r was analyzed by gas chromatography i n 4 minutes. Procedures - Steady State. Exp&UmzvvtA. To approximate a d i f f e r e n t i a l r e a c t o r an conversions were kept belo CO below 6.3 kPa were used. The t o t a l pressure was kept constant at 108.3 kPa f o r a l l the runs. For any p a r t i c u l a r s e t o f VQQ and P Q 2 > runs a t d i f f e r e n t values of W / F Q Q were conducted by v a r y i n g the flowrates o f O 2 , CO and He i n such a manner that the P 0 2 and Pco f e d stayed constant. The procedure was repeated f o r v a r i o u s combinations o f P Q and P ^ Q . T O a s c e r t a i n the e f f e c t o f tempera n a < a t u r e , one p a r t i c u l a r s e t o f P^o 02 P different temperatures. 2

p

w

a

s

r e

e a t e a
v a r i o u s runs were conducted a t d i f f e r e n t values o f W / F Q « F i g u r e 1 shows the r e s u l t s of some such experiments. If the p l u g flow assumptio haves i n a d i f f e r e n t i a l manner, a p l o t o f XQQ V S . W / F Q Q should be l i n e a r w i t h the slope equal to the r e a c t i o n r a t e . However, as i s evident from F i g u r e 1, s l i g h t curvature p e r s i s t s i n each p l o t . T y p i c a l c a l c u l a t i o n s r e v e a l e d that i n t r a and i n t e r p a r t i c l e heat and mass t r a n s f e r problems should not e x i s t a t the o p e r a t i n g cond i t i o n s . The r e a c t i o n r a t e s , t h e r e f o r e , were obtained by evaluat i n g the slope o f each curve a t the o r i g i n and as such can be called i n i t i a l rates of reaction, R Q . A p l o t o f l o g R Q V S . l o g PQ2 was l i n e a r i n d i c a t i n g that a power-law form o f expression should c o r r e l a t e the data w e l l . The order o f r e a c t i o n w i t h respect t o oxygen was 0.41. 0

E f f e c t o f Carbon Monoxide on Reaction Rate. F i g u r e 2 shows data a t VQ^ = 2.0 kPa and a t v a r i o u s values o f P Ç Q . T h i s graph i s s t r i k i n g l y d i f f e r e n t from that shown i n F i g u r e 1. One can r e a d i l y conclude that Pco has l i t t l e o r no e f f e c t on the r e a c t i o n r a t e and, t h e r e f o r e , the r e a c t i o n order w i t h respect to CO i s zero. V S . W/FCO

XQQ

E f f e c t o f Temperature on Reaction Rate. Plots of X vs. were obtained a t P Q • 2.0 kPa and Pco = 2 . 3 kPa f o r three d i f f e r e n t temperatures. The values o f R obtained from these graphs were p l o t t e d a g a i n s t 1/T to o b t a i n an a c t i v a t i o n energy of 1.273 χ 1 0 J/mol. c o

W / F

C

O

2

Q

5

E m p i r i c a l Rate Expression and Search f o r a Reaction Mechanism. Based on the steady s t a t e r e s u l t s , the i n i t i a l r a t e expression can be represented a s : Q Q m 3.9 χ 10 9

R

q

=

5

-1.273 χ 10 /RT _ 0.412 e P ^ Q

(1)

The e m p i r i c a l r a t e expression suggests only that an elemen­ t a r y step i n v o l v i n g a s u r f a c e s i t e and gaseous oxygen i s the r a t e

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

274

CHEMICAL REACTION ENGINEERING

3.0

ι

1

1

1

W/E , 0

Figure 1.

r

g(cat)h/mol

Effect of P on conversion at 488.6 Κ when P o = 2.3-2.4 kPa Key to P (kPa): • , 4.2; 0,2.0; and Δ , 0.8. 0t

C

(1).

0t

W/ffc>. g(cat)h/mol Figure 2. Results of CO partial pressure studies (1) at 488.6 Κ when P kPa. Key to P (kPa): 0,1.6; · , 2.3; Δ , 2.9; • , 3.4; V, 4.0; andO, 4.5.

0t

co

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

= 2.0

23.

PERTi AND KABEL

Dynamic Discernment of Catalytic Kinetics

275

determining s t e p . The need f o r performing f u r t h e r experiments, which would be more d i s c r i m i n a t i n g i n nature and provide more i n formation r e g a r d i n g surface-gas i n t e r a c t i o n , i s obvious. Such a need was adequately f u l f i l l e d by performing dynamic o r unsteady s t a t e experiments. Transient Kinetics A t o t a l o f 39 dynamic experiments were performed. These experiments i n v o l v e d one, two o r three components ( O 2 , CO and/or C O 2 ) i n the r e a c t o r . The step change could be imposed on any o f the components. Given the l e n g t h l i m i t a t i o n on t h i s paper, i t i s impossible to d e s c r i b e the r e s u l t s o f a l l the experiments and t o proceed l o g i c a l l y t o the c o n c l u s i o n s . However, t o g i v e the reader an adequate exposure t w i l l be d i s c u s s e d i n d e t a i s t a t e d . Complete d e t a i l s on the r e s e a r c h are a v a i l a b l e elsewhere (2)·

One-Component Experiments I n v o l v i n g CO - ReAlLÙtb, These experiments were done to o b t a i n the dynamic response o f the r e a c t o r to a step i n c r e a s e i n CO c o n c e n t r a t i o n f o r cases i n which the c a t a l y s t was p r e t r e a t e d w i t h oxygen f o r 1, 16 and 66 hours. The pretreatment was done i n a stream o f helium having an oxygen conc e n t r a t i o n o f 0.49 mol/m at 488 Κ and 108.3 kPa. A f t e r the p r e ­ treatment, pure helium was passed through the c a t a l y s t bed to purge any unadsorbed oxygen from the system. Gas a n a l y s i s a f t e r purging showed no t r a c e of O 2 , CO o r CO2 i n the r e a c t o r e f f l u e n t . The O 2 , CO and CO2 c o n c e n t r a t i o n p r o f i l e s a f t e r a CO step from zero t o 0.6 mol/m were obtained f o r a l l three experiments. I t was found that C O 2 i s formed as a r e s u l t o f i n t r o d u c i n g CO i n t o the r e a c t o r i n a l l three experiments (Figure 3 ) . The amount o f CO2 formed, as can be seen from the areas under the CO2 responses, increased w i t h i n c r e a s i n g times o f oxygen pretreatment. I n c r e a s ­ i n g pretreatment time beyond 66 h d i d not a l t e r the CO2 response. For one hour o f c a t a l y s t pretreatment i n O 2 , the concentra­ t i o n o f CO2 d e c l i n e s a f t e r a sharp i n c r e a s e a t the s t a r t . F o r longer oxygen pretreatment times the amount o f CO2 formed i n ­ creases s l o w l y , goes through a maximum a t around 6 minutes and then d e c l i n e s . Along w i t h the appearance o f C O 2 , d i s t i n c t amounts o f O 2 a l s o appeared i n the e f f l u e n t f o r the 16 and 66 h O2 pretreatment cases. These O 2 responses are sharp w i t h maxima around one minute and f i n i s h i n g around 8 minutes. No t r a c e o f O2 was found i n the case w i t h only 1 hour O 2 pretreatment. 3

3

IntOAp/ieXatioη. A q u a l i t a t i v e e x p l a n a t i o n f o r these f i n d i n g s can be put forward by examining the i d e a l s u r f a c e s formed by c r y s t a l l i n e c o b a l t oxide, [ C o ] [ C o ] V I [ 0 " * ] 4 , which i s a normal s p i n e l . I t i s formed by c l o s e c u b i c packing o f oxygen 2 +

I V

3 +

2

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

276

CHEMICAL REACTION ENGINEERING

anions w i t h the t r i v a l e n t and d i v a l e n t c o b a l t c a t i o n s l o c a t e d i n the o c t a h e d r a l and t e t r a h e d r a l spacings w i t h i n and between anion l a y e r s 03). I f a u n i t c e l l i s s e c t i o n e d i n the [ 1 0 0 ] d i r e c t i o n , v a r i o u s planes w i l l be obtained as shown i n F i g u r e 4 . In t h i s F i g u r e the l o c a t i o n s of C o , C o , and 0 ~ w i t h i n the c r y s t a l s t r u c t u r e of the normal s p i n e l are shown along w i t h some nomenc l a t u r e and an i n d i c a t i o n of the s i t e s f o r oxygen a d s o r p t i o n . I t has been shown that C o i s r e s p o n s i b l e f o r CO o x i d a t i o n . Thus, surfaces ending i n 1 / 8 and 3/8 l a y e r s i n F i g u r e 4 should be c a t a l y t i c a l l y a c t i v e . On these s u r f a c e s one can v i s u a l i z e three d i s t i n c t s i t e s : t r i v a l e n t c o b a l t i o n , [Co], l a t t i c e oxygen, [ O L ] , and a v a c a n c y , D , generated by removal of the l a t t i c e oxygen. A s s o c i a t e d w i t h these s u r f a c e s , three d i s t i n c t forms of oxygen can e x i s t : l a t t i c e oxygen, 0 ^ , oxygen adsorbed on [Co], 0 ç , and oxygen adsorbe have a l s o reported the oxygen on a c o b a l t oxide s u r f a c e . In the experiment with 1 hour of oxygen pretreatment, a l l 0 ^ and some 0Q must have been generated. Upon i n t r o d u c i n g CO, i t would at f i r s t r e a c t with 0 to form some adsorbed carbonate s p e c i e s . The subsequent d e s o r p t i o n of CO2 must be f a s t e r than i t s formation. T h i s would e x p l a i n the r a p i d r i s e and slow d e c l i n e of the CO2 response. As CO2 keeps forming, the number of 0Q will d e c l i n e and u l t i m a t e l y v a n i s h . A f t e r t h a t , CO would r e a c t with s t r o n g l y bound 0 L to c r e a t e v a c a n c i e s , O L In the 16 hours pretreatment case, the pretreatment time was probably l o n g enough to form a l l O L and 0 ç . In a d d i t i o n , some OQ could form. The appearance of O2 along with CO2 suggests that some of the weakly bound O Q i s r e l e a s e d due to i n t e r a c t i o n of CO with the s u r f a c e . CO then r e a c t s with the remaining O Q and the r e s u l t i n g 0 « C 0 adsorbs at 0 . T h i s would e x p l a i n the delay i n the C O 2 response and the maximum which occurs roughly when the O 2 response has f i n i s h e d . The CO2 maximum occurs when the excess O Q i s d r i v e n o f f the s u r f a c e to expose enough a c t i v e s u r f a c e f o r CO2 to form. At that i n s t a n t the remaining O Q has enough adjacent [ O L ] s i t e s a v a i l a b l e to adsorb the CO2 formed by r e a c t i o n of CO with O Q . I f the form of the CO2 i s assumed to be the same as that formed i n the 1 hour pretreatment case, i t s d e s o r p t i o n w i l l be f a s t causing the CO2 response to d e c l i n e afterwards. Schematicall y , the r e a c t i o n can be represented as: 2 +

3 +

2

3 +

L

o

O

C

o

O

o

L

fcofo Co - 0

L

° 0 fco - 0

L

° c o 9 o / 9 P °Co (

- Co + CO + Co - 0 - 5 - Co ·* 1/2 L

'jco^

0

L

0

2

+ Co - 0

|co L

- 0

L

- Co

The 66 hours oxygen pretreatment was long enough to form a l l p o s s i b l e O L , 0Q and O Q on the s u r f a c e . The presence of more O Q probably caused more CO2 to form i n the same manner as d e s c r i b e d f o r the 16 hour case. O

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

PERTi AND KABEL

0

Dynamic Discernment of Catalytic Kinetics

5

10

15

20

25

30

35

277

>300

TIME, min Figure 3. CO and O responses caused by step increase in CO overoxidized (pretreated in O ) catalyst (1). t

t

g

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

278

CHEMICAL REACTION ENGINEERING

Two-Component Experiments I n v o l v i n g a Reaction Mixture. In these experiments step i n c r e a s e s and decreases i n CO c o n c e n t r a t i o n (0.25 mol/m3) were made i n the presence o f continuously flowing oxygen and helium. The oxygen c o n c e n t r a t i o n was 0.21 mol/m . At no stage p r i o r to the CO step i n c r e a s e d i d oxygen pretreatment exceed a one hour p e r i o d . The step i n c r e a s e experiment i s q u i t e s i m i l a r to the one d e s c r i b e d i n the previous s e c t i o n f o r 1 hour oxygen p r e t r e a t m e n t e x c e p t that oxygen flow was not stopped p r i o r to the CO step i n c r e a s e i n t h i s case. The CO2 responses caused by the CO step i n c r e a s e and decrease are p l o t t e d i n F i g u r e 5. The CO2 response due to CO step i n c r e a s e r i s e s q u i c k l y and then d e c l i n e s u n t i l a steady s t a t e i s obtained. E a r l y , when the c o n c e n t r a t i o n of the adsorbed oxygen on the s u r face i s l a r g e s t , the maximum amount o f CO2 i s observed i n the r e sponse. T h i s response the t i o n on the s u r f a c e d e c l i n e from the gas phase oxygen. A f t e r about one hour a steady s t a t e i s achieved when the r a t e of removal of adsorbed oxygen equals that of regeneration. In the 1 hour pretreatment case, d e s c r i b e d earl i e r , the CO2 response showed a s i m i l a r r a p i d r i s e and slow dec l i n e i n d i c a t i n g f a s t formation and desorption of C O 2 . However, no oxygen was present i n the gas phase to regenerate the s u r f a c e i n that case and hence no steady s t a t e formation o f CO2 occurred. The CO2 response due to a step decrease i n CO c o n c e n t r a t i o n i n d i c a t e s that s u f f i c i e n t CO2 must be adsorbing on the s u r f a c e during r e a c t i o n , to be observed desorbing upon stoppage of the CO flow. The CO2 response due to a step decrease i n both CO and O2 i s a l s o shown i n F i g u r e 5 and i s i d e n t i c a l to that when only the CO flow was stopped. T h i s r u l e s out the p o s s i b i l i t y o f any r e a c t i o n between adsorbed CO ( i f any) and gas phase oxygen because otherwise the CO2 responses should have been d i f f e r e n t i n the presence or absence of 0 2 · 3

C o l l e c t e d Experimental Observations and Deduced Conclusions. Many conclusions can be reached from the above s t u d i e s and others not d e s c r i b e d here. A l l conclusions are c o l l e c t e d here. They are followed by a mechanistic i n t e r p r e t a t i o n . • C a t a l y s t s t a t e changes • Catalyst deactivation i s reversible • CO2 has l i t t l e e f f e c t on rate of reaction

· No r e v e r s i b l e O2 a d s o r p t i o n · No r e v e r s i b l e CO a d s o r p t i o n · S u b s t a n t i a l r e v e r s i b l e CO2 adsorption

• No e f f e c t of 0 and CO on CO2 adsorption • CO2 adsorption i s l e s s on e x t e n s i v e l y reduced c a t a l y s t • CO2 adsorption occurs on s i t e s other than r e a c t i o n sites

• CO2 desorption i s more r a p i d than formation • C O 2 formation and d e s o r p t i o n i s more r a p i d than regeneration o f oxygen s i t e • No r e a c t i o n occurs between adsorbed CO and gaseous O2

2

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

PERTi AND KABEL

Dynamic Discernment of Catalytic Kinetics

2.0

1

1

1

Curve Symbol CÇResponse to 1.6

Ο

Α ν

Ε

A

A

Ο—Ο Step Increase of CO . Step Decreases of COand 0 Ο—Ο Step Decrease of COJ 2

1.2

1

Α

5 0.8

Ο

d ο

Q4

1

ο

ο

12

"Î6

4β0

">24

TIME, min Figure 5.

CO Responses to step changes in CO (or CO and O ) concentration the presence of oxygen (I). t

t

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

CHEMICAL REACTION ENGINEERING

280 • 3 kinds of oxygen A. lattice B. adsorbed ( r e a c t i v e ) C. adsorbed (weakly bound) • Weakly bound oxygen i n h i b i t s CO2 formation

3 kinds of s i t e s on o x i d i z e d catalyst A. l a t t i c e oxygen B. where r e a c t i v e oxygen i s adsorbed C. where C0£ and weakly bound oxygen are adsorbed P a r a l l e l mechanisms e x i s t to produce CO2 on reduced c a t a l y s t

A P o s s i b l e Reaction Mechanism The proposed r e a c t i o n mechanism i s one which i s c o n s i s t e n t with the f i n d i n g s o f a l l the experiments performed and with the work of other authors. Th mechanis i based ideal t a l l i n e c o b a l t oxide s u r f a c REACTION STEPS FOR 1/2

0

2

+

C

0

+

[ 0

L

[Co] 4- [ 0 ]

L

Step 3

2

ADDITIONAL STEPS FOR PROLONGED OXIDATION AND

[o ] + L

o

1/2

2 [0 ] · 0 L

Q

»[o ] · o L

2

+ CO

>l/2 0

L

•

L

+ CO + CO +

• D

o

2

L

+

co

2

Step 4 + [0 ] · C0 L

2

+

[0 ] L

Step 5

SUBSEQUENT REACTION Step 6

2

• [o ] + co L

SUBSEQUENT REACTION

0

ADDITIONAL STEPS FOR PROLONGED REDUCTION AND

[o ]

Step 2

C0„

L

]

[o ] + co

· CO

L

Step 1

+ [Co]-Sl2H* [Co] · 0 Co

[Co] · 0 Co

[o ]

STEADY-STATE REACTION

Step 7

2

Steps 1 to 3 represent the mechanism by which the r e a c t i o n proceeds at steady s t a t e . I f the c a t a l y s t i s exposed to oxygen f o r a prolonged p e r i o d of time, a d d i t i o n a l a d s o r p t i o n of oxygen represented by step 4 can take p l a c e . I f such an o x i d i z e d c a t a ­ l y s t i s brought i n t o contact w i t h a r e a c t i o n mixture, the r e a c t i o n can proceed v i a a combination of steps 5 and 3 as w e l l as v i a steps 1 to 3 depending upon the extent of s u r f a c e o x i d a t i o n . Re­ d u c t i o n of the s u r f a c e i s represented by step 6. On a reduced s u r f a c e the r e a c t i o n can proceed v i a step 7 as w e l l as v i a steps 1 to 3 depending upon the extent of r e d u c t i o n of the s u r f a c e . At steady s t a t e the r e a c t i o n proceeds v i a a d s o r p t i o n of oxy­ gen at [Co]. The reasons f o r choosing 0Q as the oxygen respon­ s i b l e f o r CO o x i d a t i o n are many. Boreskov (5) concluded that at 488 Κ the r e a c t i o n must mainly proceed by a "concerted" mechanism. O

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

23.

PERTi AND KABEL

Dynamic Discernment of Catalytic Kinetics

281

He found that below 5 7 3 K, the r a t e o f s u r f a c e r e d u c t i o n of C 0 3 O 4 i s much slower than the r a t e of CO. o x i d a t i o n . Thus, p a r t i c i p a ­ t i o n o f 0 i n CO o x i d a t i o n a t 488 Κ i s u n l i k e l y . I f O L were con­ sumed i n CO o x i d a t i o n a t steady s t a t e , one would expect regenera­ t i o n o f O L to be f a s t . Experimental evidence suggests the oppo­ s i t e , i . e . that c a t a l y s t r e g e n e r a t i o n i s slow. Formation o f monodentate carbonate ( [ 0 L ] * C 0 2 i n step 2 ) along w i t h b i d e n t a t e c a r ­ bonate had been s p e c t r o s c o p i c a l l y observed on C 0 3 O 4 s u r f a c e s upon CO a d s o r p t i o n by H e r t l (6) and Goodsel ( 7 ) . Formation o f these s p e c i e s r a t h e r than c a r b o n y l type s p e c i e s i n d i c a t e the r o l e s played by O L and 0 ^ . Step 2 c o u l d proceed v i a an i n t e r m e d i a t e step i n which b i d e n t a t e carbonate i s formed as shown: L

ο

sr

0

oco — [Co]-0

C o

[ 0 J

+ [ 0 ] + CO + [Co] L

[0 ]-C0

[Co] +

Experimental evidenc t i o n on the c a t a l y s t i s u n a f f e c t e d by the presence o r absence o f the r e a c t i o n . T h i s i n d i c a t e s that r e v e r s i b l e a d s o r p t i o n o f C O 2 must be t a k i n g p l a c e on s i t e s other than those on which oxygen adsorb*?. I t was a l s o found that the presence or absence o f oxy­ gen does not a f f e c t the r e v e r s i b l e a d s o r p t i o n o f CO2 on an o x i ­ d i z e d c a t a l y s t w h i l e the amount o f C O 2 a d s o r p t i o n over reduced c a t a l y s t i s s i g n i f i c a n t l y lower. A l l these f a c t s j u s t i f y a s s i g n ­ ment o f s i t e [ 0 ] f o r CO2 a d s o r p t i o n . The i r r e v e r s i b i l i t y o f step 1 i s i n d i c a t e d by a r a p i d O2 r e ­ sponse t o an O 2 step decrease i r r e s p e c t i v e o f the time of O 2 ex­ posure. S i m i l a r l y , the r a p i d i t y of the CO response to a step de­ crease o f CO from r e a c t i o n c o n d i t i o n s a t steady s t a t e i n d i c a t e s the i r r e v e r s i b i l i t y o f step 2 . H e r t l (6) found that the o n l y product o f thermodesorption o f C 0 3 O 4 , preexposed t o CO, i s C O 2 . In other words, CO adsorbs i r r e v e r s i b l y on C 0 3 O 4 . L

Coherence o f Steady S t a t e and Dynamic R e s u l t s . A steady s t a t e r a t e e x p r e s s i o n based on steps 1 t o 3 can be d e r i v e d by assuming step 3 to be i n e q u i l i b r i u m and the r a t e s o f formation and consumption o f 0Q t o be e q u a l : O

l 2 3

k

_ "

D

k

l

(

K

3

k

+

K

C0

P

P

)

2

C0

0

P

0 2 1/2

P

1

/

The i n i t i a l r a t e e x p r e s s i o n w i t h Ρβθ£ k

° k

k l

l 2 k

ρ P

0

P

1 Λ 2

C0 /

2

P

0

2

1

+ k +

k

/

0 u

+

2

,

2

k

=

. ;

2 3 CO K

P

0i s :

2

Ρ

2 C 0 P

1/2

I f step 1 i s r a t e c o n t r o l l i n g , k-^ P Q ( 3 ) reduces t o :

2

«

k

2

P

a C

O

n

d

equation

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

282

CHEMICAL REACTION ENGINEERING

R

=

C

^ Ρ

1 Θ

/

2

(4)

2

Equation (4) i s similar i n functional form to equation (1) which was obtained from the steady state experiments. If the steady state data are correlated with equation (3) the result i s : P

4 χ 10-8 R

o

=

χ

10

4

Po

0

Ϊ72

~k 1

C

Ρ

± Θ

2

/

Ζ

1 / 2 9

— 5 +

4

χ

10

( 5 )

*

P

C

O

For the values of P Q and P used experimentally, the f i r s t term in the denominator ranges from one-half to one-twentieth of the second term. The minor contribution of the VQ^-I^ term ex­ plains the observed orde 0.5 of equation (4) an to be found by close examination of Figure 2. 2

C

O

Conclusions The steady state experiments took a year to carry out and yielded useful information, but limited insight. The dynamic kinetic studies, performed i n four months on a conventional fixedbed reactor with minor equipment modification, revealed a wealth of information. These experiments made i t possible to propose a reaction mechanism. The use of dynamic kinetic studies i s strongly recommended for the study of heterogeneous catalysis. Acknowledgements The authors wish to acknowledge the effective collaboration of Gregory J . McCarthy. Financial aid was provided by the National Science Foundation, Exxon Education Fund, Ε. I. duPont de Nemours and Company, and Union Carbide Corporation. Literature Cited 1. 2. 3. 4. 5. 6. 7.

Kabel, R. L.; P e r t i , D. Proceedings of XXth National Con­ vention of IMIQ, Acapulco, Mexico, 1980. Perti, D. Ph.D., Thesis, The Pennsylvania State University, University Park, PA, 1980. Fyfe, W. S. "Geochemistry of Solids;" McGraw-Hill, New York, 1964. Halpern, B.; Germain, J . E. J . Catal. 1975, 37, 44. Boreskov, G. K. Kin, i Kat. 1973, 14, 7. Hertl, W. J . Catal. 1973, 31, 231. Goodsel, A. T. J. Catal. 1973, 30, 175.

RECEIVED May

11,

1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

24 Hydrogenation Function of Fresh and Deactivated Hydrocracking Catalysts: Cyclohexene Hydrogenation S. R. POOKOTE, J. S. DRANOFF, and J. B. BUTT Northwestern University, Department of Chemical Engineering and Ipatieff Laboratory, Evanston IL 60201

A systemati genation f u n c t i o vated commercial hydrocracking c a t a l y s t s is reported u s i n g cyclohexene hydrogenation as a probe r e a c t i o n . The c a t a l y s t s were hydrocracking c a t a l y s t s , both f r e s h and d e a c t i v a t e d up t o p e r i o d s of two y e a r s . Hydrogenation a c t i v i t y is shown t o be r e l a t e d t o s u l f u r content, while ESR s t u d i e s i n d i c a t e a c o r r e l a t i o n between activity and MO in the c a t a l y s t . A p o s s i b l e mechanism o f d e a c t i v a t i o n is change in the o x i d a t i o n s t a t e o f Mo as induced by s u l f u r deposition. 5+

Hydrocracking c a t a l y s t s a r e b i f u n c t i o n a l i n nature and can be d e a c t i v a t e d by v a r i o u s mechanisms i n c l u d i n g poisoning of t h e a c i d i c f u n c t i o n by bases, formation o f i n a c t i v e s u l f i d e phases, and coke d e p o s i t i o n ( 1 ) . Some general aspects of d e a c t i v a t i o n i n hydrocracking have r e c e n t l y been d i s c u s s e d ( 2 ) . A p a r t i c u l a r problem, addressed here, i s that p r o p e r l y c o n t r o l l e d coke burning for r e g e n e r a t i o n appears t o r e t u r n f u l l a c t i v i t y f o r the a c i d i c f u n c t i o n , however f u l l hydrogénation a c t i v i t y i s not recovered. In t h i s study a s e r i e s o f f r e s h , d e a c t i v a t e d and regenerated hydrocracking c a t a l y s t s were i n v e s t i g a t e d as to hydrogénation a c t i v i t y u s i n g cyclohexene hydrogénation as a probe r e a c t i o n . The d e a c t i v a t e d m a t e r i a l s were obtained from both p i l o t and commercial u n i t s operated f o r p e r i o d s up t o two years. S p e c i f i c s of t h e hydrogénation f u n c t i o n were i n v e s t i g a t e d experimentally a f t e r p r e poisoning a c i d i c a c t i v i t y by NH^ chemisorption. Experimental C a t a l y s t s . The commercial c a t a l y s t s samples, a l l o f s i m i l a r composition, were s u p p l i e d by AMOCO O i l . These c o n t a i n MoO^ and CoO as hydrogénation components. The c r a c k i n g component i s a

0097-6156/82/0196-0283$06.00/0 © 1982 American Chemical Society In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

284

CHEMICAL REACTION ENGINEERING

c r y s t a l l i n e a l u m i n o s i l i c a t e i n an amorphous Si02/Al2Û3 m a t r i x . Table I g i v e s a d e s c r i p t i o n of m a t e r i a l s i n v e s t i g a t e d . Both p r e s u l f i d e d and n o n p r e s u l f i d e d c a t a l y s t s were i n v e s t i g a t e d ; most r e s u l t s presented-here p e r t a i n to p r e s u l f i d e d samples. The standard pretreatment c o n d i t i o n s were N ,lh,25°C; No-H2S,365 ; N2,lh,25°; N H 3 p u l s e to saturation,25°; N 2 purge,25 . The time employed i n the N2^S step was such t h a t the weight r a t i o of c a t a l y s t to H S was u n i t y . 0

2

2

Reaction. A c o n v e n t i o n a l f l o w r e a c t o r system was used to measure cyclohexene hydrogénation k i n e t i c s a t 150 6

1 2

e ( c H ) K^.mlh ^ 6

6

__

««._

204 2.3

88a 227

2.9

98

1.9

a

93° 65

a

0.18

b

0.18

c

—

7.5

b

4.0

C

—

10. o

b

10.5°

—

7.5 9.4

b

C

—

b

88° a, Experiment; b, S i m u l a t i o n w i t h independently determined para­ meters; c, Simulation w i t h f i t t e d parameters; d, see Appendix. Discussion The benzene y i e l d s given by the data o f F i g u r e s 4 and 5, 87% at 204°C and 88% a t 227°C, may be compared w i t h computed e q u i l i ­ brium y i e l d s of 13% and 19%, based on i n l e t c o n d i t i o n s . T h i s c l e a r l y shows the advantage of the continuous annular chromato­ g r a p h i c r e a c t o r over, say, a t u b u l a r r e a c t o r . The comparison i s not e n t i r e l y s t r a i g h t f o r w a r d , because d i l u t i o n o f the cyclohexane by He c a r r i e r as i t d i s p e r s e s c i r c u m f e r e n t i a l l y s h i f t s the e q u i l i ­ brium toward products; t h i s would have to be taken i n t o account i n any q u a n t i t a t i v e comparison. The data show o n l y p a r t i a l s e p a r a t i o n of benzene and cyclohexane. T h i s p a r t i a l s e p a r a t i o n must r e s u l t i n p a r t i a l suppression of the back r e a c t i o n , and must a l s o c o n t r i b u t e to the observed y i e l d enhancement ( i n a d d i t i o n to the d i l u t i o n e f ­ fect). Comparison o f product peak widths i n F i g u r e s 4 and 5 w i t h peak widths of weakly adsorbed N i n F i g u r e 2 i n d i c a t e s that spreading due to d i s p e r s i v e flows dominates peak broadening due to adsorp­ t i o n . D i s p e r s i o n causes s u f f i c i e n t peak o v e r l a p that i t seems r e a ­ sonable to a t t r i b u t e f a i l u r e to observe l a r g e r r e a c t i o n y i e l d s to t h i s f a i l u r e of s e p a r a t i o n . For example, the l i q u i d - s o l i d c o n t i n u ­ ous annular chromatographic r e a c t o r , where d i s p e r s i o n was s i g n i f i ­ c a n t l y l e s s , gave 100% y i e l d s f o r the h y d r o l y s i s o f methyl formate (4^, 5 ) . L i m i t a t i o n of y i e l d enhancement due to d i s p e r s i o n w i l l l i k e l y occur i n any g a s - s o l i d r e a c t o r o f t h i s c o n f i g u r a t i o n . I t may be p o s s i b l e t o overcome t h i s d i f f i c u l t y by p l a c i n g t h i n p a r t i ­ t i o n s i n the annulus as a b a r r i e r to t r a n s p o r t i n the c i r c u m f e r e n ­ t i a l d i r e c t i o n . However, w i t h t h i s arrangement, a x i a l d i s p e r s i o n i n the r e s u l t i n g tubes would be manifested as output peak broaden2

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

25.

WARDWELL E T A L .

Continuous Reaction Gas Chromatography

305

ing, and the remedy would not be completely e f f e c t i v e . Better s e p a r a t i o n , hence b e t t e r performance, would be obtained i n s y s ­ tems having l a r g e r d i f f e r e n c e s i n a d s o r p t i o n c o e f f i c i e n t s than those found f o r the s p e c i e s i n t h i s i n v e s t i g a t i o n . I n connection with t h i s i t should be noted that s e p a r a t i o n i s poorer a t higher temperatures, s i n c e the a d s o r p t i o n c o e f f i c i e n t s decrease with i n ­ c r e a s i n g temperature. Legend of Symbols c^

f l u i d phase c o n c e n t r a t i o n s

Ε

d i s p e r s i o n constant

F

f r a c t i o n o f bed fed

Κ

reaction rat

L

reactor length

M

number o f c e l l s about r e a c t o r circumference

m

c i r c u m f e r e n t i a l c e l l counting

η

a x i a l c e l l counting

n^

surface concentrations

Ρ

P e c l e t number based on r e a c t o r l e n g t h

_ e, L

index

index

Q

flow r a t e

t

time

U

linear velocity

X

conversion

^ef

e q u i l i b r i u m c o n v e r s i o n based on feed c o n d i t i o n s

y

circumferential direction

ζ

axial direction

3^

a d s o r p t i o n constant

ε

void fraction

η

efficiency

σ

variance

Acknowledgment T h i s work was supported by the U.S. Department o f Energy un­ der Contract No. DE-AC02-76ER02945. We are g r a t e f u l to Amoco O i l Co., N a p e r v i l l e , I l l n o i s , f o r f u r n i s h i n g the c a t a l y s t used i n t h i s work.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

306

CHEMICAL REACTION ENGINEERING

Literature Cited 1. 2.

Giddings, J. C. Anal. Chem. 1962, 34, 37. Fox, J. B . ; Calhoun, R. C . ; Eglinton, W. J. J . Chromatog. 1969, 43, 48. 3. Scott, C. D . ; Spence, R. D . ; Sisson, W. G. J . Chromatog. 1976, 126, 381. 4. Cho, Β. K . ; Carr, Jr., R. W.; A r i s , R. Chem. Engr. S c i . 1980, 35, 74. 5. Cho, Β. K . ; Carr, R. W.; A r i s , R. Sep. S c i . and Tech. 1980, 15, 679. 6. Roginskii, S. Z . ; Yanovskii, M. I.; Gaziev, G. A. Dokl. Akad. Nauk. S.S.R. 1961, 140, 1125. 7. Matsen, J. M . ; Harding, J. W.; Magee, E . M. J . Phys. Chem. 1965, 69, 522. 8. Wetherold, R. G . ; Wissler 1974, 133, 181. 9. Wardwell, A. W. Ph.D. Thesis, University of Minnesota, Minneapolis, MN, 1981. 10. P o l l i t z e r , E . L.; Hayes, J. C . ; Haensel, V. Adv. Chem. 1970, 97, 20. Appendix A r e a c t o r e f f i c i e n c y , η, defined by eq. 1A, i s used i n t h i s work. ^. ». « * « conversion o f chromatographic r e a c t o r n=fraction o f bed fed χ ττττ—: : — °„ . — e q u i l i b r i u m conversion a t i n l e t c o n d i t i o n s (1A) r

I t provides a comparison o f the p r o d u c t i v i t y o f the chromatogra­ phic r e a c t o r w i t h the p r o d u c t i v i t y t h a t would be obtained i f the annulus were f e d uniformly, ( f r a c t i o n o f bed f e d = 1 ) and reacted to a s p e c i f i e d conversion (conversion o f r e a c t o r / e q u i l i b r i u m con­ v e r s i o n < 1 ) . This e f f i c i e n c y i s thus a measure o f the penalty p a i d f o r using only a p o r t i o n o f the bed t o c a r r y out the r e a c ­ tion. I t i s a c o n s e r v a t i v e f i g u r e , however, s i n c e i t ignores the b e n e f i t o f s e p a r a t i n g r e a c t a n t and products. A measure o f the chromatographic r e a c t o r as a separator as w e l l as a r e a c t o r i s the recovery, R. conversion

v

In eq. 2A the y i e l d i s a y i e l d a t p u r i t y , the amount o f d e s i r e d product that can be removed from the r e a c t o r a t s p e c i f i e d p u r i t y . In t h i s work a p u r i t y o f 99% was s p e c i f i e d . Thus the recovery i s the f r a c t i o n of the product that can be removed a t the s p e c i f i e d purity. R E C E I V E D April 2 7 , 1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

26 Catalyst Decay During Hydrotreatment of a Heavy Coal Oil HONG JU CHANG, MAYIS SEAPAN, and BILLY L . CRYNES Oklahoma State University, School of Chemical Engineering, Stillwater, OK 74078

A trickle-bed reactor was used to study catalyst deactivation durin wt% SRC and proces catalys 324, NiMo/Al having monodispersed, medium pore diam­ eters. The catalyst zones of the reactors were sep­ arated into five sections, and analyzed for pore sizes and coke content. A p a r a l l e l fouling model is developed to represent the experimental observations. Both model predictions and experimental results con­ sistently show that: 1) the coking reactions are parallel to the main reactions, 2) hydrogenation and hydrodenitrogenation a c t i v i t i e s can be related to catalyst coke content with both time and space, and 3) the coke severely reduces the pore size and re­ s t r i c t s the catalyst efficiency. The model i s s i g ­ nificant because i t incorporates a variable d i f f u s i v i t y as a function of coke deposition, both time and space profiles for coke are predicted within pellet and reactor, activity i s related to coke content, and the model is supported by experimental data.

C a t a l y s t d e a c t i v a t i o n by coke d e p o s i t i o n i s a major concern i n upgrading c o a l - d e r i v e d o i l s . Coke forms as a r e s u l t s of a s e ­ quence o f side r e a c t i o n s which may be s i m p l i f i e d as f o l l o w s :

I f coke forms mainly by route 1 only, then t h i s i s p a r a l l e l f o u l ­ ing; i f mainly by routes 2 and 3, i t i s s e r i e s ; and i f e q u a l l y by a l l three routes, then i t i s independent f o u l i n g . John e t a l (Γ) i n d i s t i l l a t e s c a t a l y t i c c r a c k i n g s t u d i e s con­ cluded that coke on the c a t a l y s t cannot be a measure o f a c t i v i t y .

0097-6156/82/0196-0309$06.00/0 © 1982 American Chemical Society In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

CHEMICAL REACTION ENGINEERING

310

Instead, they proposed a time on stream theory to model the c a t a l y s t deactivation* However, i n an e a r l i e r work by Voorhies (2), a l i n e a r c o r r e l a t i o n between conversion and coke on c a t a l y s t f o r fixed-bed c a t a l y t i c c r a c k i n g was d e r i v e d . Rudershausen and Watson (3) a l s o observed the s i m i l a r behavior. Coke on c a t a l y s t can reduce the a c t i v i t y by covering the a c t i v e s i t e s and b l o c k i n g the pores. The e f f e c t s of pore s i z e on c a t a l y s t performance d u r i n g h y d r o t r e a t i n g c o a l o i l s i n t r i c k l e - b e d r e a c t o r s have been studied experimentally by Ahmed and Crynes (4_) and by Sooter (5) . The pore s i z e e f f e c t s i n other s t u d i e s are a l s o reported (6, _7, 8). Prasher e t a l . (9) observed that the e f f e c t i v e d i f f u s i v i t i e s of o i l s i n aged c a t a l y s t s were severely reduced by coke d e p o s i t i o n . T h e o r e t i c a l work by Masamune and Smith (10), who a p p l i e d act i v e s i t e coverage to account f o r i n t r i n s i c a c t i v i t y decay, pred i c t e d carbon p r o f i l e s i on stream and T h i e l e modulus ant d e p o s i t i o n i s heavier a t the o u t s i d e of the p e l l e t f o r p a r a l l e l f o u l i n g ; whereas, d e p o s i t i o n i n s i d e i s heavier f o r s e r i e s f o u l i n g . At a high T h i e l e modulus where d i f f u s i o n l i m i t a t i o n i s severe, the f o u l a n t d e p o s i t i o n i s always heavier at the o u t s i d e of the p e l l e t r e g a r d l e s s of the mechanism. E s s e n t i a l l y the same r e s u l t s were shown by Chiou and Olson (11) who extended Masamune and Smith's work to account f o r the e f f e c t of pore s t r u c t u r e . Froment and B i s c h o f f (12) developed a model to p r e d i c t the conv e r s i o n s and coke p r o f i l e s i n a fixed-bed r e a c t o r by assuming s e v e r a l r e l a t i o n s h i p s between a c t i v i t y and bulk coke content i n the c a t a l y s t p e l l e t . The r e s u l t s show that coke d e p o s i t i o n decreases toward r e a c t o r e x i t f o r p a r a l l e l f o u l i n g but i n c r e a s e s toward the e x i t f o r s e r i e s f o u l i n g . A l l of these models have been l i m i t e d to only p a r t i a l repr e s e n t a t i o n of c a t a l y s t coking-decaying phenomena i n a fixed-bed reactor. No experimental data have shown c o n s i s t e n c y between the many f e a t u r e s i n c l u d i n g f o u l i n g mechanism, c a t a l y s t a c t i v i t y , pore s i z e and coke p r o f i l e s i n both the p e l l e t and the t r i c k l e - b e d r e actor. In t h i s study experimental data on coke contents, coketime and p o s i t i o n p r o f i l e s , pore s i z e s and c a t a l y s t a c t i v i t i e s r e s u l t i n g from a t r i c k l e - b e d r e a c t o r are presented to demonstrate the r e l a t i o n s h i p s and c o n s i s t e n c i e s . A p a r a l l e l f o u l i n g model based on a c t i v e s i t e coverage and pore blockage i s developed and extended to the fixed-bed r e a c t o r performance of a c a t a l y s t proc e s s i n g a heavy c o a l o i l . Experimental The o i l feedstock used i n t h i s study was a 30 wt% SRC-I and 70 wt% process solvent mixture c o n t a i n i n g 87.2 wt% carbon, 6.73 wt% hydrogen, 1.40 wt% n i t r o g e n , 0.50 wt% s u l f u r and 0.097 wt% ash, having an i n i t i a l b o i l i n g p o i n t of 242C and with 32 wt% b o i l ing at higher than 454C. The c a t a l y s t was S h e l l 324, a NiMo/Al

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

26.

CHANG E T A L .

Catalyst Decay During Hydrotreatment 3

311

2

c a t a l y s t having a s u r f a c e area o f 150 χ 1 0 m /kg, a pore volume 3

3

of 0.42 χ 1 0 ~ m /kg and a narrow pore s i z e d i s t r i b u t i o n a t 11.0 nm. A 0.5 m by 0.013 m t r i c k l e - b e d r e a c t o r equipped w i t h auto­ matic temperature, pressure and flow c o n t r o l s and adequate s a f e t y monitoring systems was used i n t h i s study. The c a t a l y s t was c a l ­ cined and p r e s u l f i d e d before startup. The nominal o p e r a t i o n a l con­ d i t i o n s were: temperature, 400C; p r e s s u r e 13.9 MPa; l i q u i d v o l ­ ume space time, 2.50 hours; and h y d r o g e n - t o - o i l r a t i o , 1780 s t d . m H2/m o i l . During shutdown, the r e a c t o r was cooled q u i c k l y with a h i g h flow of hydrogen t o prevent excess coking. The used c a t a l y s t s were separated i n t o f i v e s e c t i o n s , 0.1 meter each, ex­ t e n s i v e l y e x t r a c t e d with p y r i d i n e , and d r i e d i n a h i g h vacuum oven. Thus, the coke content i n t h i s study i s d e f i n e d as p y r i d i n e i n s o l u b l e carbonaceous m a t e r i a bustion i n a i r . Specia t i o n which could badly mask the a c t u a l v a l u e s o f coke c o n t e n t s . The pore volumes and pore s i z e s were measured w i t h a Micromerit i c s Model 910 mercury porosimeter by assuming a c o n t a c t angle o f 130 degrees. O i l products were r o u t i n e l y analyzed f o r hydrogen and n i t r o g e n contents w i t h a Perkin-Elmer Model 240B elemental a n a l y z e r . More d e t a i l s on t h i s experimental work have been r e ­ ported by Crynes (13). 3

3

Experimental R e s u l t s Six experimental runs were made a t e s s e n t i a l l y the same op­ e r a t i n g c o n d i t i o n s but w i t h v a r i o u s d u r a t i o n s to o b t a i n param­ e t e r s as f u n c t i o n s of time on stream. Coke p r o f i l e r e s u l t s a r e shown i n F i g u r e 1. Note that coke content i s h i g h a t the r e a c t o r entrance and the slope of the p r o f i l e g r a d u a l l y i n c r e a s e s to a maximum then l e v e l s o f f (at 153 h o u r s ) . The maximum a c t i v i t y zone (low coke content) w i t h i n the r e a c t o r g r a d u a l l y moves down t o the reactor exit. T h i s type of p r o f i l e i m p l i e s that the coking r e ­ a c t i o n s f a l l i n t o the p a r a l l e l p a t t e r n shown by Froment and B i s c h o f f (12). The coke contents from d i f f e r e n t s e c t i o n s of each run were averaged over the r e a c t o r , and the r e s u l t s a r e p l o t t e d i n F i g u r e 2. Most coke forms d u r i n g the f i r s t 40 hours on stream. Note that during s t a r t u p and w i t h i n the f i r s t hour o f o p e r a t i o n , n e a r l y 5 wt% coke has accumulated. F i g u r e 3 suggests a r e l a t i o n s h i p between c a t a l y s t a c t i v i t y ( i n terms o f hydrogen and n i t r o g e n contents i n the product o i l ) and coke content. F i g u r e 4 shows that coke has s e v e r e l y blocked the pore mouths. These pore s i z e s have been e x p e r i m e n t a l l y de­ termined and not c a l c u l a t e d from a pore volume-surface area r e ­ l a t i o n s h i p . A d d i t i o n a l Auger analyses support the bulk a n a l y s i s r e s u l t s and f u r t h e r r e v e a l that coke accumulates predominately w i t h i n the outer edges of the p e l l e t s . With i n c r e a s i n g time on stream, the coke penetrates more deeply w i t h i n the p e l l e t u l t i ­ mately a c h i e v i n g a maximum v a l u e o f 14 wt%.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

F/gare i .

Cofa? pro/ites m iricfcfe bed reactor for 4 experimental runs. Key: tion; Δ , O, 0, and • , experimental data.

, model predic­

ο

2 2

M W

2

â

M

δ

H

> ο

M

S

Ο

Ν)

— ιu>*

Figure 2. Average coke content over reactor vs. time on stream. Key: prediction; Δ, experimental data.

, model

Κ)

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

Figure 3. Catalyst activity vs. average coke content over reactor. Key: Ο, Δ , experimental data.

, model prediction;

ο

2

W M

2

W

Η δ

w > ο

»—»

26.

CHANG E T AL.

Figure 4.

Catalyst Decay During Hydrotreatment

Most frequent pore diameter vs. catalyst coke content. Key: model prediction; Δ, experimental data.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

CHEMICAL REACTION ENGINEERING

316 Discussion

A model based on p a r a l l e l f o u l i n g was developed t o represent these experimental o b s e r v a t i o n s . The f o l l o w i n g assumptions were made: (1)

The r e a c t i o n s can be described by two simple f i r s t order p a r a l l e l r e a c t i o n s (route 1 of the scheme presented e a r l i e r ) : k A

(2) (3) (4) (5) (6)

a

• P r o d u c t s , and A

Coking r a t e i s much slower than the main r e a c t i o n s r a t e . The r e a c t o r i s i s o t h e r m a l throughout and i s i d e a l p l u g flow. There i s a n e g l i g i b l the p e l l e t s . Pores a r e f i l l e d w i t h l i q u i d throughout the r e a c t i o n s . E f f e c t i v e d i f f u s i v i t y o f the r e a c t a n t versus pore s i z e f o l ­ lows the S a t t e r f i e l d e t a l . c o r r e l a t i o n (14): D

(7)

k Q —>Coke

A

A

7

Ae ^Vp ^ k =

xp

46 X

]

M

Pores a r e uniform and p a r a l l e l to each other: PD - PD (ε /ε )** ο ρ po

(8)

[2]

u

J

The c a t a l y s t p o r o s i t y i s reduced by the coke: ε

- ε

- Q (ρ /ρ )

[3]

This model i s s i g n i f i c a n t because: 1) a v a r i a b l e d i f f u s i v i t y as a f u n c t i o n of coke content i s i n c o r p o r a t e d , 2) coke content p r o f i l e s both w i t h i n a p e l l e t and the r e a c t o r bed a r e p r e d i c t e d with time and space, 3) c a t a l y s t a c t i v i t y i s r e l a t e d to coke con­ tent, thus w i t h time and space a l s o , and 4) the model i s supported by experimental data. The c o n s e r v a t i o n equations r e p r e s e n t i n g the i n t r a p a r t i c l e de­ a c t i v a t i o n i n non-dimensional form f o r s p h e r i c a l geometry a r e given as f o l l o w s :

η

D

9

2

γ

Ρ

.

,r 3x^ ρ

P

9 y

3D

+ _ 9x P

p

. 2D

-r— + — 3x P

χ P

y

, 0

%

~ P

3x

- hf A

/1

\

m

u2

(1-q ) y - h p Ρ q f t - M n

π

_!^P_ z

1

ε -rr* σθ ρ

Γ/1

= 0 [AJ u

J

ν ί5

D = 3ε Εχρ[-4.6λ /(1-γς ) ] ο

ρ

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

[6]

26.

317

Catalyst Decay During Hydrotreatment

CHANG ET AL.

Initial and boundary conditions are: ê θ - 0 and 0 < χ < 1, y ρ - ρv 9

@ χ

β χ

The

ρ

- 1 and θ

ρ

> 0,

ρ

= 0 and θ

ρ

> 0,

y

y

p

= 1, q ρ 9

= 0, ε = 1, D = 1

Η

9

= 1 also

[8]

- 0

[9]

dimensionless equations over the r e a c t o r bed i t s e l f 3y

3y

b

_

+ Ε _

b

b

are:

3q

b

+

G

n

A

y

b

= 0 and -gg-

I n i t i a l and boundary c o n d i t i o n s 8 6 @ x

[7]

9

= n y q

b

[

1

0

]>

[

u

]

are:

• 0 and 0 < ^ < 1, y • 1, q = 0 and 9 > 0, y = 1 b

b

fe

- 0 also

[12] [13]

b

The e f f e c t i v e n e s s f a c t o r s and η , defined as the r a t i o s o f the a c t u a l r e a c t i o n r a t e s a t time θ to^the maximum r e a c t i o n r a t e s on a c l e a n c a t a l y s t , are obtained n u m e r i c a l l y from equations [4] [9]. An e x p l i c i t f i n i t e d i f f e r e n c e method was used to s o l v e the p a r t i a l d i f f e r e n t i a l equations without f u r t h e r s i m p l i f i c a t i o n s . D e n s i t i e s , p o r o s i t i e s and c l e a n c a t a l y s t pore diameters were meas­ ured experimentally. The maximum coke content i s assumed t o be that which f i l l s the pore completely. The t o r t u o s i t y i s taken as 2.3, as discussed by S a t t e r f i e l d e t a l . (14). The r a t e constants, bulk d i f f u s i v i t y , c r i t i c a l s o l u t e diam­ e t e r and i n t r i n s i c r a t e decaying orders were v a r i e d to o b t a i n the data f i t . The r e s u l t i n g r a t e constants are 1.13 χ 1 0 " m /(s) (kgc a t a l y s t ) f o r the main r e a c t i o n , 0.948 χ 10" m /(s) ( k g - c a t a l y s t ) f o r coking i n terms of hydrogénation o r 3.704 χ 1 0 ~ m /(s) (kgc a t a l y s t ) i n terms o f hydrodenitrogenation. The c r i t i c a l s o l u t e diameter of 3.3 nm, bulk d i f f u s i v i t y o f 0.55 χ 1 0 " m /s, orders of d e a c t i v a t i o n of h a l f f o r the main r e a c t i o n and second order f o r coking, and the corresponding T h i e l e modulus, 11.4, f o r the main r e a c t i o n a t c l e a n c a t a l y s t c o n d i t i o n s a l l f a l l w i t h i n reasonable ranges which have been reported. Second order d e a c t i v a t i o n f o r the coking r e a c t i o n i n d i c a t e s that the r e a c t i o n may take dual s i t e s , w h i l e the h a l f order d e a c t i v a t i o n f o r the main r e a c t i o n i n ­ d i c a t e s that the small molecules l e s s s u b j e c t i v e to coking may s t i l l be able to access the s i t e s r e s t r i c t e d by coke. 6

9

3

3

9

9

3

2

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

318

CHEMICAL REACTION ENGINEERING

The coke p r o f i l e s i n the r e a c t o r bed can be p r e d i c t e d e x c e l l e n t l y by the model as shown by the s o l i d l i n e s i n F i g u r e 1. Figure 2 shows good consistency i s a l s o obtained f o r the average coke content over the r e a c t o r bed versus time on stream. Note that w i t h i n the time p e r i o d of r e a c t o r s t a r t u p p l u s one hour of operat i o n , the average coke content of the r e a c t o r bed i s a l r e a d y a t about 5 wt%. The model cannot be a p p l i e d to t h i s s t a r t u p and i n i t i a l p e r i o d with the r a p i d t r a n s i e n t s of temperature, a c t i v i t y " s p i k e " and c o n c e n t r a t i o n . However, compensation f o r t h i s i n t e r v a l can be made by a time t r a n s l a t i o n of the model: a model time of 36 hours i s f i x e d a t an experimental time of zero. A temperature d i f f e r e n c e of more than 20C between the center of the bed and outer w a l l of the r e a c t o r i n the startup stage has been observed i n our l a b o r a t o r y f o r some experiments. About three-fourths of t h i s d i f f e r e n c e i s across th a c t o r a t reasonably lowe coke formation and to b e t t e r maintain the c a t a l y s t a c t i v i t y i s im portant, i f not c r i t i c a l . The model p r e d i c t s that the dependencies of hydrogénation and hydrodenitrogenation a c t i v i t i e s on the r e a c t o r coke content are stronger than l i n e a r , and are s a t i s f a c t o r i l y supported by the experimental data as shown i n F i g u r e 3. The p r e d i c t e d pore s i z e coke content r e l a t i o n s h i p i s shown i n F i g u r e 4. The trend i s cons i s t e n t with the experimental data, although data a t h i g h coke l o a d i n g l i e above the p r e d i c t e d l i n e . Two reasons may have cont r i b u t e d to t h i s : 1) the contact angles f o r catalyst-mercury and coke-mercury may be d i f f e r e n t and 2) the mercury porosimetric method could be l i m i t e d to measuring small pore s i z e s . Conclusion A p a r a l l e l f o u l i n g model has been developed to represent experimental observations f o r h y d r o t r e a t i n g a c o a l o i l i n a t r i c k l e bed r e a c t o r over a commercial NiMo/Al c a t a l y s t . T h i s model accur a t e l y p r e d i c t s coke p r o f i l e s with time and r e a c t o r p o s i t i o n , and hydrogénation and hydrodenitrogenation as f u n c t i o n s of coke content. The f o l l o w i n g conclusions can be drawn from t h i s study. (1)

(2) (3) (4)

C a t a l y s t coke content i s a good measure of a c t i v i t y . Both hydrogénation and hydrodenitrogenation can be r e l a t e d to coke content. Coke s e v e r e l y reduces the pore s i z e s and r e s t r i c t s the c a t alyst efficiency. Poorly c o n t r o l l e d high temperatures during s t a r t u p can r e s u l t i n excess coking r e a c t i o n . The c a t a l y t i c coking r e a c t i o n may r e q u i r e dual c a t a l y s t s i t e s , whereas small s i z e r e a c t a n t s which are l e s s s u b j e c t i v e to coking may be a b l e to access the s i t e s covered by the coke.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

26.

CHANG E T A L .

Catalyst Decay During Hydrotreatment

:

Legend of Symbols C D D

= = D

Concentration o f r e a c t a n t i n l i q u i d , kg/m Dimensionless e f f e c t i v e d i f f u s i v i t y , / D

=

Dimensionless groups, Ε = Q /

h

=

T h i e l e Modulus, h

k L m,η PD q

= = = = =

Q

=

r

=

c

M

h

e

A

e

o

Bulk and e f f e c t i v e d i f f u s i v i t y , m /s

E, G

SD Τ t χ

e

2

A' A e -

r

3

D

A

A

= Y4 e

P

k p

/ D A

k A f

T q

>

G

5 5k

p

Q

7 C

k

A b M Af
)

(26)

V ^ , ]

Z

with ξ - r / r and θ « v / r . Figure 3 i l l u s t r a t e s the change i n the average CaO conversion during the complete g a s i f i c a t i o n of a char p a r t i c l e f o r d i f f e r e n t values of , and « C * * Pl * based on parameter values corresponding to g a s i f i c a t i o n of an I l l i n o i s #6 c o a l and i t has been assumed that 10% CaS i s formed i n the p y r o l y s i s stage, i . e . χ » 0.1. Again as i n the e q u i l i b r i u m case, we see that CaS can indeed form w i t h i n the char p a r t i c l e even though i t would not be s t a b l e i n the ambient gas. Initially, the CaO conversion increases as the d i f f u s i o n r e s i s t a n c e i n the char causes H2O and CO2 t o react with the char before they can o x i d i z e the CaS. However, as the g a s i f i c a t i o n f r o n t moves inward, the conversion goes through a maximum s i n c e the p r o t e c t i v e char s h e l l shrinks a l l o w i n g i n c r e a s i n g amounts of CaS to become o x i ­ dized back to CaO. There i s a net g a i n i n CaO conversion during g a s i f i c a t i o n . The s i z e of t h i s gain depends on the r e l a t i v e mag0

0

T

i e

e x a n l

2

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

e

s

344

CHEMICAL REACTION ENGINEERING

Figure 3. Average CaO conversion during char burnout for A, JCÎ = 25.0 and «C« = 0.025; B, & = 5.0 and J& = 0.005; and C, JCi = 5.0 and JC* = 0.05. Key: · , Experimentally obtained CaO conversions with Illinois #6 coal at 140°C (14).

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

28.

JENSEN ET

AL.

345

Char Gasification

nitudes of the r a t e constants f o r the CaO/CaS r e a c t i o n s . The model p r e d i c t i o n , Figure 3B, shows good agreement with the e x p e r i ­ mentally determined CaO conversions. Concluding Remarks The model and the r e s u l t s presented here i l l u s t r a t e the physicochemical processes involved i n char g a s i f i c a t i o n with s i m u l t a ­ neous s u l f u r capture. In p a r t i c u l a r , they demonstrate that d i f f u ­ s i o n l i m i t a t i o n s i n the g a s i f i c a t i o n r e a c t i o n s enable the conver­ s i o n of CaO to CaS w i t h i n the char even though CaS formation i s not f e a s i b l e at bulk gas c o n d i t i o n s . Furthermore, t h i s f i r s t v e r ­ s i o n of the model c o r r e c t l y p r e d i c t s the trends observed e x p e r i ­ mentally. Future e f f o r t i n t h i s area w i l l focus on q u a n t i t a t i v e comparisons of model p r e d i c t i o n designed g a s i f i c a t i o n experiments Legend o f c

C

t CaO

»e e

\

Symbols

t o t a l gas phase concentration

Τ ν

temperature front velocity

i n i t i a l concentration of CaO effective diffusivity e m i s s i v i t y of char

x^

mole f r a c t i o n of

γ ε

r a t i o of d i f f u s i v i t i e s porosity

a c t i v a t i o n energy

ζ

h

heat t r a n s f e r c o e f f i c i e n t

χ ΔΗ

enthalpy of r e a c t i o n j k

V j

Aq r S

r a t e constants see eqns. (5-7) r e l a t i v e r a t e of CaO convers i o n to carbon g a s i f i c a t i o n r e l a t i v e r a t e of CaS oxida­ t i o n to carbon g a s i f i c a t i o n length pore surface has retreated r a d i a l coordinate s p e c i f i c i n t e r n a l surface of char time

species

dimensionless r a d i a l coordinate,

r/r ο

ρ

d e n s i t y of porous char

ρ 4>

d e n s i t y of carbon T h i e l e modulus

ci

k

ci D

conversion

of

4

S

co

50

CaO

Subscripts: b bulk ο initial Superscripts: * c o n d i t i o n s where pore walls merge

Acknowledgment One of the authors (KFJ) would l i k e to thank Exxon Research and Engineering Company f o r a s t i m u l a t i n g summer appointment. H e l p f u l d i s c u s s i o n s with Professors Sarofim and Longwell and t h e i r a s s o c i a t e s are g r a t e f u l l y acknowledged.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

CHEMICAL REACTION

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ENGINEERING

Literature Cited [1] [2] [3] [4]

[5] [6] [7] [8] [9] [10] [11] [12] [13] [14]

Freund, H. and Lyon, R. Κ., Comb. Flame 1982, 45 191. A t t a r , Α., F u e l 1978, 57 201. Freund, H., Lyon, R. K., and Bartok, W., I n t . Conf. Coal Science, Dusseldorf, West Germany, September 1981. M u l l e r , C. H., S c h o f i e l d , Κ., Steinberg, M. and Broida, H. Ρ., 17th Symp. ( I n t . ) Combustion, The Combustion I n s t i t u t e , P i t t s b u r g h , 1979, 867. S r i n i v a s , B. and Amundsen, N. R., Can. J. Chem. Eng. 1980, 58, 476. Sundaresan, S. and Amundsen, N. R., Ind. Eng. Chem. Fundam. 1980, 19 351. Jüntgen, H., Carbon 1981, 19 167. Ruth, L. Α., Squires Technol. 1972 6 1009 A t t a r , A. and Dupuis, F., Ind. Eng. Chem. Process Design Develop. 1979, 18 607. Simons, G. A. and F i n s o n , M. L., Comb. Sci. Tech. 1979, 19 227. B h a t i a , S. K. and Perlmutter, D. D., AIChE J. 1981, 27 226. Gavalas, G. R., AIChE J. 1980, 26 577. Gavalas, G. R., Comb. Sci. Tech. 1981, 24 197. Freund, H., et al., to be p u b l i s h e d .

R E C E I V E D April 27,

1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

29 Nitric Oxide Reduction by Hydrogen and Carbon Monoxide over Char Surface Fundamental Kinetics for Nitric Oxide Emission Control from Fluidized-Bed Combustor of Coal TAKEHIKO FURUSAWA, MIKIO TSUNODA and DAIZO KUNII University of Tokyo, Department of Chemical Engineering, Bunkyo-Ku, Tokyo, 113 Japan

The rate o gen and carbon monoxide over a char surface was measured and compared with the rate of noncatalytic "NO" reduction by char which has been previously reported to have a significant effect on "NO" emis­ sion control in a fluidized bed combustor of coal. In the presence of hydrogen and carbon monoxide, the surface catalyzed reduction of "NO" controlled the overall "NO" destruction. Thus the presence of hydrogen and carbon monoxide decreased the comsumption of carbon to nearly zero. The rate was significantly enhanced by hydrogen over the tempera­ ture range employed for the fluidized bed combustor. The ratio of formed ammonia to consumed "NO" is de­ creased with an increased temperature. The c o n t r o l o f n i t r i c oxide emission from a f l u i d i z e d bed c o a l combustor has been e x t e n s i v e l y i n v e s t i g a t e d and i t was found that the l e v e l o f n i t r i c oxide emission was determined by the r e l a t i v e c o n t r i b u t i o n o f n i t r i c oxide formation and r e d u c t i o n p r o cesses. (1_,2) There i s a great need f o r q u a n t i t a t i v e i n f o r m a t i o n concerning the r a t e o f these processes.(2) The n o n c a t a l y t i c r e d u c t i o n o f n i t r i c oxide by i n s i t u formed char i s considered one of the s i g n i f i c a n t r e a c t i o n s which c o n t r o l n i t r i c oxide emission and a d e t a i l e d k i n e t i c study was c a r r i e d out. C2,_3,4) The present authors demonstrated that t h i s r e a c t i o n proceeded even under an excess a i r c o n d i t i o n and that the r a t e i s enhanced by the c o e x i s t i n g oxygen up to 750°C.(5,6) Besides the n o n c a t a l y t i c r e a c t i o n , carbon monoxide may have a s i g n i f i c a n t e f f e c t on n i t r i c oxide r e d u c t i o n by char.(7) Roberts e t a l . ( 8 ) r e ported that the gas phase r e a c t i o n s i n the n i t r i c oxide r e d u c t i o n play a minor r o l e and that the absence o f a major gas phase r e a c t i o n o f NO and c o a l n i t r o g e n i n t o N2 r e q u i r e s the p a r t i c i p a t i o n of a surface which c a t a l y z e s r e a c t i o n s . Char i s considered t o

American Chemical © 1982 AmxHcaa CttcmKm Society

1155

16th St. N. W.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; Washington, 0. C. 20036 ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

CHEMICAL REACTION ENGINEERING

348

provide such s u r f a c e s . The o b j e c t i v e of the present study i s to i n v e s t i g a t e the e f f e c t of char s u r f a c e on "NO" r e d u c t i o n by hydrogen and carbon monoxide and to e v a l u a t e the r e l a t i v e importance of "NO" r e d u c t i o n by hydrogen and carbon monoxide and n o n c a t a l y t i c r e d u c t i o n by c h a r . Experimental Apparatus and Procedure Three d i f f e r e n t carbon p a r t i c l e s were used i n these e x p e r i ments; char which was produced by the c a r b o n i z a t i o n of non-coking T a i h e i y o c o a l a t 800°C, a c t i v a t e d carbon produced from petroleum r e s i d u a l s , and g r a p h i t e o f h i g h p u r i t y . The u l t i m a t e a n a l y s i s o f these carbons are given i n Table I . Table I Char and a c t i v a t e Ultimate A n a l y s i s [dry%] Char* Activated Carbon**

C 75.0

H 1.6

N 0.7

S 0.2

0 0.9

Ash 21.6

97.2

1.4

0.1

0.1

1.1

0.1

Physical properties Materials Char* A c t i v a t e d Carbon**

Dp [microns] 500 ^ 700 450

3

Pb [g/cm ] 0.67 0.60 e

*Char: produced from T a i h e i y o c o a l ; p y r o l y s i s temperature: 800 C * * A c t i v a t e d Carbon: "Kureha beads" produced from petroleum residuals Before use, the carbon p a r t i c l e s were d r i e d i n a i r u n t i l cons t a n t weight was a t t a i n e d . The samples were immediately weighed to an accuracy of 1 mg and then mixed w i t h quarz sand of a s i m i l a r s i z e . The p r e l i m i n a r y experiments confirmed that "NO" r e d u c t i o n by hydrogen and carbon monoxide was not c a t a l y z e d by quartz sand. The r e s u l t i n g mixtures were packed i n t o a 20 mm I.D. quartz g l a s s r e a c t o r tube, whose o v e r a l l l e n g t h i s 1000 mm, t o a predetermined height of 30 mm so that a s u f f i c i e n t c o n v e r s i o n l e v e l c o u l d be a t t a i n e d over the temperature range employed by t h i s experiment. D e t a i l s of a s i m i l a r experiment can be found elsewhere. (4) The r e a c t o r tube was brought to the r e q u i r e d temperature under an atmosphere of argon. A mixture of n i t r i c oxide and c a r bon monoxide or hydrogen, d i l u t e d by argon was then introduced i n t o the r e a c t i n g p a r t of the quartz tube. The gaseous r e a c t i o n products were i n t e r m i t t e n t l y withdrawn from the r e a c t o r and anal y z e d by a chemiluminescent NOx analyzer and a gaschromatograph. Ammonia was measured by d e t e c t o r tube method. The scope of the experiment i s shown i n Table I I .

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

29.

FURUSAWA ET AL.

Nitric Oxide Reduction

349

Table I I Scope o f experiment Carbonaceous M a t e r i a l : Gaseous reducing agent

Char CO

H2

Reaction temperature (°C) Residence time ( m i l l i s e c o n d )

530^900 0.96^180

500^900 1.27^243

580^900 1.64*116

NO c o n c e n t r a t i o n i n i n e r t gas (PPM)

1940^2000

1650^2480 113M.17

1340*2500 113*116

4.45^5.71 91.6^98.9

3.60*7.67 94.4*96.0

Ratio o f C0/H2 t o NO at the i n l e t Carbonaceous M a t e r i a l * Gaseous reducing agent

0.0 Activated

Carbon CO

H

2

Reaction temperature (°C Residence time ( m i l l i s e c o n d NO c o n c e n t r a t i o n i n i n e r t gas (PPM) Ratio of CO/H2 t o NO at the i n l e t

295

0.0

1290^1330 113M.17

1480*2360 104*107

5.88^6.06 97.4^98.2

4.81*7.28 91.6*95.4

Experimental R e s u l t s and D i s c u s s i o n Experimental C o n d i t i o n s . The r e a c t i o n r a t e constant was determined by v a r y i n g the flow r a t e o f the Ar-N0-C0 mixed gas e n t e r i n g the r e a c t o r tube and measuring the decrease i n the con­ c e n t r a t i o n o f n i t r i c oxide l e a v i n g the tube. Our p r e v i o u s experiment concerning n i t r i c oxide r e d u c t i o n by char p a r t i c l e s whose s i z e i s shown i n Table I i n d i c a t e d the f i l m r e s i s t a n c e can be i g n o r e d . The e f f e c t o f heat produced by the r e a c t i o n may a l s o be n e g l e c t e d s i n c e the c o n c e n t r a t i o n o f n i t r i c oxide was extremely low. Thus the temperature could be assumed uniform throughout the bed. The c o n c e n t r a t i o n o f n i t r i c oxide employed f o r the e x p e r i ­ ment was l e s s than 3000 ppm. Therefore the holdup o f carbon p a r t i c l e s could be assumed t o have been constant d u r i n g the time i n t e r v a l r e q u i r e d f o r the experiment. During the experiments, the c a t a l y t i c e f f e c t s o f the char s u r f a c e was found t o reduce the con­ sumption o f char t o n e a r l y z e r o . As the height o f the f i x e d bed used i n the present p a r t o f the experiment was about 50 times l a r g e r than the diameter o f the p a r t i c l e s , the flow w i t h i n the bed may be assumed t o be a plugflow. E f f e c t o f Carbon Monoxide on N i t r i c Oxide Reduction by Char. The e f f e c t s o f carbon monoxide on n i t r i c oxide r e d u c t i o n by char was analyzed by changing the gas flow r a t e o f the r e a c t a n t and the r a t i o o f c o n c e n t r a t i o n o f carbon monoxide t o n i t r i c oxide a t the i n l e t o f the r e a c t o r . T h i s r a t i o d e f i n e d as α was chosen t o be three extreme cases: α - 4*7.16, α = 47.3*48.8, and α = 91.6*98.9. The i n i t i a l s e r i e s o f experiments were c a r r i e d out f o r α = 4*7.6

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CHEMICAL REACTION ENGINEERING

to i n v e s t i g a t e the m a t e r i a l balances o f the r e a c t i o n . r e s u l t s are shown i n Table I I I ( a ) . Table I I I

T y p i c a l m a t e r i a l balance and product

Typical

composition

(a) N0-C0-Char r e a c t i o n systems Temperature [°C]

Residence [N0]intime [N0]out [millisecond] [PPM] 3.80 5.67 7.A3 11.21

[C0]in[C0]out [PPM]

980 1390 1770 2150

[N2]out

1010 1520 1720 2410

[C02]out

[PPM]

[PPM]

520 742 836 1017

1077 1647 2101 2822

(b) N0-H -Char r e a c t i o n 2

Temperature Residence [NO]in[°C] time [NO]out [ m i l l i s e c o n d ] [PPM] 800

2.73 3.90 5.28 5.31 6.86

[H ]in[H ]out [PPM] 2

[N ]out 2

[C0 ]out 2

[NH ]out

[PPM]

[PPM]

3

2

680 1030 1280 1380 1460

660 700 1020 1290 1380

[PPM] 377 439 565 610 697

25 23 46

190 230 280 320 360

T h i s i n d i c a t e s that the amount of carbon d i o x i d e formed by t h i s experiment c o i n c i d e d with the amounts of both carbon monoxide and n i t r i c oxide consumed. Thus the use of carbon monoxide reduced the consumption of carbon t o approximately zero and the char p r o ­ v i d e d c a t a l y t i c s u r f a c e s f o r n i t r i c oxide r e d u c t i o n by carbon monoxide as:

NO + CO + C0 + V N 2

2

(1)

2

In order to evaluate the r e l a t i v e importance of the above s u r f a c e c a t a l y s e d "NO" r e d u c t i o n and the n o n c a t a l y t i c "NO" reduc­ t i o n by char, which was p r e v i o u s l y known as a f i r s t order r e a c t i o n with respect to "NO", 2N0 + C •* C0

2

+ N

(2)

2

the r a t e was evaluated by assuming that the s u r f a c e c a t a l y s e d r e a c t i o n was a l s o f i r s t order with r e s p e c t to n i t r i c oxide concen­ t r a t i o n . The r e a c t i o n r a t e o f the f i r s t order r e a c t i o n i n a one dimensional i n t e g r a l flow r e a c t o r can be obtained as: Jin ( C ) o u t / ( C ) i n N 0

N 0

- £n(l-X) - -k0

(3)

where θ i s e f f e c t i v e r e s i d e n c e time of the r e a c t a n t w i t h i n the l a y e r of carbonaceous m a t e r i a l s . F i g u r e 1 i n d i c a t e s t h a t £n(l-X) i s l i n e a r l y dependent on Θ. Thus the r e a c t i o n i n the presence of carbon monoxide c o u l d a l s o be analyzed as a f i r s t order r e a c t i o n w i t h respect to n i t r i c oxide. The r e s u l t s obtained together w i t h

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

FURUSAWA ET AL.

Nitric Oxide Reduction

351

Figure 1. Integral analysis of reaction data, char-CO-NO system. Key: · , 700°C, 4.3 CO/NO ratio; Δ, 800°C, 6.2 CO/NO ratio; and • , 900°C, 6.0 CO/NO ratio.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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CHEMICAL REACTION ENGINEERING

the p r e v i o u s r e s u l t s f o r NO-char n o n c a t a l y t i c r e a c t i o n s are shown i n F i g u r e 2. Any s i g n i f i c a n t e f f e c t o f carbon monoxide on the r a t e of n i t r i c oxide r e d u c t i o n could not be observed f o r α = 4*7.16 w h i l e the s i g n i f i c a n t l y enhanced r a t e o f "NO" r e d u c t i o n was observed f o r α • 91.6*98.9 and α - 47.3*48.8. However, the e f f e c t o f carbon monoxide on the "NO" r e d u c t i o n r a t e was reduced over the h i g h e r temperature range employed f o r f l u i d i z e d bed com­ b u s t i o n of c o a l . E f f e c t o f Hydrogen on N i t r i c Oxide Reduction by Char. The f i r s t s e r i e s of experiments were c a r r i e d out to i n v e s t i g a t e the m a t e r i a l balances which r e f l e c t the r e a c t i o n mechanism. The t y p i c a l composition of the r e a c t i o n products f o r char are shown i n Table I I I ( b ) . The amount o f n i t r i c oxide decomposed c o i n c i d e d w e l l w i t h the amount of carbon d i o x i d T h i s i n d i c a t e s that the r e a c t i o n was a l s o c a r r i e d out c a t a l y t i c a l l y over char s u r f a c e s i n c e the c a t a l y t i c e f f e c t o f quarz sand used f o r d i l u t i n g char p a r t i c l e s was not observed. The a d d i t i o n of hydrogen reduced the consumption o f carbon to almost z e r o . The products were n i t r o g e n and ammonia. NO + H H 0 + VzN N0 + /2H + NH + H 0 2

2

2

5

2

3

2

(4) (5)

The r a t i o o f the formed ammonia to the consumed n i t r i c oxide was measured by changing the r e s i d e n c e time and m a i n t a i n i n g the r e a c t i o n temperature constant. T h i s r a t i o was constant at each temperature and was decreased by the i n c r e a s e d temperature. This i s shown i n F i g u r e 3(a) and 3 ( b ) . T h i s i n d i c a t e d that the n i t r i c oxide was p r i m a r i l y reduced to both ammonia and n i t r o g e n and that the secondary decomposition o f ammonia could be assumed to be negligible. In the second s e r i e s o f experiments, r a t e s were measured by v a r y i n g the flow r a t e o f the Ar-N0-H2 mixture w h i l e keeping the r a t i o of hydrogen to n i t r i c oxide approximately constant. As shown i n F i g u r e 4, the -£n(l-X) i s a l s o l i n e a r l y dependent on the r e s i d e n c e time o f the r e a c t a n t . The a r r h e n i u s p l o t obtained i s a l s o shown i n F i g u r e 2. The r a t e of "NO" r e d u c t i o n f o r α=3.7*7.7 i s not even s l i g h t l y i n c r e a s e d by the presence o f hydrogen, the a c t i v a t i o n energy appeared to be the same as that f o r the noncata­ l y t i c "NO" r e d u c t i o n by char. The r a t e was a l s o measured by i n c r e a s i n g the r a t i o o f hydro­ gen to n i t r i c oxide to α = 91.6*95.4. A d r a s t i c a l l y enhanced r a t e was observed as shown i n F i g u r e 2. The a c t i v a t i o n energy of the i n c r e a s e d r a t e c o i n c i d e d w i t h that obtained f o r the Char-CO-NO system. The r a t e was so s i g n i f i c a n t l y enhanced f o r α = 91.6*95.4 that the r a t e over a h i g h e r temperature range, which i s o f p r a c ­ t i c a l importance i n a f l u i d i z e d bed combustor, could not be measured by the present experimental system. I f the r a t e could be e x t r a p o l a t e d , the r a t e should be much higher than the r a t e o f the

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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Nitric Oxide Reduction

Figure 2. Rate of NO reduction by char and catalytic NO reduction by hydrogen and CO over char surface. The a denotes the ratio of CO/H concentration to NO at inlet. t

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354

CHEMICAL REACTION ENGINEERING

0

1000

2000

Λ [NO]

(ppm)

Figure 3a. Nitric oxide consumed by catalytic reduction by hydrogen is propor­ tional to NH formed. Key: • , 700°C, 7.5 HJNO ratio; Δ, 750°C, 5.2 H /NO ratio; O, 800°C, 7.0 H /NO ratio; A , 850°C, 7.3 H NO; and · , 900°C, 7.6 HJNO ratio. S

t

t

t

o

-3 0.9 1.0 1.1 1.2 1.3 1 / Τ x 10 ( K ) 3

Figure 3b.

0

-1

Temperature dependence of NH formation. Key: · , char; Δ, acti­ vated carbon. S

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

29.

355

Nitric Oxide Reduction

FURUSAWA ET AL.

NO-Char r e a c t i o n system. Therefore an excess i n hydrogen i s expected t o play an important r o l e i n NOx r e d u c t i o n i f the f l u i d i ­ zed bed combustor i s operated under staged a i r f i r i n g . Discussions. A c t i v a t e d carbon was used to i n v e s t i g a t e the e f f e c t o f carbon monoxide and hydrogen on "NO" r e d u c t i o n . The r e s u l t s are shown i n Figure 5. For α = 3.60*8.06 no s i g n i f i c a n t enhancement was observed. The m a t e r i a l balance o f the a c t i v a t e d carbon-CO-NO system i n d i c a t e d t h a t a n o n - c a t a l y t i c r e a c t i o n p r e ­ dominated "NO" r e d u c t i o n by the a c t i v a t e d carbon. However, i n the case o f the a c t i v a t e d carbon-H2-N0 system, the c a t a l y t i c r e a c t i o n predominated the r a t e . A product d i s t r i b u t i o n s i m i l a r t o the char-H2-N0 system was obtained. For α = 91.6*98.9, an a c c e l e r a t e d r a t e was a l s o observed. The a c t i v a t i o n energy o f the a c t i v a t e d carbon-CO-NO system c o i n c i d e an excess carbon monoxid CO-NO systems. Therefore the increased r a t e could not be a t t r i b ­ uted t o the impurity o f the char d e r i v e d from c o a l . The data ob­ tained f o r a c t i v a t e d carbon a r e compared w i t h the data f o r char i n Table IV. As was shown i n Figure 2, the enhancement o f the r a t e was reduced with the increased temperature. However a continuous­ l y i n c r e a s i n g r a t e was observed i n the case o f the carbon-H2-N0 system. A d e t a i l e d i n v e s t i g a t i o n i s expected i n the f u t u r e . Table IV

Carbonaceous material Char Activated carbon Graphite

A c t i v a t i o n energy and mechanism of "NO" r e d u c t i o n

A c t i v a t i o n Energy [kcal/mol] and mechanism Gaseous reducing agent CO H a* - 91.6*98.9 a* = 91.6*96.0 none 23.9** 21.6** 57.2 2

44.0

23.3

22.2

25.0**

* a denotes the r a t i o o f c o n c e n t r a t i o n o f gaseous reducing agent to "NO" c o n c e n t r a t i o n a t the i n l e t o f the r e a c t o r ** "NO" i s reduced by c a t a l y t i c r e a c t i o n s *** f o r α = 4 * 7 "NO" i s reduced by n o n c a t a l y t i c r e a c t i o n Concluding Remarks The r e d u c t i o n o f n i t r i c oxide by char i n the presence o f hydrogen o r carbon monoxide was c a r r i e d out over a temperature range o f 500*900°C. The r e a c t i o n could be analyzed by assuming f i r s t order with respect t o n i t r i c oxide. The predominant mecha­ nisms a r e the c a t a l y t i c r e d u c t i o n o f n i t r i c oxide by hydrogen o r carbon monoxide over char s u r f a c e . The r a t e obtained under α = 4*7 was approximately equal t o the r a t e o f n o n c a t a l y t i c r e d u c t i o n o f

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CHEMICAL REACTION ENGINEERING

0

50

100 3

L /U x 10 (sec)

Figure 4.

Integral analysis of reaction data, char-H -NO t

system. Key:

-0-,

630°C, 3.8 Hg/NO ratio;-U- 700°C, 4.9 H /NO ratio;-A750°C, 5.2 H /NO ratio; - · - , 800°C, 4.5 H /NO ratio;—£>,- 700°C 7.5 HJNO ratio; -Ο-, 800°C, 7.0 H /NO ratio. t

t

t

t

t

Activated cartxxi

a 0 4.8-73 9 1 - 9 8 9Φ-98 10

CO

H2

Ο

•Δ

•

•A

—

7 10' υ

Φ

îo'h

10 « 8

9

10 11 12 13 1 /Τ x 10 (°K ) 4

Figure 5.

- 1

Rate of NO reduction by activated C and catalytic NO reduction by hydrogen and CO over activated C surface.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

29.

FURUSAWA ET A L .

Nitric Oxide Reduction

357

n i t r i c oxide by char. The r a t i o of produced ammonia t o the con­ sumed n i t r i c oxide decreased w i t h an i n c r e a s e d temperature. Under an excess hydrogen and carbon monoxide atmosphere, the r a t e of "NO" r e d u c t i o n was s i g n i f i c a n t l y i n c r e a s e d . The r a t e enhanced by an excess carbon monoxide appear to approach the r a t e of noncata­ l y t i c r e d u c t i o n by char w i t h the i n c r e a s e d temperature. However, the r a t e was d r a s t i c a l l y a c c e l e r a t e d by an excess i n hydrogen which might p l a y an important r o l e i n NOx emission c o n t r o l of a f l u i d i z e d bed combustor operated by staged a i r f i r i n g . The same phenomena were observed i n the case of a c t i v a t e d carbon. Thus these r e s u l t s are not r e s t r i c t e d to the type of carbon employed by this investigation. Legend of Symbols k : f i r s t order r e a c t i o [se ] X : extent of the r e a c t i o n θ : r e s i d e n c e time of r e a c t a n t w i t h i n the l a y e r of m a t e r i a l s [sec]

carbonaceous

Acknowledgments T.F. wishes to express h i s thanks to G r a n t - i n - A i d f o r Energy Research (No 56045030) of the M i n i s t r y of Education, Science and Culture. Literature Cited 1. 2. 3. 4. 5. 6.

7. 8.

Beér, J.M.; Sarofim, A.F.; Chan, L.; Sprouce, A. Proc. 5th Int. Conference on F l u i d i z e d Bed Combustion, 1977, p.577. Furusawa, T.; Honda, T.; Takano, J . ; K u n i i , D. F l u i d i z a t i o n Proc. 2nd Eng. Found. Conf: Cambridge U n i v e r s i t y P r e s s , 1978. Beér, J.M.; Sarofim, A.F.; Lee, Y.Y. Proc. 6th I n t . Conference on F l u i d i z e d Bed Combustion, 1980, p.942. Furusawa, T.; K u n i i , K.; Yamada, N.; Oguma, A. I n t . Chem. Eng. 1980, 20, p.239-244. K u n i i , D.; Wu, K.T.; Furusawa, T. Chem. Eng. S c i . 1980, 35, p.170-177. K u n i i , D.; Furusawa, T.; Wu, K.T., Ed. J.R. Grace and J.M. Matsen; " F l u i d i z a t i o n " ; Plenum P u b l i s h i n g Corp: New York, 1980; p.175. Beér, J.M.; Sarofim, A.F. P r i v a t e Communication. Cowley, L.T.; Roberts, P.T. Paper submitted f o r p r e s e n t a t i o n at the F l u i d i z e d Combustion Conference, 28-30th Jan., 1981, h e l d a t the Energy Research I n s i t u t e , Univ. of Cape Town, South A f r i c a .

RECEIVED May

11,

1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

30 Transient Simulation of Moving-Bed Coal Gasifiers 1

WEN-CHING Y U and MORTON M . D E N N

2

University of Delaware, Newark, D E 19711 JAMES WEI Massachusetts Institute of Technology, Cambridge, M A 02139

A model fo transien simulatio f radial and axial compositio pressurized dry ash and slagging moving bed gasi fiers is described. The model is based on mass and energy balances, thermodynamics, and kinetic and transport rate processes. Particle and gas temperatures are taken to be equal. Computation is done using orthogonal collocation in the radial variable and exponential collocation in time, with numerical integration in the axial direction. The transient response to feed rate changes is found to be approximately first order, but dependent on the direction of the change. Strategies for changes in operating level have been studied. The proposed use o f c o a l g a s i f i c a t i o n r e a c t o r s i n e l e c t r i c power systems w i l l r e q u i r e that the g a s i f 1 e r respond t o both l a r g e and small t r a n s i e n t s , i n c l u d i n g turndown t o , and s t a r t u p from, a hot banked s t a t e . We describe here a model f o r t r a n s i e n t s i m u l a t i o n o f r a d i a l and a x i a l composition and temperature p r o ­ f i l e s i n a p r e s s u r i z e d moving bed g a s i f i e r l i k e the dry ash L u r g i r e a c t o r o r the BGC/Lurgi s l a g g e r . The countercurrent system i s shown s c h e m a t i c a l l y i n Figure 1. The model i s based on fundamental thermodynamic, k i n e t i c , and t r a n s p o r t p r o p e r t i e s , and hence i t can be used t o determine e f f i c i e n t operating and c o n t r o l p o l i c i e s f o r load f o l l o w i n g , s t a r t u p and shutdown, and changes i n feed p h y s i c a l and chemical p r o p e r t i e s .

1 2

Current address: Ε. I. DuPont de Nemours & Co., Inc., Seaford, D E 19973 Current address: University of California, Berkeley, CA 94720

0097-6156/82/0196-0359$06.00/0 © 1982 American Chemical Society In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

360

C H E M I C A L R E A C T I O N ENGINEERING

product gas

coal

Drying

Zone

Devolatilization

(

coal gas, tar

oil d r i v e n off

Thermally

ο ο NI C ο

/

Neutral

Gasification •

Zone and\

Zone

( l i t t l e or no o x y g e n ) Endothermic

u C o m b u s t i o n Zone (oxygen r i c h gas) Exothermic

ash

steam

+ unreacted carbon Figure 1.

a i r or oxygen

Schematic of a counter-current moving bed coal gasifier.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

30.

Υ ϋ ET A L .

Moving-Bed Coal Gasifiers

361

The model development has been d e s c r i b e d i n d e t a i l elsewhere QL» .?)· S o l i d and gas are assumed t o be a t the same temperature, and the f o l l o w i n g chemical r e a c t i o n s a r e assumed t o occur:

AC + 0

+ 2 (λ - 1)C0 +

2

(2 - X ) C 0

2

(1)

C + H 0

Î

CO + H

C + C0

2

î

2C0

(3)

C + 2H

2

t

CH

(4)

t

C0 + H

2

CO + H 0 2

(2)

2

4

2

R a d i a l d i s p e r s i o n o f mass and heat i s i n c l u d e d . A x i a l d i s p e r s i o n o f mass i s always n e g l i g i b l e , but a x i a l heat d i s p e r s i o n must be i n c l u d e d a t low throughputs. The mass balance f o r each gaseous s p e c i e s i s o f the form

i from one through s i x r e p r e s e n t s steam, oxygen, hydrogen, carbon monoxide, carbon d i o x i d e , and methane, r e s p e c t i v e l y ; j from one through four represents r e a c t i o n s one through f o u r , r e s p e c t i v e l y . The mass balance f o r f i x e d carbon i s w r i t t e n i n terms o f f r a c t i o n o f unreacted f i x e d carbon,

F

Ρ- + Σ α,, R = (1 - ε) & c 3Ϊ ' 7 j *J " " 3t j=l T

u

4

V

i

w

(7)

F£ i s the molar feed f l u x o f f i x e d carbon, and s u b s c r i p t 7 r e f e r s t o f i x e d carbon. F i n a l l y , the energy balance leads to the f o l l o w i n g equation f o r the temperature d i s t r i b u t i o n , w i t h p a r t i c l e and gas temperatures taken t o be e q u a l :

dz Tec [ερ gcv g + (1 - ε)p c g Vg

3T ]

S VS

dt

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

(8)

362

CHEMICAL REACTION ENGINEERING

Boundary c o n d i t i o n s a r e as f o l l o w s : 3C « 0 a t r=0 and r ; i-1,2,

6

o

C i

C. a t ζ = 0 ; 1-1,2, io

6

w = 1 at ζ = L

k

a f 9Z

« (Η g

(9a)

(9b) (9c)

- Η ) (T-T, ) a t z=0 S

(10a)

D

k

a

f3z

= 0 a t z=L

(10b)

k

r

Ρ Br

- 0 a t r=0

(10c)

k

r

f3r

= -h (T-T ) a t r=r w o

(lOd)

r i s the r a d i u s o f the i n n e r w a l l . Equations (10a) and (10b) are not r i g o r o u s l y c o r r e c t when there i s r a d i a l d i s p e r s i o n , but they d i f f e r n e g l i g i b l y from the one-term approximation t o the exact boundary c o n d i t i o n s developed by Young and F i n l a y s o n (3)· A x i a l d i s p e r s i o n of heat i s important only a t throughputs l e s s than t e n percent o f f u l l l o a d ; the appropriate equations a t h i g h e r through­ puts are obtained by s e t t i n g k to zero i n Equations (8) and (10). a

The w a l l c o o l i n g has a major e f f e c t when there are l a r g e changes i n r e a c t o r throughput. When t u r n i n g down a g a s i f i e r , the temperature o f the bed w i l l be lowered due t o heat l o s s t o the environment, and the thermal boun­ dary l a y e r w i l l penetrate inwards t o the c e n t r a l core. The i n c r e a s e d r e s i d e n c e time p r o v i d e s time f o r excess steam to react w i t h carbon. These e f f e c t s c o n t r i b u t e to lowering the maximum temperature i n a d r y ash g a s i f i e r l i k e the L u r g i , and the combustion zone moves upwards. 01) Orthogonal c o l l o c a t i o n on two f i n i t e elements i s used i n the r a d i a l d i r e c t i o n , as i n the s t e a d y - s t a t e model ( 1 ) , w i t h J a c o b i and s h i f t e d Legendre polynomials as the approx­ imating f u n c t i o n s on the i n n e r and outer elements, r e s p e c ­ tively. E x p o n e n t i a l c o l l o c a t i o n i s used i n the i n f i n i t e time domain (4, 5). The approximating f u n c t i o n s i n time have the form

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

30.

Y U ET A L .

Moving-Bed Coal Gasifiers

-t y ( z , r , t ) = y ( z , r , ~ ) + e*

N+l Σ i-1 d. ( z , r ) t i-1 " i

363

(11)

The c o l l o c a t i o n p o i n t s a r e the r o o t s o f (12) where Ι Λ i s the Laguerre

polynomial (13)

L

n

=

e

t

t

"

P

" 4

{

e

"'

t

P

^ >

T h i s approximating scheme r e q u i r e s that the process be s t a b l e and approach a new stead state p r o f i l e s are required steady s t a t e model. The approximating scheme converts the system o f p a r t i a l d i f f e r e n t i a l equations t o a s e t o f o r d i n a r y d i f f e r e n t i a l equations i n the a x i a l s p a t i a l c o o r d i n a t e . The d e t a i l e d equations a r e contained i n Yu e t a l . ( 2 ) . The advantage o f r e d u c t i o n i n t h i s manner i s that the t r a n s i e n t l o c a t i o n o f the combustion zone does not have t o be known a p r i o r i , but can be found i n the course o f the i n t e g r a t i o n s . Gear i n t e g r a t i o n , which i s designed f o r s t i f f systems, i s used t o s o l v e the two p o i n t boundary value problem i n the a x i a l d i r e c t i o n . There a r e three parameters i n e x p o n e n t i a l c o l l o c a t i o n : ρ; N; and a c h a r a c t e r i s t i c time, A t . D i f f e r e n t values o f ρ have been used, and no d i f f e r e n c e has been observed; ρ = 0 was used i n the s i m u l a t i o n s that f o l l o w . The number o f c o l ­ l o c a t i o n p o i n t s (N + 1) i s e q u i v a l e n t t o the r e c i p r o c a l of the step s i z e i n f i n i t e d i f f e r e n c e methods; the more p o i n t s used, the greater i s the accuracy, but the more time consuming the s o l u t i o n . The s e n s i t i v i t y o f the s o l u t i o n t o Ν and At i s shown i n F i g u r e 2, which shows the movement o f the combus­ t i o n zone i n an a d i a b a t i c d r y ash g a s i f i e r when the throughput i s reduced t o 80% o f f u l l l o a d a t constant feed r a t i o s . Four c o l l o c a t i o n p o i n t s appear t o give reasonable accuracy, and were used i n the s i m u l a t i o n s that f o l l o w , with two c o l l o ­ c a t i o n p o i n t s i n the r a d i a l d i r e c t i o n . The boundary c o n d i t i o n on f i x e d carbon (w • 1) a t ζ • L was s a t i s f i e d t o w i t h i n 0.003; t h i s e r r o r corresponds t o an average u n c e r t a i n t y o f 0.02 i n the normalized l o c a t i o n z/L o f the maximum temperature. The base case f o r a l l c a l c u l a t i o n s shown here i s a 3.7 m diameter d r y ash air-blown L u r g i r e a c t o r w i t h a 3.0 m

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

364

CHEMICAL REACTION ENGINEERING

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

30.

YU ET AL.

365

Moving-Bed Coal Gasifiers

high r e a c t i o n zone, g a s i f y i n g I l l i n o i s No. 6 c o a l a t 25 atm w i t h a steam-to-oxygen r a t i o o f 6.7, a f i x e d carbon-to-oxygen 2 r a t i o o f 2.80, and an oxygen f l u x o f 0.155 kg/m sec ( 6 ) . The t r a n s i e n t s r e s u l t i n g from t u r n i n g the feed f l u x e s down p r o p o r t i o n a l l y from f u l l load t o 80, 50, and 30% throughput were s t u d i e d without c o n s i d e r i n g a x i a l thermal d i s p e r s i o n . Temperature and f i x e d carbon p r o f i l e s i n the c e n t r a l core ( r / r • 0.49) and the boundary l a y e r ( r / r - 0.93) a r e shown i n F i g u r e s 3 and 4, r e s p e c t i v e l y , f o r turndown t o 30%. The f i n a l steady s t a t e i s reached i n about 40 hours. The f r a c ­ t i o n a l approach t o the new steady s t a t e i n the c e n t r a l core i s p l o t t e d on semi-logarithmic coordinates i n F i g u r e 5. A s t r a i g h t l i n e on such a p l o t i n d i c a t e s a f i r s t - o r d e r r e s ­ ponse. T h i s i s a p a r t i c u l a r l results, since difference taken. The r e l a t i v e e r r o r i s l a r g e s t f o r turndown to 80%. Within the accuracy used t o s a t i s f y the boundary c o n d i t i o n at ζ = L, the three curves cannot be d i s t i n g u i s h e d from the r e s u l t f o r turndown t o 50%. The apparent f i r s t - o r d e r time Q

Q

constant (time t o reach a v a l u e o f e ^) ranges from a p p r o x i ­ mately s i x t o nine hours, depending on the amount o f turndown. The pseudo-steady-state a n a l y s i s f o r s m a l l t r a n s i e n t s used by Yoon e t a l . (7)» which i s based on the speed o f the thermal wave, a l s o gives an apparent f i r s t - o r d e r response, but the computed time constant i s two t o three hours. I t has been shown (1) that the carbon-to-oxygen r a t i o must be i n c r e a s e d when the r e a c t o r i s turned down i n order to keep the combustion zone from moving up i n the bed. The movement o f the combustion zone w i t h time i s shown i n Figure 6 f o r a number o f feed r a t i o programs w i t h turndown to 50% throughput. A sudden i n c r e a s e o f the f i x e d carbonto-oxygen r a t i o t o the new steady-state value w i l l lower the combustion zone a l i t t l e i n i t i a l l y , and then r a i s e i t t o the f i n a l steady s t a t e . Compared w i t h other programs, a sudden i n c r e a s e o f the feed f l u x r a t i o o f 0/0^ i s an e f f e c t i v e way to turn down a g a s i f i e r . The f r a c t i o n a l approach t o steady s t a t e f o l l o w i n g an i n c r e a s e i n the throughput from 30, 50, and 80% t o f u l l load i s shown i n F i g u r e 7. There i s a s i n g l e time constant o f about three hours. The t r a n s i e n t time f o r s t a r t u p i s s h o r t e r than f o r turndown because a sudden i n c r e a s e o f the f l u x i n c r e a s e s the flame v e l o c i t y .

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

366

CHEMICAL REACTION ENGINEERING

2400

H 1500

1250

4

1000 ο

0

Figure 3.

Η

750

Η

500

2 4 6 8 10 AXIAL DISTANCE ABOVE GRATE, ft

Temperature profiles at r/r = 0.49 for turndown from full to 30% load. Key: 1,0 h; 2,9.4 h; 3,33.1 h; and 4,77.6 h. 0

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

30.

YU ET AL.

Moving-Bed Coal Gasifiers

m 2400°

'

2000

^ 1600 Lu or

Si 1200 ω CL

ω 800

400

Ο Ο Figure 4.

2 4 6 8 10 AXIAL DISTANCE ABOVE GRATE, ft

Temperature profiles at r/r = 0.93 for turndown from full to 30% load. Key: 1,0 h; 2,9.4 h; 3,33.1 h; and 4,77.6 h. 0

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

368

CHEMICAL REACTION ENGINEERING

TIME, hr Figure 5. Fractional approach to the new steady-state in central core (r/r = 0.49) for turndown from full to various partial loads. Key: O, turndown to 80%; • , turndown to 50%; and Δ , turndown to 30%. 0

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

30.

Y U ET A L .

369

Moving-Bed Coal Gasifiers

X

10

20

X

30 TIME, hr

40

50

60

Figure 6. Movement of the combustion zone with time for a number of feed ratio programs with turndown to 50% load.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

Figure 7. Fractional approach to the new steady-state at r/r = 0.49 for turning up the gasifier to full load from various initial loads. Key to initial output: O, 80%; Q 50%; and Δ, 30%. 0

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

30.

YU

ET

371

Moving-Bed Coal Gasifiers

AL.

When the throughput i s turned down to below 10% o f f u l l l o a d , a x i a l d i s p e r s i o n i s important and i s i n c l u d e d i n the energy equation. F i g u r e 8 shows the t r a n s i t i o n to a 1% throughput, s i m u l a t i n g the approach to a banked c o n d i t i o n , w i t h the f i x e d carbon-to-oxygen feed r a t i o changed to 3.5 a t time zero. The time constants w i t h a x i a l d i s p e r s i o n are s i m i l a r to the other turndown c a l c u l a t i o n s . In the s l a g g i n g g a s i f i e r , the low steam-to-oxygen feed r a t i o and the h i g h temperature burner gas keep the combustion zone low, and t u r n i n g down the throughput does not change the l o c a t i o n of the combustion zone. The major change occurs i n the boundary l a y e r , where the g r e a t e r r e l a t i v e importance of heat l o s s t o the w a l l decreases the c o n v e r s i o n and hence the thermal e f f i c i e n c y Unlik th dr h gasifier th t r a n s i e n t time i s not c o n t r o l l e wave, and the t r a n s i e n y computed time t o reach a new steady s t a t e f o l l o w i n g turndown to 30% throughput i s f i v e hours, and i t i s one-half hour f o l l o w i n g turnup from 30% t o f u l l l o a d . The major t r a n s i e n t i s the heat t r a n s f e r between the bed and the water j a c k e t . At the h i g h e r flow r a t e , the thermal boundary l a y e r i s t h i n n e r and the c o n v e c t i o n term i s more important, and hence r e t a r d s the t r a n s i e n t .

0

Figure 8.

2 4 6 8 AXIAL DISTANCE ABOVE GRATE, ft

10

Temperature profiles for turndown to 10% (F.C./O = 3.5) from full load (F.C./Ot = 2.8); 1,0 h; 2,9.4 h; 3,33.1 h; and 4, 77.6 h. t

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

CHEMICAL REACTION ENGINEERING Symbols

molar c o n c e n t r a t i o n

o f species i

heat c a p a c i t y of gas (g), s o l i d (s) s p a t i a l c o e f f i c i e n t o f approximating f u n c t i o n diffusivity molar feed f l u x o f f i x e d carbon w a l l heat t r a n s f e r c o e f f i c i e n t convective heat c a p a c i t y f l u x o f gas(g),

solid(s)

enthalpy o f r e a c t i o n j a x i a l (a) height o f r e a c t i o n zone Laguerre polynomial radial

coordinate

reactor inner

radius

apparent r a t e of r e a c t i o n j time c h a r a c t e r i s t i c time i n e x p o n e n t i a l

collocation

temperature blasrt (b), w a l l (w) temperature gas s u p e r f i c i a l v e l o c i t y f r a c t i o n o f unreacted f i x e d carbon axial

coordinate

s t o i c h i o m e t r i c c o e f f i c i e n t of s p e c i e s i i n r e a c t i o n j v o i d f r a c t i o n o f bed s e l e c t i v i t y parameter f o r o x i d a t i o n r e a c t i o n density of s o l i d

( s ) , gas (g)

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

30.

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Moving-Bed Coal Gasifiers

373

Acknowledgment T h i s work was supported by the E l e c t r i c Power Research Institute.

Literature Cited 1.

Yu, W. C . ; Denn, M. M.; Wei, J. "Radial Effects in Moving Bed Coal Gasifiers," AIChE annual meeting, New Orleans, Nov. 8-12, 1981.

2.

Yu, W. C . ; Denn, M. M.; Wei, J. "Two Dimensional Steady State and Transient Modeling of Moving Bed Coal Gasifiers," report to Electric Power Research Institute, RP-1268-1, in press (1982).

3.

Young, L. L.; Finlayson, B. A. Ind. Eng. Chem. Fundam., 12, 412 (1973).

4.

Guertin, E. W.; Sorensen, J . P; Stewart, W. E. Comp. & Chem Eng., 1, 197 (1977).

5.

Birnbaum, I.; Lapidus, L. Chem. Eng. S c i . , 33, 455 (1978).

6.

Yoon, H.; Wei, J.; Denn, M. M. Chem Eng. S c i . , 34, 231 (1979).

7.

Yoon, H.; Wei, J.; Denn, M. M. AIChE J., 25, 429 (1979).

Received April 27, 1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

31 Simultaneous Mass Transfer of Hydrogen Sulfide and Carbon Dioxide with Complex Chemical Reaction in an Aqueous Diisopropanolamine Solution P. M . M . B L A U W H O F F

1

and W. P. M . V A N SWAAIJ

Twente University of Technology, P.O. Box 217, 7500 A E Enschede, The Netherlands

The simultaneous aqueous 2.0 M diisopropanolamin (DIPA) is studied both experimentally and theoretically. The absorption phenomena observed, depend largely on the extent of depletion of the amine in the mass transfer zone and can be classified into three regimes: 1 negligible interaction, 2 medium interaction and 3 extreme interaction between H2S and CO2 absorption. In the latter regime, desorption of one of the gaseous components is observed a l ­ though, based on its overall driving force, ab­ sorption would be expected. We studied these phenomena experimentally in a wetted wall column and two stirred cell reactors and evaluated the results with both a penetration and a film model description of simul­ taneous mass transfer accompanied by complex liquid-phase reactions [5,6]. The experimental results agree well with the calculations and the existence of the third regime with its desorption against overall driving force is demonstrated in practice (forced desorption or negative enhance­ ment factor). The removal o f the a c i d components H 2 S and CO2 from gases by means of alkanolamine s o l u t i o n s i s a w e l l - e s t a b l i s h e d process. The desc r i p t i o n o f the H 2 S and CO2 mass t r a n s f e r f l u x e s i n t h i s process, however, i s very complicated due to r e v e r s i b l e and, moreover, i n t e r a c t i v e l i q u i d - p h a s e r e a c t i o n s ; hence the r e l e v a n t p e n e t r a t i o n model based equations cannot be solved a n a l y t i c a l l y [63. Recently we, t h e r e f o r e , developed a numerical technique i n order t o c a l c u l a t e H S and CO2 mass t r a n s f e r rates from the model equations [ 6 ] . 2

1

Current address: Koninklijke/Shell Laboratorium Amsterdam, P.O. Box 3003, 1003 AA Amsterdam, The Netherlands. 0097-6156/82/0196-0377$06.00/0 © 1982 American Chemical Society In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

378

CHEMICAL REACTION ENGINEERING

In t h i s i n v e s t i g a t i o n we c a r r i e d out experiments with s i m u l ­ taneous a b s o r p t i o n o f H 2 S and CO2 i n t o aqueous 2.0 M d i i s o p r o p a n o l ­ amine (DIPA) s o l u t i o n s a t 25 °C. The r e s u l t s are evaluated by means o f our mathematical mass t r a n s f e r model both i n p e n e t r a t i o n and f i l m theory form. The l a t t e r v e r s i o n has been d e r i v e d from the p e n e t r a t i o n theory mass t r a n s f e r model [ 5 ] . The experiments may be d i v i d e d i n t o three regimes: 1st w i t h n e g l i g i b l e i n t e r a c t i o n between the H 2 S and CO2 mass t r a n s f e r r a t e s , r e a l i z e d a t r e l a t i v e l y low gas-phase c o n c e n t r a t i o n s , 2nd w i t h medium i n t e r a c t i o n and 3 * w i t h extreme i n t e r a c t i o n , r e s u l t i n g i n d e s o r p t i o n o f one o f the gaseous components a g a i n s t i t s o v e r a l l driving force. Under c o n d i t i o n s p r e v a i l i n g i n i n d u s t r i a l and l a b o r a t o r y absorbers o p e r a t i n g a t steady s t a t e , only the f i r s t two regimes can be a t t a i n e d . The t h i r d regime can probably be r e a l i z e d only under t r a n s i e n t operatin r(

Theory The l i q u i d - p h a s e r e a c t i o n s . The r e a c t i o n between HoS and aqueous alkanolamines i s instantaneous and r e v e r s i b l e [ 7 J : R N H 2 + HS"

H S + R NH 2

(1)

2

2

CHS"] [R NH+] 2

\ S

(

" CH S] fR NH] 2

2

)

2

Everywhere i n the l i q u i d , e q u i l i b r i u m (1) i s e s t a b l i s h e d due t o i t s instantaneous nature. For CO2 we c o n s i d e r only the r e v e r s i b l e r e a c t i o n w i t h primary and secondary alkanolamines as shown i n the o v e r a l l r e a c t i o n equation [7]: C0

+ 2 R NH

2

R NC00~ + R NH

2

2

2

(3)

2

with [R NC00"] I^NH*] 2

K

co,

=

5

~

2

(

Γ"" -

CC0 ] [ R N H ] 2

4

)

2

2

Reaction

(3) proceeds a t a f i n i t e o v e r a l l r a t e , expressed by [ 8 ] : . [R-NCOO ] [R,NH*] k CC0 ] [R.NH] (5) 2 ^2 Κ " ΠΓΝΗΤ VAJ2 ^ In f a c t the r e a c t i o n scheme i s c o n s i d e r a b l y more complicated than suggested by equation (3) [ 9 ] and consequently more complicated r a t e equations are proposed i n l i t e r a t u r e [3,9]. F o r the purpose of t h i s work, however, equation (5) was found t o be s u f f i c i e n t l y a c c u r a t e . Other C O 2 c o n v e r t i n g r e a c t i o n s , as w e l l as the h y d r o l y s i s of the carbamate i o n , are slow compared t o r e a c t i o n (3) and hence are not i n c o r p o r a t e d i n the model. -

1

2

J

oJ

2

2

2

a a j

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

31.

BLAUWHOFF AND VAN SWAAU

HtS and CO

Mass Transfer

2

379

The mass t r a n s f e r model. In our previous work [6] the mass t r a n s f e r model equations and t h e i r mathematical treatment have been d e s c r i b e d e x t e n s i v e l y . The r e l e v a n t d i f f e r e n t i a l equations, d e s c r i b i n g the process of l i q u i d - p h a s e d i f f u s i o n and simultaneous r e a c t i o n s o f the species according to the p e n e t r a t i o n theory, are summarized i n t a b l e 1. Recently we d e r i v e d from t h i s p e n e t r a t i o n theory d e s c r i p t i o n a f i l m model v e r s i o n , which i s i n c o r p o r a t e d i n the e v a l u a t i o n o f the experimental r e s u l t s . D e t a i l s on the f i l m model v e r s i o n are given elsewhere [ 5 ] . The process o f mass t r a n s f e r and simultaneous r e a c t i o n s i s g r a p h i ­ c a l l y represented i n f i g u r e 1· In an a b s o r p t i o n s i t u a t i o n H 2 S and CO2 d i f f u s e from the bulk o f the gas-phase t o the i n t e r f a c e and are i n dynamic e q u i l i b r i u m w i t h t h e i r r e s p e c t i v e l i q u i d - p h a s e concen­ t r a t i o n s . From the i n t e r f a c e , H 2 S and CO2 d i f f u s e towards the l i q u i d bulk and both r e a c according t o o v e r a l l r e a c t i o n t r a n s p o r t r a t e s t o the net conversion r a t e s o f the species i n v o l v e d both i n r e a c t i o n ( 1 ) and ( 3 ) ( R 2 N H and R 2 N H 2 ) , determine the extent o f d e p l e t i o n o f R 2 N H and surplus o f R2^H5 hence d e t e r ­ mine the i n t e r a c t i o n between the r e a c t i o n s ( 1 ) and ( 3 ) . The de­ p l e t i o n o f R 2 N H and the surplus o f R 2 N H 2 i n t e r f a c e can be estimated u s i n g an approach s i m i l a r t o e.g. Ramachandran and Sharma [ 1 0 ] . a n Q 4

a

t

t

n

e

A s u b s t a n t i a l amine conversion by H 2 S and CO2» combined w i t h a r e l a t i v e l y high a b s o r p t i o n mole f l u x o f one o f the gaseous com­ ponents, e.g. H 2 S , gives r i s e to an i n t e r e s t i n g f e a t u r e induced by the i n t e r a c t i o n o f the l i q u i d - p h a s e r e a c t i o n s . Due t o the r e l a t i v e l y high amine conversion r a t e i n the p e n e t r a t i o n zone and the consequent d e p l e t i o n o f amine, the competitive C02~amine r e a c t i o n i s reversed and l o c a l l y produces amine and f r e e C O 2 . This l o c a l CO2 c o n c e n t r a t i o n can exceed i t s i n t e r f a c i a l c o n c e n t r a t i o n and leads t o d i f f u s i o n o f p a r t o f the CO2 towards the gas phase (see f i g u r e 2 ) . The n e t r e s u l t w i l l be d e s o r p t i o n o f C 0 2 , although based on i t s o v e r a l l d r i v i n g f o r c e , a b s o r p t i o n would have been expected. Consequently the enhancement f a c t o r of CO2 y i e l d s negative v a l u e s . P r e v i o u s l y we d e f i n e d t h i s phenomenon as f o r c e d d e s o r p t i o n o r negative enhancement f a c t o r [ 2 , 6 ] . No experimental evidence of t h i s phenomenon has been a v a i l a b l e u n t i l now. In general the r a t e of mass t r a n s f e r o f e.g. H 2 S may be expressed by: ο [H S] 2

CH S]? 2

-

g

Γ

~ 1

H S 2

k

= k,

1

SH S 2

m

H

S 2

'

k l H

o v

H S

»*«îl [H S] 2

g

2

s

2 '

f H

2

S

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

( ) 6

CHEMICAL REACTION ENGINEERING

T a b l e 1. P e n e t r a t i o n t h e o r y e q u a t i o n s f o r t h e mass t r a n s f e r model (boundary c o n d i t i o n s as u s u a l i n p e n e t r a t i o n t h e o r y [6 ] ) . the c a r b o n d i o x i d e r e a c t i o n 2

3[C0 ]

3 [C0 ]

2

9

=

k

balance:

D C 0

2

"

k

2

C C 0

2

3 C R

2

N H : I

+

[R NC00"][R NH ]

2

2

2

+

2

[R^NH]

the t o t a l

carbon d i o x i d e b a l a n c e :

3[C0~] £-

2

3[R NC00~]

3 [CO-]

0

+

±

3t

s Π

3t

—

C0

2 χ

2

^

2

Ô [R NCOO"] 2

+

D

~2

R NCOO 2

t o t a l sulphur

balance: 2

3

C

H

2

S

]

3

, -9[HS~] _ _

at

=

at

H

D

S

2

C

H

3 χ

2

S

]

2

. _ +

2

3 [HS~]

H S "

D

3 χ

2

t o t a l amine b a l a n c e +

3[R NH]

3[R NH ]

2

2

+

3t

at

+

2

the a c i d

2

N H

2

=

3t

2

D R

3 [R NH]

2

3 [R NH +

2

3[R NCOO~]

2

+ 2

2

D

R NH

^2

2

2

]

+

+

_

3 [R NCOO ] 2

D

r

2

N

C

0

°

3^

balance:

3[H S] at

+

3[C0 ]

2

at

+

2

3[R NH ]

2

2

at

+

3 [H S]

2

2

=

D

H S

2

2

3 [C0 ] °

C 0

2

+

3 CR NH ]

2

+

+

2

2

+

R

° 2

N H

2

2

+

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

'

H

C 0

m

2

m

2

'°°

2

H

. 2

2

S

+

+

penetration

"

2

CXU

2

H„S

zone

0

2

2

2

2

t

R„NH„+ 2""2

R NH =^ir R N H +

D

I R NH

2R NH = ^

Liquid

+

+

2

D R NH

R NC00 o

HS

t

2

9

^R NCOO

—~D.

2 +

'HS

Scheme of the absorption process with interaction by the common product R NH * and reactant R NH.

C0

H S

m

Figure 1.

2

S

*H S 2

Interface

382

CHEMICAL REACTION ENGINEERING

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

BLAUWHOFF AND VAN SWAAU

31.

383

H S and CO* Mass Transfer t

where: CH S3Î 2

(7) [H S]^ 2

and: .

k

!

(8)

For CO2 an expression analoguous t o equation (6) can be d e r i v e d . The values o f the enhancement f a c t o r s i n (6) and i t s CO2 analogon, f f l g and fc(>2 P c t i v e l y , a r e obtained from our mass t r a n s f e r model and account f o r the i n t e r a c t i o n between H 2 S - and C02-amine reactions. I f the amine d e p l e t i o n i a b s o r p t i o n s i t u a t i o n i s n e g l i g i b l e , the mass t r a n s f e r f l u x e s are independent o f each other and the r e s p e c t i v e enhancement f a c t o r s may be obtained e a s i l y from a n a l y t i c a l s o l u t i o n s o f s i n g l e gas mass t r a n s f e r models. r e s

e

2

Selectivity. I n many cases i t i s d e s i r e d t o remove H 2 S s e l e c t i v e l y from a gas stream, r e j e c t i n g CO2 t o the h i g h e s t p o s s i b l e extent. I t i s , t h e r e f o r e , u s e f u l t o introduce the s e l e c t i v i t y f a c t o r S, being a y a r d s t i c k f o r the process s e l e c t i v i t y independent o f mass t r a n s f e r d r i v i n g f o r c e s [ 8 ] : C C 0

J

C C 0

H S 9 2

[H S]?

'

2

3

2 1 2 g " ^SCÔT" — C0 2 ]

(9)

J

[H S]£ ° E which y i e l d s a f t e r s u b s t i t u t i o n o f equation (6) and i t s C 0 analogon: _ ! _ ι 0

2

J G

M

S

2

2

+

êC0 S . — p i k

_ 1 — K

m

9

SH S 2

C0

o

k

2

+

lC0

o

f

2

C0

K

3 :

H S lH S H S 2

2

=

ovH S 2_ K

* m

k o

2

ov

(

1

0

)

c o Z

2

and represents the r a t i o o f the o v e r a l l mass t r a n s f e r c o e f f i c i e n t s . Our a b s o r p t i o n experiments i n the regime w i t h n e g l i g i b l e i n t e r a c t i o n are e n t i r e l y gas-phase l i m i t e d with respect t o H 2 S , as was checked using the a n a l y t i c a l mass t r a n s f e r e x p r e s s i o n of Secor and B e u t l e r [ 1 1 ] . The CO2 a b s o r p t i o n i s i n the p s e u d o - f i r s t order regime and hence the s e l e c t i v i t y f a c t o r can be s i m p l i f i e d t o :

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

384

CHEMICAL REACTION ENGINEERING

-V

s

,

k g C 0

S m

2

C0

2

8

^ 2 ^ ° \ θ

P l o t t i n g of S versus kgj^s slope l/mco

2

/k [R NH]°D 2

,

2

Experimental procedures

s n o u

C 0 2

and

5

S ^

2

^

(11) 2

^

%

^

^ ^ y i e l d a l i n e a r dependency with

and y - a x i s i n t e r c e p t

1.

results.

N e g l i g i b l e and medium i n t e r a c t i o n regimes. Experiments were c a r r i e d out with an aqueous 2.0 M DIPA s o l u t i o n at 25 °C i n a s t i r r e d - c e l l r e a c t o r (see réf. [1]) and a 0.010 m diameter wetted w a l l column (used only i n e g l i g i b l i n t e r a c t i o regime ref [ 4 , 5 ] ) . Gas and l i q u i d mass t r a n s f e r r a t e s wer gas-phas analyse excep f o r C 0 i n the wetted w a l l column where due to low C 0 gas-phase conversion, a l i q u i d - p h a s e a n a l y s i s had to be used [ 5 ] . In the n e g l i g i b l e i n t e r a c t i o n regime some 27 experiments were c a r r i e d out i n both r e a c t o r s . The s e l e c t i v i t y f a c t o r s were c a l c u l a t e d from the measured H S and C0 mole f l u x e s and are p l o t t e d versus kgjj^s 2

2

2

2

i n f i g u r e 3. The dependency i s l i n e a r , as p r e d i c t e d by equation (11). The p s e u d o - f i r s t order C0 -DIPA r e a c t i o n r a t e constant c a l c u l a t e d from the slope i s : k D I P A 1200 s ~ l , which i s s l i g h t l y higher than found i n our separate k i n e t i c s study [3,5] (800 s " ) . Two s e r i e s of experiments were c a r r i e d out i n the medium i n t e r ­ a c t i o n regime at a constant entrance gas flow r a t e , c o n t a i n i n g 50% of H S or C 0 and v a r y i n g concentrations of the other component (0, 20, 30, 40 and 50%). Measured and c a l c u l a t e d ( p e n e t r a t i o n and f i l m theory) mole f l u x e s are shown i n f i g u r e 4 a,b as a f u n c t i o n of the v a r i e d c o n c e n t r a t i o n s . The D I P A f l u x i s obtained from a f l u x balance equation (JoiPA JH S 2 Jc0 )· f i g u r e 4a i t obvious that J D I P A remains constant w i t h i n c r e a s i n g C 0 concen­ t r a t i o n , implying that the maximum enhancement given by complete DIPA d i f f u s i o n l i m i t a t i o n i s r e a l i z e d . The measured H S molef l u x e s f a l l between f i l m and p e n e t r a t i o n theory c a l c u l a t i o n s while C 0 agrees more with the f i l m theory. For each experimental r u n , measured and c a l c u l a t e d s e l e c t i v i t y f a c t o r s are shown i n f i g u r e 5 a,b. The values measured are r a t h e r s c a t t e r e d due to experimental i n a c c u r a c i e s but the f i l m theory c a l c u l a t i o n seems to y i e l d the minimum values of the s e l e c t i v i t y f a c t o r s and hence should be p r e f e r r e d f o r ( c o n s e r v a t i v e ) absorber design. 2

β

2

1

2

2

β

+

F

2

r

o

m

2

2

2

2

Extreme i n t e r a c t i o n regime. The experimental set-up i s given i n f i g u r e 6. The s t i r r e d - c e l l r e a c t o r was operated batchwise with respect to the l i q u i d and semi-batchwise w i t h r e s p e c t to the gas-phase which was a l s o c i r c u l a t e d by means of a p e r i s t a l t i c pump over an i n f r a r e d spectrophotometer f o r C 0 d e t e c t i o n . The experiments s t a r t e d w i t h e q u i l i b r a t i o n of ~ 720 ml 0.35 mole 2

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

BLAUWHOFF AND VAN SWAAU

HtS

and

COt

Mass Transfer

385

Figure 5. Selectivity factor S as a function of kg a In the negligible interaction regime. Key: O, stirred cell reactor; +, wetted wall column, cocurrent; and X, wetted wall column (countercurrent). Ht

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

386

CHEMICAL REACTION ENGINEERING

Ο JH2S •

—

JDIPA

calculated JH£JDIf^penetration th.) calculated JH2S,JDIFA(film th.)

Ίξ

ΐξ -

β [C02l (moles/ft ) 3

g

2u"

Ο Jc02'2x) • —

JDIPA calculated JQ)2 » -OlPA (penetration th.) calculated JC02. DIPA (Mm th.) J

ι 5

»

1 1

I 0

1

lH2S]g (moles/m ) 3

5

1

1 20

·»

Figure 4. Measured and calculated molefluxesas a function of gas-phase concen­ tration in the medium interaction regime in a stirred cell reactor at 40 rpm.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

31.

BLAUWHOFF AND VAN SWAAU

H*S and

CO*

Mass Transfer

Figure 5. Measured and calculated selectivity factors as a function of gas-phase concentration in a stirred cell reactor at 40 rpm. Key: O, measurements; , penetration theory; and ,filmtheory.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

388

CHEMICAL REACTION ENGINEERING

Figure 7. A typical example of measured concentration curves during extreme interaction experiments. Key: · , [H S] ; and O, [CO ] . t

g

g

g

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

31.

BLAUWHOFF AND VAN SWAAU

H S and CO* Mass Transfer t

389

CC>2/mole DIPA c o n t a i n i n g 2.0 M s o l u t i o n a t 25 °C. E q u i l i b r a t i o n was checked by the IR-spectrophotometer and a f t e r t h i s , H 2 S was introduced i n t o the system a t a constant flow r a t e . The H 2 S gasphase c o n c e n t r a t i o n was obtained from the combination o f the pressure readings ( H 2 S + C O 2 ) and the I R - e x t i n c t i o n ( C O 2 ) . D i r e c t l y on admittance o f H S, CO2 desorbed from the s o l u t i o n i n t o the gas-phase and thus immediately r e s u l t e d i n a p o s i t i v e o v e r a l l (absorption) d r i v i n g f o r c e , but d e s o r p t i o n continued. A f t e r some 20-30 minutes the H 2 S flow was stopped to enable r e - e q u i l i b r a t i o n . I t was observed that CO2 was again absorbed i n t o the s o l u t i o n to almost the i n i t i a l e q u i l i b r i u m (see f i g u r e 7 f o r a t y p i c a l example). T h i s unambiguously proves t h a t the recorded c o n c e n t r a t i o n curves i n the gas-phase a r e due t o r e a c t i o n processes i n the p e n e t r a t i o n zone and have nothing to do w i t h bulk e q u i l i b r i u m which would not have lead t o r e - a b s o r p t i o H2S was n e g l i g i b l e (0.0 bulk e q u i l i b r i u m . 2

Two experimental runs were performed. The H 2 S - and CO2 mole f l u x e s were obtained from the measured c o n c e n t r a t i o n curves by numerical d i f f e r e n t i a t i o n and are p l o t t e d i n f i g u r e 8a,b together with p e n e t r a t i o n and f i l m model c a l c u l a t i o n s . I t i s evident that f o r c e d d e s o r p t i o n can be r e a l i z e d under p r a c t i c a l c o n d i t i o n s and can be p r e d i c t e d by the model. In g e n e r a l , measured H 2 S mole f l u x e s are between the v a l u e s p r e d i c t e d by the models, whereas the CO2 f o r c e d d e s o r p t i o n f l u x i s l a r g e r than c a l c u l a t e d by the models. The CO2 a b s o r p t i o n f l u x , on the other hand, can c o r r e c t l y be c a l c u l a t e d by the models. T h i s probably i m p l i e s that the r a t e o f the r e v e r s e r e a c t i o n , i n c o r p o r a t e d i n equation ( 5 ) , i s underestimated. Moreover, i t should be kept i n mind that e s p e c i a l l y the r e s u l t s o f the c a l c u l a t i o n s i n the f o r c e d d e s o r p t i o n range are very s e n s i t i v e to i n d i r e c t l y obtained parameters ( d i f f u s i o n , e q u i l i b r i u m constants and mass t r a n s f e r c o e f f i c i e n t s ) and the numerical d i f f e r e n t i a t i o n technique a p p l i e d . Conclusions The phenomena d u r i n g simultaneous a b s o r p t i o n o f H 2 S and CO2 a r e c l a s s i f i e d i n t o three-regimes w i t h d i f f e r e n t extents o f i n t e r a c t i o n . I n the f i r s t regime ( n e g l i g i b l e i n t e r a c t i o n ) , the mole f l u x e s may be d e s c r i b e d by simple s i n g l e gas a n a l y t i c a l mass t r a n s f e r expressions and an e x p r e s s i o n f o r the s e l e c t i v i t y f a c t o r at complete H 2 S gas-phase l i m i t a t i o n i s d e r i v e d . I n the medium i n t e r a c t i o n regime, the mole f l u x e s measured f a l l between penet r a t i o n and f i l m theory c a l c u l a t i o n s . I n the extreme i n t e r a c t i o n regime, f o r c e d d e s o r p t i o n i s obtained both e x p e r i m e n t a l l y and t h e o r e t i c a l l y . The measured mole f l u x e s agree f a i r l y w e l l w i t h the c a l c u l a t i o n s , however with the e x c e p t i o n o f the CO2 d e s o r p t i o n f l u x which i s l a r g e r than c a l c u l a t e d . T h i s l a t t e r o b s e r v a t i o n may be a t t r i b u t e d to an incomplete d e s c r i p t i o n o f the r e v e r s e r e a c t i o n rate.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

Figure 8a. Measured and calculated mole fluxes during extreme interaction experiments. Key: · , J ; O, J ; , penetration theory; and ,filmtheory. Ht8

COft

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

Figure 8b. Measured and calculated mole fluxes during extreme interaction experiments. Key is the same as in Figure 8a.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

CHEMICAL REACTION ENGINEERING

392 Legend o f Symbols f k kl,kg r 2

Ζ

enhancement f a c t o r r e a c t i o n r a t e constant (eqn.(5)) liquid/gas-phase mass t r a n s f e r c o e f f i c i e n t reaction rate dimensionless p e n e t r a t i o n depth a t t T , e

defined by : Ζ = x/J ο 1/8

mVmole s m/s mole/m^ s

vDco

π

τ

2

bulk liquid/gas

Literature Cited 1. Beenackers, A . A . C . M . 15, 25. 2. Blauwhoff, P.M.M., Assink, G . J . B . , van Swaaij, W.P.M., Proceedings NATO ASI, Turkey, August 1981. 3. Blauwhoff, P.M.M., Versteeg, G . F . , van Swaaij, W.P.M., to be published. 4. Blauwhoff, P.M.M., Van Swaaij, W.P.M., to be published. 5. Blauwhoff, P.M.M., Ph.D. Thesis, Twente University of Technology, the Netherlands, 1982. 6. Cornelisse, R . , Beenackers, A . A . C . M . , van Beckum, F . P . H . , Van Swaaij, W.P.M., Chem. Eng. Sci., 1980, 35, 1245. 7. Danckwerts, P . V . , Sharma, M.M., Chem. Eng. 1966, 10, CE 244. 8. Danckwerts, P . V . , "Gas-Liquid Reactions", McGraw-Hill, New York, 1970. 9. Danckwerts, P . V . , Chem. Eng. S c i . 1979, 34, 443. 10. Ramachandran, P . Α . , Sharma, M.M., Chem. Eng. S c i . 1971, 26, 349. 11. Secor, R . M . , Beutler, J.A., AIChE J. 1967, 13, 365. Received April 27, 1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

32 Hydrodynamics and Mass Transfer in Pulsing Trickle-Bed Columns J. R. B L O K

1

and A . A . H . DRINKENBURG

Rijksuniversiteit Groningen, Department of Chemical Engineering, Nijenborgh 16, 9747 A G Groningen, The Netherlands

In concurrent downward-flo trickl bed f 1 mete in height and wit and 20 cm, filled with different types of packing material, gas-continuous as well as pulsing flow was realized. Residence time distribution measure­ ments gave information about the liquid holdup, its two composing parts: the dynamic and stagnant holdup and the mass transfer rate between the two. Pulse characteristics were provided by electrical conductivity measurements, viz. frequency, holdup in- and outside the pulses, pulse velocity and pulse height. Mass transfer between gas and liquid was measured with a carbonate/bi-carbonate buffer solution flow­ ing through the bed while absorbing carbon dioxide from the air flow. A l l data together lead to a cor­ relation for the mass transfer rate, that fits the data within twenty per cent. One o f the main advantages o f a c o n c u r r e n t l y operated packed c o l umn i s the high throughput r a t e o f gas and l i q u i d . The disadvantage, that only one t h e o r e t i c a l mass t r a n s f e r stage can be a t tained i s g e n e r a l l y overcome by the l a r g e absorbing c a p a c i t y o f the l i q u i d phase, be i t chemically or p h y s i c a l l y . Several r a t e determining steps can be d i s t i n g h u i s e d i n the mass t r a n s f e r p r o cess ( 1 ) . The hydrodynamics c o n t r o l the mass t r a n s f e r r a t e from gas to l i q u i d and the same from l i q u i d to the s o l i d , o f t e n c a t a l y t i c , p a r t i c l e s . In c o n c u r r e n t l y operated columns not only the g a s - c o n t i nuous flow regime i s used f o r o p e r a t i o n as w i t h countercurrent flow, but a l s o the p u l s i n g flow regime and the d i s p e r s e d bubble flow regime (2). Many chemical r e a c t o r s perform a t the border be1

Current address: Shell Nederland Chemie b.v., Vondelingenweg 601, 3194 AJ Rotterdam-Hoogvliet, The Netherlands. 0097-6156/82/0196-0393$06.00/0 © 1982 American Chemical Society In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

394

CHEMICAL REACTION ENGINEERING

tween gas-continuous and p u l s i n g flow, o f t e n j u s t w i t h i n p u l s i n g flow. Reason i s the enlarged mass t r a n s f e r r a t e i n t h i s s i t u a t i o n coupled to the i n t e n s i v e r a d i a l mixing of the l i q u i d that i n c r e a s e s the heat t r a n s f e r r a t e while decreasing the extent of a x i a l mix­ ing. R e l a t i o n s of the r a t e of mass t r a n s f e r between gas and l i q u i d and the i n f l u e n c e of the stagnant and dynamic holdup were not r e ­ searched i n t e n s i v e l y , u n t i l the present work, although papers on the general subject have been presented (3-6) . L a t e l y an i n t e r e s t i n g paper about mass t r a n s f e r from l i q u i d to s o l i d i n p u l s i n g flow was presented by Luss and co-workers ( 7 ) . One of the main drawbacks i n the p u b l i s h e d data w i t h the p a r t l y exception of (7) i s the absence of i n f o r m a t i o n regarding the hydrodynamic p r o p e r t i e s of the system, i n f o r m a t i o n that could con­ nect these phenomena w i t our l a b o r a t o r y we have s t u d i e f e r e n t types of packing, ranging from Raschig r i n g s to c a t a l y s t p e l l e t s and polypropylene mattings. Some of the r e s u l t s we p r e ­ sent i n t h i s paper, r e s t r i c t e d to Raschig r i n g s , although other types of packing confirm the behaviour. T r a n s i t i o n from gas-continuous

to p u l s i n g flow

P u l s i n g flow i s found when, s t a r t i n g from the gas-continuous flow regime, gas and l i q u i d flow r a t e s are i n c r e a s e d . G e n e r a l l y one observes an i n c r e a s e of the l i q u i d holdup i n the gas-continuous flow regime when the l i q u i d flow r a t e i s increased at constant gas r a t e . However, at a c e r t a i n p o i n t pulses develop i n the bed and t h e r e a f t e r the holdup i n c r e a s e s o n l y f a i n t l y . F i g u r e 1 p r e ­ sents some r e s u l t s f o r 2.5 mm Raschig r i n g s i n a column of 1 meter length and 10 cm diameter, f o r the air/water system. The r e s u l t s were obtained by residence time d i s t r i b u t i o n measurements. P u l s i n g s e t s i n at the p o i n t i n d i c a t e d by an arrow. I t ap­ pears from many more experiments, that the t r a n s i t i o n i s found f o r a constant value of the r e a l l i q u i d v e l o c i t y f o r each type of packing and each system. F i g u r e 2 shows that the l i q u i d holdup obeys an exponential r e l a ­ tion:

I

= 4.48

* 10~

0.265 * (S/u )

2

For the t r a n s i t i o n p o i n t we N.

- 0.08

Since v ^

u

= it/g

β e x

*"**

to

then f i n d a constant Froude number: 0.09

(2)

r

P e s s i o n can be r e w r i t t e n , w i t h the a i d

of equation (1), as (u )/(e d ) l t

p

(1)

« constant

(u /s) g t

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

BLOK AND DRINKENBURG

Pulsing Trickle-Bed Columns

395

Figure 1. Relative liquid holdup versus real liquid velocity. Key: · , u = m/s; Δ, u = 0.81 m/s; V , u = 0.61 m/s; • , u = 0.41 m/s; X, u = 0.20 m/s; and O, u = 0.10 m/s. g

g

g

g

1.3

g

g

Figure 2.

Relative liquid holdup versus S/u in the pulsingflowregime. System is air-water. Key: ·, 2.5 χ 2.5; and Χ,4χ4 Raschig rings. g

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

396

CHEMICAL REACTION ENGINEERING

the constant being 0·042 i n case Ν =0.09. F i g u r e 3 shows the experimental v a l u e s , i n c l u d i n g a number o f data on a d i f f e r e n t packing geometry as presented by S i c a r d i , Gerhard and Hofmann ( 8 ) . Pulse frequency and holdup For l i q u i d flow r a t e s , higher than the t r a n s i t i o n p o i n t , the f r e ­ quency of the p u l s e s i n c r e a s e s l i n e a r l y with the r e a l l i q u i d v e ­ l o c i t y , f i g u r e 4. U l t i m a t e l y a t h i g h frequencies the pulses o v e r l a p and we a r r i v e i n the d i s p e r s e d bubble flow regime. Thus we consider the pulses to be zones of the bed already i n the d i s p e r s e d bubble flow, spaced by moving compartments that a r e s t i l l i n the gas-continuous flow regime. T h i s concep t r a n s f e r and mixing phenomena t i o n s (9) where i t appears that above the t r a n s i t i o n p o i n t the pressure drop can be c o r r e l a t e d l i n e a r l y w i t h the pulse frequency. Pulses a r e to be considered as porous to the gas flow as i s shown when we p l o t the pulse v e l o c i t y versus the r e a l gas flow r a t e , f i g u r e 5. Above a s u p e r f i c i a l gas v e l o c i t y o f approx. 1 m/s the pulse v e l o c i t y becomes more or l e s s constant, t h e r e f o r e gas must be pushed through the pulses from top to bottom. Indeed, the l i q u i d holdup i n the p u l s e , although h i g h , i s not f i l l i n g up a l l the v o i d s , l u c k i l y l e a v i n g the p o s s i b i l i t y o f a h i g h mass t r a n s f e r r a t e i n the pulse i t s e l f . F i g u r e 6 shows t h e l i q u i d holdup i n s i d e and o u t s i d e the pulse (the base holdup) as measured w i t h the e l e c ­ t r i c a l c o n d u c t i v i t y c e l l s . β i s the average holdup c a l c u l a t e d from the residence time d i s t r i b u t i o n . Mass t r a n s f e r between stagnant and dynamic holdup Residence time d i s t r i b u t i o n measurements, together w i t h a theore­ t i c a l model, provide a method to c a l c u l a t e the r a t e o f mass t r a n s ­ f e r between the l i q u i d f l o w i n g through the column, the dynamic holdup, and the stagnant pockets o f l i q u i d i n between the p a r t i ­ c l e s . We have chosen the cross flow model (10). I t has to be noted that the model s t a r t s from the assumption that the flow p a t t e r n has a steady-state c h a r a c t e r , which i s i n c o n f l i c t w i t h r e a l i t y . Nevertheless, average values of the number of mass t r a n s f e r u n i t s can be c a l c u l a t e d as w e l l as the p a r t o f the l i q u i d being i n the stagnant s i t u a t i o n . The f o l l o w i n g equations then h o l d :

Ν =

k SH (3) U

L

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

32.

BLOK AND DRINKENBURG

Pulsing Trickle-Bed Columns

• X

+ 0 φ

•

f

• •

397

columndiameter Packing 0.2 m RR 4 mm. 0.1 m RR 4 mm. 0.05 m RR 4 mm. 0.1 m RR 2.5 mm. 0.05 m RR 2.5 mm. 0.3 m RR 10 mm. 0.3 m CC 12 mm. 0.15 m CC 6 mm. 0.08 m CC 5 mm.

10 CC= Ceram. C y l .

10

Fr = .O90

1(f 10"

10" eVd7 Figure 3.

Correlation for the transition from gas-continuous to pulsing flow. All systems are air-water. Left of the line is gas-continuous flow (S).

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

398

CHEMICAL REACTION ENGINEERING

9

jp[Hz]

8

γ

7 6

'0

5 A 3 2 1

5

U

6

7

8

l

10

11

12

Fr=O080

Figure 4. Pulse frequency versus real liquid velocity. Raschig rings 2.5 mm. Key to u :O 0.025 m/s;^ 0.021 m/s;jer, 0.018 m/s;-&, 0.014 m/s; and , 0.011 m/s. Uncircled: col diam. 5 cm; circled: col. diam. 1 cm. L

t

f

0

1

2

3 —

Figure 5.

Vg ( m/s )

Pulse velocity vs. real gas velocity.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

4

32.

BLOK AND DRINKENBURG

Pulsing Trickle-Bed Columns

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

399

400

CHEMICAL REACTION ENGINEERING

M

M

2 01 S

d

3

M

3

2 2

F i g u r e 7 presents r e s u l t s f o r N, f i g u r e 8 f o r β as a f u n c t i o n o f the t o t a l holdup. From f i g u r e 8 i t can be seen that the stagnant p a r t o f the holdup decreases very r a p i d l y w i t h the t o t a l holdup, as can be expected, but a l s o with i n c r e a s i n g pulse frequency. From the v a l ­ ues of Ν the corresponding mass t r a n s f e r c o e f f i c i e n t i s found and appears to be constant i n the p u l s i n g flow regime. A l l t h i s leads to the i d e a that the pulses r e f r e s h p a r t s of the l i q u i d that i s stagnant i n between the p u l s e s , but i s a c t i v a t e d i n the p u l s e , e s ­ p e c i a l l y by i t s h i g h l y t u r b u l e n t f r o n t Mass t r a n s f e r from gas

liqui

pulsing

regim

The value of k^a, a being the g a s - l i q u i d contact area per u n i t v o l ­ ume, k^, the corresponding l i q u i d s i d e mass t r a n s f e r c o e f f i c i e n t , i s c o n s i d e r a b l y higher i n the p u l s i n g than i n the gas-continuous flow regime. I t has been t r i e d i n the past, and p a r t i a l l y successf u l l , to c o r r e l a t e the mass t r a n s f e r data to the energy d i s s i p a ­ t i o n r a t e i n the bed. We made the premise, that pulses are p a r t s of the bed a l r e a d y i n the d i s p e r s e d bubble flow regime and t h e r e ­ f o r e must a c c r e d i t f o r an i n c r e a s e i n the t r a n s f e r r a t e propor­ t i o n a l to t h e i r presence i n the bed. The a c t u a l value of k a was measured by a b s o r p t i o n of carbondioxide from a i r i n t o a b u f f e r s o l u t i o n of potassium-carbonate and b i ­ carbonate. Care was taken that the mass t r a n s f e r c o e f f i c i e n t i t ­ s e l f was not enhanced by the chemical r e a c t i o n , although the com­ p o s i t i o n o f the b u f f e r s used guaranteed a s u b s t a n t i a l d r i v i n g f o r c e f o r mass t r a n s f e r over the whole length of the column. L i t ­ erature about the subject i s abundant and here r e f e r r e d to (11, 12, L

J3). The carbondioxide content o f the a i r was measured a t the entrance and e x i t o f the bed by an i n t e r f e r o m e t e r . From f i g u r e 9 i t becomes c l e a r that indeed the mass t r a n s f e r r a t e i n c r e a s e s q u i t e l i n e a r l y w i t h the pulse frequency. T h i s sup­ p o r t s the i d e a that the value of k a indeed can be s p l i t up i n t o p a r t s produced by the gas-continuous zones and the p u l s i n g zones i n the bed. Taking the a c t i v e pulse h e i g h t as 0.05 m and the pulse v e l o c i t y as 1 m/s, we d e r i v e f o r the mass t r a n s f e r c o e f f i c i e n t i n the gascontinuous zone, k , a value of 10 ** m/s and i n the pulse proper, k , a v a l u e of 6 * 10 m/s. These values compare very w e l l w i t h those given i n l i t e r a t u r e (_5, 6) f o r both gas-continuous and d i s ­ persed bubble flow regimes. An estimate of k^ can a l s o be made by means o f the p e n e t r a t i o n theory, t a k i n g the r e s p e c t i v e l i q u i d i n and outside the pulse as the b a s i c f o r the c a l c u l a t i o n of the conL

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

32.

BLOK AND DRINKENBURG

*· f m

~#

Ο

—I

1

1

2

1

3

* *

1

4

401

Pulsing Trickle-Bed Columns

1

5

·

··*·

1

6

1

7

β

ψ

·

1

8

—

1

9

1

10

1

11

Τ­

12

v [iô f] L

2

Figure 7. Number of transfer units versus real liquid velocity. Raschig rings 4 mm. Key to column diameter: ·, 20 cm; ψ, 10 cm; and A, 5 cm.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

402

CHEMICAL REACTION ENGINEERING

Figure 8. Static holdup versus total holdup for various pulse frequencies. Raschig rings 4 mm. Key: Ο , 0 Hz; · , 2 Hz; +, 1 Hz; X, 3 Hz; Δ , 4 Hz; A, 5 Hz; and V, >6Hz.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

32.

BLOK AND DRINKENBURG

τ 1

Pulsing Trickle-Bed Columns

1

1

1

1

1

1

2

3

4

5

6

7 -~

Figure 9.

403

1

1

8 f [Hz]

9

The relation between k and the pulse frequency. L

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

CHEMICAL REACTION ENGINEERING

404

ο 4 mm κ 4 mm • 2.5 m m • 2.5mm

A

RR 5 c m column φ R R 10 " RR 5 " " " R R 10 "

6mm RR •π1

0.1

—

Figure 10.

8 "

"

" (GJQnetto)

.58 •4 -2-2 U Ug Se SI (units) L

Final correlation for k a. L

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

-r-n 10

32.

BLOK AND DRINKENBURG

Pulsing Trickle-Bed Columns

405

t a c t time between gas and l i q u i d w h i l e f l o w i n g over one p a r t i c l e . Then we f i n d the values as presented i n the t a b l e : Table I : l i q u i d s i d e mass t r a n s f e r c o e f f i c i e n t c a l c u l a t e d with the p e n e t r a t i o n theory 2.5 mm r i n g s -4 1.7 * m m/s , 8.1 * m m/s

4 mm r i n g s -4 1.5 * 10 m/s , 6.4 * 10 m/s

k_ Lc k Lp Taking a l l measurements together, i t can be shown t h a t : T

a

.-4 „ -1.2 =5*10 * S * £ Λ

(5)

L and,

s i n c e the l i q u i d holdup i s known, ,0.4 a = 0.46 S

^-2.2 0.58 ε U U 11 S F i g u r e 10 then presents the c o r r e l a t i o n and the experimental A confidence l i m i t o f 20% encloses a l l data. A

l

(6) data.

Conclusion I t i s shown, that the performance o f a p u l s i n g packed column can be s p l i t up i n t o i t s two component p a r t s , the p u l s e s and the zones i n between p u l s e s . The p u l s e s can be d e s c r i b e d as p a r t s o f the bed already i n the d i s p e r s e d bubble flow regime; the zones-in between the p u l s e s as p a r t s o f the bed s t i l l i n the gas-continuous regime. The pulse frequency i s l i n e a r l y dependent upon the r e a l l i q u i d v e ­ l o c i t y . The p r o p e r t i e s o f the p u l s e , l i k e holdup, v e l o c i t y and height a r e q u i t e independent upon a l l the parameters except gas flow r a t e . Combination o f the e m p i r i c a l l y found c o r r e l a t i o n s f o r these pulse p r o p e r t i e s i n a model i n which the p a r t s of the bed i n the gascontinuous resp. d i s p e r s e d bubble flow are weighted, leads to a c o r r e l a t i o n o f the mass t r a n s f e r r a t e with p r e d i c t i v e v a l u e . The use of a p u l s i n g t r i c k l e bed seems very important i n those cases where s i d e r e a c t i o n s may take p l a c e i n the stagnant holdup.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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CHEMICAL REACTION ENGINEERING

Legend of Symbols a d f g H k M Ν S u ν 3 ε

p

s p e c i f i c area g a s - l i q u i d contact p a r t i c l e diameter p u l s e frequency a c c e l a r a t i o n due to g r a v i t y h e i g t h of the bed mass t r a n s f e r c o e f f i c i e n t moment number of t r a n s f e r u n i t s s p e c i f i c area packing superficial velocity real velocity holdup porosity

m /m

bed

-1 s -2 m/s m m/s 2, 3 m /m m/s "4/

3

K ,

Subscripts 01, 2, 3 c d g 1 ρ s t

moment-order gas-continuous dynamic gas liquid pulse stagnant transition

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

S a t t e r f i e l d , C.N.; AIChEJ 1975, 2J, 209. Charpentier, J.C.; Chem. Engng. Jourη. 1976, 21, 161. R e i s , L.P.; IEC Proc. Pes. Dev. 1967, 6, 486. G i a n e t t o , Α.; Specchia, V.; B a l d i , G.; AIChEJ 1973, 916. H i r o s e , T.; Toda, M.; Sato, Y.; Journ. Chem. Engng. Japan 1974, 2, 187. S y l v e s t e r , N.D.; P i t a y a p u l s a r n , P.; IEC Proc. Pes. Dev. 1975, ^4, 421. Chou, T.S.; Worley, F.L.; Luss, P. IEC Fund. 1979, _l

1/3 L.

i-0

( a b Li/I*) +

1

(

I

4

)

the summation i n Eq.14 by an i n t e g r a l , leads to 2/3

2/3

μ

τ

1

/

3

1/3

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

33.

CRINE AND L'HOMME

Percolation Theory

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

415

416

CHEMICAL REACTION ENGINEERING

i n which Θ has been r e p l a c e d by the value given by Eq.10. can put Eq.15 i n dimensionless form = 1.74 f d

2/3 Z

/

J

w

Re

1/3 L

1

x" / Ga L

3

(a d ) g

2/3

We

(16)

p

T h i s equation i s reproduced i n F i g u r e 5 f o r d i f f e r e n t values o f The experimental system considered i n t h i s f i g u r e c o n s i s t s of water f l o w i n g through a bed of 3 mm diam. spheres w i t h a poro­ s i t y equal to 0.35. The pressure drop i s assumed to be n e g l i g i b l e (6 «pTg). Comparison o f Eq.16 w i t h the c o r r e l a t i o n proposed by Speccnia e t a l . (18), f o r the low g a s - l i q u i d i n t e r a c t i o n regime, L G

0

= 3.86 ε · d

3 5

Re

0

'

5 4 5

Ο ^ ' "

0

(a d ) '

6 5

(17)

i s shown i n F i g u r e 5. Th very s a t i s f y i n g . The apparent l o g - s l o p e o f Eq.16 versus R e equals 1 - 2/3 . By comparison w i t h Eq.17, t h i s y i e l d s a mean i r r i g a t i o n r a t e o f about 0.7 i n the range 0.1 to 10 kg/m s, i . e . , a parameter 1^ o f roughly 0.3 kg/m s. T h i s value i s i n good agreement w i t h the range found when a n a l y z i n g the i r r i g a t i o n r a t e c o r r e l a t i o n s (see F i g u r e 4 ) . The averaged value o f apparent r e a c t i o n r a t e i s obtained r e a d i l y u s i n g the same procedure as f o r the i r r i g a t i o n r a t e . L

w

2

2

a

< r

a > = IP ^ 0.146 „ -0.071 = 1.617 R e Ga

C E

L

„v (4)

L

E v a l u a t i o n o f L i q u i d - S o l i d Contacting

Efficiency

T r a c e r methods proposed by Schwartz e t a l . (19) and Colombo et a l . (21) were used t o determine t o t a l and e x t e r n a l c a t a l y s t c o n t a c t i n g e f f i c i e n c y . These techniques have been d e s c r i b e d elsewhere (22). T o t a l c o n t a c t i n g e f f i c i e n c y , ï)ç d e f i n e d as the f r a c t i o n of t o t a l ( e x t e r n a l and i n t e r n a l ) c a t a l y s t area contacted by l i q u i d can be obtained by: 9

β

(K } (u } A app l a l n a TF μ u (K ) " ( la~ ιΜ^ρ A

L F

m

( d i f f e r e n c e i n f i r s t moment f o r adsorbing and nonadsorbing t r a c e r impulse response i n t r i c k l e - f l o w ) ( d i f f e r e n c e i n f i r s t moment o f the above two t r a c e r s i n l i q u i d f i l l e d column a t same l i q u i d flow-rate) (1)

and i t has been shown t o be u n i t y i n the hydrocarbon systems used (20, 22). E x t e r n a l c o n t a c t i n g e f f i c i e n c y , n , d e f i n e d as the f r a c t i o n o f e x t e r n a l c a t a l y s t area i n contact with f l o w i n g l i q u i d i s obtained a s : C E

_r eo'app Λ (D ) , M eo

m

η

0Ε

LF T T

(apparent e f f e c t i v e d i f f u s i v i t y i n t r i c k l e - f l o w ) ( e f f e c t i v e d i f f u s i v i t y i n l i q u i d f i l l e d column) ^2)

where the d i f f u s i v i t i e s a r e e x t r a c t e d from the v a r i a n c e o f the impulse response. Tracer s t u d i e s a l s o give i n f o r m a t i o n on dynamic holdup (22).

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

432

CHEMICAL REACTION ENGINEERING

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

34.

EL-fflSNAWI ET

AL.

Trickle-Bed Reactors

433

w i t h an average e r r o r of -2.5% and standard d e v i a t i o n of the e r r o r of 8.7%. Both dynamic s a t u r a t i o n and l i q u i d - s o l i d c o n t a c t i n g e f f i c i e n c y are found to c o r r e l a t e w e l l w i t h l i q u i d mass v e l o c i t y , not to c o r r e l a t e w i t h Reynolds number alone, to i n c r e a s e w i t h i n c r e a s e d l i q u i d v e l o c i t y and t o decrease w i t h i n c r e a s e d p a r t i c l e diameter. Surface t e n s i o n f o r c e s do not seem to p l a y a r o l e i n t r i c k l e - f l o w regime but become important i n the high g a s - l i q u i d i n t e r a c t i o n (pulsing) regime. Equations (3) and (4) e s t a b l i s h a r e l a t i o n s h i p between c o n t a c t i n g e f f i c i e n c y and dynamic s a t u r a t i o n : 0.244 "CE

=

(5)

1 , 0 2

Discussion

of R e a c t i o n Studies i n a T r i c k l e - B e d

Reactor

R e a c t i o n s t u d i e s wer F i g u r e 5. Both 0.5% Pd and 2.5% Pd c a t a l y s t s were used i n cyclohexane and A.C.S. grade hexane s o l v e n t s . In F i g u r e 6 experimental r e s u l t s f o r c o n v e r s i o n as a f u n c t i o n of l i q u i d s u p e r f i c i a l v e l o c i t y are compared to the p r e d i c t i o n s of model Ml f o r the 0.5% Pd c a t a l y s t and cyclohexane s o l v e n t . Equa­ t i o n (4) i s used to p r e d i c t c o n t a c t i n g e f f i c i e n c y . The c o r r e l a ­ t i o n of Dwivedi and Upadhyay (26) i s used to evaluate f l o w i n g l i q u i d to s o l i d mass t r a n s f e r c o e f f i c i e n t , k^s, and the c o r r e l a ­ t i o n of Goto and Smith (24) i s used t o determine the g a s - l i q u i d v o l u m e t r i c mass t r a n s f e r c o e f f i c i e n t , (ka)g£. The B i o t number on the i n a c t i v e l y wetted s u r f a c e , B i - kgLS Vp/D ex, of 7 i s based on the assumed stagnant l i q u i d f i l m mean thxckness of 0.01 cm. F i g u r e 6 (curve 1) i l l u s t r a t e s that the a v a i l a b l e mass t r a n s f e r c o r r e l a t i o n s are inadequate i n p r e d i c t i n g the observed e x p e r i ­ mental r e s u l t s . T h i s i s to be expected s i n c e these c o r r e l a t i o n s are based on data obtained i n absence of r e a c t i o n . I t i s known that t r a n s p o r t c o e f f i c i e n t s are enhanced by the presence of r e a c t i o n and t h i s has been shown i n t r i c k l e - b e d s a l s o (27). This n e c e s s i t a t e s i n t r o d u c t i o n of two enhancement f a c t o r s : E\ f o r the f l o w i n g l i q u i d - s o l i d mass t r a n s f e r c o e f f i c i e n t , k^s, and E2 f o r the v o l u m e t r i c g a s - l i q u i d mass t r a n s f e r c o e f f i c i e n t , ( k a ) j t . Comparison of experimental and p r e d i c t e d c o n v e r s i o n when the t r a n s p o r t c o e f f i c i e n t s as c a l c u l a t e d from the c o r r e l a t i o n s are m u l t i p l i e d by v a r i o u s assumed values of t h e i r r e s p e c t i v e enhance­ ment f a c t o r s i s a l s o shown i n F i g u r e 6. Agreement w i t h data seems only a c h i e v a b l e when both Εχ and E2 are l a r g e r than u n i t y . The b e s t f i t (minimizing the sum of the squares of the d e v i a t i o n s ) of the data i s obtained w i t h Εχ - 2.5, E2 - 5.7 and B i n =5.2 (dashed l i n e i n F i g u r e 6 ) . The s i m p l i f i e d lumped parameter model (M2) can a l s o be used to match the data of F i g u r e 6. T h i s suggests the f o l l o w i n g c o r r e l a t i o n s f o r the o v e r a l l mass t r a n s f e r c o e f f i c i e n t s i n presence of r e a c t i o n . s

D

e

g

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

434

CHEMICAL REACTION ENGINEERING

U g (cm/sec) L

Figure 6. Predicted and experimental reactor conversions as a function of liquid superficial velocity. [Model Ml]—Bi = 5.2. Key: A, experimental results. D

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

34.

23.0

Sc

0 , 4 L

435

Trickle-Bed Reactors

EL-HiSNAWi ET AL.

1.3

1^

(6)

(7)

Model p r e d i c t i o n s a r e now t e s t e d a g a i n s t experimental r e s u l t s f o r cyclohexane s o l v e n t and 2.5% Pd c a t a l y s t , hexane (A.C.S. grade) s o l v e n t and 0.5% Pd and 2.5% Pd c a t a l y s t . The r e s u l t s a r e presented i n F i g u r e s 7-9. The p r e d i c t i o n s o f model Ml a r e based on unchanged enhancement f a c t o r s f o r the l i q u i d s o l i d and g a s - s o l i d mass t r a n s f e r c o e f f i c i e n t s o f « 2.5 and E 2 = 5.7, r e s p e c t i v e l y w e l l i n the same s o l v e n l y s t (Figure 7 ) . However, the simpler model (M2) p r e d i c t s r e a c t o r performance b e t t e r i n a d i f f e r e n t s o l v e n t (hexane) on both c a t a l y s t s (Figures 8-9). T h i s suggests that t r a n s p o r t c o e f f i c i e n t s k and kgLg obtained from equations (6) and (7) and used i n model M2 a r e l e s s a f f e c t e d by change i n r e a c t i o n r a t e s than the enhancement f a c t o r s Εχ and E 2 which a r e used with model Ml. The assumption that the f r a c t i o n (1-TICE) °f e x t e r n a l c a t a l y s t s u r f a c e i s dry, as used by some other i n v e s t i g a t o r s (11), r e s u l t s i n a very l a r g e B i p which cannot e x p l a i n o r even match the observed experimental r e s u l t s . Dryout o f a c a t a l y s t s u r f a c e appears p o s s i b l e only when much l a r g e r temperature gradients a r e present. On the other hand the assumption o f TlcE 1 everywhere leads to u n r e a l i s t i c dependence o f mass t r a n s f e r c o e f f i c i e n t s on l i q u i d v e l o c i t y . Matching the data w i t h a s i n g l e parameter model (an o v e r a l l mass t r a n s f e r c o e f f i c i e n t ) r e s u l t s i n too high an e f f e c t o f v e l o c i t y on such a parameter and i n the l o s s o f model predictive a b i l i t y for d i f f e r e n t solvents. s

=

Conclusions Dynamic t r a c e r t e s t s can be used t o determine dynamic holdup and c a t a l y s t c o n t a c t i n g which i n t r i c k l e - f l o w regime can be c o r r e l a t e d w i t h Reynolds and G a l l i l e o number. A simple r e a c t o r model f o r gas l i m i t i n g r e a c t a n t when matched t o experimental r e s u l t s f o r one s o l v e n t and one c a t a l y s t a c t i v i t y p r e d i c t s r e a c t o r performance w e l l f o r d i f f e r e n t c a t a l y s t a c t i v i t i e s and i n other s o l v e n t s over a wide range o f l i q u i d v e l o c i t i e s .

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

436

CHEMICAL REACTION ENGINEERING

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

34.

EL-msNAWi

ET AL.

Trickle-Bed Reactors

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

437

438

CHEMICAL REACTION ENGINEERING

Figure 9.

Reactor conversion as junction of liquid superficial velocity (hexane solvent). Bi = 8.6. Key is the same as in Figure 8. D

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

34.

EL-HiSNAWi ET A L .

439

Trickle-Bed Reactors

Legend o f Symbols a Bi

D

- i n t e r f a c i a l area (see s u b s c r i p t s f o r meaning) - B i o t number on i n a c t i v e l y wetted or dry c a t a l y s t k

< gLS V /De p

S

e x

)

5 i ^ - B i o t number on a c t i v e l y wetted c a t a l y s t ( k

v

s

o

r

k

V

D

LS p/°e e x s p / e S x) S reactant c o n c e n t r a t i o n i n l i q u i d l i q u i d reactant c o n c e n t r a t i o n d i f f u s i v i t y o f gaseous reactant i n the l i q u i d phase e f f e c t i v e d i f f u s i v i t y o f gaseous reactant i n the c a t a l y s t pellet - e f f e c t i v e mean p a r t i c l e diameter (6 V p / S ) - G a l l i l e o number ( d 3 g P L / U L ) - dynamic l i q u i d holdu - s t a t i c external l i q u i - adsorption e q u i l i b r i u - r a t e constant per u n i t c a t a l y s t volume - mass t r a n s f e r c o e f f i c i e n t ( i s i n g l e o r m u l t i p l e s u b s c r i p t ) - t o t a l r e a c t o r length - Reynolds number (dp u g Ρχ/μΐ.) - Schmidt number ( U I / P L D ) - e x t e r n a l area of c a t a l y s t p a r t i c l e - liquid superficial velocity - p a r t i c l e volume - volume o f the a c t i v e c a t a l y s t l a y e r - l i q u i d reactant conversion - a x i a l coordinate - bed p o r o s i t y - c a t a l y s t e f f e c t i v e n e s s f a c t o r (completely wetted p e l l e t ) - t o t a l contacting e f f i c i e n c y " external contacting e f f i c i e n c y - parameter (eq. T9) - f i r s t mement o f the impulse response - liquid viscosity - l i q u i d density - p e l l e t modulus ( V / S ) A / D - a c t i v e s h e l l modulus ( V / S A /D - dynamic s a t u r a t i o n (%/eg) - gas reactant A - adsorbing t r a c e r - apparent value - at gas-liquid equilibrium - gas-liquid - l i q u i d - i n a c t i v e l y wetted s o l i d - liquid - liquid filled - l i q u i d a c t i v e l y wetted s o l i d - nonadsorbing t r a c e r - l i q u i d feed c o n d i t i o n s - o v e r a l l (gas-active l i q u i d - s o l i d ) - two phase flow - l i q u i d r e a c t a n t (a-methylstyrene) e

CA C a

D

E

dp GaL % Hgg k ki L Re^ v

SCL

S ugL Vp V X(X ζ ε η T)Q ^CE λ μ y PL φ φ cop A a app e g£ gLS L LF LS na ο s TF α e x

s

Β

L

3

" -

A

S

ex

2

2

p

L

A

p

V

e x

s

E

e x

V

E

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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Acknowledgements Support o f the Chemical Reaction E n g i n e e r i n g Laboratory i n which t h i s work was performed by Amoco O i l , Monsanto Company and S h e l l Development i s t r u l y a p p r e c i a t e d .

Literature Cited 1. Germain, Α . ; L'Homme, G. Α . ; Lefebvre, Α. "Chemical Engineering of Gas-Liquid-Solid Catalytic Reactions"; L'Homme, G. Α . , E d . ; Cebedoc, Liege, 1978, ρ 265. 2. Satterfield, C. Ν. AIChE J. 1975, 21, 209. 3. Goto, S.; Levec, J.; Smith, J. M. Cat. Rev.-Sci. Eng. 1977, 15, 187. 4. M i l l s , P. L.; Duduković, M. P. Chem. Eng. S c i . 1980, 35, 2267. 5. Gianetto, Α . ; Baldi G . Specchia V . Sicardi S AIChE J. 1978, 24(6), 1087 6. Germain, Α . ; Lefebvre, Α . ; L'Homme, G. A. Adv. Chem. 1974, 133, 164. 7. Sedricks, W.; Kenney, C. N. Chem. Eng. S c i . 1973, 38, 559. 8. Goto, S.; Smith, J. M. AIChE J. 1975, 21, 714. 9. Levec, J.; Smith, J. M. AIChE J. 1976, 22, 159. 10. Satterfield, C. N . ; Ozel, F. AIChE J. 1973, 19, 1259. 11. Herskowitz, M . ; Carbonell, R. G . ; Smith, J. M. AIChE J. 1979, 25, 272. 12. Koros, R. M. Proc 4th Int. Symp. React. Eng. Dechema, Heidelberg, 1976, V o l . 1, ρ Ι Χ - 3 7 2 . 13. Germain, Α . ; Crine, M . ; Marchot, P . ; L'Homme, G. A. ACS Symp. Ser. 1978, V o l . 65, ρ 411. 14. Turek, F.; Lange, R. Chem. Eng. S c i . 1981, 36, 569. 15. Ma, Y. H. D.Sc. Thesis, MIT, 1966. 16. White, D. E.; Litt, M . ; Heymuch, G. J. I&EC Fundamentals 1974, 13, 143. 17. Jawad, A. Ph.D. Thesis, Univ. Birmingham, England, 1974. 18. El-Hisnawi, A. A. D.Sc. Thesis, Washington University, St. Louis, 1981. 19. Schwartz, J. G . ; Weger, E.; Duduković, M. P. AIChE J. 1976, 22, 953. 20. M i l l s , P. L . D.Sc. Thesis, Washington Univ. St. Louis, 1980. 21. Colombo, A. J.; Baldi, G . ; Sicardi, S. Chem. Eng. S c i . 1976, 31, 1101. 22. M i l l s , P. L.; Duduković, M. P. AIChE J. 1981, 27, 893. 23. M i l l s , P. L.; Duduković, M. P. 2nd World Congress on Chem. Eng. Montreal, October 1981, V o l . 3, ρ 143. 24. Goto, S.; Smith, J. M. AIChE J. 1975, 21, 706. 25. Charpentier, J. C. "Chemical Engineering of Gas-Liquid-Solid Catalyst Reactions"; L'Homme, G. Α . , E d . ; Cebedoc, Liege, 1979; ρ 78. 26. Dwivedi, P. Ν . ; Uphadhyay, S. Ν. I&EC Process Des. Develop. 1977, 16, 157. 27. Baldi, G . ; Sicardi, S. Chem. Eng. S c i . 1975, 30, 617. Received April 27, 1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

35 Exothermic Gas Absorption with Complex Reaction: Sulfonation and Discoloration in the Absorption of Sulfur Trioxide in Dodecylbenzene R. M A N N , P. KNYSH, and J. C . A L L A N University of Manchester Institute of Science and Technology, Department of Chemical Engineering, Manchester, M60 1QD England Experimental measurements of absorption fluxes and colour developmen between sulphur trioxid carried out i n a s t i r r e d c e l l absorber. A model with two parallel reaction paths representing sulphonation and discolouration has been applied to analyse the exothermic absorption accompanying conversions up to 70%. The results show that the two reactions have similar activation energies and that temperature increases greater than 100°C occur at the interface during absorption. The absorption enhancement factor exhibits a maximum value as l i q u i d phase conversion proceeds. G a s - l i q u i d r e a c t o r s present a number o f i n t e r e s t i n g problems i n r e a c t o r a n a l y s i s and design which a r i s e from the c o u p l i n g o f mass t r a n s f e r and chemical r e a c t i o n processes. Thus, the d i f f i c u l t y o f r e s o l v i n g the r e l a t i v e c o n t r i b u t i o n s o f filmwise and bulkwise r e a c t i o n remains unsolved f o r a l l but the s i m p l e s t k i n e t i c s . Such d i f f i c u l t i e s are compounded when thermal e f f e c t s and s i g n i f i c a n t heat r e l e a s e accompany the a b s o r p t i o n and r e a c t i o n . W h i l s t e a r l y work i n d i c a t e d that f o r carbon d i o x i d e a b s o r p t i o n heat r e l e a s e c o u l d not be expected t o be s i g n i f i c a n t O ) , Van de Vusse had a l r e a d y remarked i n 1966 (2) that the a b s o r p t i o n o f c h l o r i n e i n t o a hydrocarbon c o u l d produce flames a t the i n t e r f a c e . Around that time the heat e f f e c t s accompanying ammonia a b s o r p t i o n were estimated t o g i v e i n c r e a s e s o f around 15°C across the mass t r a n s f e r f i l m (3)> and subsequently f u r t h e r treatments q u a n t i f i e d temperatures up t o 40°C (4,5,6). Systems i n v o l v i n g the a b s o r p t i o n o f S0~ i n t o organic l i q u i d s i n v o l v e s u r f a c e temperatures up t o 100°C higher than the bulk (7) and Beenackers has experimentally observed s u r f a c e b o i l i n g f o r a b s o r p t i o n o f SO^ i n benzene ( 8 ) . The i n d u s t r i a l sulphonation o f high b o i l i n g l i q u i d s l i k e l i n e a r a l k y l benzenes can i n theory give r i s e t o very h i g h temperatures s i n c e evaporative c o o l i n g does not occur before thermal degradation temperatures a r e reached. 0097-6156/82/0196-0441$06.00/0 © 1982 American Chemical Society In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

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CHEMICAL REACTION ENGINEERING

D i s c o l o u r a t i o n o f l i q u i d product i n the manufacture o f detergent sulphonates from liquids like dodecylbenzene is a problem a s s o c i a t e d w i t h the s e v e r i t y o f sulphonation c o n d i t i o n s . High p r o d u c t i v i t y o f r e a c t o r s tends to be l i m i t e d by the formation o f c o l o u r i n g agents which may moreover be malodourous. A lack o f r i g o u r i n i n t e r p r e t i n g mass t r a n s f e r effects i n gas-liquid sulphonation w i t h SO- has r e s u l t e d i n an ad-hoc v a r i e t y o f r e a c t o r types ranging from sparged r e a c t o r s (9)· through f a l l i n g film r e a c t o r s (1£) w i t h scraped s u r f a c e r e a c t o r s (JO and spray r e a c t o r s i n between. A l i q u i d - l i q u i d r e a c t o r u s i n g SO- d i s s o l v e d i n l i q u i d SOg has even been proposed (^2) t o by-pass problems o f g a s - l i q u i d systems. Precise quantitative design o f e f f i c i e n t direct sulphonation r e a c t o r s which minimise d i s c o l o u r a t i o n and permit high p r o d u c t i v i t y a t h i g h SO- c o n c e n t r a t i o n s , r e q u i r e s knowledge o f the basic reaction kinetics* d th heat d transfe o c c u r r i n g a t the i n t e r f a c e t r a n s f e r d i s p l a y c o m p l e x i t i e analogou isothermal c a t a l y s t p e l l e t s and m u l t i p l i c i t i e s a r e p r e d i c t e d t o occur a c r o s s the t r a n s f e r f i l m s (13)* Laminar J e t Experiments A f u l l s e t o f dodecylbenzene laminar j e t experiments a t c a r e f u l l y c o n t r o l l e d SO^ c o n c e n t r a t i o n s from 3$ t o 30% have been undertaken. The theory o f a b s o r p t i o n with pseudo f i r s t order r e a c t i o n , i n c o r p o r a t i n g the i n f l u e n c e o f i n t e r f a c e temperature i n c r e a s e on s o l u b i l i t y d r i v i n g f o r c e r e d u c t i o n , and u s i n g the s i m p l i f i c a t i o n t h a t the heat t r a n s f e r f i l m i s much t h i c k e r than the mass t r a n s f e r f i l m as shown i n F i g . 1, has been used t o produce the estimates o f i n t e r f a c i a l temperature shown i n F i g . 2. At the highest 30$ SO- composition, the i n t e r f a c e temperature a t the base o f the 14mm diameter j e t i s estimated t o be 114 C above the datum o f 25°C. The k i n e t i c parameters f or £he r a t e o f r e a c t i o n o f SO- have been estimated to be A = 1.24 X 10 and Ε = 24,700 c a l / m o l e " ( 14). For these k i n e t i c parameters the h a l f - l i f e o f SO- d u r i n g a b s o r p t i o n v a r i e s g r e a t l y with j e t l e n g t h as shown i n F i g . ? f o r 30$ SO-. The value o f the Hatta number a t the base o f the laminar j e t i n c r e a s e s from 1.78 f o r 3$ SO- t o 479 f o r 30$ SO-, p l a c i n g the r e a c t i o n i n the f a s t regime. ^ ^ 9

1:5

S t i r r e d C e l l Experiments A g a s - l i q u i d s t i r r e d c e l l r e a c t o r with a w e l l d e f i n e d plane i n t e r f a c e permits a study o f the heat and mass t r a n s f e r e f f e c t s throughout the e n t i r e range o f dodecylbenzene c o n v e r s i o n up t o 100$. Experiments have been c a r r i e d out u s i n g a 900ml charge o f l i q u i d dodecylbenzene (Dobane JN a l k y l a t e ) with continuous feed o f SO- d i l u t e d with n i t r o g e n . Samples o f the bulk l i q u i d phase were p e r i o d i c a l l y withdrawn and analysed f o r sulphonic a c i d and f o r degree o f d i s c o l o u r a t i o n by measuring the absorbance at a wavelength o f 420 nm. The conversion-time behaviour f o r v a r i a t i o n i n gas phase composition a t a f i x e d o v e r a l l gas flowrate and s t i r r e r speed i s

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

35.

MANN ET AL.

Exothermic Gas Absorption

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

443

444

CHEMICAL REACTION ENGINEERING

0.1

0.2 gas phase mol

Figure 2.

0.3 f r a c t i o n o f SO

Interface temperature rise at the jet surface.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

35.

MANN ET A L .

Exothermic Gas Absorption

Figure 3. Reaction half-life of SO* at jet surface.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

445

446

CHEMICAL REACTION ENGINEERING

shown i n F i g . 4 ( a ) . I t i s c l e a r that gas phase composition a f f e c t s the absorption r a t e . F i g . 4(b) shows the e f f e c t o f v a r y i n g the s t i r r e r speed from 100 t o 500 rpm and i n t h i s case no s i g n i f i c a n t e f f e c t can be detected. On the other hand, F i g . 4(c) i n d i c a t e s t h a t the gas flowrate a t a f i x e d composition i n f l u e n c e s the f l u x and hence the conversion achieved i n a given time. Whilst t h i s might be taken t o i n d i c a t e gas-phase c o n t r o l l e d mass t r a n s f e r , care i s necessary i n drawing such a conclusion because heat release a f f e c t s s o l u b i l i t y (hence d r i v i n g f o r c e ) i n a complicated way and a l s o changes chemical enhancement f o r a f i n i t e a c t i v a t i o n energy. At any r a t e , i t i s necessary t o a c c u r a t e l y assess interfacial temperatures i n these experiments because o f the p o s s i b i l i t y that these could a f f e c t the d i s c o l o u r a t i o n r e a c t i o n s . F i g . 5 shows how the d i s c o l o u r a t i o n developed i n these semibatch experiments i s c o r r e l a t e d against conversion At low conversion l e v e l s up t c o n d i t i o n s do not a f f e c Beyond 50$, there i s some evidence that under severe conditions ( i e . 30$ SO-) the degree o f d i s c o l o u r a t i o n i s a c c e l e r a t i n g . However f o r the purposes o f i n i t i a l assessment, the by-product colour can be represented by a p a r a l l e l r e a c t i o n where the sulphonation and discolouration reactions have similar activation energies. Brostrom's c o l o u r r e s u l t s a r e d i f f e r e n t , and shown i n F i g . 5 f o r comparison (15). Exothermic Absorption with Two P a r a l l e l Reactions The

r e a c t i o n scheme i s t h e r e f o r e product sulphonic

acid

d i s c o l o u r i n g by-product Within the mass transfer film dodecylbenzene i s described by 2 2 D

d

°A

dx

2

A

=

-D

d p

C

B

dx

=

the

reaction

(k^T) + k (T))C 2

A

of

C

SO-

B

with

(1)

2

2

06j"§

=

(ΔΗ

subject t o the boundary

c

A

= Cc .(T.)

Κ 1

^(Τ)

T»

. χ = 0

J

ÛH

conditions

A

Cg*

+

and

R 2

k (T))C 2

c

A

= c

C

B

=

Τ

C

A b

B b

A

C

B

(2)

l

X

J-^

=

(3)

Τ. χ = x„ 'b H The i n t e r f a c i a l and bulk boundary c o n d i t i o n s are assumed quasi-stationery with respect t o the timewise increase i n conversion o f Β (dodecylbenzene) and the v a r i a t i o n o f unreacted

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

4^ ^4

Figure 4a. Influence of gas phase composition in a stirred cell reactor.

1'

î

ξ

i

I

>

W H

y*

Χ Χ

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

ο In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

Figure 4c. Influence of gas massflowrate in a stirred cell reactor.

vo

î

3· /M

1

tanhjM

1

F i n a l l y , F i g . 8 i n d i c a t e s the s e n s i t i v i t y w i t h r e s p e c t t o v a r i a t i o n i n a c t i v a t i o n energy f o r the by-product r e a c t i o n . I f the two p a r a l l e l r e a c t i o n s d i d have d i f f e r e n c e s o f the order o f + 10 k c a l mol" , then v a r i a t i o n o f gas phase composition (at f i x e d Ν and G) as per F i g . 4 ( a ) , would give a wide spread o f absorbance behaviour, caused by d i f f e r e n c e s i n i n t e r f a c i a l temperature.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

M A N N ET A L .

200 *·

Y

A b

453

Exothermic Gas Absorption

- 0.098

170

140

110

À

80 20

Ô

40

time Figure 6a.

minutes

Interface temperature predictions as y b varies, when N = 400 rpm. A

100 rpm

120 time Figure 6b.

minutes

Interface temperature predictions as N varies, when yAI, = 0.049.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

ta

I Ah

F/gwre 7. Enhancement factor behavior through a semi-batch. Conditions: y , 0.049; N, 400 rpm; and G, 2.324 mol/s.

ta

H

s

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982. 9

E = 35 kcal/mol; and —

, Et =

t

E.

Figure 8. Discoloration: sensitivity to activation energy. Key:

t

,E

= 15 kcal/mol; · · ·,

Ln

ϊ

I

?

Β*

s-

1

?

>

H

w

I

to

CHEMICAL REACTION

456

ENGINEERING

Legend o f Symbols A^

pre-exponential factor of i t h reaction pre-exponent s t i r r e d c e l l s p e c i f i c surface

area

Cj

c o n c e n t r a t i o n o f component I

Dj

d i f f u s i v i t y o f component I

Ε

a b s o r p t i o n enhancement f a c t o r

E^^

a c t i v a t i o n energy o f i t h r e a c t i o n

G

gas molar flow rate

k

r e a c t i o n r a t e constant

k

l i q u i d phase mass t r a n s f e r c o e f f i c i e n t

x

k

gas phase mass t r a n s f e

M

Hatta number a t i n t e r f a c e temperature

Ν

s t i r r e r speed

Τ

temperature

A sulphur t r i o x i d e

χ

position i n transfer film

Β dodecylbenzene

XJJ

t h i c k n e s s o f mass t r a n s f e r f i l m

b bulk value

^

t h i c k n e s s o f mass t r a n s f e r f i l m

Superscript

Ot

thermal d i f f u s i v i t y

Subscripts

* i n t e r f a c e value

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

Danckwerts P . V . , Appl. S c i . Res. 1953, A3, 383 Van de Vusse, J.G., Chem. Engng. Sci 1966, 21, 631 Chiang, S.H. and Toor, H . L . , A . I . C h . E . J l . 1964, 10, 398 Clegg, G.T. and Mann, R., Chem. Engng. S c i . 1969, 24, 321 Mann, R., and Clegg, G . T . , Chem. Engng. S c i . 1975, 30, 97 Ikemizu, Κ., Int. Chem. Eng. 1979, 19(4), 611 Mann, R., and Moyes, H . , A . I . C h . E . J l . 1977, 23, 17 Beenackers, A.C.M. and Swaaji, W.P.N. Chem. Eng. Jl. 1978, 15, 25 S i l v i s , S . J . and Ballestra M . J . J. Am. O i l Chem. Soc. 1963, 40, 618 Knaggs, E.A. and Nussbaum, M.S. Soap Chem. Spec. 1962, 38, 145 Mutzenberg, A.B. and Giger, A. Trans. I . Chem. Engrs., 1968, 46, T187 Lohr, J.W., J. Am. O i l Chem. Soc. 1958, 35, 532 Allan, J.C., and Mann, R., Submitted to Can. Jl. Chem. Eng. Allan, J.C., M.Sc. Thesis University of Manchester, 1978 Brostrom, Α . , Trans. I . Chem. Engrs. 1975, 53, 26 Van Krevelen, D.W. and Hoftijzer, P . J . Rec. Trav. Chim. 1948, 67, 563 Wilke, C.R. and Chang, P. A . I . C h . E . J l . 1955, 1, 264 Shoji, H. and Majima, K. J. Am. O i l Chem. Soc. 1963, 40, 179

Received April 27,

1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

36 Analysis of Chemical and Physical Processes During Devolatilization of a Single, Large Particle of Wood R. WAI C H U N C H A N and BARBARA B. KRIEGER University of Washington, Department of Chemical Engineering, Seattle, WA 98195

The detailed product distribution (tar,gases,char,and components in each flux pyrolysis of a experimentally investigated. Previous mathematical models of wood pyrolysis were extended and predictions of density and temperature profiles were in agreement with experimental data. The rate of heat transfer and particle length are shown to alter the reaction product distribution with a larger tar fraction occuring for realistically large particles. A desire f o r optimal energy recovery w i t h i n the f o r e s t products industry has caused i n t e r e s t i n s t o k e r - b o i l e r s i m u l a t i o n Q). I f the v o l a t i l e s from a s i n g l e p a r t i c l e can be a c c u r a t e l y predicted and optimized, combustor design can be improved. Although processing small p a r t i c l e s might be d e s i r a b l e , s i z e reduction of f i b r o u s wood p a r t i c l e s i s d i f f i c u l t and expensive. Knowledge of the e f f e c t s o f p a r t i c l e s i z e , wood anisotropy, moisture content, and species type on v o l a t i l e s r e l e a s e can a i d i n b e t t e r fuel mixture preparation and process design f o r chemicals production. Owing to the r e l a t i v e u n i f o r m i t y of composition ^15^21^10 ^' * k °* mineral matter ( l e s s than 0.5% a s h ) , and regular but a n i s o t r o p i c physical s t r u c t u r e , wood represents an i n t e r e s t i n g model f o r study of other s o l i d f u e l s such as o i l shale and coal. These w i l l a l s o be d e v o l a t i l i z e d i n thermally l a r g e p a r t i c l e s i n such a p p l i c a t i o n s as underground g a s i f i c a t i o n , or small s c a l e commercial combustion. Models of wood p y r o l y s i s and combustion have been developed to a i d i n f i r e s a f e t y and have treated various p h y s i c a l and chemical phenomena (3-9). Several studies have determined volatiles composition from r a p i d p y r o l y s i s of small p a r t i c l e s (10-13). However, few studies have combined modeling of heat transfer e f f e c t s and d e t a i l e d experimental r e s u l t s ( 8 ) . To our knowledge, no study has measured v o l a t i l e s composition as a f u n c t i o n of time from d e v o l a t i l i z i n g l a r g e p a r t i c l e s of wood. a c

0097-6156/82/0196-0459$06.00/0 © 1982 American Chemical Society In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

CHEMICAL REACTION ENGINEERING

460

Brief Description of Mathematical Model The properties of vood(7,14) were used to analyze time scales of physical and chemical processes during wood pyrolysis as done in Russel, et al (_15) for coal. Even at combustion level heat fluxes, intraparticle heat transfer is one to two orders of magnitude slower than mass transfer (volatiles outflow) or chemical reaction. A mathematical model reflecting these facts is b r i e f l y presented here and detailed elsewhere(16). It predicts volatiles release rate and composition as a function of particle physical properties, and simulates the experiments described herein in order to determine adequate kinetic models for individual product formation rates. A one dimensional model is presented for heat transfer and reaction in a cylindrica time-varying radiation carrier gas and radiative loss at both faces are also treated. Within the pellet, heat is transfered by conduction and absorbed by reaction. The volatiles from chemical reaction are assumed to be in thermal equilibrium with the solid, and cool i t during volatiles outflow. They are assumed to flow toward the heated face only which has been experimentally v e r i f i e d 0 8 ) to be a valid approximation. This analysis extends previous models(6,7) by including additional effects, more extensive treatment of variable properties, and different boundary conditions. Volatiles release rate is computed as the instantaneous value of the change in density integrated over the pellet length and currently ignores the mass transfer resistance within the wood. This approach was taken f i r s t since wood is highly porous and the chemical model is simple. Kinetic parameters for weight loss rate(2) were used. For a more complex mechanism, best f i t , experimental, product formation rate parameters for devolatilizing small particles of c e l l u l o s e ( l l ) and non-stoichiometric parameters times the rate coefficients for wood(26) were both used. The experiments described below indicate which product species require series-parallel mechanisms. The heat of reaction for wood is not well known (6,17) and depends on the extent of secondary reactions within the wood (19) (also dependent on particle size). In this model, i t is treated as a parameter. The energy and mass balances and rate of reaction equations are given in Table 1 together with boundary conditions, nomenclature, and values of the physical properties. Thermal conductivity and thermal d i f f u s i v i t y are assumed to be l i n e a r functions of the density (verified by Wong^20) and McClean(14)). The porosity and heat capacity C are linear functions of their i n i t i a l and final values using the ?atio, eta, as follows: Ρ

η =

~P

·

S

= ne

Q

+

(l-n)

e ; c

q?

s

= nCp

Q

+

(l-n)

Cp c

The variation in gas remaining in the solid is neglected since i t is small compared to the amount of volatiles outflow . The equations are solved in dimensionless form by codes (21) using the method of f i n i t e differences. In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

36.

C H A N A N D KRIEGER

Devolatization of Wood

461

B r i e f D e s c r i p t i o n of Experiments A schematic diagram of the experimental apparatus i s shown i n F i g . 1. A high i n t e n s i t y ^ x e n o n arc lamp provides a constant e x t e r n a l heat f l u x (4-12 cal/cm /s) t o one face of a c a r e f u l l y positioned wood p e l l e t . The r e d u c t i o n i n net r a d i a t i o n a r r i v i n g at the s u r f a c e during high rates of v o l a t i l e s outflow i s q u a n t i f i e d i n Chan(22) and Kashiwagi(23). The e v o l v i n g gases are swept by helium c a r r i e r gas through a glass r e a c t o r designed to prevent t a r condensation on the window f a c i n g the lamp. T r a c e r s t u d i e s on this r e a c t o r showed a residence time d i s t r i b u t i o n (RTD) c h a r a c t e r i z e d by a P e c l e t number of 3-5. V o l a t i l e products e v o l v i n g from the p e l l e t a r e quenched by helium and a dry ice-acetone t r a p . Uncondensed gases are sampled above the t r a p as a f u n c t i o f tim b programmabl chromatographic (GC) samplin machine. The time and s p a t i a y pelle i s measured by an X-ray technique described by Lee, e t a l . A f t e r the experiment i s completed, the gas samples are s e q u e n t i a l l y analyzed by GC, t a r samples and r e a c t o r washings are analyzed by GC/MS according to a s l i g h t m o d i f i c a t i o n o f the procedure described i n Ref. 24. Char and unreacted p o r t i o n s are weighed and analyzed. Small p e l l e t s have t o t a l mass l e s s than 0.5 g r e q u i r i n g c a r e f u l experimental techniques. The 1. cm diameter p e l l e t s are c a r e f u l l y l a t h e d from a s l a b of lodgepole pine wood with uniform g r a i n d i r e c t i o n , d r i e d , thermocouples (chromel-alumel, 0.005 i n . diam.) are placed at three depths, and the wood i s i n s e r t e d i n the r e a c t o r . The heated face temperature i s measured approximately by an. i n f r a - r e d pyrometer which was c a l i b r a t e d with thermocouples at the s u r f a c e . A s l i g h t p o s i t i v e pressure i s applied to the unheated f a c e . Since the runs are lengthy and complex i n t e r a c t i o n s are present, the experiments are performed according to a Box-Behnken design(25) i n which the f a c t o r s studied are: e x t e r n a l heat f l u x ; particle d e n s i t y , l e n g t h , g r a i n d i r e c t i o n ( f o r wood); composition (wood, cellulose, l i g n i n , c o a l , s h a l e ) . P r e l i m i n a r y model runs i n d i c a t e d s u i t a b l e l e v e l s f o r these f a c t o r s and only the main e f f e c t s of particle length on some compositions w i l l be reported here (22). One advantage of a Box-Behnken design i s hidden r e p l i c a t i o n ; thus the data f o r each particle length roughly corresponds to the average of 4 runs(22). R e s u l t s and D i s c u s s i o n The a b i l i t y to p r e d i c t v o l a t i l e s r e l e a s e rate and composition i s of interest f o r furnace simulations (1)· F i g . 2 presents c a l c u l a t e d v o l a t i l e s f l u x as a f u n c t i o n of time i n dimensional form f o r three p e l l e t lengths using the experimentally determined time-dependent surface f l u x of 3-4 cal/cm"/s and a s i n g l e r e a c t i o n to d e s c r i b e weight loss. T h i s f i g u r e i s to be compared to the

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

s

p

g

C

P g

"g

s

0

p .

c

0

Specific heat of char

4 0

=

}

V- (K- VT)

g

Ε Η h Κ

g

g

q e

c

0

M · VT + ΔΗ r 8 Ρ

3T 3X

0, Q

C

P.

ε

0 CP.

A

1

4

Q

Q

4

- T );

- 9.493 χ 10~ ρ + 1.0962 χ 10 s

Α

= {0.4η + (1-η) 0.85} = {0.6η + (1-η) 0.25} cal/g-°

= 0.4

« 0.2 g/cc; 25% of p

=0.25 cal/g-°K

- 300°K

= 2.5 χ 10 sec"

Constants :

- -K - g + h(T - T ) + ωσ(Τ

s

3p s , ,. -E/RT - - ( p - p ) k exp

At t > 0, X

Activation energy Heat of reaction Convective heat transfer coefficient Thermal conductivity of substrate Pre-exponential coefficient

Specific heat of the substrate

C P Q I n i t i a l s p e c i f i c heat of substrate

Cp

Cp

Chemical Reaction:

0;

8T -

- T ) and M

g

4

s

M

Cp

ΰρ^ Specific heat of v o l a t i l e s

Cp

Nomenclature:

Q

s

T = T ,

K | | = h(T - T ) + ωσ(Τ

At t > 0, X - L,

At t • 0, ρ

Boundary Conditions

8t

+ V

M_

+ (1 - e.) P

Mass Balance:

{ e

Energy Equation:

TABLE 1 - Details of the Mathematical Model

In Chemical Reaction Engineering—Boston; Wei, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

F r a c t i o n o f unreacted m a t e r i a l Stefan-Boltzman constant Emissivity

Substrate density

I n i t i a l substrate density

Density of v o l a t i l e s

Char d e n s i t y

Substrate p o r o s i t y

I n i t i a l substrate porosity

D i s t a n c e from the s u r f a c e Char p o r o s i t y

Gas constant Chemical r e a c t i o n r a t e Time Temperature Ambient temperature

Surface heat f l u x

Mass f l u x o f v o l a t i l e s

Length o f p e l l e t

Q

g

g

s Q

= 9.6 χ 1 0 "

= {0.4, 0.6, 0.8} g/cm

0

Q

P q

3

2

4

( s i m i l a r t o Kung (6) and Kansa, e t a l

Dimensionless Groups:

= e x p e r i m e n t a l l y measured time v a r i a t i o n

= {5.7, 4.93, 4.22} c a l / c m - s e c

= {0.5, 1.0, 1.5} cm

L

2

= {100, 0, -100} c a l / g

q(t)

2

cal/cm -s-°K

cal/s-cm -°K

1 2

3

H

5

= 1.356 χ 1 0 "

- 0.37

= 0.85

= 1.2 χ 1 0 " g/cm

3

=0.25 cal/g-°K

S

(cal/cm-sec-°K; 0.24