Chemical Reaction Engineering—Houston 9780841204010, 9780841204966, 0-8412-0401-2

Table of contents :
Title Page......Page 1
Half Title Page......Page 3
Copyright......Page 4
ACS Symposium Series......Page 5
FOREWORD......Page 6
PdftkEmptyString......Page 0
PREFACE......Page 7
1 Design and Operation of a Novel Impinging Jet Infrared Cell-Recycle Reactor......Page 9
Design Factors......Page 10
Experimental Performance......Page 14
Comments......Page 19
Literature Cited......Page 20
2 Performances of Tubular and Loop Reactors in Kinetic Measurements......Page 21
Apparatus......Page 23
Results and evaluation......Page 26
Comparison......Page 28
Recommendations......Page 31
Experimental Procedure......Page 32
Experimental Results......Page 33
Discussion......Page 36
Literature Cited......Page 42
Thermal methods and Instrumentation......Page 43
A bench scale heat flow calorimeter [2,3,9,10,11]......Page 45
Kinetics......Page 47
Assessment of thermal hazards......Page 49
Heat transfer coefficients......Page 51
Nomenclature......Page 54
Literature cited......Page 55
5 Adsorption Studies at Reaction Conditions—Reactor Development and Evaluation for Transient Studies at Millisecond Rates......Page 56
Reactor Design Features......Page 57
Data Collection and Reduction......Page 59
Experimental Results......Page 60
Acknowledgement......Page 65
Literature Cited......Page 66
Experimental......Page 67
Reactor Model......Page 68
Results and discussion......Page 71
Summary......Page 74
References......Page 75
7 Experimental and Theoretical Study of the Simultaneous Development of the Velocity and Concentration Profiles in the Entrance Region of a Monolithic Convertor......Page 76
Theoretical Part......Page 77
Experimental Part......Page 79
Discussion......Page 83
Notation......Page 85
Literature Cited......Page 86
Equipment......Page 87
Mathematical Models......Page 90
Results......Page 93
Roman.......Page 99
Subscripts and Superscripts......Page 100
Literature Cited......Page 101
1. Hysteresis......Page 102
2. Effect of Multiple Channels......Page 107
5. Literature Cited......Page 112
10 Poisoning in Monolithic Catalysts......Page 114
The Assumptions of the Model and its Equations......Page 115
Method of Solution......Page 117
Results and Conclusions......Page 118
Nomenclature......Page 123
Greek Symbols......Page 124
Literature Cited......Page 125
11 Micromixing Phenomena in Continuous Stirred Reactors Using a Michaelis-Menten Reaction in the Liquid Phase......Page 126
Experimental :......Page 127
Treatment of experimental data......Page 128
Results......Page 130
The "shrinking aggregate" model (S.A. model)......Page 131
Equivalence between the SA model and the IEM model......Page 134
Notation......Page 138
Lit erature cited......Page 139
Model......Page 141
Mathematical Analysis......Page 144
Results......Page 145
VELOCITY PROFILE ANALYTIC SOLUTION FOR NONUNIFORM VISCOUS FLOW......Page 150
Acknowledgement :......Page 152
REFERENCES......Page 153
13 Comparison of the Performances of Various Fermentors and Selection Criteria......Page 154
Experimental Results and Interpretation.......Page 155
Conclusions.......Page 160
Literature Cited......Page 163
Materials and Methods......Page 164
Reaction Model......Page 165
Results and Discussion......Page 166
Literature Cited......Page 173
Runaway Analysis of Polymerizations and Copolymerizations......Page 174
Experimental Tests of the Runaway Parameters......Page 181
Symbols......Page 185
Subscripts......Page 186
Literature Cited......Page 187
16 Comparison of Different Determination Methods for Effective Thermal Conductivity of Porous Catalysts......Page 188
Experimental Methods......Page 189
Experimental Results......Page 194
Discussion and Conclusion......Page 196
Symbols......Page 198
Literature......Page 199
17 Interpretation of Catalyst Deactivation by Fouling from Interactions of Pore Structure and Foulant Deposit Geometries......Page 200
Outline of the Theory......Page 201
Comparison of Theory and Experiment for a HDS Catalyst......Page 206
Acknowledgement......Page 211
Literature Cited......Page 212
18 Operational Flexibility Consideration in the Design of Multitubular Reactors......Page 213
Model of the Multitubular Reactor......Page 214
Comparison of Reactor Configurations......Page 216
Mixed Flow Configurations......Page 219
Conclusions......Page 221
Nomenclature......Page 222
Literature Cited......Page 223
19 Pore Plugging Model for Gas-Solid Reactions......Page 224
b. Product Layer Diffusion......Page 225
2. Analytical Evaluation of the Plugging Time......Page 227
3. Perturbation Solution for Small Times......Page 228
4. Comparison with Experimental Data for Sulfation of Fully Calcined Limestone......Page 230
5. Perturbation — Collocation Method of Solution......Page 231
7. Notation......Page 233
8. Literature Cited......Page 236
2. Experimental Equipment and Procedure......Page 237
(A) The Axially Dispersed Plug Flow Model......Page 238
(B) Depth by Depth Analysis......Page 241
Results of Overall Analysis......Page 242
7.1 A Model for Prediction of the Radial Conductivities......Page 246
7.3 The Axial Conductivity (ka)......Page 248
Literature Cited:......Page 251
II. Experimental......Page 253
IV. Deactivation of a Single Catalyst Particle......Page 254
V. Metal Removal and Catalyst Life in a (Simulated) Stirred-Tank Reactor......Page 259
VI. Effect of Metal Deposition on the Desulfurization Activity......Page 261
List of Symbols......Page 263
Literature Cited......Page 266
1. Cracking coil design equations......Page 267
2. Fire box heat transfer......Page 269
3. Simulation procedure......Page 272
4. Results......Page 273
Subscripts......Page 276
Literature Cited......Page 277
Theory......Page 278
Determination of the Realtime Activity Kinetics......Page 283
Realtime Activity Predictions......Page 284
Literature Cited......Page 287
24 Heuristic Approach to Complex Kinetics......Page 288
Rule 1:......Page 291
Rule 5:......Page 293
Rule 8:......Page 294
Rule 10:......Page 295
Conclusions......Page 297
Literature Cited......Page 298
25 Kinetics of Catalytic Liquefaction of Big Horn Coal......Page 299
Experimental......Page 300
Results and Discussion......Page 305
Literature Cited......Page 307
26 Development of Reaction Models for Complex Gas Phase Reactions......Page 309
Experimental Methods......Page 310
Mathematical Methods......Page 311
Results and Discussion......Page 312
Summarising and Concluding Remarks......Page 318
Literature Cited......Page 320
Reaction Kinetics; Regime of Mass Transfer with Chemical Reaction......Page 321
Experimental......Page 322
Results and Discussion......Page 323
Nomenclature......Page 329
Literature Cited......Page 330
28 Axial Mixing of Liquid in Packed Bubble Columns and Perforated Plate Columns of Large Diameter......Page 331
Summary......Page 338
Literature cited:......Page 341
1. INTRODUCTION......Page 342
2. KINETIC MODEL......Page 343
3. MODEL OF THE GAS-LIQUID REACTOR......Page 345
4. SIMULATION OF A PLANT OXIDATION SECTION BY MEANS OF TISFLO......Page 346
5. OPTIMIZATION......Page 347
6. FINAL REMARKS......Page 349
LIST OF SYMBOLS......Page 351
7. LITERATURE CITED......Page 352
30 Detailed Analysis of CO2-Interphase Mass Transfer in a Bubble Column to Prove the Validity of a Design Model......Page 353
Gas Hold up and Interfacial Area......Page 354
Model Assumptions......Page 356
Model Equations......Page 358
Description of Measured Profiles......Page 360
Acknowledgement......Page 364
Literature Cited......Page 365
31 Determination of Fluid Dynamic Parameters in Bubble Column Design......Page 366
Literature cited:......Page 376
32 Catalyst Effectiveness Factor in Trickle-Bed Reactors......Page 378
Review of Previous Models......Page 379
Mathematical Model For Reaction In Partly Wetted Catalyst Pellets......Page 382
Discussion......Page 384
Nomenclature......Page 387
Literature Cited......Page 389
33 Modeling the Slugging Fluidized Bed Reactor......Page 391
Results and Discussions......Page 397
NomencIature......Page 398
Literature Cited......Page 401
34 Modeling of a Trickle-Bed Reactor: The Hydrogenation of 2-Butanone on a Ruthenium Catalyst......Page 402
Experimental Set-up......Page 403
Experimental Result......Page 405
Topological Model of the Liquid Distribution in a Trickle-Bed......Page 408
Mathematical Model of Mass Tranfers in a Trickle-Bed Reactor......Page 411
List of symbols......Page 413
Literature cited......Page 414
35 Determination of the Extent of Catalyst Utilization in a Trickle Flow Reactor......Page 416
Selection of a System to Determine Maximum Catalyst Utilization......Page 419
Results and Discussion......Page 423
Conclusions......Page 425
Literature Cited......Page 426
The Two-Phase Theory Examined......Page 427
Fluidised Bed Reactor Model......Page 429
List of Symbols......Page 435
Literature Cited......Page 437
37 Multiphase Kinetic Studies with a Spinning Basket Reactor......Page 438
Experimental......Page 439
Results and Discussion......Page 441
Abstract......Page 447
Literature Cited......Page 449
Experimental Part......Page 450
Theoretical Part......Page 452
Results and Discussion......Page 455
Nomenclature......Page 462
Literature Cited......Page 463
39 Limit Cycle Phenomena during Catalytic Oxidation Reactions over a Supported Platinum Catalyst......Page 464
Experimental Considerations......Page 465
Experimental Results......Page 466
Discussion of Results......Page 471
Abstract......Page 474
Literature Cited......Page 475
Positive Feedback and Capacity Effects.......Page 476
Results of Analysis of Two Models......Page 477
Some Experimental Observations and Computed Results......Page 481
Greek Letters......Page 485
Literature Cited......Page 486
1. Mathematical model......Page 487
3. Numerical calculations......Page 488
4. Frequency of limit cycle......Page 489
5 . Amplitude of temperature oscillations......Page 492
7. Experimental results......Page 494
Notation......Page 499
"Literature Cited"......Page 500
42 Effect of Periodic Operation on the Selectivity of Catalytic Reactions......Page 501
Experimental......Page 502
Theoretical......Page 504
Results......Page 505
Discussion......Page 511
Notation......Page 513
Literature Cited......Page 514
43 Dynamic Studies of Acetylene Hydrogenation on Nickel Catalysts......Page 515
Experimental Materials and Methods......Page 516
Results and Discussion......Page 517
Literature Cited......Page 524
44 Multiple Steady States of a Moving Bed Reactor—Theory and Experiment......Page 526
Theory......Page 527
Boundary conditions......Page 528
Calculated region of multiple solutions......Page 529
Experimental results......Page 531
Nomenclature......Page 535
Literature cited......Page 536
RFBR Cell Model......Page 537
Uniqueness, Multiplicity, and Stability......Page 538
Selectivity Effects......Page 544
Conclusions......Page 546
Literature Cited......Page 548
1. Formulation of the problem......Page 549
2. The method of control......Page 550
3· The ideal control......Page 552
4. The influence of time lag......Page 553
5. Nonlinear analysis......Page 555
Literature Cited......Page 557
Introduction......Page 558
Case 1 - Plant Scale Reactor......Page 561
Case 2 - Pilot Unit Scale Reactor......Page 564
Nomenclature......Page 565
Literature Cited......Page 568
SO2-Oxidation Kinetics......Page 569
Experimental......Page 570
Analysis of Purely Kinetic Data......Page 573
Kinetics of The Liquid Diffusion Regime......Page 577
List of Symbols......Page 581
Literature Cited......Page 582
A......Page 583
B......Page 584
C......Page 585
D......Page 587
E......Page 588
F......Page 589
G......Page 590
H......Page 591
K......Page 592
M......Page 593
O......Page 595
P......Page 596
R......Page 598
S......Page 600
T......Page 601
Z......Page 603

Citation preview

Chemical Reaction EngineeringHouston

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

Chemical Reaction EngineeringHouston Vern W . Weekman, Jr.,

EDITOR

Mobil Research and Development Company

Dan Luss,

EDITOR

University of Houston The Fifth International Symposium on Chemical Reaction Engineering co-sponsored by the American Chemical Society, the American Institute of Chemical Engineers, the Canadian Society for Chemical Engineering, and the European Federation of Chemical Engineering, held at the Hyatt Regency Hotel, Houston, T X , March 13-15,

1978.

65

ACS SYMPOSIUM SERIES

AMERICAN

CHEMICAL

SOCIETY

WASHINGTON, D.C. 1978

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

Library of Congress CIP Data International Symposium on Chemical Reaction Engineering, 5th, Houston, Tex., 1978. Chemical reaction engineering—Houston. (ACS symposium series; 65 ISSN 0097-6156) Bibliography: p. Includes index. 1. Chemical engineering—Congresses. 2. Chemical reactions—Congresses. I. Weekman, Vern W. II. Luss, Dan, 1938III. American Chemical Society. IV American Chemical Society. ACS symposiu TP5.I67 1978 ISBN 0-8412-0401-2

660.2'9'9 77-25340 ACSMC 8 65 1-619 (1978)

Copyright © 1978 American Chemical Society All Rights Reserved. T h e 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. T h i s consent is given o n 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. T h i s 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 works, for resale, or for information storage and retrieval systems. T h e citation of trade names and/or names of manufacturers i n 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 i n any way be related thereto. PRINTED IN THE UNITED STATES OF AMERICA

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

ACS Symposium Series Robert F. Gould, Editor

Advisory Board Kenneth B. Bischoff Donald G . Crosby Jeremiah P. Freeman E. Desmond Goddard Jack Halpern Robert A . Hofstader James P. Lodge John L. Margrave Nina I. McClelland John B. Pfeiffer Joseph V . Rodricks F. Sherwood Rowland Alan C. Sartorelli Raymond B. Seymour Roy L. Whistler Aaron Wold

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

FOREWORD The ACS SYMPOSIU

a medium for publishing symposia quickly in book form. The format of the SERIES parallels that of the continuing ADVANCES IN CHEMISTRY SERIES except that in order to save time the papers are not typeset but are reproduced as they are submitted 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 SYMPOSIUM 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—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

PREFACE

has, as in past symposia, provided an excellent forum for reviewing recent accomplishments in theory and application. This international symposium series grew out of the earlier European Symposia on Chemical Reaction Engineering which began in 1957. In 1966, as part of the American Chemical Society Industrial and Engineering Chemistry Division's Summer Symposium series, a meeting was devoted to chemical reaction engineering and kinetics. This meeting highlighted the great interest and activity in this field in the United States, and led the organizers to join with the America European Federation of Chemical Engineers in organizing International Symposia on Chemical Reaction Engineering. The first symposium was held in Washington in 1970 and was followed by symposia in Amsterdam (1972), Chicago (1974), and Heidelberg (1976). These meetings consistently attract experts in the field who have submitted many more papers than can be accommodated. This year was no exception with more than 130 papers being submitted, only 48 of which could be accepted. Again, the international flavor was maintained with more than one-half the papers coming from Western Europe, in addition to one each from Russia, Japan, Australia, and Canada. While industrial participation was not as extensive as anticipated (30% ), it did show clearly the increasing and productive application of Reaction Engineering tools to industrial problems. The meeting format maintained three plenary review lectures each morning and three parallel, original paper sessions in the afternoon. The nine plenary review papers are being published in the American Chemical Society Symposium Series as a separate volume. We acknowledge financial support from the National Science Foundation, American Chemical Society-Petroleum Research Fund, Shell Oil Co., Mobil Oil Corp., and Exxon Co. A

V E R N W . W E E K M A N , JR.

D A N Luss

Mobile Research Corp. Princeton, NJ

University of Houston Houston, T X

October 1977 xi

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

Organizing Committee for the Fifth International Symposium on Chemica

Vern W . Weekman, Jr., Editor Dan Luss, Editor

Members: Chandler H . Barkelew (Shell Development Co.) K. B. Bischoff (University of Delaware) John B. Butt (Northwestern University) James M. Douglas (University of Massachusetts) Hugh M. Hulburt (Northwestern University) Donald N. Miller (Dupont Co.)

xii In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

1 Design and Operation of a Novel Impinging Jet Infrared Cell-Recycle Reactor R.

LEUTE

and I. G .

DALLA

LANA

Department of Chemical Engineering, University of Alberta, Edmonton, Alberta, Canada

In the study of chemisorbed species on catalyst surfaces, the application of infrared spectroscopic methods has developed from the early in situ studies of Eischens and Pliskin [1] to rather detailed surface kinetics measurements [5]. The variety of techniques which have been described [1,2,3,4,5,6,7,8] increase i n their effectiveness with their a b i l i t y to discriminate between the spectra of adsorbed species which are relevant to the reaction mechanism and spectra of spurious adsorbed species. These approaches may be c l a s s i f i e d using this c r i t e r i o n as follows: (i)

I n t r i n s i c Rates/Surface Spectra Transients Measured D i r e c t l y . Under reaction conditions where adsorbed reactants, intermediates, and products display significant IR absorption band i n t e n s i t i e s , the transient intensities may be quantita­ t i v e l y monitored. Considerable detailed studies are required to correlate these intensities with surface concen­ trations.

(ii)

Global Rates/Surface Spectra Static or Transient. By carrying out studies i n an IR cell - c i r c u l a t i o n flow reactor, a cause-and-effect r e l a t i o n between reactant concentration and specific band intensities may be discerned. Such mechanistic insights may be useful i n developing more r e l i a b l e forms of rate expressions.

(iii)

Indirect Studies of Adsorption and Surface Reactions. The observation of selected spectral band intensities attributed to chemisorbed species are assumed to be related to the surface reactions involved. I f the spectra are recorded at room temperature, the presence of spurious spectra may occur. Generally, additional experimental evidence is required to demonstrate the relevance of such observations to the kinetics of the c a t a l y t i c reaction.

©

0-8412-0401-2/78/47-065-003$05.00/0

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

4

CHEMICAL REACTION ENGINEERING—HOUSTON

This paper d e s c r i b e s the development of an improved v e r s i o n of the IR cell-recycle r e a c t o r (type ( i i ) ) which is to be used to study the mechanism and kinetics of r e a c t i o n s of 2-propanol on v a r i o u s alumina c a t a l y s t s . While t h i s r e a c t i o n does not have direct commercial i m p l i c a t i o n s (dehydration or dehydrogenation), it e x h i b i t s many of the characteristics which make it very s u i t a b l e to demonstrate the usefulness of the IR technique. Design Factors The yin AAXU technique i n v o l v e s c a t a l y s t p e l l e t s i n the form of very t h i n wafers, about 40 mg/cm2 alumina content. The h i g h s u r f a c e area, about 4 m^/cm^- of IR beam c r o s s - s e c t i o n , enables s u f f i c i e n t adsorbed species to i n t e r a c t w i t h the IR beam even a t r e l a t i v e l y low s u r f a c e coverage that s p e c t r a w i t h good I n s t u d y i n g s o l i d - c a t a l y z e d gas-phase r e a c t i o n s , the back­ ground s p e c t r a r e s u l t i n g from the gas-phase are u s u a l l y e l i m i n a t e d by use of a double-beam IR spectrophotometer, i n which the sample c e l l i s matched w i t h an " i d e n t i c a l " reference c e l l without c a t a l y s t i n i t . V a r i a t i o n s i n pressure and/or temperature between sample and reference c e l l s i n c r e a s e the d i f f i c u l t y of matching the two c e l l s . When the c a t a l y s t wafer i s placed t r a n s v e r s e t o the flow of gases through the IR c e l l - r e a c t o r , the flow p a t t e r n s w i t h i n the c e l l l e a d to c o n c e n t r a t i o n gradients along the a x i s of the IR beam, and between the f r o n t and r e a r s u r f a c e concentrations on the wafer. Under r e a c t i o n c o n d i t i o n s , these aspects l i m i t the s e n s i t i v i t y of the technique because of low s u r f a c e coverages a t r e a c t i o n temperatures. The new c e l l attempts t o e l i m i n a t e many of these o b j e c t i o n a b l e f e a t u r e s . Figure l a describes a t y p i c a l geometry f o r previous c e l l designs. I t should be evident that i t i s d i f f i c u l t to o b t a i n values of the i n t r i n s i c r e a c t i o n r a t e because of the uneven c o n t a c t i n g between the gas and wafer a t v a r i o u s p o i n t s on the wafer s u r f a c e . High r e c i r c u l a t i o n r a t e s w i t h i n such a steadys t a t e r e c y c l e r e a c t o r provide d i f f e r e n t i a l values of the r e a c t i o n r a t e , but these g l o b a l values are u n l i k e l y to equal i n t r i n s i c r a t e s ( n e g l e c t i n g , f o r the moment, i n t r a p a r t i c l e d i f f u s i o n ) . C o m p a t i b i l i t y of flow p a t t e r n s between the IR c e l l and an i d e a l continuous s t i r r e d - t a n k r e a c t o r are r e q u i r e d as a minimum c o n d i t i o n . Since the mode of h e a t i n g the wafer l i k e l y i n v o l v e s IR-transparent windows being a t temperatures lower than those of the wafer, compensation f o r temperature gradients may a l s o be required. Figure l b describes the proposed geometry of the improved IR c e l l - r e a c t o r . This r e c y c l e r e a c t o r i s t o be capable of being operated i n e i t h e r open (flow) o r c l o s e d (batch) modes of o p e r a t i o n . The r e a c t o r u n i t i s maintained a t the r e a c t i o n temper­ ature (up t o 400°C) and the pump and sampling system are maintained at a constant u s u a l l y lower temperature (220°C) t o ensure maximum

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

Figure 1.

(a)

OLDER TYPE IR REACTOR CELLS

Geometrical arrangement and flow patterns in typical and improved ir cell-reactors

(b)

NEW IR REACTOR C E L L

6

CHEMICAL REACTION ENGINEERING—HOUSTON

l o n g e v i t y of equipment. F i g u r e 2 d e s c r i b e s the i n f o r m a t i o n flow between the IR spectrophotometer and an IBM/1800 computer system which are i n t e r f a c e d . The s p e c t r a l data are monitored at wave number i n t e r v a l s as low as 0.2 cm over the complete s p e c t r a l scan range of the spectrophotometer (about 700 to 4000 cm"" , corresponding to a maximum of about 16,000 data p o i n t s ) . The "% t r a n s m i s s i o n " versus "wave number" p o i n t s are t r a n s m i t t e d i n d i g i t i z e d form to the computer from a b s o l u t e encoders. At p r e s e n t , the complete s p e c t r a l scan may be monitored and s t o r e d i n a d i s k f i l e and r e t r i e v e d at a l a t e r time. The coupled Model 621 spectrophoto­ meter w i t h IBM/1800-compatible i n t e r f a c e was purchased some time ago from Perkin-Elmer. The improved c e l l u t i l i z e s axisymmetric j e t s of feed gas impinging upon both s i d e l e n t f i e l d over most of r e a c t i o n r a t e s to approximate i n t r i n s i c r e a c t i o n r a t e s at h i g h f l o w - r a t e s and i n the absence of pore d i f f u s i o n . The new c o n f i g u r a t i o n shown i n F i g u r e 1 i s housed i n an oventype enclosure c o n t r o l l e d at the temperature, T 3 , by i n t e r n a l a i r c i r c u l a t i o n . I n a d d i t i o n to the oven h e a t e r , a second heater about the i n l e t s e c t i o n , packed w i t h g l a s s beads, r a i s e s the c i r c u l a t i n g gas temperature from the reduced temperature i n the pump compart­ ment to T j . Because of heat l o s s e s from the IR windows, the tem­ perature d i f f e r e n c e , T - T , could range as h i g h as 50°C This not only changes the d e n s i t y of the f l o w i n g gas but a l s o r e s u l t s i n a c o n s i d e r a b l e d e v i a t i o n of the t r u q temperature of the c a t a l y s t wafer from the measured values T . A d d i t i o n a l heaters p l a c e d around the ends of the two c y l i n d r i c a l s e c t i o n s compensated f o r the window heat l o s s e s . In t h i s way, the temperatures, T and T 3 , could be matched w i t h i n 0.5°C, and the w a l l temperature would be expected to d i f f e r from T (or T3) only i f the c a t a l y t i c r e a c t i o n e x h i b i t e d severe thermal e f f e c t s . With g r e a t l y improved mass t r a n s f e r r a t e s normal to the wafer s u r f a c e , one would a l s o expect from s i m i l a r i t y c o n s i d e r a t i o n s enhanced heat t r a n s f e r between the wafer s u r f a c e and the impinging gas j e t . Such adjustments among the three monitored temperatures enabled the r e f e r e n c e c e l l IR beam to compensate n e a r l y e x a c t l y f o r the sample c e l l gas phase absorption spectra. By changing the c o n f i g u r a t i o n of the two c e l l s i n the sample compartment of the IR spectrophotometer t h i s enables the d e t e r ­ mination of e i t h e r r e c i r c u l a t i n g gas composition or p l o t t i n g of the b a s e l i n e spectrum f o r the c a t a l y s t wafer. With the two c e l l s i n the double-beam mode, the c a t a l y s t b a s e l i n e and surface s p e c t r a are recorded. I f the reference c e l l was p l a c e d i n the sample beam and an a i r gap i n the r e f e r e n c e beam, q u a n t i t a t i v e absorption s p e c t r o ­ scopy was p o s s i b l e . The IR c e l l s thus provide i n f o r m a t i o n l e a d i n g to both r e a c t i o n r a t e s and m e c h a n i s t i c i n s i g h t s concerning adsorbed species at r e a c t i o n c o n d i t i o n s . When used as a r e c i r c u l a t i n g batch r e a c t o r , the spectrophotometer-computer i n t e r f a c e can monitor but not record the "% t r a n s -1

1

3

2

2

2

2

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

LEAUTE AND DALLA LANA

Infrared Cell-Recycle Reactor

X = Wave Length (abscissa) Y = Transmittance (ordinate) X

I

= analog signal, Wave Length, 5 digits

Y

1

= analog signal, Transmittance, 3 digits

Linear Encoder Shaft Encoder

IR Spectra Source

Encoder Readout/ I nterf ace

Y1 I

~TT X| I

lY I

i_t

X-Y Recorder

Figure 2.

i

l X Display Y Display

Information flow between ir spectrophotometer and digital computer

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

8

m i s s i o n " at a f i x e d " s p e c t r a l frequency" ( u s u a l l y that of a s p e c i ­ f i e d absorption band). At present, the drum chart on the IR recorder p l o t s the time - absorption band i n t e n s i t y r e l a t i o n c o r ­ responding to t r a n s i e n t r e a c t i o n c o n d i t i o n s . The time constant of the spectrophotometer thermocouple sensor was s u f f i c i e n t l y s m a l l that the t r a n s i e n t r e a c t i o n r a t e s could be recorded. Experimental

Performance

1. Mass Transfer Performance t e s t s were designed to t e s t f o r micromixing or f o r mass t r a n s f e r performance and thus, to f a c i l i ­ t a t e d e f i n i t i o n of the c e l l design s p e c i f i c a t i o n s . L i m i t e d reac­ t i o n data had been recorded f o r the 2-proposal r e a c t i o n over alumina. Figure 3 summarize were observed i n a protptyp wafer m a t e r i a l . A i r flows between 10 and 50 t/m±n were passed through the c e l l and the corresponding s u b l i m a t i o n r a t e s , mg/min, were recorded. Since the c e l l geometry was h e l d constant f o r a s e r i e s of flow r a t e s and the temperatures were always at room temperature, the coordinates of Figure 3 show the measured s u b l i ­ mation r a t e s versus flow r a t e r a t h e r than Reynolds number. The exponent of the flow parameter (given by the slope of the l i n e ) i s seen to remain n e a r l y constant over a wide range of c o n d i t i o n s v e r i f y i n g that the t u r b u l e n t flow regime i s maintained. The i n f l u e n c e of changing the o r i f i c e s i z e used to create the j e t s , and of the spacing between the o r i f i c e and the wafer upon mass t r a n s f e r r a t e s are a l s o shown. In a d d i t i o n to the above t e s t s w i t h the new design, mass t r a n s f e r r a t e s were a l s o observed f o r c e l l - r e a c t o r s of the o l d type, w i t h wafers p o s i t i o n e d both p a r a l l e l and transverse to flows. These t e s t s suggest t h a t i n such geometries much of the stream bypasses the wafer surface making i t d i f f i c u l t to o b t a i n i n t r i n s i c r a t e s of r e a c t i o n . Furthermore, c o n t a c t i n g of the gas flow w i t h l o c a l i z e d p o r t i o n s of the periphery of the wafer r e s u l t e d i n abnormally h i g h l o c a l mass t r a n s f e r r a t e s . F i g u r e 3 demonstrates that o l d type c e l l designs provide mass t r a n s f e r performance i n f e r i o r to that observed w i t h the impinging j e t s . By c a l c u l a t i n g mass t r a n s f e r c o e f f i c i e n t s from the u s u a l equation f o r the r a t e of s u b l i m a t i o n , gmol/(min)(g c a t a l y s t ) . r

s

=

k

g

a

(C

. surface

-C) o

and using the bulk gas phase c o n c e n t r a t i o n , C =0, and e x t e r n a l area, a=10 cm , some experimental c o e f f i c i e n t s could be compared to values estimated from p u b l i s h e d c o r r e l a t i o n s . Table 1 shows these r e s u l t s . 2

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

Table 1 Comparison of Mass Transfer C o e f f i c i e n t s (cm/sec) Model Flat plate i n perpendicular flow Sphere of equal area i n a packed bed Experimental wafer, c o n v e n t i o n a l geometry Experimental wafer, new geometry

Flow = 10 l/min 1.3 cm/sec

Flow = 50 l / m i n 2.9 cm/sec

2.1

5.4

1.6

3.0

3.7

9.2

Table 1 and F i g u r e 3 both i l l u s t r a t e the marked s u p e r i o r i t y of the new IR c e l l - r e a c t o r design i n promoting mass t r a n s f e r at the wafer s u r f a c e . However, i t s t i l l remains to be demonstrated t h a t under r e a c t i o n c o n d i t i o n s , i n t r i n s i c r a t e s of r e a c t i o n may be obtained at the flow r a t e s mentioned.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

10

2. Mixing W i t h i n C e l l The a n a l y s i s of performance w i t h i n a d i f f e r e n t i a l bed-recycle r e a c t o r i s u s u a l l y compared to t h a t of a continuous s t i r r e d - t a n k r e a c t o r . By operating the r e a c t o r w i t h an i n e r t wafer and by i n t r o d u c i n g a l c o h o l to the feed as a step change i n c o n c e n t r a t i o n , the mixing performance of t h i s r e a c t o r may be compared to t h a t p r e d i c t e d f o r an i d e a l CSTR of comparable volume. Figure 4 i l l u s t r a t e s such a comparison and i n d i c a t e s s u b s t a n t i a l agreement w i t h the i d e a l behaviour. I t may be expected that c h a n n e l l i n g , s t a g n a t i o n of some f l o w , e t c . are absent from the r e c y c l e r e a c t o r w i t h i n the range of performance of the pump. 3. Double-beam Compensation f o r Gas Phase A b s o r p t i o n When r e c o r d i n g IR s p e c t r a at r e a c t i o n temperature, the IR beams are attenuated by the number of molecules i n the beam path. Since the gas phase p o p u l a t i o n i s l i k e l y only one or two orders of magnitude g r e a t e r than th the wafer s u r f a c e , i t i u a t i o n i n the two c e l l s be balanced as w e l l as p o s s i b l e . For example, a pressure drop between the two c e l l s n e c e s s i t a t e s h e a t i n g the upstream c e l l to reduce i t s gas d e n s i t y to that i n the down­ stream c e l l . S i m i l a r l y , d i f f e r e n c e s i n temperature between the c e l l s must a l s o be compensated. Such inbalances between reference and sample c e l l gas phases r e q u i r e d c a l i b r a t i o n s ^ t o determine the values of T^ r e q u i r e d , f o r a f i x e d value of T (= T3) and given c i r c u l a t i o n r a t e at v a r i o u s i s o p r o p a n o l concentrations i n the gas-phase, to blank out gas phase absorption s p e c t r a . F i g u r e 5 shows how s p e c t r a l bands i n the 1200-1500 cm r e g i o n from gas phase i s o p r o p a n o l can be a l t e r e d be changing T j . Curve B represents n e a r - e x t i n c t i o n of the back­ ground whereas curves A and B represent under- and over-compensa­ tion, respectively. 4. Dehydration of 2-Propanol over Alumina The p r e l i m i n a r y measurements of s p e c t r a f o r adsorbed species w i l l be used to i l l u s t r a t e how the mechanism of r e a c t i o n may be c l a r i f i e d . The main f e a t u r e of the IR c e l l - f l o w r e a c t o r i s i t s c a p a b i l i t y of determining s p e c t r a at r e a c t i o n c o n d i t i o n s . Most published work on the dehydration of i s o p r o p a n o l by alumina describes Zn A^Lta s t u d i e s w i t h s p e c t r a recorded w i t h the c e l l at room temperature. Figure 6 r e v e a l s a b s o r p t i o n bands i n s e l e c t e d regions of the spectrum f o r s e v e r a l c o n c e n t r a t i o n l e v e l s of i s o p r o p a n o l vapour. Each curve, A, B, or C, represents a s p e c t r a l scan at steady-state r e a c t i o n c o n d i t i o n s w i t h a l l r e a c t i o n parameters except feed composition of i s o p r o p a n o l being kept constant. I f d i f f e r e n t curves (A, B, and C) r e s u l t , the adsorbed species a s s o c i a t e d w i t h the s p e c t r a are considered to be germane to the r e a c t i o n mechanism. In the event that the s p e c t r a l bands do not change the adsorbed species are considered to be spurious. Subsequently, the r e a c t o r may be operated i n a batch mode and the questionable band moni­ tored c o n t i n u o u s l y . The f a i l u r e of t h i s band to change w i t h the extent of r e a c t i o n would provide e x t r a support to the view that the band i s a s s o c i a t e d w i t h a by product species not i n v o l v e d i n the dehydration mechanism. 2

-1

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

LEAUTE AND DALLA LANA

Infrared Cell-Recycle Reactor

Figure 4. Comparison between ideal CSTR and improved cell-reactor to step change in input concentration

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

12

CHEMICAL REACTION ENGINEERING—HOUSTON 1

1

1

1

110

1

1

T 2 = 2 8 7 . 8 ° C - A l c o h o l 5.5% A: T1 = 2 2 6 . 5 ° C B: T1=251.5°C C: T1 = 2 7 3 . 5 ° C

100

c | 80 (0

-4

70

60

\J

u 1

1

1500

1400

1

1300

I

I

1200

1100

Frequency, cm"

I

1000

1

Figure 5. Compensation of gas-phase adsorbance between reference and sample cells

Baseline without alcohol Alcohol Partial Pressure = 2.1 cmHg Alcohol Partial Pressure = 3.2 cmHg

Catalyst Weight = 0.151 g Temperature = 246.1°C

Free O H Groups

3800

3600

CH

3

3000

Stretching

2800

Low Frequency Region

1600

Frequency, c m "

1400 1

Figure 6. Steady-state spectral scans for dehydration of isopropanol at reaction conditions

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

1.

LEAUTE AND DALLA LAN A

Infrared Cell-Recycle Reactor

13

The s t e a d y - s t a t e s p e c t r a l scans when recorded on the IBM/1000 may be processed. ( i ) t o s u b t r a c t the b a s e l i n e of the c a t a l y s t wafer from each s p e c t r a l scan at v a r y i n g p a r t i a l pressures of the i s o p r o ­ panol; ( i i ) to s u b t r a c t one s p e c t r a l scan at (P - , - ) i from another s p e c t r a l scan a t of the change i n band i n t e n s i t i e s at given band f r e q u e n c i e s . A p r e l i m i n a r y i n t e r p r e t a t i o n of the s p e c t r a shown i n Figure 6 would suggest the f o l l o w i n g o b s e r v a t i o n s . The f r e e h y d r o x y l groups on the surface of alumina p r o g r e s s i v e l y disappear, A to B to C, w i t h i n c r e a s i n g reactant c o n c e n t r a t i o n , i s o p r o p a n o l . This i m p l i e s that the a l c o h o l hydrogen bonds to these hydroxyl s i t e s but i t i s not c l e a r whether the a l c o h o l 0 o r H atom i n i t s h y d r o x y l group i s i n v o l v e d The s t r e t c h i n g v i b r a t i o n panol a l s o d i s p l a y d i r e c t correspondence between t h e i r surface c o n c e n t r a t i o n and that of the i s o p r o p a n o l vapour c o n c e n t r a t i o n . This i n f o r m a t i o n suggests that isopropanol adsorption on y a l u m i n a i n v o l v e s more than one adsorption band, i . e . both hydroxyl and emthyl groups are bonded and l i k e l y to d i f f e r e n t s i t e s on the surface of alumina. In the low frequency r e g i o n , region I r e l a t e s t o carbon chain s k e l e t a l v i b r a t i o n s and r e g i o n I I to symmetrical C-H deformation v i b r a t i o n s i n the methyl group. Both of these observations are i n accord w i t h a m u l t i - s i t e a d s o r p t i o n model. Region I I I shows the s t r e t c h i n g v i b r a t i o n f o r a carboxylate species formed on the s u r f a c e . Since the band i n t e n s i t i e s i n region I I I do not change w i t h i s o p r o p a n o l vapour c o n c e n t r a t i o n , the s p e c t r a are considered i n c i d e n t a l to the r e a c t i o n mechanism. With J C Q a d d i t i o n a l experiments, i t should be p o s s i b l e to d i s t i n g u i s h which surface s i t e s on the alumina are s p e c i f i c a l l y i n v o l v e d and thus t o propose a r e a c t i o n mechanism compatible w i t h such chemical evidence. During the above s p e c t r a l measurements, steady-state r e a c t i o n r a t e s i n the r e c i r c u l a t i o n r e a c t o r were a l s o determined. These r a t e s may then be used to t e s t the k i n e t i c model r e s u l t i n g from observations o f the s p e c t r a of adsorbed s p e c i e s . Comments 1.

11

The use of a " s i n g l e - w a f e r c a t a l y t i c r e c y c l e r e a c t o r system r e q u i r e s s t r i c t a t t e n t i o n to o p e r a t i n g parameters, i f one a s p i r e s to o b t a i n i n t r i n s i c r a t e s of r e a c t i o n . By modifying the flow past the wafer to ensure h i g h l y t u r b u l e n t c o n d i t i o n s on both s i d e s of the wafer, mass t r a n s f e r r a t e s may be more than doubled over those observed i n the o l d design of c e l l s i n which flow i s transverse t o the wafer s u r f a c e . This i n d i c a t e s that the u t i l i z a t i o n of both s i d e s of the wafer i s g r e a t l y improved and that the average mass t r a n s f e r r a t e s are a l s o enhanced.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

14

CHEMICAL REACTION ENGINEERING—HOUSTON

2.

I d e a l mixing (CSTR) i s obtained w i t h the r e c i r c u l a t i n g rates a v a i l a b l e from the bellows pump used to t h i s system. The corresponding residence time d i s t r i b u t i o n f u n c t i o n i s not of value i n the a n a l y s i s of the k i n e t i c s s i n c e i t i s a n t i c i p a t e d that n o n - l i n e a r r a t e expressions w i l l be encountered. The usefulness of a combined I R - k i n e t i c s study i n e s t a b l i s h i n g a more r e l i a b l e k i n e t i c model i s apparent. The processing of such data to a s c e r t a i n which s p e c t r a l bands are s i g n i f i c a n t i s u s u a l l y a very tedious chore. By i n t e r f a c i n g the IR spectrophotometer to a d i g i t a l computer, a number of data processing s i m p l i f i c a t i o n s are e v i d e n t . F u l l use of t h i s s i t u a t i o n has not yet been a t t a i n e d i n t h i s program. Whether or not improved r e s o l u t i o n of minor s p e c t r a l bands r e s u l t s from an o n l i n e computer f a c i l i t y s t i l l remains to be demon­ strated for this reactio The problem of i s o l a t i n r e a c t i o n r a t e s measured i n a single-wafer r e a c t o r appears to have been reduced but not n e c e s s a r i l y s o l v e d . If r e l a t i v e i n t e n s i t i e s of absorption bands e x h i b i t e d by reactants or r e a c t i o n intermediates can be a s c e r t a i n e d as a f u n c t i o n of time, i t may be p o s s i b l e to check r a t e expressions based upon a s i n g l e step being r a t e - c o n t r o l l i n g . Many extensions of t h i s technique (using the new r e a c t o r ) are evident i n the study of c a t a l y t i c k i n e t i c s . Some aspects worth pursuing i n c l u d e : ( i ) a study of pore d i f f u s i o n under c o n t r o l l e d c o n d i t i o n s ; v a r y i n g wafer thickness at constant p o r o s i t y should provide a d i r e c t means of 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 as a f u n c t i o n of wafer t h i c k n e s s . ( i i ) the r o l e of t r a c e amounts of c a t a l y s t promoters or i n h i b i t o r s may be examined using IR techniques and c o r r e l a t e d d i r e c t l y w i t h steady-state r e a c t i o n r a t e s .

3.

4.

5.

Acknowledgements F i n a n c i a l support of t h i s p r o j e c t by the N a t i o n a l Research C o u n c i l of Canada i s g r a t e f u l l y acknowledged. Literature Cited 1. 2. 3. 4. 5. 6. 7. 8.

Eiechens, R.P., Pliskin, W.A., Advan. Cata., (1957), 9, 662. Heyne, H., Tompkins, F.G., Proc. Roy. Soc., (1966), A292, 460. Baddour, R.F., M o d e l l , M., and Goldsmith, R.L., J . Phys. Chem. (1968), 72, 3621. Dent, A.L., and Kokes, R.J., J . Phys. Chem, (1970), 74, 3653. Tamaru, K., O n i s h i , T., Fukada, K., Noto, Y., Trans. Faraday Cos., (1967), 63, 2300. Thornton, R., Ph.D. t h e s i s , U n i v e r s i t y of Delaware 1973, Shih, Stuart Shan San, Ph.D. t h e s i s , Purdue U n i v e r s i t y , 1975. London, J.W., B e l l , A.T., J . Cat., (1973), 31, 36-109.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

2 Performances of Tubular and Loop Reactors in Kinetic Measurements G E R H A R D L U F T , R A I N E R R Ö M E R , and F R I T Z H Ä U S S E R Institut für Chemische Technologie der Technischen Hochschule Darmstadt, 61 Darmstadt, Petersengstrasse 15, West Germany

I n d u s t r i a l reactor terogenous c a t a l y t i s i t i v e i f the reaction conditions or the cooling rates are suddenly changed. They can be operated only i n a small range i n order to avoid damage to the apparatus or to the catalyst by super heating, also to avoid loss i n y i e l d by side reactions, favoured at high tempera­ tures. In a d d i t i o n , poor accuracy in the rate data, as well as i n the mass and heat transfer parameters,do not allow to calculate the exact concentration and temperature p r o f i l e s inside the reactor. This leads to incorrect p r e d i c t i o n of the reactor's dynamic behaviour. There­ fore these data should be determined as accurately as possible. For the measurement of reaction rates, d i f f e r e n t i a l reactors having extremely short catalyst beds or i n t e ­ g r a l reactors with r e l a t i v e long catalyst beds are often used. In the f i r s t type of experimental reactor, the concentration and temperature gradients within the catalyst beds are n e g l i g i b l y small. Due to t h i s fact, the reaction rate point data can be measured, provided the small concentration differences can be accurately analyzed. In the i n t e g r a l reactor, the change i n con­ centration i s much higher. There i s i n general no d i f ­ f i c u l t y analyzing the concentrations of the reacting species but, the reaction rates have to be determined from the concentration curves by c a l c u l a t i o n and cannot often be related to the fast changing temperature. Be­ cause of these obvious disadvantages, the s o - c a l l e d loop reactors are being used more and more i n k i n e t i c studies. In loop reactors, the extremely small concen­ t r a t i o n and temperature gradients desired within the short catalyst bed, along with s u f f i c i e n t l y high con­ centration difference between the reactor i n l e t and the ©

0-8412-0401-2/78/47-065-015$05.00/0

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTO^

Integral Tubular Reactor

Loop Reactor Figure 1.

Differential Reactor

Stirred-Tank Reactor Types of laboratory reactors

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

2.

LUFT ET AL.

Tubular and Loop Reactors

17

o u t l e t , can be r e a l i z e d by r e c y c l i n g a p a r t o f t h e react i o n products. In o r d e r t o see how t h e s e advantages c o u l d be r e a l i zed i n p r a c t i c e , t h e performance o f a l o o p r e a c t o r was compared w i t h t h a t o f a c o n v e n t i o n a l l y - b u i l t i n t e g r a l r e a c t o r . I n t h i s comparison t h e c a p a b i l i t y t o handle a c t u a l i n d u s t r i a l c a t a l y s t s , t h e s e t t l i n g time o f changing experimental c o n d i t i o n s , the d i f f i c u l t y of the m a t h e m a t i c a l e v a l u a t i o n o f t h e measured d a t a were cons i d e r e d . The a c c u r a c y o f t h e d a t a s f o r s c a l e up p r o b lems was checked i n a p i l o t p l a n t . F o r t h e r e a c t i o n , the o x i d a t i o n o f o-xylene w i t h a vanadiumpentoxide c a t a l y s t , an i n d u s t r i a l l y important p r o c e s s , was chosen. Apparatus The d e s i g n o f t h changes i n t h e r e a c t i o r e , c o n c e n t r a t i o n and throughput i n a wide range. I t s core i s a d i f f e r e n t i a l r e a c t o r d i r e c t l y c o u p l e d t o t h e blower. I t sucks t h e r e a c t a n t s through t h e c a t a l y s t bed and r e c y c l e s p a r t o f i t . T h i s d e s i g n a l l o w s o n l y a s m a l l dead volume and a s m a l l p r e s s u r e drop a c r o s s t h e c a t a l y s t bed even a t h i g h f l o w r a t e s . F u r t h e r m o r e , t h e whole a p p a r a t u s i s compact and t h e r e f o r e i t can e a s i l y be m a i n t a i n e d a t c o n s t a n t temperature. The s m a l l temp e r a t u r e and c o n c e n t r a t i o n g r a d i e n t s w i t h i n t h e catalyst bed, n e c e s s a r y f o r t h e k i n e t i c measurements, can^be r e a l i z e d by r e c y c l i n g p a r t o f t h e gas about 12 m /h. I t i s v e r y l a r g e compared t o t h e feed and c o r r e s p o n d s t o r e c y c l e r a t i o s o f l o o t o 5oo, a l s o s u f f i c i e n t f o r t h e a p p r o p r i a t e study o f highly-exothermic reactions. The r e c y c l e r a t i o can be changed w i t h r e s p e c t t o t h e r e a c t i o n c o n d i t i o n s by changing t h e speed o f r o t a t i o n o f t h e blower. The blower i s d r i v e n by an asynchronousmotor whose r o t o r i s f i x e d t o t h e s h a f t o f t h e blower. I t i s separ a t e d from t h e s t a t o r by means o f a p r e s s u r e tube i n o r d e r t o e x c l u d e any l e a k a g e . The i n t e g r a l a p p a r a t u s ( F i g . 3) c o n s i s t s o f a tubul a r r e a c t o r o f 1 m-length. In o r d e r t o measure t h e conc e n t r a t i o n , about 2o sampling t a p s a r e i n s t a l l e d a l o n g the tube. Through each sampling t a p , a thermocouple i s passed t o determine t h e temperature p r o f i l e . The a i r i s f e d through d r i e r s , f l o w meters and h e a t e r s b e f o r e e n t e r i n g v a p o r i z e r , where x y l e n e i s e v a p o r a t e d . T h i s a i r - x y l e n e m i x t u r e , c o n t a i n i n g about o.9 i:ol% x y l e n e , i s f e d t o t h e t o p o f t h e t u b u l a r r e a c t o r . The p h t h a l i c a n h y d r i d e , l e a v i n g t h e r e a c t o r i s washed and condensed by water i n a s p r a y tower. The r e a c t i o n heat i s removed by an e f f i c i e n t c o o l i n g system i n which d i p h e n y l (Dow therm) i s v a p o r i z e d .

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

18

CHEMICAL REACTION ENGINEERING—HOUSTON

Figure 2.

Loop reactor

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

2.

LUFT ET AL.

Tubular and

19

Loop Reactors

j 1 2 3 4 5 6 7

Figure 3.

Xylene storage Filter Metering pump Reactor Spray absorber Vaporizer Air pre heater

8 9 10 11 12 13

Rotameter Adsorber - Dryer Air regulater Savety switch Filter

Tubular reactor for the oxidation of xylene

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

20

CHEMICAL REACTION ENGINEERING—HOUSTON

R e s u l t s and e v a l u a t i o n The measurements i n b o t h r e a c t o r s were c a r r i e d out at steady s t a t e . The c a t a l y s t a c t i v i t y was m a i n t a i n e d at a l l times, t e s t i n g a t r e g u l a r i n t e r v a l s f o r any l o s s in activity. The r e s u l t s o f a t y p i c a l experiment a r e shown i n F i g . 4 . The c o n c e n t r a t i o n o f t h e r e a c t a n t s i s p l o t t e d v e r s u s a m o d i f i e d r e s i d e n c e time. The r e s i d e n c e time c o u l d be v a r i e d a l o n g t h e range l - l o g.h/mole by changing t h e throughput and t h e q u a n t i t i y o f c a t a l y s t . The temperature was k e p t c o n s t a n t a t 41o°C. The x y l e n e c o n c e n t r a t i o n i n t h e feed c o u l d be i n c r e a s e d up t o 1 , 3 mol %, which i s h i g h e r than the lower e x p l o s i o n l i m i t . As i t can be seen from t h e c u r v e s , t h e concent r a t i o n of the xylen increasing residenc r e a c t i o n product p h t h a l i c a n h y d r i d e (PSA) i n c r e a s e s f i r s t , then d e c r e a s e s a t h i g h r e s i d e n c e t i m e s due t o i t * o x i d a t i o n forming CO and C G . A l s o t h e c o n c e n t r a t i o n ofth intermediate products tolualdehyde (TCL) and p h t h a l i d e (PI) which a r e c o n s i d e r e d t o g e t h e r f o r s i m p l i c i t y , pass through a maximum. In t h e i n t e g r a l r e a c t o r , t h e e x p e r i m e n t s c o u l d not be c a r r i e d out i s o t h e r m a l l y ( F i g . 5 ) . The temperature ( l e f t ordinate) r i s e s s t e e p l y i n the f i r s t part of the c a t a l y s t bed, p a s s e s through a d i s t i n c t maximum and dec r e a s e s a g a i n by the c o o l i n g . The x y l e n e i s almost c o m p l e t e l y c o n v e r t e d . The concent r a t i o n o f t h e PSA i n c r e a s e s a t f i r s t s t e e p l y , then t e n d s t o l e v e l o f f i n t h e lower p a r t o f t h e r e a c t o r . Carbonmonoxide (CO) and c a r b o n d i o x i d e as w e l l as malei c a n h y d r i d e which was d e t e c t e d a t a low c o n c e n t r a t i o n , i n c r e a s e s t e a d i l y a l o n g the c a t a l y s t bed whereas t h e curve o f t o l u a l d e h y d e and p h t h a l i d e show a maximum s i m i l a r t o t h e loop r e a c t o r e x p e r i m e n t s . The e v a l u a t i o n o f t h e e x p e r i m e n t s i n both r e a c t o r s was based on t h e mechanism o f t h e o x i d a t i o n . The conc e n t r a t i o n p r o f i l e s measured i n t h e i n t e g r a l r e a c t o r , as w e l l as t h e f i n i t e s l o p e i n t h e o r i g i n o f t h e conc e n t r a t i o n - r e s i d e n c e time c u r v e s from t h e loop r e a c t o r , r e v e a l t h a t , t h e x y l e n e i s c o n v e r t e d by s i m u l t a n e o u s r e a c t i o n s t o the products p h t h a l i c a n h y d r i d e , p h t h a l i d e , t o l u y l a l d e h y d e , CO and C G . The d i s t i n c t maximum o f t h e p h t h a l i d e - and t o l u a l d e h y d e - c o n c e n t r a t i o n curve i n d i c a t e s t h a t these a r e i n t e r m e d i a t e p r o d u c t s which a r e converted mainly t o phthalicanhydride i n a consecutive s t e p . From t h e d e c r e a s e o f t h e P S A - c o n c e n t r a t i o n a t h i g h r e s i d e n c e t i m e s i t may be concluded t h a t , t h i s s p e c i e s o x i d i z e t o CO, CG , as w e l l a s water and t o a lower extend, t o MSA. F o r t h e e v a l u a t i o n o f t h e ex2

2

2

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

2.

LUFT ET AL.

21

Tubular and Loop Reactors

IrW/Ho Residence time Figure 4.

Results of loop-reactor experiments

450|

— —

Length

Figure 5.

Concentration and temperature distribution in integralreactor

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

22

CHEMICAL REACTION ENGINEERING—HOUSTON

p e r i d e n t a l r e s u l t s , i t i s considered u s e f u l to s i m p l i f y the mentioned r e a c t i o n scheme; t h u s , the concent r a t i o n s of t o l u a l d e h y d e and p h t h a l i d e were i n c l u d e d t o g e t h e r . The s m a l l q u a n t i t i e s of MSA were n e g l e c t e d . At the h i g h r e c y c l i n g r a t i o s the loop r e a c t o r o p e r a t e s as an i d e a l s t i r r e d - t a n k r e a c t o r . T h e r e f o r e , the r e a c t i o n r a t e can immediately be determined from the d i f f e r e n c e i n c o n c e n t r a t i o n between the feed and the o u t l e t , the throughput and the q u a n t i t y of c a t a l y s t . T h e r a t e e q u a t i o n , d e s c r i b i n g the consumption of x y l e n e and the f o r m a t i o n of the r e a c t i o n p r o d u c t s , are c o n s i d e r e d t o be pseudo f i r s t o r d e r . The parameter of the r a t e equations, vhich are the f r e q u e n c y f a c t o r s and the a c t i v a t i o n e n e r g i e s , are determined by l e a s t square methods. In the abov 6b) measured r a t e , f i meters, w r e p r e s e n t a p p r o p r i a t e weight f a c t o r s and N i s the number of measured v a l u e s . Because the r a t e e q u a t i o n s c o u l d be d i f f e r e n t i a t e d w i t h r e s p e c t t o the unknown k i n e t i c parameters, the o b j e c t i v e f u n c t i o n was m i n i m i z e d by a s t e p w i s e r e g r e s s i o n . The s t e e p c o n c e n t r a t i o n and temperature p r o f i l e s i n the i n t e g r a l r e a c t o r d i d not a l l o w t o determine the r e a c t i o n r a t e s immediately. T h e r e f o r e , the o b j e c t i v e f u n c t i o n c o n t a i n s the measured and the c a l c u l a t e d conc e n t r a t i o n s i n s t e a d of the r e a c t i o n r a t e s , a l s o the t e m p e r a t u r e s because of the n o n i s o t h e r m a l r e a c t o r beh a v i o u r . The k i n e t i c parameters must be o b t a i n e d by d i r e c t s e a r c h t e c h n i q u e s l i k e the d e r i v a t i v e f r e e simp l e x method of N e l d e r and Mead. Comparison Comparing the two l a b o r a t o r y r e a c t o r s i t may be n o t i c e d t h a t the loop r e a c t o r i s more e x p e n s i v e . A l though the q u a n t i t y , o f c a t a l y s t and the volume of the l o o p r e a c t o r i s s m a l l , compared t o the i n t e g r a l r e a c t o r , the r e c y c l i n g of a l a r g e volume of gas r e q u i r e s a c o m p l i c a t e d blower. Hoivever, c e r t a i n advantages and d i s a d v a n t a g e s r e s u l t from the d i f f e r e n t c o n c e n t r a t i o n and temperature d i s t r i b u t i o n i n both r e a c t o r s . Because of the u n i f o r m c o n c e n t r a t i o n and temperature i n s i d e the loop r e a c t o r , the c o n c e n t r a t i o n of the r e a c t a n t s c o u l d be measured o n l y i n the r e a c t o r j n l e t and o u t l e t to determine the r e a c t i o n r a t e . The s t e e p c o n c e n t r a t i o n and temperat u r e g r a d i e n t s i n s i d e the i n t e g r a l r e a c t o r r e q u i r e measurements at many s p o t s a l o n g the tube. T h i s becomes r a t h e r e x p e n s i v e i n time i f s e v e r a l components are t o be a n a l y z e d as i n the o x i d a t i o n of x y l e n e . In the e v a l u a t i o n of the e x p e r i m e n t a l r e s u l t s the d i s t r i b u t i o n of c o n c e n t r a t i o n and temperature appear

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

2.

LUFT ET AL.

23

Tubular and Loop Reactors

^L_ToUPI-^ Xylene \

§—••PSA 12 *C0*C02

3

Xylene

r *.

-(k

x

r

Phthali canhydride

o

r

.-El/RT

• k

o

. « -

3

E

/

3

R

T

E

• k

o

.«- S'*T

5

).x

x

PSA*

Tolu — aldehyde j r

Phthalide

CO, c o

TOL*PI

'CO*C0

2

s

k

o T « "

E

l

k

= o3-*'

2

/

E

3

Figure 6a.

R

T

/

R

'

T

X

k

X " o4

,

e

"

E

(

,

/

k

R

• *X * o 2 - « '

T

E

x

*

2

/

R

T

TOL*Pl

-

*PSA

Rate equations

N #

=

] > w

x

( r

x

- ?

w

*

x

(r

PSA PSA"'PSA

1

w

(r

• ^> TOL*PI TOL*Pl " *TOL*Pl

N •

X PSA TOL PI

w

]> CO,C0

Xylene PhthoJic anhydride Tolu—at deny de Phthalide

Figure 6b.

(r 2

C0,C0

N W ? r

?

2

" CO C0 i

) 2 2

Number of runs Appropriate weight factor Reaction rate, calculated - * - , measured

Objective function

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

}

24

CHEMICAL REACTION ENGINEERING—HOUSTON

Length

[cm]

•

Figure 7. Comparison of the loop-reactor data with pilot plant experiments

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

2.

LUFT ET AL.

Tubular and

25

Loop Reactors

t o be the b a s i c f a c t o r s i n t r o d u c i n g d i f f i c u l t y . The l o o p r e a c t o r can be d e s c r i b e d by simple a l g e b r a i c e q u a t i o n s of which the c o e f f i c i e n t s , p e r t a i n i n g t o the unknown f r e q u e n c y f a c t o r s and a c t i v a t i o n e n e r g i e s , can be o b t a i n e d by s t e p w i s e r e g r e s s i o n . In the case of the i n t e g r a l r e a c t o r , the e s t i m a t i o n parameters are more c o m p l i c a t e d and r e q u i r e s more computation time because of the n e c e s s i t y f o r n u m e r i c a l i n t e g r a t i o n of a s e t of d i f f e r e n t i a l e q u a t i o n s . In o r d e r t o check the a c c u r a c y of the measured data and c o l l e c t i n f o r m a t i o n f o r s c a l e - u p , a d d i t i o n a l exp e r i m e n t s were c a r r i e d out i n a p i l o t p l a n t and the r e s u l t s were compared w i t h t h e s e p r e v i o u s l y o b t a i n e d i n the l a b o r a t o r y r e a c t o r s . The p i l o t p l a n t r e a c t o r c o n s i s t e d of a tube l e n g t h t a k e n from a I t was f i l l e d w i t h about 1 kg c a t a l y s t p e l l e t s . The measured temperature- and c o n c e n t r a t i o n p r o f i l e s are p l o t t e d i n F i g . 7 v e r s u s the l e n g t h of the c a t a l y s t bed. The p o i n t s are e x p e r i m e n t a l l y determined whereas the t h i c k - l i n e c u r v e s have been c a l c u l a t e d u s i n g the k i n e t i c c o n s t a n t s o b t a i n e d i n the l o o p r e a c t o r exp e r i m e n t s . A c l o s e agreement between the e x p e r i m e n t a l r e s u l t s of the p i l o t r e a c t o r and the c a l c u l a t e d v a l u e s i s apparent. O n l y the c a l c u l a t e d CO and CG concentrat i o n s are a l i t t l e h i g h , c a u s i n g a l s o a h i g h e r temperature maximum. 2

Recommendations As the e x p e r i m e n t s i n the l o o p r e a c t o r can be carried out i s o t h e r m a l l y and at c o n s t a n t c o n c e n t r a t i o n s and the i n f l u e n c e of mass t r a n s f e r can be e x c l u d e d by a h i g h flow r a t e and s m a l l c a t a l y s t p e l l e t s , the l o o p r e a c t o r i s t o be recommendated f o r k i n e t i c s t u d i e s . F u r t h e r advantages are the f l e x i b i l i t y of the r e a c t o r w i t h r e s p e c t t o changes i n e x p e r i m e n t a l c o n d i t i o n s and l a s t but not l e a s t the u n c o m p l i c a t e d e v a l u a t i o n of the measured d a t a . The i n t e g r a l r e a c t o r shows some advantages i n the study of the p r o d u c t q u a l i t y and s e l e c t i v i t y because t e c h n i c a l c o n d i t i o n s can e a s i l y be i n c o r p o r a t e d . Furthermore, i t i s p o s s i b l e t o measure s i m u l t a n e o u s l y the heat cond u c t i v i t y i n the c a t a l y s t bed and the heat t r a n s f e r c o e f f i c i e n t through the r e a c t o r w a l l . The d i f f i c u l t i e s i n the e v a l u a t i o n of the e x p e r i m e n t s depend s t r o n g l y on the m a t h e m a t i c a l model which has t o be chosen. The e v a l u a t i o n i s c e r t a i n l y more comp l i c a t e d i f the r e a c t o r must be d e s c r i b e d by a twod i m e n s i o n a l model because o f s t e e p r a d i a l temperature g r a d i e n t s as we have observed i t i n the p h t h a l i c anhydrid reactor.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

3 Kinetic Measurements of the Hydrogenation of Carbon Monoxide (Fischer-Tropsch Synthesis) Using an Internal Recycle Reactor A. ZEIN EL DEEN, J. JACOBS, and M. BAERNS Lehrstuhl für Technische Chemie, Ruhr-Universität Bochum, Postfach 102148, D-4630 Bochum, West Germany

The Fischer-Tropsch-synthesi r e s t during the l a s t years. Its goal being nowadays the formation of mainly lower o l e f i n s as chemical feed­ -stocks (1-5). From t h i s point of view k i n e t i c measure­ ments on the hydrogenation of CO have been performed in an i n t e r n a l recycle reactor with a d i f f e r e n t l y pretreated c a t a l y s t containing oxides of i r o n , manganese, zinc and potassium. Catalysts containing manganese have been described recently (4,5) as suited for producing short-chain o l e f i n s such as ethylene and propylene. The experimental r e s u l t s of t h i s investigation are discussed with respect to product d i s t r i b u t i o n and the rate determining step of the synthesis r e a c t i o n . Experimental Procedure The i n t e r n a l recycle reactor as described elsewhere (6) used for the experiments was charged with about 60 g of c a t a l y s t which was thermally pretreated and reduced with hydrogen before the synthesis r e a c t i o n . During the synthesis recycle r a t i o s (recycled volume per time and weight of c a t a l y s t divided by space v e l o c i t y under ope­ r a t i n g conditions) of more than 20 were used to estab­ lish ideal mixing as well as isothermal operation and to avoid transport l i m i t a t i o n due to f i l m resistance. The measurements were conducted i n two d i f f e r e n t regions of c a t a l y s t performance: After reduction and operation of about 5 to 10 hrs under synthesis condi­ tions the a c t i v i t y reached a constant l e v e l where i t remained for upto 60 to 70 hrs during which the k i n e t i c measurements were performed; thereafter the a c t i v i t y decreased continously. The analysis of the reaction mixture (H2, CO, C02, and the various C1- to C4-hydrocarbons) was c a r r i e d out by gaschromatography. © 0-8412-0401-2/78/47-065-026$05.00/0 In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

3.

ZEIN

27

Measurement of Carbon Monoxide Hydrogénation

E L DEEN

Experimental Conditions The p e l l e t i z e d c a t a l y s t (D = 3,7 nun, L = 6,2 mm) was t h e r m a l l y t r e a t e d f o r 20 h r s a t 300°C and s u b s e q u e n t l y r e d u c e d w i t h H2 f o r 50 h r s a t 3 00°C ( c a t a l y s t A) and a t 500°C ( c a t a l y s t C ) . These t r e a t m e n t s r e s u l t e d i n d i f f e r e n t s u r f a c e a r e a s S and average pore d i a m e t e r s A:

2

13,4 m /g

d

= 4,6 nm

(meso-pores)

= 3,8 nm

(meso-pores)

Ρ C:

2

10,4 m /g

d

The t o t a l pore volume amounted i n b o t h c a s e s t o 0.4 cm /g. C a t a l y s t C was used i n two d i f f e r e n t forms: F i r s t , i t was used the c a t a l y s t (C-II t i o n s s i m i l a r t o s y n t h e s i s (T = 258 t o 323°C, ρ(total) = 5 ; 10 and 15 bar) a t a l e v e l o f c o n v e r s i o n o f about 40 % r e s u l t i n g i n some d i s i n t e g r a t i o n b e f o r e k i n e t i c t e s t s were c o n d u c t e d . The k i n e t i c measurements w i t h c a t a l y s t s A, C-I and C - I I were performed under t h e f o l l o w i n g c o n d i t i o n s : 3

Catalyst

T[°C]

P

total

[

b

a

r

]

Space

veloci­

x

co

[ % ]

t y (STP)[1/h] A 233-270 5 ; 1 0 ; 1 5 366-4480 8-65 C-I 323 5; 10 872-3752 8-34 C-II 309-335 10; 15 1180-5580 18-45 The f e e d gas was i n a l l i n s t a n c e s composed o f 40.1 v o l - % CO, 39.3 v o l - % H2 and 20.4 v o l - % A r . Experimental

Results

The CO was c o n v e r t e d under a l l c o n d i t i o n s t o about 45 t o 48 % C02 t h u s , r e s u l t i n g i n a n e a r l y c o n s t a n t r a t i o of CO-to H 2 - c o n v e r s i o n o f 1.4 t o 1.6. T h i s means t h a t t h e water formed d u r i n g t h e hydrogénation i s m a i n l y r e duced t o H2. The f o r m a t i o n o f c a r b o n and/or c a r b o n a c e ous m a t e r i a l i n s o l u b l e i n x y l e n e was a l m o s t n e g l i g i b l e . The remainder o f CO i . e . a p p r o x i m a t e l y 52 t o 55 % y i e l d e d hydrocarbons o f which o n l y t h e C1- t o C 4 - f r a c t i o n i s q u a n t i t a t i v e l y d e t a i l e d i n the following. Selectivity. The s e l e c t i v i t y o f t h e h y d r o c a r b o n f o r m a t i o n i s a l m o s t independent on C O - c o n v e r s i o n and p a r t i a l p r e s s u r e o f c a r b o n monoxide and hydrogen i n t h e range s t u d i e d f o r t h e c a t a l y s t s A and C-I d u r i n g t h e p e r i o d o f c o n s t a n t a c t i v i t y as e x e m p l i f i e d i n F i g u r e 1 A/B; t h e s e l e c t i v i t y i s , however, dependent upon t h e c a t a l y s t used, c a t a l y s t A p r o d u c i n g s i g n i f i c a n t l y l e s s C1- t o C4-hydrocarbons t h a n c a t a l y s t C-I and a l s o a

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

I "

Γ"

60

Π

Γ—-f

ο

ο

-

"*1

!

C0

20 Ί

Α

2

I

I

J

Γ

CK

4

~Ο

2

J

I

1

J

I

1

or

_J Ί

Γ­

co

• •

ο

I

I

1

2

• à

ACJ° ι

(

r

1—

L· C

•gi- 2^

*4

11

Η

^2 6 î

Ο

1

1

1—

rê^b

η

η

Q

2 /νβ_ΛθΟ_Οο—«Ο

0

'

C3H °

ι

I

3

8

I—

π

1

1

Γ

1

1

1

•

A

ο-

2 0

C H 8

Ο—Ο-

.^S-g-oo-Ot9-aa> ι

ι

C4H10 I

I

LO

20 X

R N

[%]

-

C4H10" *

L

60

I

20 X

C O

[%)

CO

Figure 1. Dependence of selectivity S on CO-conversion X(CO). (A) catalyst A; Τ = 256°C; F(total) = 15 (\J), 10 (O), 5 (A) bar; (B) catalyst C-I; Τ = 322°C; F(total) = 10 (·), 5(A) bar.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

3.

Measurement of Carbon Monoxide Hydrogénation

E L DEEN

zEiN

29

s m a l l e r p o r t i o n o f o l e f i n s . T h i s d i f f e r e n c e may be, however, due t o t h e d i f f e r e n t temperatures o f r e a c t i o n ; f o r c a t a l y s t C a h i g h e r one was n e c e s s a r y t o o b t a i n measurable c o n v e r s i o n s a t o t h e r w i s e comparable c o n d i t i o n s . The e f f e c t o f temperature i s d i s c u s s e d l a t e r i n some more d e t a i l . A change o f s e l e c t i v i t y i s , however, o b s e r v e d d u r i n g c a t a l y s t d e a c t i v a t i o n (Table I ) ; i n t h e Table I; Effect of operating time on performance of catalyst A with respect to conversion X(%) and selectivity S(C-atom%) at constant., temperature (256°C), pressure (10 bar) and space velocity (822 h" S.T.P). time [h]

2,42

26,87 31,30 29,10 27,33 28,02 27,75 27,02 25,10 23,20 18,00 1,49

X

CO H CO H

X

2

X

8,08 11,83 21,52 35,75 47,50 63,67 79,17 95,42

/X

2

s(co ) 52,33 46,52 S(CH ) 2,57 3,45 S(C H ) 0,45 0,73 S(C H ) 2,57 3,77 S(C H ) 0,78 1,12 S(C H ) 3,65 5,30 s(i-c ) 0,04 0,13 S(n-C ) 0,82 1,09 S (1-C+i-C+i-C) 3,01 4,44 S(t-2-C4n-C ) 0,67 0,86 S(c-2-C+3-M-C(1)) 0,33 0,45 2

4

2

6

2

4

3

8

3

6

4

4

4

4

4

4

Zh

5

5

4

46,67 49,69 48,07 50,81 50,52 47,77 46,59 3,92 4,46 4,71 4,65 4,51 4,98 5,04 0,82 0,99 1,11 1,15 1,11 1,27 1,34 4,19 4,72 4,75 4,54 4,18 4,50 4,27 1,13 1,28 1,28 1,30 1,22 1,27 1,29 5,77 6,37 6,53 6,20 5,96 6,29 6,12 0,07 0,11 0,11 0,11 0,11 0,12 0,13 1,13 1,28 1,25 1,22 1,18 1,27 1,25 4,78 5,16 5,25 4,94 4,77 5,06 4,87 0,86 0,95 0,96 0,94 0,96 1,00 0,99 0,48 0,51 0,53 0,50 0,52 0,52 0,47

67,21 67,86 69,83 75,52 74,55 76,36 75,05 74,06 72,37

l a t t e r case the r a t i o of o l e f i n to p a r a f f i n d i m i n i s h e s a l t h o u g h t h e a b s o l u t e amount o f t h e v a r i o u s o l e f i n i c hydrocarbons s t a y s c o n s t a n t . Activity. The a c t i v i t y o f t h e c a t a l y s t s was quant i t a t i v e l y e x p r e s s e d by t h e r a t e o f r e a c t i o n a s moles of component consumed o r formed r e s p e c t i v e l y p e r time and weight o f c a t a l y s t which c o u l d be measured d i r e c t l y by d e f i n i t i o n o f t h e r e c y c l e r e a c t o r . The a c t i v i t y was g r e a t e s t f o r c a t a l y s t A when compared w i t h C on an e q u a l temperature b a s i s ; t h e a c t i v i t y o f C - I I was h i g h e r t h a n C - I . The l a t t e r dependence i s p r o b a b l y caused by t h e s m a l l e r p a r t i c l e s i z e o f C - I I which was o b t a i n e d d u r i n g p r e t r e a t m e n t . The v a r i o u s o v e r a l l r e a c t i o n r a t e s were found t o be o n l y s l i g h t l y dependent on c a r b o n mon o x i d e p a r t i a l p r e s s u r e as i s shown i n T a b l e I I f o r t h e t h r e e c a t a l y s t s ; t h e dependence on ρ(CO) i s n o t v e r y

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL

30

REACTION

ENGINEERING—HOUSTON

Tfrfrle I I ; C o r r e l a t i o n between reduced r e a c t i o n rate r /p ±

pressure of r

i

/ p

H

*

a

k

i

, p

CO

CO C H 2

5

n.

108

4

and

partial

rooie/fg-cat.-h'bar)

Catalyst A Component i V 1 0

H

cgrbon monoxide

Catalyst k^lO

-0.22

0.53

5

n

116

±

0.22

R 2 (

C-I PCO>

0.41

Catalyf it Jc^lG

C-II

R (P 2

223

0.04

3.64

-0.31

0.88

5.08

0.22

0.63

7.42

0.20

0.39

1.94

-0.39

0.85

2.73

0.15

0.30

4.22

0.13

0.21

C

2 6

H

0.22

+0.18

0.64

0.30

0.43

0.69

0.57

0.27

0.81

C

H

3 6

1.72

-0.40

0.65

2.38

0.14

0.28

2.85

0.32

0.47

C

3 8

H

0.20

+0.01

0.01

0.24

0.22

0.42

0.27

0.41

0.74

C

H

4 8

1.11

-0.46

C

4 10

H

0.17

-0.10

pressure range of CO Temperature

to

1.8 T

R

-

5.2

bar

1.8

e

255-1 C

T

R

to -

3.8 bar 321±1 • c

2.9

T

R

to -

C O

)

0.03

5.6 bar 322-1 C e

s i g n i f i c a n t as can be d e r i v e d from the c o r r e l a t i o n c o ­ e f f i c i e n t R [p(CO)] which i s a l s o g i v e n i n t h i s t a b l e . T h i s r e s u l t i s i n agreement w i t h e a r l i e r p u b l i c a t i o n s (7,8) assuming t h a t t h e r a t e i s p r o p o r t i o n a l o n l y t o p(H2) and not i n any way t o ρ(CO) when the a c t i v e s u r ­ f a c e i s a l m o s t c o m p l e t e l y c o v e r e d w i t h CO. The temperature dependency o f the o v e r a l l r e a c t i o n r a t e s was d e r i v e d from A r r h e n i u s p l o t s ( F i g u r e 2) f o r which r e a c t i o n r a t e s measured a t comparable c o n v e r s i o n s and e q u a l p a r t i a l p r e s s u r e s o f CO and H2 were used. The a p p a r e n t a c t i v a t i o n e n e r g i e s E and t h e p r e e x p o n e n t i a l r e a c t i o n r a t e s r are l i s t e d i n Table I I I f o r c a t a l y s t s A and C - I I . The a c t i v a t i o n e n e r g i e s f o r the i n d i v i d u a l compounds o b t a i n e d f o r the two c a t a l y s t s a r e a l m o s t equal c o n s i d e r i n g t h a t the accuracy of E i s approxi­ m a t e l y 5 t o 10 %. 2

a

0

a

Discussion Based on the a f o r e communicated e x p e r i m e n t a l r e s u l t s some s p e c i f i c a s p e c t s o f the r e a c t i o n scheme and o f the r a t e d e t e r m i n i n g s t e p s o f the F i s c h e r - T r o p s c h - s y n t h e s i s a r e d i s c u s s e d i n the f o l l o w i n g . Product d i s t r i b u t i o n . A r e l a t i o n s h i p between the r a t e o f f o r m a t i o n o f the i n d i v i d u a l hydrocarbon and i t s c h a i n l e n g t h may be f o r m u l a t e d by the f o l l o w i n g e q u a t i o n when assuming t h a t the c a r b o n s k e l e t o n i s b u i l t up by s t e p w i s e a d d i t i o n of one c a r b o n atom t o an adsorbed

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

ZEiN

EL

DEEN

Measurement of Carbon Monoxide

Figure 2.

Hydrogénation

Arrhenius diagram for reaction rates

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

32

T a b l e I I I : Apparent a c t i v a t i o n energy E f o r r a t e s ———-——— a o f CO-consumption and h y d r o c a r b o n f o r m a t i o n . a

r =

r . e x p ( -- E / R T ) , r ο Q

a

=

r

o*

Compound *a

4.0·10

CH

4

C H 2

4

C

2 6

C

3 6

C

3 8

C

C

X

8.5- 1 0

7

3.6- 1 0

6

H

2.3-10 1.7·10

r

o

5.0-10

7

26.4

2.6·10

8

32.2

25.8

8.8·10

5

26.2

26.4

1.4·10 4 3.4-10 4.3·10 4 4.7-10*

24.1 28.5

22.4

3

22.5 1.9·10 3.5 t o 3.7

H

4 10

C0

2 >

25.6

H

4 8

4

bar

25.2 26.2

5

26. 1

3.4 t o 3.6

3.6 t o 3.7

3.7 t o 3.8

12 t o 19

22 t o 28

%

°c

Τ

1

7

5.7- 1 0 4

H

c o

' CO>

4.0·10

H

P

P

2

1)

1 )

Ο

CO

H

Catalyst C-II

Catalyst A r

f ( p

309

233 t o 271

^ m o l e / ( g - c a t a l y s t χ h)

2 )

t o 335

kcal/mole

growing c h a i n and t h a t t h e p r o b a b i l i t y o f c h a i n growth W i s independent o f c h a i n l e n g t h : r

= A

V co

w

"

r i s the r a t e of formation of p a r a f f i n plus o l e f i n of c a r b o n number n. As e x e m p l i f i e d i n F i g u r e 3 t h e e x p e r i ­ mental r a t e d a t a c a n be r e p r e s e n t e d by t h e above c o r r e ­ l a t i o n . The c o n s t a n t s A and W have been e v a l u a t e d f o r the v a r i o u s e x p e r i m e n t a l c o n d i t i o n s and a r e l i s t e d i n T a b l e IV; A i n c r e a s e s and W d e c r e a s e s s l i g h t l y w i t h temperature. P o s t u l a t i n g t h a t t h e l i n e a r p l o t can be extended t o carbon numbers n>4 t h e t o t a l s e l e c t i v i t y f o r t h e f o r m a t i o n o f s t r a i g h t c h a i n p a r a f f i n s and a o l e f i n s 5jS [C-atom%] c a n be c a l c u l a t e d : n

n

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

3.

zEiN

EL

Measurement of Carbon Monoxide Hydrogénation

DEEN

10 6

r

co

2

1 0

1 2

3

4

C A R B O N NUMBER Figure 3. Correlation between the rate of formation of straight chain paraffins plus α-olefins (r ) and carbon number η (catalyst C - I / , F(CO) = 3.5 bar, ?(H ) = 3.7 bar) n

2

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

33

CHEMICAL REACTION ENGINEERING—HOUSTON

34

r—

S

)

=

^ n

n=°° η A W n=0

r

n

f

= 0

—

0

n

dn = A/ (lnW)'

The v a l u e s o f £ s a r e g i v e n i n T a b l e IV; t h e amounts t o about 44 %. C o n s i d e r i n g t h a t t h e l e c t i v i t y towards C02 i s a p p r o x i m a t e l y 48 % 8 % o f s e l e c t i v i t y a r e t o be c o n t r i b u t e d t o hydrocarbons and oxygenated compounds. n

average average s e ­ the missing branched

Table IV: Parameters A and W of the product d i s t r i b u t i o n c o r ­ r e l a t i o n and cumulative s e l e c t i v i t y ^ S

n

of s t r a i g h t

chain-hydrocarbons

Catalyst A

T

R

e

ΑΊ0

2

C a t a l y s t C II

W

T

s.*

c

R

A-10

2

W

In' c--atom %

°c

C-a torn %

233

3,13

0,776

49

309

4,88

0,697

38

245

3,76

0,776

58

316

5,17

0,704

42

254

4,34

0,755

55

322

5,44

0,687

39

263

4,20

0,732

43

329

5,53

0,679

37

270

4,57

0,724

44

335

6,00

0,655

34

S

CO

a

*

4

5

-

5

0

C-atom %

Rate d e t e r m i n i n g s t e p and a c t i v a t i o n energy. The m o d i f i e d T h i e l e - m o d u l u s (J) i s commonly used as a means f o r e v a l u a t i n g whether a r e a c t i o n i s e f f e c t e d by pore d i f f u s i o n (j)) : 2

$ =

R . r.·0 Ρ P C(H ).D 1

2

V

e f f

For the F i s c h e r - T r o p s c h - s y n t h e s i s the q u e s t i o n a r i s e s on what k i n d o f d i f f u s i o n c o e f f i c i e n t t o base t h e c a l ­ c u l a t i o n . When a p p l y i n g a gas phase d i f f u s i o n c o e f f i ­ c i e n t φ amounts t o about 0,001 t o 0,01; hence, pore d i f f u s i o n s h o u l d be e x c l u d e d . I t i s , however, known that the pores o f the c a t a l y s t a r e f i l l e d with high b o i l i n g l i q u i d hydrocarbons as was a l s o o b s e r v e d i n

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

3.

ZEIN

EL

Measurement of Carbon Monoxide Hydrogénation

DEEN

35

t h i s study. T h e r e f o r e i t seems a p p r o p r i a t e t o s u b s t i t u t e f o r the r e a c t a n d s the l i q u i d phase d i f f u s i o n c o e f f i c i e n t s and t h e i r s o l u b i l i t y i n the l i q u i d hydrocarbons as a measure o f c o n c e n t r a t i o n . When u s i n g e s t i mated v a l u e s f o r the m o l e c u l a r d i f f u s i o n c o e f f i c i e n t based on Π 0 ) and f o r the s o l u b i l i t y of H2 (VjJ moduli a r e o b t a i n e d i n the o r d e r o f 20 t o 50 r e s u l t i n g i n e f f e c t i v i n e s s f a c t o r s o f 0.3 t o 0.1. T h i s c l e a r l y sug­ g e s t s t h a t t h e r a t e o f CO-consumption i s s t r o n g l y i n ­ f l u e n c e d by p o r e d i f f u s i o n . The magnitude o f the ap­ p a r e n t a c t i v a t i o n e n e r g i e s as l i s t e d i n T a b l e I I I , how­ ever, i s comparable t o the t r u e a c t i v a t i o n e n e r g i e s o f the s y n t h e s i s as proposed by (J^) . I t might t h e r e f o r e be assumed t h a t t h e measured v a l u e s of E a r e not e f ­ f e c t e d by pore d i f f u s i o v a l u e s . In t h i s cas the a c t i v e s u r f a c e would have t o o c c u r by another me chanism than pore d i f f u s i o n ; s u r f a c e d i f f u s i o n has been suggested e a r l i e r (J_3) · a

Performance o f c a t a l y s t s A and C - I I . C a t a l y s t C - I I reduced a t 500°C was l e s s a c t i v e than A reduced a t 300 °C. The d i f f e r e n c e i n a c t i v i t y which i s e x e m p l i f i e d by the r e a c t i o n r a t e s of CO i n T a b l e V i s g r e a t e r than c o u l d be e x p l a i n e d by the s m a l l e r s u r f a c e a r e a of C - I I . Table V: E f f e c t o f c a t a l y s t pretreatment on a c t i v i t y c a l c u l a t e d a c c o r d i n g to the k i n e t i c d a t a o f Table I I I . Temp. 1

3

r

° - co

mole g-cat.'h

e

C Cat. A Cat.C-II

250

270

3.9 (0.6)

300

9.2 +)

(1.4)

330 +)

(29.4) (83.8) +)

5.0

+)

15.6

I t i s c o n c l u d e d t h a t t h e number o f a c t i v e s i t e s per u n i t a r e a d e c r e a s e s by t h e h i g h temperature r e d u c t i o n . There a r e minor d i f f e r e n c e s i n s e l e c t i v i t y o f the two c a t a l y s t s as i s shown i n T a b l e VI f o r e t h y l e n e and ethane. The s e l e c t i v i t y towards e t h y l e n e i s i n the temperature range i n v e s t i g a t e d s l i g h t l y h i g h e r f o r c a t a l y s t C - I I as compared w i t h A. C o n s i d e r i n g ethane i t s s e l e c t i v i t y can be l o o k e d a t as n e a r l y c o n s t a n t . Hence, the main d i f f e r e n c e o f the two c a t a l y s t s i s their activity. To e l u c i d a t e the mechanism o f the d e c r e a s e i n a c t i v i t y i n v e s t i g a t i o n s are p r e s e n t l y i n progress to determine t h e number o f a c t i v e s i t e s o f t h e c a t a l y s t s .

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

36

T a b l e V I : E f f e c t o f c a t a l y s t pretreatment on s e l e c t i v i t y (C-atom %) c a l c u l a t e d a c c o r d i n g t o t h e k i n e t i c data o f Table I I I . Temp.

C a t a l y s t C-II

Catalyst A S(C )

S(C )

250

3.5

0.6

5.8

(4.3)

+ )

(0.6)

+ )

(7.2) >

270

3.8

0.8

4.8

(4.2)

+ )

(0.6)

+ )

(7.0)

300

(4.1)

+ )

(4.4)

+ )

°C

2

330

S (C )/S(C2) s ( c )

+

(3.7) > +

(1.4) >

(3.1)

+ )

S(C2)/S(C )

s(c )

2

2

2

2

2

+

4.2

0.6

7.0

4.1

0.6

6.8

+ )

c a t a l y s t was n o t operate

Ac knowledgement T h i s work was s u p p o r t e d by Ruhrchemie AG, Oberhausen and t h e M i n i s t r y f o r R e s e a r c h and Technology o f t h e Fed. Rep. o f Germany. Literature Cited (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

(11) (12) (13)

Büssemeier B., F r o h n i n g C.D., C o r n i l s Β., Hydroc. P r o c . (1976) 11, 105. German P a t e n t A p p l i c . DAS 2.536.488 (16.8.1975). German P a t e n t A p p l i c . DOS 2.518.982 (29.4.1975). German P a t e n t A p p l i c . DOS 2.518.964 (29.4.1975). German P a t e n t A p p l i c . DOS 2.507.647 (19.2.1975). B e r t y J.M., Chem. Engng. P r o g r . (1974) 70, 78. Anderson R.B., Seligmann Β., S c h u l t z J . F . , Kelly R., Elliot M.A., I n d . Engng. Chem. (1952) 44, 391. Dry M.E., S h i n g l e s T., B o s h o f f L . J . , J. Catal. (1972) 25, 99. Satterfield C.N., "Mass T r a n s f e r in Heterogeneous Catalysis", 138, M.I.T. P r e s s , London 1970. Weast R.C. ( e d i t o r ) "Handbook o f C h e m i s t r y and P h y s i c s " F59(n-Hexane), CRC-Press, C l e v e l a n d / O h i o 1974. K ö l b e l H., Ackermann P., E n g e l h a r d t F., E r d ö l und Kohle (1965) 9 ( 3 ) , 153. Anderson R.B., H o f e r L . J . E . , J. Chem. Eng. Data (1960) 5, 511. B r ö t z W., S p e n g l e r H., Brennstoff-Chem. (1950) 31, 97.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

4 Thermal and Kinetic Design Data from a Bench-Scale Heatflow Calorimeter W.

REGENASS

CIBA-GEIGY

Ltd.,

Department of Chemical Engineering, Basel, Switzerland

THERMAL AND KINETIC DESIGN DATA FROM A BENCH-SCALE HEATFLOW CALORIMETER In this paper, a heat flow calorimeter designed for the investigation of i n d u s t r i a l organic reactions i s presented. This instrument i s extensively used for the elucidation of reaction kinetics and for the assessment of thermal hazards. I t also per­ mits the determination of heats of reaction, specific heats and heat transfer coefficients, and due to its accurate controls, i t is an ideal "mini-pilot-reactor". Attempts to use heat evolution as an indicator for the kinetics of chemical reactions are as old as thermochemistry. Nowadays thermal methods are firmly established for the i n v e s t i ­ gation of s o l i d / s o l i d , gas/solid and curing reactions, and they are widely used for biochemical reactions. There i s an adequate supply of instruments for this type of work. However, it i s only i n the l a s t few years that calorimeters suited to the requirements of process development have been described i n the literature [1,2,3,4], and no such instrument i s available commercially to date. Therefore, chemical engineers often are not aware of the potential of thermal methods. Thermal methods and Instrumentation As an introduction for the chemical engineer not familiar with thermal methods, a short review on instrumentation i s given here. The most important feature for classifying thermal methods is certainly the treatment of the evolved heat. In accumulation methods (adiabatic and isoperibolic calorimetry), the sample i s well insulated from its environment and its temperature change is used as a measure of the extent of conversion. In heat transfer or heat flow methods, the evolved heat flow to the environment i n ©

0-8412-0401-2/78/47-065-037$05.00/0

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

38

CHEMICAL REACTION ENGINEERING—HOUSTON

a measurable way, w h i l e the sample temperature remains near i t s s e t p o i n t j here the measured r a t e o f heat flow i s p r o p o r t i o n a l t o the r a t e o f c o n v e r s i o n . For k i n e t i c work and hazards assessment, heat flow methods are t o be p r e f e r e d . Heat f l o w c a l o r i m e t e r s may be c l a s s i f i e d f u r t h e r w i t h respect to the method o f heat t r a n s f e r c o n t r o l . I n p a s s i v e systems, heat flow i s induced by temperature changes o f the sample due t o p a r t i a l accumulation o f the evolved heat. I n a c t i v e systems, a heat t r a n s f e r c o n t r o l l e r causes heat t r a n s f e r induced by the s l i g h t e s t d e v i a t i o n o f the sample temperature from i t s s e t p o i n t . Three heat flow c o n t r o l p r i n c i p l e s are mainly used i n a c t i v e systems: 1) P e l t i e r heat t r a n s f e r 2) Compensation h e a t i n constant temperatur c o n t r o l l e d e l e c t r i c heater i s so adjusted t h a t the sample temperature i s kept a t i t s s e t p o i n t , i . e . the h e a t i n g power i s complementary t o the heat r e l e a s e of the sample) 3) adjustment o f the environment temperature Heat flow measurement i s s t r a i g h t forward w i t h the f i r s t two p r i n c i p l e s ? there a r e two methods i n connection w i t h p r i n c i p l e 3) : 31) use o f the temperature d i f f e r e n c e across the sample w a l l as a measure o f heat flow 32) heat balance on the heat t r a n s f e r f l u i d (jfj [VJ. Another c h a r a c t e r i s t i c f e a t u r e o f heat f l o w c a l o r i m e t e r s i s sample s i z e . The micro-methods ( d i f f e r e n t i a l - t h e r m a l a n a l y s i s = DTA, d i f f e r e n t i a l scanning c a l o r i m e t r y = DSC) are q u i c k and r e q u i r e l i t t l e experimental e f f o r t , b u t they p r o v i d e no means o f adding r e a c t a n t s d u r i n g measurements, and heterogeneous samples cannot be mixed. A l l micro-methods use a twin (or d i f f e r e n t i a l ) design t o e l i m i n a t e d i s t u r b i n g e f f e c t s , i . e . an i n e r t sample i s exposed to the same environment c o n d i t i o n s as the sample under i n v e s t i ­ g a t i o n and the d i f f e r e n c e o f the two heat flows i s recorded. Laboratory (research type) heat flow c a l o r i m e t e r s (with sample s i z e s o f 20 t o 200 ml) are a v a i l a b l e from v a r i o u s suppliers. These instruments are very accurate b u t they have l i m i t e d ranges of a p p l i c a t i o n w i t h r e s p e c t t o temperature, p r e s s u r e , c o r r o s i o n r e s i s t e n c e and h a n d l i n g o f r e a c t a n t s . Two bench-scale heat f l o w c a l o r i m e t e r s (with a sample s i z e of 0.3-2.5 l i t r e s ) have been d e s c r i b e d : a design o f Hub QÛ , p a r t i c u l a r l y s u i t a b l e f o r work under r e f l u x c o n d i t i o n s , and the instrument presented i n t h i s paper, which i s a s i n g l e sample a c t i v e heat flow c a l o r i m e t e r , u s i n g the heat flow c o n t r o l method 31) . More comprehensive reviews on thermal a n a l y s i s instrumenta­ t i o n are found i n r e f e r e n c e s and HQ.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

4. REGENASS

Thermal and Kinetic Design Data

A bench s c a l e heat flow c a l o r i m e t e r

39

ΓΣ.1.2..1Ω.Ill

For the requirements o f process development and process s a f e t y i n v e s t i g a t i o n , a bench s c a l e heat flow c a l o r i m e t e r has been developed and b u i l t . F i g u r e 1 o u t l i n e s i t s p r i n c i p l e . The s t i r r e d tank r e a c t o r (A) i s surrounded by a j a c k e t i n which a heat t r a n s f e r f l u i d i s c i r c u l a t e d a t a very h i g h r a t e . A cascaded c o n t r o l l e r (B) a d j u s t s the temperature o f the c i r c u l a t i o n loop (C) so t h a t heat t r a n s f e r through the r e a c t o r w a l l e q u i l i b r a t e s the heat e v o l u t i o n i n the r e a c t o r . I n j e c t i o n o f thermostated hot or c o l d f l u i d i s used t o a d j u s t the temperature i n the loop. The r a t e o f heat t r a n s f e r q (which equals the r a t e o f heat e v o l u t i o n ) i s r e l a t e d t o the observed temperature d i f f e r e n c e Δτ between the j a c k e t f l u i d and the r e a c t i o n mixture by the r e l a t i o n q = U · A · ΔΤ = f c where the c a l i b r a t i o n f a c t o r f i s the product o f U, the o v e r a l l heat t r a n s f e r c o e f f i c i e n t , and A the a c t i v e (= wetted) heat t r a n s ­ f e r a r e a . Because both A and U depend on the r e a c t o r contents and on the s t i r r i n g c o n d i t i o n s , s p e c i f i c c a l i b r a t i o n i s r e q u i r e d . T h i s i s done by producing a known heat i n p u t r a t e t o the r e a c t i o n mixture by means o f an e l e c t r i c heater (D). The need o f frequent c a l i b r a t i o n i s o f some inconvenience as compared w i t h heat balance c a l o r i m e t e r s . On the o t h e r hand, t h e method chosen permits the use o f an u n i n s u l a t e d g l a s s r e a c t o r and thus a l l o w s v i s u a l o b s e r v a t i o n o f phase changes, c o l o u r changes and m i x i n g c o n d i t i o n s . T h i s i s a d i s t i n c t advantage f o r process development work. Our standard instrument, which i s shown i n f i g . 2 , i s equipped w i t h a r e f r i g e r a t i o n u n i t , e l e c t r o n i c c o n t r o l s f o r temperature programming; automatic c a l i b r a t i o n and w i t h f e e d i n g systems (not shown) f o r gases, s o l i d s and l i q u i d s . Thus, a l l standards operations c a r r i e d out w i t h i n d u s t r i a l s t i r r e d tank r e a c t o r s can be performed. The s p e c i f i c a t i o n s are as f o l l o w s : r e a c t o r temperature : -20 t o 200°C temperature programm : i 1 t o 200°/hour pressure (glass r e a c t o r ) : - 1 t o 2 bar volume o f r e a c t o r : 0.5/2.5 l i t r e s (exchangeable) volumen o f r e a c t a n t : 0.3-2.5 l i t r e s s e n s i t i v i t y : 0.5 Watts f o r low v i s c o s i t y r e a c t i o n mixtures heat removal c a p a c i t y : 500 Watts ( f o r temp. >· 30°C) response time (to a step change o f the heat r e l e a s e r a t e ) : 20 seconds f o r 50%, 200 seconds f o r 99% o f the f u l l s i g n a l . c

S p e c i a l u n i t s f o r h i g h temperature (250°C), low temperature (-60°C, f l l ] ) and moderate pressure (50 bar) are a l s o i n use.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

40

D

Figure 1. Bench scale heat flow calorimeter

Figure 2. Bench scale heat flow calorimeter

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

4.

REGENASS

Thermal and Kinetic Design Data

41

F i g . 3 presents a t y p i c a l heatflow r e c o r d o f an i s o t h e r m a l run. I n the example a c e t i c anhydride was hydrolyzed a t 25°. The f o l l o w i n g events are i n d i c a t e d : (A) I n i t i a t i o n o f the r e a c t i o n by instantaneous a d d i t i o n o f 0.88 moles o f a c e t i c anhydride t o a l a r g e amount o f 0.1 η aqueous HCl (B) dynamic l a g (heat flow t o the j a c k e t has t o e q u i l i b r a t e w i t h heat r e l e a s e i n the r e a c t o r ) (C) heat e v o l u t i o n decreasing e x p o n e n t i a l l y ( f i r s t order r e a c t i o n ) (D) c a l i b r a t i o n (superimposed on r e a c t i o n ) Thermal data The r a t e o f heat e v o l u t i o n which i s o f primary i n t e r e s t f o r s a f e t y and design c o n s i d e r a t i o n s observed temperature d i f f e r e n c The t o t a l heat o f r e a c t i o n f o l l o w s by i n t e g r a t i n g the surface under the heat flow curve. Heat c a p a c i t i e s and s p e c i f i c heats are obtained from tempera­ ture programmed runs. When t h e r a t e o f imposed temperature change Τ i s a l t e r e d , there i s a step change i n heat flow (s i n f i g . 4 ) : Aq = Δ(Τ)

· (w + m C , ) r ρ r In t h i s r e l a t i o n w denotes the p r o p o r t i o n a t e heat c a p a c i t y o f the c a l o r i m e t e r (a q u a n t i t y which depends on temperature and on the volume o f the c a l o r i m e t e r contents and has t o be c a l i b r a t e d f o r a s p e c i f i c r e a c t o r ) , m and Cp, are the mass and the s p e c i f i c heat o f the mixture under i n v e s t i g a t i o n . r

r

The e v a l u a t i o n o f heat flow data obtained from the bench s c a l e c a l o r i m e t e r has been t r e a t e d by M a r t i n [T]and Gautschi QJO]. Kinetics For s i n g l e r e a c t i o n s , the r a t e o f r e a c t i o n i s d i r e c t l y propor­ t i o n a l t o the r a t e o f heat e v o l u t i o n observed. The most common o b j e c t i o n s t o the use o f thermal methods a r e r e l a t e d t o the f a c t s t h a t most r e a c t i o n s a r e n o t s i n g l e and t h a t heat i s a very uns p e c i f i c i n f o r m a t i o n . Therefore the c o n c l u s i o n could be drawn t h a t thermal methods a r e o f l i t t l e value f o r k i n e t i c work. However, i n the authors experience on s e v e r a l hundred r e a c t i o n s o f w i d e l y d i f f e r e n t k i n d s , t h i s i s not the case.In a s u r p r i s i n g l y l a r g e number o f cases, the main r e a c t i o n i s dominating t h e r m a l l y t o such an e x t e n t , t h a t the i n f l u e n c e o f concentrations and o f temperature on the r e a c t i o n r a t e can be obtained by heat flow experiments alone. I n most other cases, thermal data provide v a l u a b l e informa­ t i o n a d d i t i o n a l t o the data obtained by c l a s s i c a l means, a f a c t which d r a s t i c a l l y speeds up k i n e t i c work. Of course, thermal methods are not appropriate f o r s e l e c t i v i t y determinations.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION

ENGINEERING—HOUSTON

Figure 3. Isothermal run of the hydrolyse of acetic anhydride

Figure 4. Temperature programmed run of a diazo-decomposition

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

4.

Thermal and Kinetic Design Data

REGENASS

43

In order to u t i l i z e c a l o r i m e t r y t o i t s f u l l e x t e n t , i t i s important to have d i f f e r e n t means o f r e a c t i o n i n i t i a t i o n a t ones d i s p o s a l . The bench-scale c a l o r i m e t e r described permits the f o l l o w i n g i n i t i a t i o n s of reaction: 1) instantaneous a d d i t i o n o f a r e a c t a n t ( f i g . 3) o r a c a t a l y s t ( f i g . 5 and 6) 2) gradual (continuous) a d d i t i o n o f l i q u i d , gaseous o r s o l i d r e a c t a n t s ( f i g . 7) 3) gradual r i s e o f temperature (as shown i n f i g . 4 f o r the f o r ­ mation o f a p h e n o l i c compound by the decomposition o f the corresponding d i a z o - s a l t : ArN^HSO^ + H 0—»-ArOH + N +H S0 ) 2

2

2

4

By temperature programmed o p e r a t i o n , heat of r e a c t i o n , s p e c i f i c heat, frequency f a c t o r and a c t i v a t i o n energy may be ob­ t a i n e d from one s i n g l e run the f o l l o w i n g parameter constant k (433 K) : 1.0-10~ s ? a c t i v a t i o n energy E: 2.1-10^ Joule/mole? heat o f r e a c t i o n ΔΗ: 2.29·10^ Joule/mole, w i t h estimated v a r i a t i o n c o e f f i c i e n t s o f 7%, 6% and 4% r e s p e c t i v e l y . 2

_1

F i g . 5 and 6 are taken from an i n v e s t i g a t i o n by M a r t i n on the i s o m e r i s a t i o n o f t r i m e t h y l p h o s p h i t e (TMP): P(0CH ) 3

3

•

CH -PO(OCH ) 3

3

2

This r e a c t i o n i s c a t a l y s e d by CH J and i n h i b i t e d by N(C H _) . F i g . 5 demonstrates the ease o f i n v e s t i g a t i n g i n f l u e n c e s on r e a c t i o n r a t e by means o f the c a l o r i m e t e r . A f t e r c a t a l y s t a d d i t i o n (marked C), there i s an immediate increase i n r e a c t i o n rate? a f t e r the a d d i t i o n o f i n h i b i t o r (marked I) there i s a f a s t exothermic r e a c t i o n between the c a t a l y s t and the i n h i b i t o r and then a decrease o f the r a t e o f i s o m e r i s a t i o n . F i g . 6 i l l u s t r a t e s the value o f d i r e c t i n f o r m a t i o n on r e a c t i o n r a t e . A f t e r c a t a l y s t a d d i t i o n there i s a t f i r s t a marked increase o f r e a c t i o n r a t e a t constant temperature, where one would expect a f i r s t order decrease. This i s due to a considerable i n ­ crease i n p o l a r i t y o f the r e a c t i o n mixture as a consequence o f conversion. The heat flow record demonstrates t h i s f a c t more e v i d e n t l y than a c l a s s i c a l conversion versus time diagram . 3

2

C

3

A comprehensive review on the k i n e t i c e v a l u a t i o n o f thermal data has been given by Wendtland and coworkers / the evaluation procedures s p e c i f i c to heat flow c a l o r i m e t r y have been t r e a t e d by Becker \Î2} , M a r t i n OQ and Gautschi [ÏQj · Assessment o f thermal hazards Thermal explosions do occur, when the heat e v o l u t i o n r a t e o f a r e a c t i o n (with a high l a t e n t a d i a b a t i c temperature r i s e ) exceeds the heat t r a n s f e r c a p a c i t y o f the r e a c t o r . Events o f t h i s type which have happened i n i n d u s t r y , may be d i v i d e d i n t o two c l a s s e s :

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

NOT INITIATED

INITIATED Watt

Κ 433 -heat flow

50

393

0 100

/

cni /-—RCL a d d e d - ν 5 0 1 / / / u

Figure 7.

Formation of Grignard compound

h 413

/! I j

/

'

temperature^ .5

1.

0

.5

j

373 353 333

1. hours

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

4.

REGENASS

45

Thermal and Kinetic Design Data

1) exothermal decomposition o r p o l y m e r i s a t i o n o f t h e r m a l l y i n s t a b l e mixtures (e.g. n i t r o compounds, b e n z y l - h a l i d e s , 2) "run away" o f an intended r e a c t i o n .

etc.)

Type 1 hazards a r e e a s i l y assessed u s i n g w e l l e s t a b l i s h e d t e s t methods [^4,15] , e.g. the t h e r m o a n a l y t i c a l micro-methods DTA or DSC? a t e s t e s t a b l i s h e d by L u t o l f \ ΐ β ] . which i s now standard i n Swiss firms? o r the "Sikarex" . However, the e l a b o r a t i o n o f safe r e a c t i o n c o n d i t i o n s (which avoid type 2 hazards) i s s t i l l a problem. Whenever p o s s i b l e , h i g h l y exothermal r e a c t i o n s are performed i n such a way, t h a t the r e a c t a n t s disappear by r e a c t i o n as they enter the r e a c t o r (semibatch o r continuous o p e r a t i o n ) . Under these c o n d i t i o n s , any accumulation o f r e a c t a n t s i n the r e a c t o r i s hazardous. I t may have 21) too low temperatur 22) i n s u f f i c i e n t mixing 23) wrong k i n e t i c assumptions (a case o f t e n encountered i n process development: the r e a c t i o n i s assumed t o be f a s t and the heat evolved a f t e r the a d d i t i o n o f the r e a c t a n t s i s n o t n o t i c e d on l a b o r a t o r y scale? then a t the p i l o t stage, there i s a run away). 24) i n c o r r e c t i n i t i a t i o n F i g . 7 demonstrates the i n v e s t i g a t i o n o f a type-24)-hazard d u r i n g formation o f a Grignard-reagent. A h a l i d e i s added gradually to magnesium suspended i n a s o l v e n t (RC1 + Mg • RMgCl). A f t e r c o r r e c t i n i t i a t i o n ( l e f t ) , the r e a c t i o n proceeds almost l i k e a n e u t r a l i s a t i o n ? w i t h o u t i n i t i a t i o n ( r i g h t ) , the r e a c t i o n does n o t s t a r t u n t i l f a r too much h a l i d e has been added, and then gets o u t of c o n t r o l . Even s l i g h t l y exothermal r e a c t i o n s may become dangerous, when a t a higher temperature an exothermal decomposition i s t r i g g e r e d o f f . For t h i s reason,the p o t e n t i a l a d i a b a t i c temperature r i s e o f i n d u s t r i a l r e a c t i o n s i s o f general i n t e r e s t . When s y n t h e t i c work i s done i n the b e n c h - s c a l e - c a l o r i m e t e r , the r e q u i r e d data are ob­ t a i n e d without a d d i t i o n a l e f f o r t . Heat t r a n s f e r c o e f f i c i e n t s F i l m heat t r a n s f e r c o e f f i c i e n t s may be estimated from flow c o n d i t i o n s and from p h y s i c a l p r o p e r t i e s . For f o r c e d convection and t u r b u l e n t flow ( i . e . c o n d i t i o n s p r e v a i l i n g i n s i d e s t i r r e d tank r e a c t o r s ) , the r e l a t i o n f \ _ ,„ %ι

(3a) i s v a l i d , where a i s a geometric f a c t o r and d i s the v e s s e l d i a ­ meter. N e g l e c t i n g the r a t i o o f the v i s c o s i t i e s i n the bulk and a t the w a l l , a rearrangement y i e l d s

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

46

CHEMICAL REACTION ENGINEERING—HOUSTON

r

2 2 λ ρ ·ο Ρ Λ

h =

1/3 2/3

(3b)

•r.

w i t h s denoting the s t i r r e r , r being the r a t i o of the a c t u a l s t i r r e r frequency f to a standard frequency f , s p e c i f i c f o r a given s t i r r e r type and v e s s e l s i z e , and g (the g r a v i t a t y a c c e l e r a ­ t i o n ) introduced to make Ζ dimensionless. In the r i g h t hand r e p r e s e n t a t i o n of (3b), f i r s t proposed by J e h l e and Oeschger [Xj], Ζ i s a property of the r e a c t o r (which can be t a b u l a t e d f o r standardized r e a c t o r s ) and γ i s a property of the l i q u i d . For v i s c o u s r e a c t i o n mixtures where we have a p a r t i c u l a r i n t e r e s t i n knowing h, th mine y, are not e a s i l y culate γ from the o v e r a l l heat t r a n s f e r c o e f f i c i e n t U i n the heat flow c a l o r i m e t e r , which i s obtained by the c a l i b r a t i o n procedure : Δ (Δτ) àq A

d

, 1 1 w 1 ' A = — = -— + τ— + -— U h. λ h D w r

= Β +

1 —— „ 2/3 Ζ -r -y c f

(4)

Here the i n d i c e s denote j a c k e t , w a l l , r e a c t i o n mixture and o a l o r i m e t e r v e s s e l , and Β i s the sum of the r e s i s t a n c e s of the w a l l and of the f i l m i n the j a c k e t . Β i s i n f l u e n c e d by the heat t r a n s f e r f l u i d , by the c i r c u l a t i o n c o n d i t i o n i n the j a c k e t and by the r e a c t i o n v e s s e l chosen. For a given s e t of equipment, Β de­ pends only on temperature and can be c a l i b r a t e d once and f o r a l l . This c a l i b r a t i o n has to be done c a r e f u l l y s i n c e Β i s the domina­ t i n g term of (4), due to the l a r g e r e s i s t a n c e of the g l a s s used as r e a c t o r w a l l . Therefore, the procedure o u t l i n e d here i s suggested f o r t y p i c a l r e a c t i o n mixtures (with v i s c o s i t i e s s i m i l a r to s u l f u r i c a c i d or higher) and not f o r l i q u i d s l i k e methanol or water. For very v i s c o u s f l u i d s , where (3) becomes i n v a l i d , Z l o k a r n i k [18] has proposed a more general r e l a t i o n . Experimental work i n t h i s flow r e g i o n i s i n progress. F i g . 8 compares a few y-values obtained experimentally i n the heat flow c a l o r i m e t e r w i t h the values c a l c u l a t e d from p h y s i c a l p r o p e r t i e s Q.9]. Table I i l l u s t r a t e s the s c a l i n g up procedure. One may conclude from t h i s t a b l e , t h a t r e l i a b l e estimates of heat t r a n s f e r c o e f f i c i e n t s are not only u s e f u l f o r design purposes, but are a l s o a v a l u a b l e c l u e f o r improving heat t r a n s f e r i n e x i s t i n g equipment. We have o f t e n found, p a r t i c u l a r l y i n g l a s s l i n e d v e s s e l s , t h a t poor c i r c u l a t i o n i n the j a c k e t c o n t r i b u t e s more to the o v e r a l l heat t r a n s f e r r e s i s t a n c e than the f i l m of the r e a c t i o n mixture.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

4.

Thermal and Kinetic Design Data

REGENASS

47

'TUT (Watt/m K) 3

2

- calcexp — • • H S0 96 % — A A Glycerol 100% 2

4

• Figure 8. Temperature depend­ 273

323

373

y

423

Table 1 L i q u i d mixture

τ [κ]

(1) Ύ

Reactor-type

' Z

(2)

( 1 )

r

h

r

( 1 )

cale

υ found

organic i n H S0

400

6100 .6 m ,(3)(5) .183 1040 350 150 (7) ±370 ί 40 320 (8) ±2000

nitrobenzene/

380

7100 ±3000

2

AICI

4

3

3

4 m , (3) (6) .153 1090 370 320 ±450 ± 50 3

naphta, aqu.ZnCl^ 330 s o l i d organic

80 (7) 3600 10 m , (3) (5) .134 480 270 ±140 ΐ 30 220 (8) ±1000

caustic fusion

500 ± 200

470

3

4 m , (4) (5) .153 3

77 70 + 30± 30

85

Remarks : (1) S i - U n i t s : watt/nr Κ (2) anchor a t s t a n d a r d i z e d frequency (3) g l a s s l i n e d s t e e l w i t h j a c k e t (4) N i - c l a d s t e e l , outside c o i l s (5) c o o l i n g by c i r c u l a t e d water (6) steam heating (7) before improving c i r c u l a t i o n (8) a f t e r improving c i r c u l a t i o n i n jacket.

American Chemical Society Library "55 16th St., N.W.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS SymposiumWashington, Series; AmericanD.C. Chemical Society: Washington, DC, 1978. 20036

48

CHEMICAL REACTION ENGINEERING—HOUSTON

Conclusions There i s an obvious need f o r thermal a n a l y s i s instruments which are s u i t e d t o the s p e c i f i c requirements of process develop­ ment. The bench-scale c a l o r i m e t e r presented i n t h i s paper i s de­ signed t o f i l l t h i s gap by p r o v i d i n g thermal and k i n e t i c informa­ t i o n i n conjunction with conventional synthetic i n v e s t i g a t i o n s . The r e a c t i o n models obtained from thermal data are as a r u l e v a l i d over a wide range of experimental c o n d i t i o n s and i n g e n e r a l p e r m i t the e l u c i d a t i o n o f the thermal s a f e t y aspects of a reaction. Used as a m i n i - p i l o t - r e a c t o r , the b e n c h - s c a l e - c a l o r i m e t e r i n many cases p r o v i d e s data which permits a d i r e c t scale-up t o p l a n t s c a l e , when c o n v e n t i o n a l means would n e c c e s s i t e a p i l o t stage. Thus, i t i s a powerful reducing c o s t and time Acknowledgment The author i s indebted t o many collègues f o r h e l p , i n p a r t i ­ c u l a r to A. Runser, H.P. Gfrôrer, A. Mauerhofer, Dr. H. M a r t i n , Dr. W. G a u t s c h i , Dr. H. Randegger, Dr. P. F i n c k and Dr. W. Kanert f o r t h e i r c o n t r i b u t i o n t o the design of the c a l o r i m e t e r and t o Dr. H.U. M e i s t e r f o r f r u i t f u l s t i m u l a t i o n and generous support. He i s a l s o o b l i g e d t o P r o f . M. Brenner and t o P r o f . D.W.T. R i p p i n f o r t h e i r support of fundamental work on the method presented.

Nomenclature A p d g h f m Pr q r Re Δτ c

Τ U w Ζ y λ

e f f e c t i v e heat t r a n s f e r area s p e c i f i c heat J kg K diameter (or t h i c k n e s s ) dimensional constant 9.81 ms f i l m heat t r a n s f e r c o e f f i c i e n t Wm -2K -1 frequency (of s t i r r i n g ) s mass (of c a l o r i m e t e r contents) kg P r a n d t l number heat f l o w r a t i o (of frequencies) Reynolds number temperature d i f f e r e n c e (between c a l o r i m e t e r contents and j a c k e t ) r a t e of temperature change o v e r a l l heat t r a n s f e r c o e f f i c i e n t Wm" K e f f e c t i v e heat c a p a c i t y of c a l o r i m e t e r v e s s e l J K " "heat t r a n s f e r p r o p e r t y " of a s t i r r e d tank Wm" K "heat t r a n s f e r p r o p e r t y " of l i q u i d heat c o n d u c t i v i t y Wm V 1 X

Z

±

_ 1

1

2

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

1

1

4. y p

REGENASS

49

Thermal and Kinetic Design Data

dynamic v i s c o s i t y density

kg m s kg m

subscripts : b : b u l k , j : j a c k e t , r : r e a c t o r contents, s: s t i r r e r , w: w a l l Literature cited 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Köhler, W. e tal.,Chem.Ing.Techn. 45 (1973), 1289 M a r t i n , H., Ph. D.Thesis, B a s e l , 1973 Regenass, W., G a u t s c h i , W., M a r t i n , H. and Brenner, Μ., Proc. 4th Int.Conf.Thermal A n a l . 3, 834, Budapest 1974 Hub, L., Ph.D.Thesis, ΕΤΗ, Z u r i c h , 1975 Becker, F. and W a l i s c h , W., Z.Phys.Chem. NF 46 (1965), 279 Swiss Patent 455 32 Regenass, W., Thermochim Wendtland, W.W., "Thermal Methods o f A n a l y s i s " , Wiley, 1974 US-Patent 3 994 164 G a u t s c h i , W., Ph.D.Thesis, ΕΤΗ, Zürich, 1975 Kanert, W., Ph.D.Thesis, B a s e l , 1977 Sestak, J. e tal.,Thermochim. Acta 7 (1973), 335 Becker, F., Chem.Ing.Techn. 40 (1968), 933 C o f f e e , R.D., AIChE-64th-Natl.Meeting (1969), P r e p r i n t 25C Eigenmann, Κ., 2nd Int.Symp. on Loss P r e v e n t i o n (1977) Lütolf, J., Staub, Reinh. L u f t 31/3 (1971), 94 J e h l e , E. and Oeschger, V., Ciba-Geigy, presented a t Dechema Jahrestagung 1968, but never p r i n t e d S l o k a r n i k , Μ., Chem.Ing.Techn. 41 (1969), 1195 G a u t s c h i , W., Ciba-Geigy, unpublished

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

5 Adsorption Studies at Reaction Conditions—Reactor Development and Evaluation for Transient Studies at Millisecond Rates R I C H A R D D. S T O L K *

and A L D R I C H

SYVERSON

Department of Chemical Engineering, Ohio State University, Columbus, OH

43210 The role of adsorptio i heterogeneou catalysi i t easily evaluated becaus sorption and reaction and the difficulty of measuring surface con centrations of reacting species on the catalyst at these conditions. Exploratory research directed toward devising a method for studying adsorption in gas-solid systems by means of a batch adsorber-reactor has been underway in this laboratory for several years. This technique provides an opportunity to examine the "adsorption" and "reaction" steps sequentially at reaction temperatures and pressures. How sharply the individual steps can be separated depends largely upon the magnitude of the differences in rates and upon the data resolution capability of the experimental apparatus. Interpretation of the transient rapid response measurements in terms of steady state operation is needed if these results are to be most useful. Recent studies in this laboratory indicate that this approach holds some promise and it is the purpose of this paper to describe the adsorber-reactor system and its performance capabilities. The most recent design provides rapid gas-solid contact in a constant volume cell with transient rates for temperature and pressure measurements in the millisecond region. Few adsorber-re actors have been devised to measure adsorption at reaction conditions. Winfield (1) described a high speed apparatus for adsorption studies at low pressure. Macarus (2) reported results on a high speed adsorption-reaction apparatus; his data were correlated with fixed bed catalyst studies of Sashihara (3) with encouraging results. The second generation high speed adsorption apparatus was built by Edwards (4) and Keller (5) and improved by Haering (6) in the early 1960's. They overcame many of the previous limitations by first treating and sealing the catalyst sample in a glass capsule which was then placed in the adsorber-reactor containing gaseous reactants at the desired temperature and *Present Address: Monsanto Enviro-Chem Systems, Inc. 800 N. Lindbergh Blvd., St. Louis, Missouri 63166 ©

0-8412-0401-2/78/47-065-050$05.00/0

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

5.

STOLK A N D SYVERSON

Adsorption Studies at Reaction Conditions

51

p r e s s u r e . The r e a c t i o n w a s i n i t i a t e d by c r u s h i n g the c a p s u l e b y remote c o n t r o l u s i n g a feedthrough d e v i c e . T h i s procedure a l l o w e d a pretreatment o f the c a t a l y s t w i t h r e a c t a n t s or products before s e a l i n g the c a p s u l e . For a binary s y s t e m either of the g a s e o u s r e a c t a n t s may be a d s o r b e d by the c a t a l y s t prior to the r e a c t i o n . Pretreating the c a t a l y s t p r o v i d e s some i n s i g h t i n t o the e f f e c t s of m u l t i - c o m p o n e n t a d s o r p t i o n at r e a c t i o n c o n d i t i o n s . The reactor d e s c r i b e d h e r e i n may be c o n s i d e r e d third g e n e r a t i o n . D a t a c o l l e c t i o n w a s f i r s t a c c o m p l i s h e d by r e c o r d i n g the a n a l o g s i g n a l s o n a tape r e c o r d e r . Later a m o d i f i e d P D P - 1 5 d u a l p r o c e s s o r d i g i t a l computer w a s d i r e c t l y c o u p l e d to the reactor i t s e l f . The equipment w a s c o m p l e t e d i n 1971 (7). S i n c e that time others i n c l u d i n g Becher (8), W o l f e (9), and N a s h (10) have u s e d the system for h i g h spee

Reactor D e s i g n Features The primary d e s i g n c o n s i d e r a t i o n w a s the arrangement of r e actor components to i n s u r e r a p i d g a s - s o l i d c o n t a c t . T h e m e a s u r ing d e v i c e s had to be c a p a b l e of operating at high temperature and have m i l l i s e c o n d time c o n s t a n t s . The parameters of i n t e r n a l and c a t a l y s t volume and their ratio are k e y elements i n a constant volume s y s t e m . The i n t e r n a l reactor volume must be m i n i m i z e d . C a t a l y s t volume w a s c h o s e n to c a u s e a d e t e c t a b l e p r e s s u r e change i n the s y s t e m d u r i n g the e x p e r i m e n t . After e v a l u a t i n g s e v e r a l d e s i g n c o n c e p t s to a c h i e v e r a p i d g a s - s o l i d c o n t a c t f o l l o w e d by e f f e c t i v e m i x i n g , a c o m b i n a t i o n " f l y w h e e l / f a n " w a s d e s i g n e d to c r u s h the g l a s s c a p s u l e and to provide gas c i r c u l a t i o n . A n i n c l i n e d grid and s c r e e n were added to separate the c a t a l y s t p a r t i c l e s from the c a p s u l e before c o n t a c t with the f l y w h e e l to reduce a t t r i t i o n . C l e a r p l a s t i c prototypes were b u i l t for e v a l u a t i o n at ambient c o n d i t i o n s . H i g h s p e e d (4000 fps) motion p i c t u r e s permitted o b s e r v a t i o n of a c a p s u l e b e i n g broken i n s i d e the r e a c t o r . E x a m i n a t i o n of the p i c t u r e s showed that g a s - s o l i d m i x i n g was e f f e c t i v e i n the m i l l i s e c o n d range and that v e r y l i t t l e d i s i n t e g r a t i o n of the c a t a l y s t o c c u r r e d . The reactor components and the a s s e m b l e d reactor are shown i n Figure 1 . Components of the reactor i n c l u d e : (1) c a p s u l e h o l d e r , (2) f l y w h e e l , (3) rotary f e e d t h r o u g h , (4) grid and s c r e e n , (5) p r e s s u r e t r a n s d u c e r , and (6) t h e r m o c o u p l e . The i n t e r n a l volume was 415 c c and h e l d a 24 c c c a p s u l e . The reactor w a s made of 304 s t a i n l e s s s t e e l and w e i g h e d about 35 p o u n d s . S p e c i f i c a t i o n s are p r e s e n t e d i n T a b l e 1 d e s c r i b i n g the upper l i m i t s of temperature and pressure for the major c o m p o n e n t s .

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

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CHEMICAL REACTION ENGINEERING—HOUSTON

Figure 1. Adsorber-reactor

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

5.

A.

B.

STOLK A N D SYVERSON

Adsorption Studies at Reaction Conditions

53

T a b l e 1 . S p e c i f i c a t i o n s for the A d s o r b e r - R e a c t o r (1) Rotary Feedthrough 450 C 6Ô"psia (2) Pressure T r a n s d u c e r 485°C 68 p s i a (3) Thermocouple 485 C (4) M a n u a l Feedthrough B e l l o w s 30 p s i a Response Time to a Step C h a n g e (Time Constant) (1) Pressure T r a n s d u c e r 2-3 m i l l i s e c o n d s (2) Thermocouple 2-10 m i l l i s e c o n d s U

The capsule h o l d e r c o n t a i n e d the a c t i v a t e d catalyst i n a s e a l e d g l a s s c a p s u l e at the start of the t e s t . The r e a c t i o n w a s i n i t i a t e d b y m a n u a l l y rotating the holder 180 d e g r e e s r e l e a s i n g the c a p s u l e into the f l y w h e e l . H i g h Speed Pressure T r a n s d u c e r . The c h a r a c t e r i s t i c s of the D a t a m e t r i c s T y p e 531 B a r o c e l p r e s s u r e transducer are shown i n T a b l e g[. It c a n be operated a s a d i f f e r e n t i a l or a b s o l u t e type up to 450 C without c o o l i n g .

A. B. C. D. E.

T a b l e II. C h a r a c t e r i s t i c s of P r e s s u r e Transducer S e n s i n g Element: c a p a c i t i v e potentiometer R i s e T i m e : 2-3 m i l l i s e c o n d s H y s t e r e s i s : L e s s than 0.2% Temperature C o e f f i c i e n t of S e n s i t i v i t y : 0.01% C A c c u r a c y at 7 5 ° C : 0.2% of Reading p l u s 0 . 0 1 % F . S .

H i g h Speed T h e r m o c o u p l e , M i c r o - m i n i a t u r e c h r o m e l - a l u m e l t h e r m o c o u p l e s h a v i n g 0 . 0 0 2 - 0 . 0 1 0 s e c o n d time c o n s t a n t s were p u r c h a s e d from B L H E l e c t r o n i c s / I n c . The thermocouple w i r e i s 0 . 0 0 1 i n c h i n d i a m e t e r . A n a m p l i f i e r w i t h a g a i n up to 1000 w a s u s e d to produce a 10 v o l t s i g n a l . D a t a C o l l e c t i o n and Reduction In the b e g i n n i n g a tape recorder w a s u s e d to record the h i g h s p e e d t r a n s d u c e r d a t a . H o w e v e r , b e c a u s e of h i g h n o i s e l e v e l i n the s y s t e m , the data c o l l e c t i o n w a s i n t e r f a c e d w i t h a m o d i f i e d P D P - 1 5 d u a l p r o c e s s o r d i g i t a l computer. C o m p a r i n g the s i g n a l - t o n o i s e r a t i o for both s c h e m e s , the former h a d a 14:1 ratio w h i l e the latter h a d a 250:1 r a t i o . The p r e c i s i o n h a s been improved from about 10 torr for the tape recorder scheme to 0 . 3 torr for the c o m puter scheme without time a v e r a g i n g the d a t a . The e l e c t r i c a l s i g n a l s from the m e a s u r i n g d e v i c e s were t r a n s mitted v i a s h i e l d e d c a b l e d i r e c t l y into the computer. Internal to

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

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CHEMICAL REACTION ENGINEERING—HOUSTON

the computer, the a n a l o g data were d i g i t i z e d to binary d e c i m a l and f i n a l l y recorded on D E C t a p e . The quantity of gas adsorbed w a s determined from the p r e s s u r e and temperature changes i n the constant volume c e l l . A f a s t r e s p o n s e pressure transducer and thermocouple monitored c o n t i n u o u s l y at a m i l l i s e c o n d f r e q u e n c y p r o v i d e d the b a s i c t r a n s i e n t d a t a . M e a s u r e m e n t of gas c o m p o s i t i o n i n s u c h a r a p i d l y changing s y s t e m i s d i f f i c u l t b e c a u s e of the n e e d to sample at high rates for a n a l y s i s . H o w e v e r , both i n i t i a l and f i n a l c o m p o s i t i o n s may be s a m p l e d when the s y s t e m i s at e q u i l i b r i u m . A p r o v i s i o n w a s made to i n s t a l l a p a i r of f i l a m e n t s for c o n t i n u o u s measurement of the gas thermal c o n d u c t i v i t y but they were not u s e d i n this s t u d y . Computer Program D e s c r i p t i o n ten i n both Fortran IV and M a c r o - 1 5 a s s e m b l e r l a n g u a g e . The p r o gram u s e d to c o l l e c t and store the data was written i n M a c r o - 1 5 language to a l l o w a 1000 c y c l e per s e c o n d s a m p l i n g r a t e . The program c a n sample three data c h a n n e l s , perform time a v e r a g e s , and make other c a l c u l a t i o n s a l l w i t h i n one m i l l i s e c o n d . It "waits" u n t i l the next m i l l i s e c o n d before r e p e a t i n g the c a l c u l a t i o n s and storage of d a t a . F i v e data sets were c o l l e c t e d during the e x p e r i m e n t . Two were at steady state prior to b r e a k i n g the c a p s u l e to evaluate the reactor c o n d i t i o n s . Thirty s e c o n d s of steady state data were c o l l e c t e d at a one s e c o n d f r e q u e n c y . One hundred data p o i n t s w i t h a one m i l l i s e c o n d s e p a r a t i o n were recorded to evaluate the n o i s e l e v e l o n the n o n - t i m e averaged d a t a . The three r e m a i n i n g data sets were a v e r a g e s b a s e d on 16 m i l l i s e c o n d v a l u e s . After the f i r s t s e c o n d of time had b e e n r e c o r d e d with m i l l i s e c o n d data p o i n t s , the s a m p l i n g rate was r e d u c e d to ten p o i n t s per s e c o n d for a ten s e c o n d p e r i o d . It w a s further r e d u c e d to one point per s e c o n d for the r e m a i n i n g p e r i o d . A t o t a l of 6390 data p o i n t s were c o l l e c t e d during the experiment l a s t i n g 15 m i n u t e s . Other computer programs were u s e d to reduce the data to p r e s sure and temperature v a l u e s . The data i n the two steady state data sets were reordered w i t h r e s p e c t to time s i n c e e a c h w a s c o l l e c t e d i n a l o o p w h i c h w a s c o n t i n u o u s l y b e i n g rewritten before the c a p s u l e b r o k e . A time b a s e w a s added to the data before b e i n g transferred to t a p e . Experimental Results In order to i l l u s t r a t e the c a p a b i l i t y of t h i s d e v i c e and p o s s i b l e areas of a p p l i c a t i o n to r e s e a r c h i n c a t a l y s i s , examples of

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

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Adsorption Studies at Reaction Conditions 55

r e s u l t s are reported i n the f o l l o w i n g c a t e g o r i e s : (a) d y n a m i c r e s p o n s e of the s y s t e m to a step p r e s s u r e c h a n g e , (b) a d s o r p t i o n rate s t u d i e s of water o n an a l u m i n a c a t a l y s t , and (c) t y p i c a l a d s o r p t i o n - r e a c t i o n r e s u l t s for c a t a l y t i c dehydration of tertiary butanol on alumina. Pressure R e s p o n s e C h a r a c t e r i s t i c s . A m e c h a n i c a l d e v i c e w a s not u s e d to i n i t i a t e the data c o l l e c t i o n b e c a u s e a f i n i t e time e l a p s e d after the c a p s u l e w a s r e l e a s e d from the holder u n t i l i t c o n t a c t e d the f l y w h e e l ; i n s t e a d a v o l t a g e change o n the t r a n s ­ ducer s i g n a l e q u i v a l e n t to 15 torr w i t h i n 10 m i l l i s e c o n d s w a s found to be the b e s t w a y to start data c o l l e c t i o n . The s y s t e m r e s p o n s e to a step change c a u s e d by b r e a k i n g an empty c a p s u l e under v a c u u m surrounde stants were c a l c u l a t e d for 63.2% r e s p o n s e to the pressure change. T h e v a l u e s of 0 . 9 and 0 . 8 m i l l i s e c o n d s were r e c o r d e d at 13 and 196 C r e s p e c t i v e l y . The r e s p o n s e time of the pressure t r a n s ­ d u c e r w a s adequate for t h i s m e c h a n i c a l s y s t e m and for the water and t - b u t a n o l s t u d i e s o n a l u m i n a . (Prior work showed that a 100 torr p r e s s u r e change o c c u r r e d i n 20-30 m i l l i s e c o n d s after the alumina w a s e x p o s e d to the a d s o r b a t e ) . 0

Transient Adsorption Studies: Water on Alumina. One e i g h t h i n c h a l u m i n a p e l l e t s (Type 100S) s u p p l i e d b y A i r Products C o r p . , Houdry D i v i s i o n were c r u s h e d i n t o s m a l l e r p a r t i c l e s and separated i n t o v a r i o u s f r a c t i o n s from - 1 0 to +200 m e s h . The alumina w a s a c t i v a t e d at 300 C at l e s s than 100 microns pressure for three h o u r s . A l l c a l c u l a t i o n s were b a s e d o n sample weight after activation. A s e r i e s of samples w a s t e s t e d u s i n g the s i z e f r a c t i o n s p r e ­ sented i n Table III. Ad s o r p t i o n - t i m e c u r v e s of t h e s e samples are shown i n Figure 3 .

- M e s h Size 12/20 C a t . W e i g h t (g) 5 . 7 7 5 Initial Conditions Pressure (torr) 787 Temperature ( C)193

20/35 7.421

770 111

20/35 7.936

35/65 7.476

65/100 6.382

784 203

782 196

783 195

F i n a l C o n d i t i o n s After 15 minutes Pressure (torr)

579

357

525

523

545

Temperature ( C) 191 Max-temp. Ob s.( C.)223

114 136

199 227

194 215

193 220

$$ϊ£λ%

( g /g)*0-52 . 1.06 . 0.47 0.51 , 0.54 * m g m / g - m i l l i g r a m m o l e s adsorbed per gram o f c a t a l y s t m

T

m

u

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

56

Figure 2.

System response to pressure change

Figure 3.

Adsorption of water on 100S alumina

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

5.

STOLK A N D SYVERSON

Adsorption Studies at Reaction Conditions

57

The c u r v e s i n Figure 3 i n t e r s e c t the time corrdinate at 1 to 2 m i l l i s e c o n d s . T h i s time l a g a r i s e s b e c a u s e of the w a y the c o m puter c o r r e c t s for the c a p s u l e v o l u m e and sets time zero w h i l e the c a p s u l e i s b r e a k i n g i n the f i r s t two m i l l i s e c o n d s . S i n c e p a r t i c l e s i z e and shape are s i g n i f i c a n t factors i n m a s s transfer c o n s i d e r a t i o n s and the s i z e and shape d i s t r i b u t i o n s w i t h i n a g i v e n mesh s i z e for t h e s e experiments are not known , q u a n t i t a t i v e e v a l u a t i o n o f transport properties may not be m e a n i n g f u l . C e r t a i n l y the p o t e n t i a l for s u c h quantitative measurements seems p o s s i b l e . In a q u a l i t a t i v e s e n s e , the c u r v e s of Figure 3 are i n the order e x p e c t e d i f m a s s transfer were a dominant f a c t o r . A d s o r p t i o n R e a c t i o n S t u d i e s : D e h y d r a t i o n of t - b u t a n o l on A l u m i n a . Previous wor r e s u l t s i n a r r i v i n g at L a n g m u i r - H i n s c h e l w o o d or H o u g e n and W a t s o n type k i n e t i c models ( 2 , 6 , 8 , 1 0 ) w h e n the amount of a d s o r p t i o n at r e a c t i o n c o n d i t i o n s has b e e n d e t e r m i n e d . The t y p i c a l r e s u l t s p r e s e n t e d here repeat some e a r l i e r experiments w i t h , h o w e v e r , a much superior a p p a r a t u s . The b a s i s for t h i s procedure for e v a l u a t i n g the c o n c e n t r a t i o n o f a b s o r b e d s p e c i e s at r e a c t i o n c o n d i t i o n s r e s t s upon b e i n g able to measure a d s o r p t i o n w h i l e a much s l o w e r r e a c t i o n step t a k e s p l a c e . If the study i s to go b e y o n d the a d s o r p t i o n s t e p , the r e a c t i o n must be of the type that p r o d u c e s a change i n p r e s s u r e at c o n s t a n t v o l u m e and temperature. Figure 4 shows portions of a t y p i c a l a d s o r p t i o n r e a c t i o n h i s t o r y for the c a t a l y t i c d e h y d r a t i o n o f t - b u t a n o l on A l u m i n a 100S w h i c h has been treated or " c o n d i t i o n e d " w i t h water (6). The r e a c t i o n w h i c h i s endothermic p r o d u c e s one mole of i s o b u t y l e n e and a mole of water for e a c h mole of t - b u t a n o L The steep d e c r e a s e i n p r e s s u r e during the f i r s t s e c o n d (approximately) w a s c a u s e d by a d s o r p t i o n , then the s l o w r i s e r e s u l t e d from the r e a c t i o n . The ratio of a d s o r p t i o n rate to r e a c t i o n rate for t h i s c a s e w a s about 1700. The temperature r o s e during the f i r s t three s e c o n d s as a r e s u l t of the heat of adsorption then f e l l b e c a u s e of the endothermic r e a c t i o n and heat l o s s to the r e a c t o r . The temperature l a g may be due i n part to the s l o w e r r e s p o n s e of the t h e r m o c o u p l e . The amount of t - b u t a n o l w h i c h w a s measured b y the drop i n p r e s s u r e from the i n i t i a l v a l u e to the minimum i s c o n s i d e r e d to be the a d s o r p t i o n at r e a c t i o n c o n d i t i o n s . The t e c h n i q u e of c o n f i n i n g the c a t a l y s t i n a c a p s u l e permits v a r i o u s treatment or a c t i v a t i o n procedures as w e l l as e x a m i n a t i o n of m u l t i - c o m p o n e n t a d s o r p t i o n e f f e c t s . For a s i n g l e reactant s y s t e m r e a c t i o n products c a n be p r e a d s o r b e d at a known quantity to a s c e r t a i n the e f f e c t t h e s e might have on reactant a d s o r p t i o n and

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

58

CHEMICAL REACTION ENGINEERING—HOUSTON

700 h

Figure 4. Adsorption-reaction pressure transient for catalytic dehydration of tert-butanol

ί 0

I

I

I

I

L

0.2

0.4

0.6

0.8

1.0

Time-seconds

Figure 5.

Effect of water on tert-butanol adsorption

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

5.

STOLK A N D SYVERSON

Adsorption Studies at Reaction Conditions

59

r e a c t i o n r a t e . To a v o i d transport or d e s o r p t i o n the i n i t i a l p a r t i a l p r e s s u r e of the products i n s i d e and o u t s i d e the c a p s u l e c a n be made e q u a l . For r e a c t i o n s w i t h more than one r e a c t a n t , the b i n a r y a d s o r p t i o n e f f e c t s c a n a l s o be m e a s u r e d . Figure 5 shows the e f f e c t o f water o n the adsorption of t - b u t a n o l on 100S a l u m i n a . A i l r u n s i n v o l v i n g t - b u t a n o l (TBA) had about the same i n i t i a l p a r t i a l p r e s s u r e . M o s t adsorption-reaction experiments r e a c h the minimum pressure i n one s e c o n d , hence the time s c a l e for Figure 5 . The top curve r e p r e s e n t s the a d s o r p t i o n of 2:1 mixture of TBA and w a t e r . T h i s curve i s o n l y s l i g h t l y above the TBA c u r v e , w h e r e a s , were the a d s o r p t i o n of the two c o m p o n ents i n d e p e n d e n t , the total a d s o r p t i o n w o u l d be 60-100% higher as c a n be s e e n by adding the two s i n g l e component c u r v e s . The lower curve r e p r e s e n t s th a b s o r b e d water e q u i v a l e n t to a pressure of 208 t o r r . The s u p p r e s s i o n of the a d s o r p t i o n of TBA by preadsorbed water i s i n d e e d substantial. A d s o r p t i o n measurements at r e a c t i o n c o n d i t i o n s have b e e n c o u p l e d w i t h f i x e d b e d k i n e t i c data to arrive at s i m p l e k i n e t i c models w i t h one or two a d j u s t a b l e parameters (2 and 6). In r e c e n t work (10) the a d s o r b e r - r e actor has b e e n u s e d as a b a t c h reactor far o b t a i n i n g k i n e t i c data up to h i g h c o n v e r s i o n s i n a d d i t i o n to i t s u s e as an a d s o r b e r . Conclusions The d e s i g n and experimental r e s u l t s for some t y p i c a l a p p l i c a t i o n s of a h i g h temperature, h i g h speed constant volume a d s o r b e r reactor have b e e n p r e s e n t e d . Preliminary experiments i n d i c a t e that a d s o r p t i o n s t u d i e s c a n p r o v i d e a better i n s i g h t i n t o transport m e c h a n i s m s and the role of a d s o r p t i o n i n heterogeneous c a t a l y s i s thereby a s s i s t i n g the development of i m p r o v e d k i n e t i c models for these complex reactions. Acknowledgement The authors thank P r o f e s s o r E . R . H a e r i n g for h i s h e l p f u l a d v i c e on the t - b u t a n o l k i n e t i c s , Professor J . T . H e i b e l for h i s a s s i s t a n c e o n the computer data a c q u i s i t i o n f a c i l i t i e s and programming and M i c h a e l Kukla for h i s h e l p o n e l e c t r o n i c s . Financial support for f e l l o w s h i p s and g r a n t s - i n - a i d from The A m e r i c a n O i l C o m p a n y , Exxon C o m p a n y , E . I . duPont C o m p a n y , M o n s a n t o C o m p a n y , H e n r y D r e y f u s T e a c h i n g F e l l o w s h i p Program and the C h e m i c a l E n g i n e e r i n g D e v e l o p m e n t Fund are gratefully acknowledged.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

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ENGINEERING—HOUSTON

Literature Cited 1. W i n f i e l d , M.E., Aust. J. of C h e m . , (1953),6, 221. 2. Macarus, D.P., Syverson,A. I&EC Proc. Design Dev, (1966), 5, 397. 3. Sashihara, T.F., Syverson, Α . , I&EC Proc. Design D e v . , (1966),5, 392. 4. Edwards, D.C., M.Sc. Thesis (1961), The Ohio State University, Department of Chemical Engineering. 5. Keller, R.M., M.Sc. Thesis (1962), The Ohio State University, Department of Chemical Engineering. 6. Haering, E.R., Syverson, Α . , (1974). J . of C a t a l y s i s , 3 2 , (3), 396-414. 7. Stolk, R.D., PhD Dissertation (1971) Th Ohi University, Departmen 8. Becher, J.H., PhD. Dissertation, (1972), The Ohio State University, Department of Chemical Engineering. 9. Wolfe, D.B., PhD. Dissertation, (1974), The Ohio State University, Department of Chemical Engineering. 10. Nash, G.L., M.S. Thesis, (1976), The Ohio State University, Department of Chemical Engineering.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

6 Methanation in a Parallel Passage Reactor E . W . DE B R U I J N , W . A . DE JONG, and C . J. VAN DER S P I E G E L Laboratory of Chemical Technology, Delft University of Technology, Delft, The Netherlands

One of the steps i n the process of making SNG via coal g a s i f i ­ cation, the methanation o attention i n recent years of the reaction, the temperature control of methanation reactors is difficult. Among the solutions proposed are the application of p a r a l l e l plate (1) and coated tube (2) reactors. I t i s also possi­ ble to apply recirculation of cold product gas, but when this i s done with conventional fixed-bed reactors the resulting high pres­ sure drop i s a disadvantage. The parallel passage reactor (PPR) recently described i n connection with S h e l l ' s Flue Gas Desulphurization Process (3) does not have this drawback because it contains shallow beds of solid reactant separated from narrow channels by wire screens, the gaseous reactants flowing through the channels with a r e l a t i v e l y low pressure drop. Such reactors could, i n p r i n c i p l e , be applied i n any process i n which large volumes of gas must be treated at minimum pressure drop, provided that sufficient capacity for absorption of the heat of reaction i s available. Ex­ amples of such processes are oxidation reactions, Fischer Tropsch synthesis and, as outlined above, carbon oxide methanation. This paper describes preliminary results of a study on this reactor using the methanation of carbon dioxide i n hydrogen at atmospheric pressure as the test reaction. Moreover, a mathematical model was formulated and used to compare computed conversions with experimental data. The objective of the first phase of this work is to obtain a rough estimate of the a p p l i c a b i l i t y of the PPR for methanation purposes. Experimental The test reaction^ C0 + 4 H CH, + 2 H 0 (ΔΗ° = -164.7 kJ/mole C0 ) 2 2 4 2 r,s 2 has been studied extensively and r e l i a b l e k i n e t i c data are a v a i l ­ able (4_) . Work on the use of this reaction i n studying the tran­ sient behaviour of an adiabatic methanator indicates that i t can be applied as a test reaction between 200 ° and 280 °C, with good o

0

o

© 0-8412-0401-2/78/47-065-063$05.00/0

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

0

64

CHEMICAL REACTION ENGINEERING—HOUSTON

r e s u l t s (5). The k i n e t i c equation used i n the present work i s given i n t a b l e 1, along w i t h the experimental c o n d i t i o n s of the i n i t i a l phase of the work. The set of c o n d i t i o n s being covered i n current work i s a l s o given i n the t a b l e , as w e l l as i n f o r m a t i o n on the i n d u s t r i a l methanation c a t a l y s t a p p l i e d . Table I The r e a c t i o n r a t e i s given by: K exp.(-E /RT)p œ

r

a

^

C02

=

C Q

mol.h

2

1

+

K

C0 pC0 2

.g

2

Experimental c o n d i t i o n s

f i r s t phase

current work

Temperature Concentration Flow T o t a l pressure Reactant

208 0,1 0,0

190 -

°C vol% Nm /h atm. 3

H, 2

224

242

1 C0

H,

2

2

C a t a l y s t : G i r d l e r G-65 Ni/AUO.; NiO/AUO. = 3 : 3 s i z e = 0,35 - 0,42 mm; S = 42,4 m /g; 2

B E T

240

1 - 1 2 CO, C0 ,

w/w;

2

H0 2

particle = 6,6 m /g 2

The equipment used i s s i m i l a r to that of r e f . 4 , except f o r the p a r a l l e l passage r e a c t o r and the gas throug>ut, which i s between 0,1 and 0,5 Nm^/h. I t c o n s i s t s of a feed p r e p a r a t i o n s e c t i o n f o r metering and c o n t r o l l i n g the reactant mixture, the PPR immersed i n a f l u i d i z e d bed thermostat and a s e c t i o n f o r o n - l i n e a n a l y s i s of feed and product gases by gas chromatography. Figure 1 shows a b l o c k diagram. The dimensions of the r e a c t o r are shown i n f i g u r e 2. The two c a t a l y s t beds are f i l l e d w i t h p a r t i c l e s of 0.35-0.42 mm; the bottom and top p a r t s of the beds c o n t a i n i n e r t m a t e r i a l of the same dimensions to ensure that the flow regime i n the channel i s completely e s t a b l i s h e d when the gas reaches the c a t a l y s t beds. Reactor Model Let ζ be the coordinate i n l o n g i t u d i n a l d i r e c t i o n and y i n l a t e r a l d i r e c t i o n and assume that the c o n c e n t r a t i o n changes caused by r e a c t i o n and mass t r a n s p o r t to the c a t a l y s t bed are s i m i l a r to that of f i g u r e 3. I f the flow regime i n the channel i s laminar and the r e a c t o r i s o t h e r m a l , and supposing that mass t r a n s p o r t i n channel screen and c a t a l y s t bed are e n t i r e l y due to d i f f u s i o n , the mass balance f o r the channel reads: ν JC y 9z d 2 y The equation contains the assumption that the d i f f u s i o n can be represented by F i c k ' s law, i n other words that flow due to the volume change by chemical r e a c t i o n can be neglected. Furthermore, a x i a l d i f f u s i o n i s not taken i n t o account. A l s o , the channel i s taken to be wide enough to consider i t as being bounded by two = ] D

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

( 1 )

6.

BRuijN E T A L .

Methanation in a Parallel Passage Reactor

65

vent COo

reactor gas conditioning

H * I GC I gas chromatograph carrier gas p

2

digital integration Figure 1.

6

5

6

Block diagram of a parallel passage reactor

mm lateral cross section

wire screen

gas channel

inert longitudinal cross section catalyst

inert Figure 2.

Dimensions of a parallel passage reactor

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

66

CHEMICAL REACTION

ENGINEERING—HOUSTON

i n f i n i t e l y wide p a r a l l e l p l a t e s . The boundary c o n d i t i o n s

are:

f| = 0 a t y = 0 ( 2 ) ; C = C a t ζ = 0 ( 3 ) ; D-|f - » - | f ^ q

B

=

f

(

a t

y

=

y

( 5 )

a n d

y-ia (4);

8c

V

=

1

a

6

e f f ^ V k y " (y^ >

The d i f f u s i o n c o e f f i c i e n t i n the w i r e screen QD i n eq.4) i s taken to be equal t o the product of the screen p o r o s i l y and the d i f f u ­ s i o n c o e f f i c i e n t i n the gas channel. Boundary c o n d i t i o n (5) must be found by i n t e g r a t i n g the mass balance over the c a t a l y s t bed, which f o r a volume w i t h thickness dy i n the x-z plane reads: eff· f £ - C < V b e d 3y 2 In t h i s equation, r ^ represents the r a t e equation of t a b l e I The e f f e c t i v e d i f f u s i o to the d i f f u s i o n c o e f f i c i e n bed p o r o s i t y and a f a c t o r f o r the t o r t u o s i t y of the d i f f u s i o n path. Both f a c t o r s are assumed t o be 3 according t o r e f . 6^. Assumptions made i n formulating the mass balance over the c a t a l y s t bed are that pore d i f f u s i o n l i m i t a t i o n i n the c a t a l y s t p a r t i c l e s can be neglected over the e n t i r e c o n c e n t r a t i o n range of e x i s t i n g i n the bed ( 5 ) , that the bed i s isothermal and homoge­ neous, and that mass t r a n s p o r t i n the bed i s e n t i r e l y due t o d i f f u ­ s i o n . The boundary c o n d i t i o n s are: B

C = C

at y = y

k

r

k

p

(8) and | | = 0 at y = y

( 7 )

w

(9)

Numerical s o l u t i o n o f the mass balance i n the c a t a l y s t l a y e r i s r e l a t i v e l y simple. However, a complete s o l u t i o n i s superfluous since we are p r i m a r i l y i n t e r e s t e d i n mass transport at Ύ Ύ^Ι t h i s transport can be c a l c u l a t e d i f the f i r s t d e r i v a t i v e of the con­ c e n t r a t i o n i n the y - d i r e c t i o n i s known. I t i s p o s s i b l e t o o b t a i n t h i s d e r i v a t i v e a n a l y t i c a l l y from equation ( 8 ) ; i f t h i s i s done the r e s u l t i s : 3C 2A — = (—Ô(BC - I n (1 + B C ) ) + i n t e g r a t i o n constant ay 2 The i n t e g r a t i o n constant can be determined w i t h boundary c o n d i t i o n (9); i f C i s the c o n c e n t r a t i o n of reactant at the r e a c t o r w a l l one f i n d s : ~ = (^y(BC - I n (1 + BC) - BC + I n (1 + BC ) ) * (10) 0 : | ^ = ν = ω = 0 , Ψ = | dr 0 < r < 1, z = 0

(8)

: ω = 0 , Ψ = \ (1-r ) 2

(9)

2 r = 1, ζ > 0:ϋ = ν = Ψ = | ^ = 0 , ω = ^-4 dr

(10)

In the numerical a n a l y s i s the r a d i a l and a x i a l d e r i v a t i v e s of the p a r a b o l i c equations are replaced by the c e n t r a l d i f f e r e n c e ap­ proximations and the backward d i f f e r e n c e approximations, r e s p e c t i v e ­ l y . Thus N-l s e t s of f i n i t e p a r a b o l i c d i f f e r e n c e equations are ob­ t a i n e d , Ν being the number of r a d i a l steps. The number* of e q u i d i s ­ tant g r i d p o i n t s i n r a d i a l d i r e c t i o n amounted to 40, w h i l e f o r the f i n i t e d i f f e r e n c e increment of ζ(= 2z/Re) a value of 1.25 10"^ was used. D e t a i l s of the numerical s o l u t i o n procedure are given elswhere (J_2). F i g u r e 1 i s a g r a p h i c a l r e p r e s e n t a t i o n of the development of the a x i a l v e l o c i t y obtained by the numerical s o l u t i o n procedure. This r e s u l t agrees q u i t e w e l l w i t h that obtained by Vrentas e t . a l . (11). The Tube Wall Catalyzed Reaction Assuming incompressible flow of a Newtonian f l u i d and no c o n t r i b u t i o n s i n the azimuthal d i r e c t i o n a mass balance f o r a d i f f e r e n t i a l element i n the en­ trance r e g i o n of the tube y i e l d s the f o l l o w i n g steady s t a t e d i ­ mensionless d i f f e r e n t i a l equation: 1^2 + !kp' poison d e p o s i t i o n r a t e constants, d e f i n e d i n eqns. ( 2 ) , (6) and (5) r e s p e c t i v e l y L l e n g t h of m o n o l i t h , 8.1 cm L t o t a l c a t a l y t i c a l l y a c t i v e s i t e s , gmole/cm Leo t o t a l amount t h a t c o u l d be adsorbed at s a t u r a t i o n , gmole/cm t t h i c k n e s s of c a t a l y t i c l a y e r , 0.0025 cm P,P fluid-phase Pecle respectively, P P f l u i d - p h a s e P e c l e t number f o r heat, P r R e [ ( a / 2 ) / L ] , 0.4 Q dimensionless parameter of s o l i d phase c o n d u c t i v i t y , [(2naLkf)/(k S )]«[L/a], 2500 Re Reynolds number, 150 r r a t e of r e a c t i o n gmole/cm sec, a l s o r a d i a l c o o r d i n a t e , cm S e f f e c t i v e s u r f a c e area of c a t a l y t i c l a y e r per volume of c a t a l y t i c l a y e r , cm /cm S c r o s s - s e c t i o n area f o r s o l i d phase, c a t a l y t i c l a y e r p l u s the ceramic r e g i o n , cm t time, sec t» time t o s a t u r a t e a v a i l a b l e s i t e , i f the poison deposited immediately, sec, 2 π a L £ S L » / π a ν c Τ temperature, °K u dimensionless c o n c e n t r a t i o n f o r CO, c o / C 0 0 ν dimensionless temperature, T/T ' w dimensionless c o n c e n t r a t i o n f o r poison p r e c u r s o r , Cp/cç-Q w = 0.0002 ζ a x i a l c o o r d i n a t e , cm

(-AH)CQ

4

2

r

3

λ

2

2

!I

f

s

c

3

v

2

3

c

2

2

v

p f

c

c

0

0

Greek Symbols t h e r m i c i t y parameter f o r CO, [k^Q o ( " ^ ) c O C O o ^ ^ t o l > 0.16 t h e r m i c i t y parameter f o r p o i s o n p r e c u r s o r , [kp,o(-AH) c a>L]/[kT ], 0 a / i , 25 A r r h e n i u s numbers f o r CO o x i d a t i o n and s e l e c t i v e poison d e p o s i t i o n r e s p e c t i v e l y , E / R T , E"/RT d i f f u s i v i t y ratio, D /D dimensionless a x i a l c o o r d i n a t e , z / L unpoisoned f r a c t i o n of a d s o r p t i o n s i t e s , ( l - c / L ) , and (1 - c^/L) r e s p e c t i v e l y f o r n o n - s e l e c t i v e and s e l e c t i v e poisoning dimensionless r a d i a l coordinate f o r f l u i d phase, r/a dimensionless r a d i a l c o o r d i n a t e f o r s o l i d phase, (r-a)/£ dimensionless Jtime, t(Dp C0 0 ^ ( v ^ ^ ) l t and [ (D c )/(LcoS 't )ft f o r s e l e c t i v e and n o n - s e l e c t i v e H

β β"

p

γ e,e

M

C 0

0

|_ § τ

a

if

o

0

ie

w

c

L S

e

2

p e

C 0 > 0

k T

o

C0

Δ ζ θ

c

v

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

œ

10.

Poisoning in Monolithic Catalysts

L E E A N D ARIS

0,0p

poisoning r e s p e c t i v e l y , approx. 0.2t/too T h i e l e moduli f o r CO and poison p r e c u r s o r , i*/kco 0^ ( ^\/kp /D respectively dimensionless a d s o r p t i o n c o e f f i c i e n t , 65.5 y , 0 e x p ( 9 6 1 / T v ) , y o , 0 - > s> ° D

y

0

to

pe

= 0

C 0

CO f ο ρ ps s w 11

121

o

s

04

T

K

C

Subscripts carbon monoxide fluid-phase value reference value, i . e . i n l e t value poison precursor poison p r e c u r s o r a t t h e s o l i d s u r f a c e solid-phase value poison deposited Superscripts poison p r e c u r s o r v a l u e a p p r o p r i a t e t o the c a t a l y t i c cup-mixing v a l u e

surface

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

Butt, J . B . , Adv. Chem. Ser., (1972), 109, 259. Hegedus, L . L . and Petersen, Ε. E.; Chem. Engng. Sci., (1974), 28, 345. Hegedus, L . L., Ind. Eng. Chem. Fundls., (1974), 13, 3, 190. Becker, E. R. and Wei, J., 4th ISCRE, Heidelberg(April 1976). Froment, G. F . and Bischoff, Κ. Β . , Chem. Engng. Sci., (1961), 16, 189. Luss, D. and Erwin, Μ. Α., AIChE J1., (1970), 16, 979. Olson, J . H . , Ind. Eng. Chem. Fundls., (1968), 7, 185. Wei, J., Adv. in Catalysis, (1975), 24, 57. Heck, R. H . , Wei, J., and Katzer, J . R., AIChE J1., (1976), 22, 477. Finlayson, B. A. and Young, L . C., AIChE J1., (1976), 22, 331. Hegedus, L . L., Baron, Κ., J1., Catalysis, (1975), 37, 127. A r i s , R. and Lee, S.-T., Chem. Engng. Sci., i n press. Smith, J . M . , "Models i n Ecology," Cambridge University Press, Cambridge, 1974.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

11 Micromixing Phenomena in Continuous Stirred Reactors Using a Michaelis-Menten Reaction in the Liquid Phase E D U A R D P L A S A R I , R E N É D A V I D , and J A C Q U E S V I L L E R M A U X Laboratoire des Sciences du Génie Chimique, C N R S - E N S I C 1, rue Grandville, 54042 Nancy Cedex, France

Micromixing phenomen work i n recent years. Their importance i s now recognized from both p r a t i c a l and fundamental points of view. In practice, micro­ mixing plays an important role when two streams of reacting fluids are put into contact and react rapidly before achieving perfect mixing on the molecular scale (e.g. combustion and precipitation reactions), or when complex reactions are carried out i n viscous media (e.g. continuous polymerization reactions). On the fundamen­ tal side, the study of coupling between reaction and mixing may y i e l d valuable information on the mechanism of turbulent mixing. In spite of the publication of many papers on the subject, micro­ mixing processes are far from being c l e a r l y understood. In one category of models, micromixing i s described i n the age space. These models are often abstract and they obviously lack a clear physical meaning. In a second category, interaction i s supposed to take place i n the physical space between neighbouring f l u i d aggregates. Three mechanisms have been invoked : 1) Random coalescence processes (1_) characterized by the i n ­ teraction frequency ω±, or the interaction time t j = Ι/ωχ. 2) mass-transfer between one particular aggregate and a bulk made up of a l l other aggregates that are s t a t i s t i c a l l y interacting with i t (2) (3_) (4_) . The parameter i s here a f i c t i t i o u s mass trans­ fer coefficient or i t s reciprocal, the micromixing time t (I.E.M. model). 3) molecular diffusion of species into the aggregates (5_) (, X 3 are mole f r a c t i o n s of ethylene, propylene, and l> 2 hexadiene r e s p e c t i v e l y i s vanadium i o n c o n c e n t r a t i o n ( m i l l i m o l e / l i t e r ) τ i s shear s t r e s s i s volumetric flow Q a, h, Κ and g are d e f i n e d i n the t e x t ±

x

x

Acknowledgement : The author i s g r a t e f u l t o R. L. Turner f o r d i s c u s s i o n s of h i s work on laminar v e l o c i t y d i s t r i b u t i o n s and f o r p o i n t i n g out the method of L. H. Thomas.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

152

CHEMICAL REACTION ENGINEERING—HOUSTON

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

Husain, A. and A. E. Hamielec, CEP Symposium Series (1976) 160 112 Sala, R., F. Valz-Griz and L. Zanderighi, Chemical Eng. S c i . (1974) 29 2205 Wyman, C. E. and L. F. Carter, CEP Symposium Series (1976) 160 1 Ghosh,M., D. W. Foster, J. P. Lenczyk and T. H. Forsyth, CEP Symposium Series (1976) 160 102 Shih, Chi-Kai, Unpublished von Rosenberg, D. V, "Methods for the Numerical Solution of P a r t i a l D i f f e r e n t i a l Equations," P-8, American Elsevier, New York, 1969 Petersen,R. E. A. an Lynn, S. and J. E Lynn, S. AIChE Journal (1977) 23 389

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

13 Comparison of the Performances of Various Fermentors and Selection Criteria J. P. E U Z E N , P. T R A M B O U Z E , and H .

VAN

LANDEGHEM

Institut Francais du Petrole, C . E . D . I . , B.P. 3, 69390,Vernaison, France

For several decade i n d u s t r i a l operation. Systemati bega y years ago, chiefly at the time of the development of processes whose main objective was the production of biomass. Our own research was carried out i n this context, and accompanied the development of fermentation processes using as substrate either hydrocarbons or methanol. Our pre-occupation was to improve the economics of the process : it was therefore necessary to find appliances which could operate with a minimum fermentor volume and low energy consumption. Our criteria of choice were therefore essentially based on biomass productivity (weight of biomass/unit of volume and time) and energy consumption per kg of dry material produced. The acquisition of comparative values for different a p p l i ­ ances i s very difficult. In fact it became apparent that the nature of the s t r a i n and fermentation conditions noticeably affected the conditions of mass transfer and consequently the overall kinetics of the cell growth. A priori oxygen and hydrocarbons are i n the same s i t u a t i o n , that means that mass transfer phenomena between two f l u i d phases will l i m i t free c e l l growth, but we shall see that hydrocarbons have a special behaviour. In fact since 1967, several authors (1_, 2_) have confirmed that the transfer of paraffins was far too rapid to be explained l i k e O2 transfer by a transfer v i a the aqueous phase : diffusion and s o l u b i l i t y coefficients are far too low. In the same way a direct transfer between the c e l l s and the hydrocarbon drops seems highly u n l i k e l y . I t was A.AIBA who i n 1969 ( 2 ) introduced the idea of pseudo-solubility or "accomodation" of the hydrocarbon i n sub-micronic drops. The v a l i d i t y of this idea has been demonstra­ ted on several occasions (3, 4_, _5, 6) which now allows to treat hydrocarbons as a soluble substrate with, however, this p a r t i c u ­ l a r i t y that the value of the saturation constant depends not only on the nature of the s t r a i n but also on the previous history of ©

0-8412-0401-2/78/47-065-153$05.00/0

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

154

CHEMICAL

REACTION

ENGINEERING—HOUSTON

the c u l t u r e . I t has i n f a c t appeared t h a t t h i s accomodation occurs only thanks to the presence i n the c u l t u r e medium of a c e r t a i n number of s t i l l not c l e a r l y i d e n t i f i e d s u r f a c t a n t s . Consequently a l i m i t a t i o n by hydrocarbons i s not more l i k e l y to occur than t h a t of other s o l u b l e s u b s t r a t s , so that i n a w e l l conducted fermentation, oxygen has every chance of being the only growth l i m i t i n g s u b s t r a t e . We know moreover that s u r f a c t a n t substances i n f l u e n c e mass t r a n s f e r s , even g a s - l i q u i d t r a n s f e r s , as a r e s u l t of m o d i f i c a ­ t i o n s of the i n t e r f a c i a l area and of the t r a n s f e r c o e f f i c i e n t (among others ( 7 ) ) . Conclusions which might be drawn on the t r a n s f e r k i n e t i c s from chemical or physico-chemical measurements are t h e r e f o r e suspect, and only d i r e c t compariso f fermentatio r e s u l t g i v e r i s e to v a l i d c o n c l u s i o n s well-known and c o n t r o l l e d however to some experimental r e s u l t s obtained by the o x i d a t i o n of sodium s u l p h i t e method. Experimental Methods. a

) " Oxydation of sodium s u l p h i t e . The method and the physico-chemical c o n s t a n t s , were borrowed from REITH ( 8 ) . b) - Fermentations. The fermentations were c a r r i e d out i n an aqueous n u t r i t i v e medium w i t h o p t i m i z a t i o n f o r the e s s e n t i a l c o n s t i t u e n t s (Ν, Κ, P, o l i g o - e l e m e n t s , v i t a m i n s ) t a k i n g care to a v o i d any d e f i c i e n c y of s o l u b l e s u b s t r a t e s . The carbon source was a η-paraffin commercial cut w i t h 12-20 carbon atoms. The s t r a i n used was a Candida T r o p i c a l i s ; a i r provided the oxygen w h i l e the n i t r o g e n supply and pH c o n t r o l (pH « 3,5) was made by ammonia i n j e c t i o n . Some e v o l u t i o n of the s t r a i n c h a r a c t e r i s t i c s allowed a s m a l l i n c r e a s e of the fermentation temperature i n the l a s t experiments (30 to 35 °C). Experimental R e s u l t s and I n t e r p r e t a t i o n . We were i n t e r e s t e d i n 3 types of fermentors d u r i n g t h i s study : - m e c h a n i c a l l y s t i r r e d fermentors - a i r - l i f t fermentors - loop fermentors. The l a s t - o n e , s t i l l undergoing experimentation w i l l thus only be r e f e r r e d to b r i e f l y . Concerning i n t e r p r e t a t i o n of the r e s u l t s we have adopted the following simplifications : - the oxygen consumption i s of 2 kg/kg of c e l l s - i n our s t i r r i n g c o n d i t i o n s the t r a n s f e r c o e f f i c i e n t k^ w i l l be taken as a constant equal to 1,80 m/h; t h i s approximation has f r e q u e n t l y been confirmed (7^ 8).

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

13.

EUZEN

ET AL.

Fermentor Performance and Selection Criteria

155

a) - M e c h a n i c a l l y s t i r r e d fermentors. F i g u r e 1 shows diagrams of 3 fermentors s t u d i e d . The f l a t - b l a d e t u r b i n e may be surrounded by a c y l i n d e r p i e r c e d w i t h openings between the t u r b i n e s and w i t h s m a l l holes at the l e v e l o f the t u r b i n e s . I t was the v e r s i o n without a c y l i n ­ der which was p r e f e r a b l y used i n the fermentation t e s t s , w h i l e d i f f e r e n t geometries were s t u d i e d more s y s t e m a t i c a l l y by the oxydation of sodium s u l p h i t e . R e s u l t s obtained are summarized i n f i g u r e 2 i n the form suggested by REITH ( 9 ) . The powers and i n t e r f a c i a l areas are thus expressed per u n i t volume of non-expanded l i q u i d phase. The power Ρ i s the sum of the one r e s u l t i n g from the i s o t h e r m i c expansion of the i n j e c t e d gas and the mechanical power absorbed by the l i q u i d phase. The i n t e r f a c i a l area method, o r e l s e c a l c u l a t e d from fermentation r e s u l t s . The f o l l o w i n g comments might be made : - the c y l i n d r i c a l b a f f l e s f i t t e d to provoke a strong shearing a c t i o n at t u r b i n e l e v e l have a negative e f f e c t f o r oxygen t r a n s ­ f e r , and serve no purpose f o r the t r a n s f e r of hydrocarbons,which w i t h a good s t r a i n are p s e u d o - s o l u b i l i z e d by the s u r f a c t a n t s ; - the energy supply i s more e f f i c i e n t l y used i f i t i s provided by a i r , r a t h e r than by s t i r r e r s ; - f o r a g i v e n energy source and f o r a g i v e n s t r a i n the r e s u l t s can be expressed a p p r o x i m a t i v e l y as f o l l o w s : Ζ = P/V L ΚΖ (1) with 0,6 < α < 0,7 100 < Κ < 200 f o r the systems used T

α

A good choice of fermentor should t h e r e f o r e be able to g i v e a Κ v a l u e of a t l e a s t 200 (a = 0,65), which i m p l i e s a k^A v a l u e c a l c u l a t e d as f o l l o w s :

\k = 1,8 * 200 Z

a

= 360 Z

a

1

(h" )

(l

f

)

b) - A i r l i f t fermentors. Two types o f fermentors were used ( f i g . 3 ) . F i v e dimensions, from 60 to 1 900 l i t e r s , were t e s t e d f o r type A. The experimental data ( t a b l e I and f i g u r e s 4 & 6 ) were, once more, c o r r e l a t e d by a law of the form suggested by WANG (J2) A = K Z with 0,6 < α < 0,7 The Κ f a c t o r i s i n f l u e n c e d by the geometry of the system, by operating c o n d i t i o n s , and by the nature of the s t r a i n . Moreover successive s e l e c t i o n s m o d i f i e d the nature o f the s t r a i n between c e r t a i n t e s t s e r i e s on a i r l i f t s . This e x p l a i n s why d i f f e r e n t performances may have been noted on s i m i l a r fermentors. Thus the s t r a i n used i n the type A 850 1 a i r l i f t r e a c t o r i s probably l e s s oxygen demanding, which would b r i n g the value of A down to a l e ­ v e l approwimately 40 % lower (arrows on f i g u r e 4 ) . The outputs being non-ambiguous magnitudes, t a k i n g energy consumption per kg a

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

156

CHEMICAL REACTION ENGINEERING—HOUSTON

Figure 2. Mechanically-stirred fermentors

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

EUZEN ET

foam

AL.

Fermentor Performance and Selection Criteria

breaker

coolant

TYPE

Β

Figure 3. Two types of airlift fermentors

Figure 4. Air lift fermentors

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

cm/s

S

V

3

26

3,5

2,75 -

780

4,20

0,5

0,65

0,58

0,13

0,47

-

3,20

1,5

590

19

0,29

0,33 4,30

800

-

1,40

12,5

0,28

3,2

2,00

370

-

1 ,50

18 590

0,75

1 ,50

278

-

1 ,15 -

-

0,56 0,77

1 ,35

250

-

0,75

9

13,5

0,89

0,17

0,74

333

-

8

0,09

0,65

1 ,55 1 ,80

287

-

1

1 ,33

-

0,41

15

1 ,70

315

-

0,7

8

_

0,26

12

1,55

287

C - LOOP FERMENTOR -

3 300

Type_R

1 900

850

235

160

60

Tyge_A

• 0,4

0,87

3,0

280

55

2,60

2,90

450

5

-

1,42

2,4

79

Β - AIR LIFT

-

1 ,38

2,6

236 220

86

3,60

1 - ε

3,40

Ε kWh/kg02

Energy Consumption

1 ,45

YoV! kg 02/nrh

Product!vi ty XF

1,95

A m2/m3

Interfacial area

450

kW/m3

Mechanical energy fraction (%)

450

(1 000 rev/mi η)

A - MECHANIC AL STIRRING -

1

V

L

Volume

Performances of some fermentors

TABLE I

Symbol s

©

v

Δ

8

8

X X 0 0 0

• •

• • •

of fig. 4, 5

00

13.

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Fermentor Performance and Selection Criteria

159

of oxygen consumed against Ζ = P / V ^ seems more s u i t a b l e . This r e p r e s e n t a t i o n avoids the ambiguity on the 0~ concentra­ t i o n i n the bulk o f the l i q u i d . Indeed, the presence o f hydrocar­ bons i n the medium provokes an important d r i f t on the 0£ measurements w i t h d i s s o l v e d O 2 probes. I f , as a f i r s t approximation, the oxygen p r o d u c t i v i t y π i s p r o p o r t i o n a l t o the i n t e r f a c i a l area π - A = Κ Z (2) we can s t a t e as s p e c i f i c energy consumption a

Ε = Ζ/π = Kj Ζ

1

α

"

(3)

This relationship i s respected ( f i g . 6 ) , and Kj depends on the s t r a i n and on the fermentation system. A l l our previous c o n c l u ­ sions a r e , o f course, confirmed by t h i s r e p r e s e n t a t i o n . I t does c l e a r l y appear t h a t , a Ζ = P / V L i s more worth bulky. The compromise between these two c o n t r a d i c t o r y f a c t o r s which, i n the absence o f other requirements, w i l l go to make up the c r i t e r i a f o r fermentor choice. c) - Loop fermentors. F i g u r e 5 shows the b a s i c designs o f a loop fermentor (10, 11). The important r e c i r c u l a t i o n ensures a good b r o t h homogeneity and permits i n t e r e s t i n g heat and mass t r a n s f e r s . The s o l e o p e r a t i o n a l p o i n t a v a i l a b l e f o r an i n d u s t r i a l p l a n t , i s l o c a t e d c l o s e t o the r e s u l t s observed f o r the other fermentors (fig. 6 ) . Conclusions. Apart from a c e r t a i n number o f requirements, the r e l a t i o n s h i p developed so f a r enable us t o draw some u s e f u l c o n c l u s i o n s r e g a r ­ ding the choice o f the fermentation system and i t s o p e r a t i n g c o n d i t i o n s . I t i s thus that mechanical systems, showing up badly i n f i g u r e s 2 and 6 , are not t o be r e t a i n e d , and t h a t , among a i r l i f t type equipment, a compromise should be sought between r e a c t i o n a l volume and energy consumption. The f a c t o r s on which t h i s compromise might be based are i n f a c t a v a i l a b l e . The h o u r l y cost o f o p e r a t i o n fermentation equipment producing X kg/h o f yeasts might be s t a t e d : c o s t = a X+ aj + a EXY + P Q

2

Q

R

+ P

Where : a^ nutrient price a^ f i x e d expenditure a^ cost o f a i r compression energy ( t a k i n g i n t o account y i e l d ) P cost o f r e a c t o r ( a m o r t i z a t i o n ) Pç cost o f compressor idem R

c

(F/h)

(4)

F/kg o f yeast F/h o f o p e r a t i o n F/kWh F/h of o p e r a t i o n

These two l a t t e r terms could be w r i t t e n as f o l l o w s :

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL

160

REACTION

ENGINEERING—HOUSTON

air out Γ Γ Τ ~ medium in i I | |

j

coolant

® medium in

coolant

k air out

m

medium out

air out

medium out

•βdesaprating pump

Figure 5.

Loop fermentors

Ε kwh/kgO?

Symbols see table I

K,= VL

0.65

(P

^ K,=

_1,0

0,30

V

1

I

,

1 0

Ψ kw Vj. m

3

Figure 6. Final comparison of the various studied fer­ mentors

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

13.

EUZEN

P

R

Fermentor Performance and Selection Criteria

ETAL.

=

(

V L

)

161

supposing the p r i c e o f the r e a c t o r depends on i t s l i q u i d volume

a

a^ a^

C 4 * s p e c i f i c operating cost o f fermentor s p e c i f i c o p e r a t i n g cost o f compressor . Thus the p r i c e o f the yeast i n F/kg would come t o :

p r i c e = a + aj/X + a E Y Q

2

Q

+ a (V )^/X + 3

L

Ύ

Ρ /Χ (F/kg) (5)

For b i g compressors γ i s i n the range of 0.8 t o 1 (13). I f f o r the sake o f s i m p l i c i t y we take γ = 1, we o b t a i n : p r i c e = a + α /Χ + Κ , Υ ^ + α^Ζ^Κα^ χ

Q

owing t o

V

L

= Ρ/Ζ,

Ρ/Χ = E Y

Q

and

X ^.Y^-Z^F/kg^)

Ε = KjZ

.

Then the optimal Ζ v a l u e i s obtained when : Ζ

. opt

Il-a

a

(K-XY a

2 4

1

0

) J

1 +αβ-α

(7)

As we have seen α i s c l o s e to 2/3, w h i l e β i s somewhere between 0,6 and 1. I t can be pointed out that a b i g s i z e fermentor has to be operated w i t h a lower P / V ^ value than a s m a l l s i z e one. We can a l s o see that the optimum P/Vt f o r l a r g e appliances which, i n 1969, was i n the r e g i o n of 1.5 kW/m^, i s tending t o evolve as a r e s u l t o f changes i n r e l a t i v e energy/investment c o s t s , towards l e s s productive u n i t s w i t h a lower s p e c i f i c ener­ gy consumption. An ambiguity does however p e r s i s t f o r a i r l i f t fermentors: the volume which we c a l c u l a t e d above i s a l i q u i d volume. However there i s no means by which, i n these a p p l i a n c e s , we can p r e d i c t and c o n t r o l the expansions. As a r e s u l t , i n i n d u s t r i a l p r a c t i c e , a very high "expansion volume" i s to be expected, w h i l e adapting the gas v e l o c i t y to the foaming p r o p e n s i t i e s o f the c u l t u r e i s an i n s i t u o p e r a t i o n . I t i s t h i s absence o f p r e c i s i o n i n the design stage, i n v o l v i n g as i t does the danger o f a c e r t a i n l a c k of homo­ g e n e i t y , which i s the weak p o i n t o f these a p p l i a n c e s . Loop fermen­ t o r s , e a s i e r to c o n t r o l from t h i s p o i n t of view, could thus represent a step foreward on c o n d i t i o n however that t h e i r u n i t volume and t h e i r energy consumption prove to be c o m p e t i t i v e . I n any case they w i l l always have an advantage i n terms o f the heat t r a n s f e r c o e f f i c i e n t s i n the r e - c i r c u l a t i o n loop. I t should a l s o be noted t h a t the c r i t e r i a of p r o d u c t i v i t y and energy consumption alone are i n s u f f i c i e n t c r i t e r i a on which to base a choice o f fermentor. The importance of m a i n t a i n i n g a homogeneous " b r o t h " c o u l d , i n f a c t , be d e c i s i v e i f , f o r example, the f u n c t i o n i n g were to be d i s t u r b e d by excessive sedimentation or foaming. On the other hand, w h i l e s u b s t r a t e y i e l d depends on

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

162

the fermentor p r o d u c t i v i t y , some o v e r s i m p l i f i c a t i o n has been made i n t h i s study and more experimental work i s needed t o f i n d out the t r u e o v e r a l l optimum f o r the process. In t h i s respect i t must never be f o r g o t t e n t h a t , w h i l e a fermentor i s c e r t a i n l y a chemical r e a c t o r , i t i s a l s o one i n which the presence o f l i v i n g substances d i s t u r b s the t r a d i t i o n a l working of the equipment, i n p a r t i c u l a r as f a r as t r a n s f e r and expansion f a c t o r s are concerned. I t i s t h e r e f o r e o n l y by comparing equipments, i n the presen­ ce o f the s t r a i n whose i n d u s t r i a l use i s being considered, that i t would be p o s s i b l e t o o b t a i n t r u l y r e p r e s e n t a t i v e c o n c l u s i o n s . L i s t o f Symbols A Ε k-^ Ρ Vg X YQ Ζ ε φΜ ΤΓ

i n t e r f a c i a l area nrVnr s p e c i f i c energy consumptio g mass t r a n s f e r c o e f f i c i e n t m/h t o t a l power kW l i q u i d volume i n fermentor m^ s u p e r f i c i a l gas v e l o c i t y cm/s pondéral b r o t h f l o w r a t e kg/h weight oxygen consumed/weight c e l l s produced t o t a l power per u n i t o f l i q u i d volume kW/m l i q u i d volume f r a c t i o n i n fermentor mechanical energy f r a c t i o n % p r o d u c t i v i t y expressed as kg C^/m o f l i q u i d . h

Literature Cited (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

B. ERDSIECK, Thesis, Eindhoven (The Netherlands) (1967) A. AIBA et alii, J. Ferment. Technol, 47, 211 (1969) F. YOSHIDA and alii, Bioeng.& Biotechn, X I I I , 215(1971); i b i d XV, 257 (1973) ; i b i d XVI, 635 (1974) M. CHAKRAVARTY et alii,ibid, XIV, 61 (1972) ; i b i d XVII, 399, (1975) D.A. WHITWORTH et alii,ibid, XV, 649 (1973) G. GOMA et alii, J . Ferment. Technol., 51, 616 (1973) A. BENEDECK et alii, Bioeng.& Biotechn., X I I I , 663 (1971) T. REITH, Thesis, Delft (1968) T. REITH, Brit. Chem. Eng. 15, 1562 (1970) H. ZIEGLER et alii, Bioeng. & Biotechn., XIX, 507 (1977) K. SCHEIER, Chem. Rundschau, 38, 18 (1976) D.I.C. WANG et alii,8e World Petroleum Congress, Panel discussion "Petroleum and Microbiology" P.152(1971) P. LEPRINCE et alii, Manuel d'Evaluation économique de procédés. Ed. Technip. Paris (1976)

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

14 Kinetic Analysis of Unbalanced Bacterial Growth in Temperature Shift T A T S U R O S A W A D A and T E T S U J I C H O H J I Department of Chemical Engineering, Faculty of Technology, Kanazawa University, Kanazawa 920, Japan SIGERU K U N O Department of Biochemistry, School of Medicine, Kanazawa University, Kanazawa 920, Japan

Attempts to assess quantitatively the bacterial growth and their physiological state have long been pursued by many i n v e s t i ­ gators. Bacteria can be cultivated i n a virtually unchanging environment for long periods during which they simply repeat the same cycle of mass increase and d i v i s i o n . Depending on culture conditions, however, a large number of physiological states ex­ ists, each of which is characterized by a particular size and chemical composition of the c e l l s (1, 2). In balanced growth with a sufficient amount of substrate, a simple relationship ex­ i s t s between the growth rate and the average mass or macromolecu­ le content of the cells, and thus the state of the balanced growth can be characterized by either the growth rate or the average mass or macromolecular content. In utilization of microorganisms for sanitary and i n d u s t r i a l purposes, it is d i f f i c u l t to maintain a constant environment for microbial growth. Since a change i n environment results usually i n a change i n the growth rate as well as the size and the chemi­ cal composition of the cells, a plausible conjecture as to the mode of growth i s difficult. We have studied a method to evalu­ ate quantitatively the unbalanced growth i n response to shifts i n environmental condition. For p r a c t i c a l reasons we chose growth temperature for environmental change. Although the cell size and composition were almost independent of the growth temperature i n a given medium containing a sufficient amount of substrate (1), it was found that a shift i n the growth temperature brought changes i n the physiological state i n a medium containing a lower concentration of substrate. In the present communication, we will present the behavior and formular expression of the bacteri­ a l growth i n t h i s unbalanced state. Materials and Methods Organism and Growth Medium. ©

The strain used throughout the

0-8412-0401-2/78/47-065-163$05.00/0

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

164

experiments was Escherichia coli BB. A b a s a l medium contained 0.25 % (NHi ) HP0i , 0.15 % NaCl, and 0.01 % MgSOi^î^O. To t h i s b a s a l medium, v a r i o u s c o n c e n t r a t i o n s o f glucose (maximum 0.5 %) were added. The pH o f t h e media was maintained a t 7.0 throughout the experiment. t

2

+

Experiment i n Batch C u l t u r e . I n a b a t c h c u l t u r e , t h e c e l l c o n c e n t r a t i o n was l e s s than 1 0 c e l l s / m l so t h a t a change i n g l u ­ cose c o n c e n t r a t i o n was n e g l i g i b l e d u r i n g t h e experiments. A t i n ­ t e r v a l s , samples were withdrawn and v i a b l e c e l l s were measured by the double agar l a y e r method. 4

Experiment i n Continuous C u l t u r e . An a l i q u o t o f o v e r n i g h t c u l t u r e was added i n a T-shaped tube (working volume = 100 ml) c o n t a i n i n g 90 ml o f t h the o p t i c a l d e n s i t y at c u l t u r e was poured i n t o a fermentor (working volume = 500 ml) con­ t a i n i n g i*00 ml o f t h e f r e s h medium. A f t e r 5 t o 6 h r s c u l t i v a t i o n , a supply o f t h e medium which contained 0.5 mg/ml glucose and had been s t o r e d i n a r e s e r v o i r was i n i t i a t e d t o s t a r t a continuous run. The schematic diagram o f t h e fermentor i s shownΛη F i g u r e 1. A g i t a t i o n was p r o v i d e d by means o f a magnetic s t i r r e r and a remov­ able b a f f l e . A i r f l o w r a t e was 2 wm. The a i r from t h e compres­ sor was s a t u r a t e d w i t h water vapor by p a s s i n g i t through a humidi­ f i e r t o p r o t e c t e v a p o r a t i o n o f t h e medium. When t h e e f f e c t o f a temperature was s t u d i e d , t h e fermentor was immersed i n a v e s s e l c o n t a i n i n g i s o p r o p y l a l c o h o l and d r y i c e . When t h e temperature o f t h e medium reached t h e d e s i r e d v a l u e , t h e fermentator was q u i c k l y t r a n s f e r r e d i n t o a new water-bath which had been a d j u s t e d t o t h e d e s i r e d temperature. T h i s method made i t p o s s i b l e t o change t h e c u l t u r e temperature w i t h i n one minute. The c o n c e n t r a t i o n o f glucose i n t h e c u l t u r e was determined a c c o r d i n g t o t h e method o f Park and Johnson (3) after centrifugat i o n (3,500 rpm, 5 min) t o remove c e l l s . 9

R e a c t i o n Model The Monod's equation (^_, , which was obtained on t h e b a s i s o f M i c h a e l i s - M e n t e n s equation f o r enzymatic r e a c t i o n , has been one o f t h e most w i d e l y accepted models, f o r a q u a n t i t a t i v e a s s e s s ­ ment o f m i c r o b i a l growth. I f b a c t e r i a are grown i n media i n which excess i n o r g a n i c n u t r i e n t s but a l i m i t i n g amount o f glucose ( c a r ­ bon source) are p r e s e n t , a s p e c i f i c growth r a t e , μ, o f t h e b a c t e ­ r i a i s s p e c i f i e d as a f u n c t i o n o f t h e c o n c e n t r a t i o n , y, o f glucose i n t h e medium, and can be expressed by the f o l l o w i n g Monod s equation: 1

f

y = y where y

m

m

y/(Ks + y )

d)

and K3 are t h e maximum v a l u e o f μ and a s a t u r a t i o n con-

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

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SAWADA ET AL.

Bacterial Growth in Temperature Shift

165

stant ( n u m e r i c a l l y equal t o t h e glucose c o n c e n t r a t i o n a t 1/2 y ) , r e s p e c t i v e l y . I t i s w e l l known t h a t y i s a f u n c t i o n o f tempera­ t u r e . Since Kg i s apparently e q u i v a l e n t t o t h e d i s s o c i a t i o n con­ stant i n t h e Michaelis-Menten s equation, l/Kg appears t o show degree o f u t i l i z a b i l i t y o f s u b s t r a t e by c e l l s and t o be a l s o a f u n c t i o n o f growth temperature. Thus, y and l/Kg may be given by f o l l o w i n g A r r h e n i u s equations. m

m

1

m

1

(2), l/K

Pm = A i exp(-Ei/RT)

s

=A

2

(3)

exp(-E /RT) 2

In our previous study (l), i t was demonstrated t h a t a content of macromolecule, such as DNA, RNA and p r o t e i n , per c e l l was ex­ pressed by an e x p o n e n t i a l f u n c t i o n o f s p e c i f i c growth r a t e : Ci = C

i 0

exp

where C^ i s a content o f macromolecule, i , per c e l l , C±Q i s a con­ t e n t o f macromolecule per c e l l a t t h e zero growth r a t e , and oti i s a f u n c t i o n o f temperature and a gradient i n t h e p l o t s o f l o g a r i t h ­ mic values o f C i against y. The value o f C i o was shown t o be con­ stant and independent o f temperature. From equations ( l ) and (h), Ci/Cio - ( C / C ) i m

i 0

y / ( K

S

+

y

(5)

)

where C ^ i s t h e macromolecular content per c e l l a t t h e maximum growth r a t e , y . Since t h e maximum growth r a t e i s obtained i n t h e presence o f a s u f f i c i e n t amount o f glucose (thus y >> Kg), C i i s a constant r e g a r d l e s s o f growth temperature. However, C i a t a l i ­ m i t i n g c o n c e n t r a t i o n o f glucose may be v a r i e d by growth tempera­ t u r e , unless E value i n equation (3) i s zero. T h i s r e l a t i o n s h i p i s i l l u s t r a t e d i n F i g u r e 2. The s o l i d l i n e s i n t h e f i g u r e r e p r e ­ sent a r e l a t i o n s h i p between y and DNA content per c e l l a t a given temperature c a l c u l a t e d from equation (h). The broken l i n e s i n d i ­ cate a r e l a t i o n s h i p between y and DNA content p e r c e l l a t a given c o n c e n t r a t i o n o f g l u c o s e , and a r e obtained by c a l c u l a t i o n o f equa­ t i o n s ( 1 ) , (3) and ( 5 ) . m

m

2

R e s u l t s and D i s c u s s i o n E f f e c t o f Temperature on \i and Kg» F i g u r e 3 shows t h e r e l a ­ t i o n s h i p between t h e s p e c i f i c growth r a t e and s u b s t r a t e (glucose) c o n c e n t r a t i o n . I n t h e f i g u r e , 1/y has been p l o t t e d against a r e c i p r o c a l o f glucose c o n c e n t r a t i o n s i n media f o r seven d i f f e r e n t growth temperatures. I t i s c l e a r from the equation ( l ) t h a t t h e i n t e r c e p t s on t h e v e r t i c a l a x i s and t h e base l i n e g i v e l / y and - l / K g , r e s p e c t i v e l y , and t h a t both y and Kg are f u n c t i o n s o f temperature. I n F i g u r e k t h e logarithms o f y and Kg are p l o t t e d a g a i n s t l / T . These Arrhenius p l o t s give s t r a i g h t l i n e s , and t h e a c t i v a t i o n energies f o r y and Kg were c a l c u l a t e d from the slopes as 8.51 and 1 5 . 7 kcal/g-mole, r e s p e c t i v e l y . I t i s obvious t h a t m

m

m

9

m

m

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTOIN

166

Feed-

1 2 3 4 5 6

• Effluent

Water-bath Ja Baffle Magneti spi Magnetic stirrer Thermometer

Figure 1.

7

Humidifier

10 Control heater 11 Oriftce

Apparatus for continuous culture

TB

Μβ2 μ%\

TA

MA2

μ

MAI 1

Chr"]

Figure 2. DNA contents per cell as a function of specific growth rate at temperatures Ύ and T . The broken lines represent the relationship at a glucose concentration of y or y,. Α

B

m

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

SAWADA

ET AL.

Bacterial Growth' in Temperature Shift

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

168 the 10

5

e x t r a p o l a t e d p o i n t s o f the l i n e s t o l / T = 0 g i v e Αχ = 7.31 h r " and A = 1.99 10 ml/mg o f equations (2) and ( 3 ) . 1

x

*

1 5

2

R e l a t i o n s h i p between Average DNA Content and μ. I n F i g u r e 5> the DNA content per c e l l was p l o t t e d a g a i n s t μ. The s o l i d l i n e s i n the f i g u r e were c a l c u l a t e d from equations ( l ) , ( 2 ) , (3) and ( 5 ) , u s i n g C D O = ^.1 * 1 0 " m g / c e l l and C = 8.5 * Η Γ mg/cell obtained i n our p r e v i o u s r e p o r t ( l _ ) . The broken l i n e s i n the f i g ­ ure were obtained by c a l c u l a t i o n o f equations ( l ) , (2) and (5). The experimental data were i n agreement w i t h the c a l c u l a t e d v a l u e . As expected from F i g . 2, i t was shown t h a t the DNA content per c e l l was independent o f growth temperature at h i g h e r glucose con­ c e n t r a t i o n s , w h i l e the DNA content decreased w i t h a l o w e r i n g o f the growth temperature a suboptimal c o n c e n t r a t i o n f glucose 1 2

1

2

D m

E f f e c t s o f Temperature S h i f t on Growth i n Batch C u l t u r e . As r e p o r t e d p r e v i o u s l y ( l ) , when the b a c t e r i a are grown i n a s u f f i c i ent amount o f s u b s t r a t e , the b a c t e r i a are capable o f adapting without any l a g t o a sudden change i n growth temperature because the p h y s i o l o g i c a l s t a t e o f the b a c t e r i a i s independent o f growth temperature under t h i s c o n d i t i o n . However, i n an i n s u f f i c i e n t supply o f g l u c o s e , the sudden upward or downward s h i f t i n tempera­ t u r e w i l l cause the b a c t e r i a t o l a g i n adapting t o a new c o n d i ­ t i o n , because the p h y s i o l o g i c a l s t a t e o f the c e l l d i f f e r s by grow­ t h temperature i n t h i s case. When the medium contains a l i m i t i n g amount o f g l u c o s e , y i , p h y s i o l o g i c a l s t a t e s o f t h e b a c t e r i a are B s t a t e at temperature T , and Αχ s t a t e at T^ ( F i g . 2 ) . When the growth temperature o f the steady s t a t e c u l t u r e i s suddenly s h i f t e d from Tg t o T&, the p h y s i o l o g i c a l s t a t e o f t h e c e l l s w i l l move from B t o A and t o A\. S i m i l a r l y a temperature s h i f t from T^ t o T w i l l cause a change i n the p h y s i o l o g i c a l s t a t e from A\ t o Βχ and to B . T h e r e f o r e , a change i n growth r a t e (as measured by c e l l number, N) may occur a f t e r some time l a g i n temperature s h i f t - u p , and an i n i t i a l overshot growth may be observed i n temperature a shift-down. These s i t u a t i o n s are probably s i m i l a r t o those obser­ ved i n s h i f t - u p t o an enriched medium or a shift-down t o a poorer medium (6^). These conjectures were v e r i f i e d i n the s h i f t - u p and shift-down experiment w i t h the batch c u l t u r e , as shown i n F i g u r e 6. Although the temperature s h i f t i n the batch c u l t u r e brought q u a l i t a t i v e l y expected r e s u l t s , i t was d i f f i c u l t t o measure c e l l mass and macromolecule c o n t e n t , because the c e l l d e n s i t y i n the c u l t u r e had t o be kept v e r y low t o m a i n t a i n the c u l t u r e at the f i x e d and much lower c o n c e n t r a t i o n o f glucose. T h e r e f o r e , a con­ tinuous c u l t u r e was c a r r i e d out t o f o l l o w changes i n the p h y s i o l o ­ g i c a l s t a t e o f c e l l s at the temperature s h i f t . 2

B

2

2

B

2

E f f e c t s o f Temperature S h i f t on Growth i n Continuous C u l ­ t u r e . At the steady s t a t e i n the continuous c u l t u r e , the c u l t u r e p o p u l a t i o n d e n s i t y i s maintained c o n s t a n t , and the s p e c i f i c growth r a t e i s equal t o the d i l u t i o n r a t e , D (the i n f l u e n t volume per hr

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

SAW ADA ET AL.

Bacterial Growth in Temperature Shift

Figure 5. Rehtionship between DNA contents per cell and the specific growth rate at various glucose concentrations and temperatures. Solid and broken lines represent the cal­ culated curves at isothermal conditions and those at the same glucose concentrations, respectively.

10.0

274* 37 °C ·'

5.0

!

5.0

2.0^ ο 1.02

% 2.0

H0.5

^ V

(α)

!

> 1 -10

1_,

1

1 2 t Chr]

3

Figure 6. Increment in cell number after a shift in temperature. Filled cir­ cles and open circles show increments in cell number with 0.5 rag/mL and 2 X 10~ mg/mL glucose, respectively, (a) Growth temperature was shifted up from 27°-37°C at t = 0. (b) Growth temperature was shifted down from 37°-27°C att = 0. 4

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

170

per t h e t o t a l volume o f medium i n t h e growth v e s s e l ) . The concen­ t r a t i o n o f glucose (y) i n t h e growth v e s s e l i s a l s o maintained constant i n t h e balance between t h e input and t h e output p l u s con­ sumption by b a c t e r i a . Thus, i t i s p o s s i b l e t o measure c e l l mass and chemical components o f c e l l s i n t h e steady s t a t e c u l t u r e under extremely low glucose c o n c e n t r a t i o n . However, t h e upward o r down­ ward s h i f t i n growth temperature under t h e c o n d i t i o n causes i n e v ­ i t a b l y a change i n t h e consumption r a t e o f glucose by b a c t e r i a as w e l l as a change i n growth r a t e , and t h e r e f o r e i t i s d i f f i c u l t t o maintain the f i x e d c o n c e n t r a t i o n o f glucose i n t h e medium before and a f t e r t h e temperature s h i f t . I f t h e temperature o f t h e steady s t a t e c u l t u r e i s suddenly lowered without changing t h e d i l u t i o n r a t e , the glucose c o n c e n t r a t i o n w i l l i n c r e a s e . And i f t h e s p e c i ­ f i c growth r a t e i s much dilutio concentration w i l l diminis from t h e v e s s e l , and t h e p h y s i o l o g i c a l s t a t e o f b a c t e r i a w i l l f i n a l l y reach t o t h e s t a t e w i t h maximal supply o f glucose at t h a t temperature (e.g. % s t a t e i n F i g . 2 ) . Therefore t h e temperature s h i f t i n the continuous c u l t u r e w i l l cause an unbalanced growth which i s more complicate than t h a t i n t h e batch c u l t u r e . During t h i s unbalanced growth, the net change i n c o n c e n t r a t i o n o f organ­ isms (x) and i n glucose c o n c e n t r a t i o n (y) can be expressed on t h e b a s i s o f Monod s model as f o l l o w s : f

dx/dt = y

m

(6)

χ y / ( K + y) - D χ s

dy/dt = - ( l / n ) y

m

(7)

χ y / ( K + y ) + D ( y - y) s

0

where t i s the time a f t e r t h e s h i f t , η i s a y i e l d c o n v e r s i o n , and y i s a i n f l u e n t s u b s t r a t e c o n c e n t r a t i o n . However, these equa­ t i o n s do not i n v o l v e a proper c o n s i d e r a t i o n o f t h e d i f f e r e n c e s i n the p h y s i o l o g i c a l s t a t e o f c e l l s before and a f t e r t h e temperature s h i f t . F i g . 7 i l l u s t r a t e s t h e experiment i n which t h e steady s t a t e c u l t u r e s w i t h the d i l u t i o n r a t e o f 0.500 h r " (a) and 0.529 hr" (b) were s h i f t e d from 37 t o 27 °C. The f i l l e d and open c i r ­ c l e s i n d i c a t e c e l l mass (measured by o p t i c a l d e n s i t y ) , x, and g l u ­ cose c o n c e n t r a t i o n , y, r e s p e c t i v e l y . The broken curves show t h e time course o f χ and y obtained by c a l c u l a t i o n o f equations (6) and ( 7 ) . I t i s apparent t h a t t h e c a l c u l a t e d curves d e v i a t e enor­ mously from t h e experimental data. These d e v i a t i o n s can probably be a t t r i b u t e d t o time l a g f o r a t t a i n i n g t o t h e new p h y s i o l o g i c a l s t a t e . From t h i s v i e w p o i n t , equations (6) and (7) were m o d i f i e d as f o l l o w s , though the m o d i f i c a t i o n i s e n t i r e l y o u t s i d e t h e scope of p h y s i o l o g i c a l i m p l i c a t i o n . 0

1

1

dx/dt = { t / ( K

L

+ t ) } y χ y / ( K + y) - D χ

dy/dt = - ( l / n ) { t / ( K where

m

L

(8)

s

+ t ) } y χ y / ( K + y) + D ( y - y) m

s

0

(9)

i s a constant. The s o l i d l i n e s i n t h e f i g u r e were ob-

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

14.

SAWADA ET AL.

î

Bacterial Growth in Temperature Shift

ChrJ

171

t Chrl

Figure 7. Time course of cell mass and glucose concentrations after the growth temperature was shifted down from 37 -27°C in the continuous culture at dilution rate = 0.500 hr (a), and 0.529 hr (b). Filled circles and open circles show cell mass and glucose concentrations, respectively. Triangles show the yield to be almost constant after and before the shift. Broken and solid lines represent calculated lines from Equations 6 and 7 and from Equations 8 and 9, respectively. 1

1

Figure 8. Relationship between a difference in DNA content per cell and K L

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

172

t a i n e d by c a l c u l a t i o n o f equations ( 8 ) and (9) as K = 0 . 3 8 h r (a) and 0 . 2 3 h r ( b ) , and show s a t i s f a c t o r y agreement w i t h the data. K L shows a time constant o f delay and should be dependent on a d i f f e r e n c e i n the s t a t e s before and a f t e r the temperature s h i f t . F i g u r e 8 i l l u s t r a t e s the r e l a t i o n s h i p between a d i f f e r e n c e i n DNA content per c e l l and K ^ . ACj) r e p r e s e n t s a d i f f e r e n c e i n DNA content per c e l l b e f o r e and a f t e r the temperature s h i f t . In a steady s t a t e o f b a c t e r i a l growth, the p h y s i o l o g i c a l s t a t e o f c e l l s , such as c e l l mass,, and macromolecular content per c e l l , i s p r i m a r i l y defined by the c u l t u r e medium and i s an expo­ n e n t i a l f u n c t i o n o f the growth r a t e a t a f i x e d temperature. When an environment o f b a c t e r i a l growth i s changed t o another s t a t e , the b a c t e r i a can adapt immediately t o the new environment, p r o v i d ­ ed t h a t the p h y s i o l o g i c a l s t a t e s i n two environmental c o n d i t i o n s are i d e n t i c a l , such as s u f f i c i e n t amount o f n u t r i e n t s t r a n s f e r r e d t o a new c o n d i t i o n i n which a d i f f e r e n t p h y s i o l o g i c a l s t a t e i s g i v e n , they r e q u i r e some time l a g t o accommodate t o t h e new c o n d i t i o n . I n the present i n v e s t i g a t i o n , i t has been shown t h a t a q u a n t i t a t i v e e x p r e s s i o n o f growth was p o s s i b l e w i t h temperature s h i f t s i n a suboptimal n u t r i e n t s u p p l y , by u s i n g t h e parameter K ^ , t h e f u n c t i o n o f the d i f f e r e n c e i n p h y s i o l o g i c a l states. L

Nomenclature Αχ, A = frequency f a c t o r s Cj) = DNA content per c e l l D = d i l u t i o n rate Ε = a c t i v a t i o n energy L» S constants Ν = c e l l number R = gas constant Τ = temperature t = time x, y = c e l l mass and glucose c o n c e n t r a t i o n s α = constant η - yield μ = s p e c i f i c growth r a t e 2

K

K

=

1

[ h r " ] , [ml/mg] [mg/cell] [hr- ] [cal/g-mole] [ h r ] , [mg/ml] [cells/ml] [cal/°K-g-mole] [°K] [hr] [mg/ml] [hr] 1

[ 1

[hr- ]

Literature Cited (1) Chohji, T . , Sawada, T . , and Kuno, S . , Appl. Environ. Microbi­ ol., (1976), 3 1 , 8 6 4 . (2) Schaechter, Μ., Maaløe, O., and Kjeldgaard, N . O., J. gen. M i c r o b i o l . , (1958), 19, 529. (3) Park, J. T . , and Johnson, M. G . , J. Biol. Chem., (1949), 181. 149. (4) Monod, J.; Ann. Rev. M i c r o b i o l . , (1949), 3, 371. (5) Monod, J.; Ann. Inst. Pasteur, (1950), 79, 390. (6) Kjeldgaard, N . O., Maaløe, O., and Schaechter, Μ., J. gen. M i c r o b i o l . , (1958), 19, 607.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

15 Nonisothermal Behavior and Thermal Runaway Phenomena in Chain Addition Copolymerization D O N A L D H . S E B A S T I A N and J O S E P H A. B I E S E N B E R G E R Department of Chemistry and Chemical Engineering, Stevens Institute of Technology, Hoboken, NJ 07030

The condition of therma actors has been characterize tures (dT/dt » 0) and an upward concavity in the temperature profile (d T/dt > 0 ) . When runaway additionally exhibits para­ metric s e n s i t i v i t y i t is termed thermal ignition (IG). Beyond the obvious consequence of large temperature rises and possible i n s t a b i l i t y , RA could cause a sharp reduction in polymer molecu­ lar weight and an increased spread in molecular weight d i s t r i b u ­ tion. 2

2

Runaway Analysis of Polymerizations and Copolymerizations A study of RA in chain polymerizations was undertaken in our laboratories with the aim of developing quantitative c r i t e r i a for predicting the onset of both RA and IG. A modification of Semenov-type dimensional analysis, together with computer simula­ tion and experimentation, have shown (1,2) that 5 independent parameter groupings characterize the thermal behavior of chain homopolymerizations: a,Β,b,ε,εΕ' . The approach of Semenov deals with the thermal energy balance. Putting temperature and concen­ tration in dimensionless form the thermal energy balance for homopolymerization appears as (1) : ι mm 1/2 . = expÎEV/l+T'ï-iiT'-T;) (0 d

The f i r s t term of the RHS of Eq. 1 can be interpreted as the rate of heat generation function while the second term as heat removal. The Semenov technique locates the c r i t i c a l temperature for RA at the point where heat generation and removal are not only equal, but their change with temperature ( i . e . , derivative with respect to Τ ) is also equal. Applying these steps to the generation and removal terms of Eq.l eliminates T',with resulting c r î t e r i a formed as functions of ' a and ε. The effect of the remaining para­ meters was investigated through numerical simulation. The impor­ tant c r i t e r i a for RA is a < 2, and for parametrically sensitive RA, Β > 20 and b > 100. Parameters Β and b are dimensionless 1

©

0-8412-0401-2/78/47-065-173$05.00/0

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

174

groupings appearing i n the monomer and i n i t i a t o r component b a l ­ ances r e s p e c t i v e l y . The a n a l y t i c a l methods employed i n the R A a n a l y s i s o f homop o l y m e r i z a t i o n a r e not immediately a p p l i c a b l e to chain a d d i t i o n c o p o l y m e r i z a t i o n . The e q u i v a l e n t expression to Eq. 1 i s λ 6

+

ηΠ»] exp Ε ^ τ ' / l + Τ

XQ22

M

2

Β

Χ

Ρ

Ε

2 2

Τ

,

/

1

+

T

'

J

1

+

m

o

/ 2

( Q|2 X

H

'

"

+ X

X

G21 ^

R

1

(

T

m

l

'

M

"

2

T

E

X

R

P

1 2

E

]

T

'

(

+

2

T

'

)

The b a s i c k i n e t i c equations f o r chain a d d i t i o n copolymeriza­ t i o n are given i n Table I f o r three t e r m i n a t i o n models: geometric mean (GM), phi f a c t o r (PF) and penultimate e f f e c t (PE). I t i s important to note the symmetr e f f e c t o f choice o f t e r m i n a t i o f u n c t i o n H. A Semenov-type a n a l y s i s cannot be a p p l i e d to Eq. 2 . The presence of four exponential terms w i t h d i f f e r e n t a c t i v a t i o n en­ e r g i e s , and the complicated f u n c t i o n a l form o f H = H/H preclude e x p l i c i t s o l u t i o n f o r a c r i t i c a l T . A more general technique based upon p h y s i c a l i n t e r p r e t a t i o n o f R A parameters has led to c o p o l y m e r i z a t i o n analogs f o r the groupings a,B,b,e and εΕ^. Each such parameter can be expressed as the r a t i o o f a p p r o p r i a t e time constants. While appearing as c o e f f i c i e n t s i n the balances, time constants serve a l s o as i n i t i a l values f o r the balance. For ex­ ample i n E q . l , note that the r e c i p r o c a l of XG» the c h a r a c t e r i s t i c time f o r heat g e n e r a t i o n , i s a l s o the value o f the heat genera­ t i o n f u n c t i o n when dimensionless c o n c e n t r a t i o n s and temperature take on t h e i r i n i t i a l values o f one. The second i n t e r p r e t a t i o n , when a p p l i e d to the generation p o r t i o n o f Eq. 2 , d e f i n e s an over­ a l l AQ f o r c o p o l y m e r i z a t i o n . S i m i l a r a t t a c k on the t o t a l monomer balance y i e l d s an expression f o r A , the c h a r a c t e r i s t i c time f o r monomer decay. In homopolymerization a n a l y s i s ( J j the time constant X j = ελβ i s c r u c i a l to the f o r m u l a t i o n o f runaway parameters a, B,b, ε and εΕ^. I t does not appear e x p l i c i t y i n any o f the d i mensionless balances, but rather i s a consequence of a Semenovtype a n a l y s i s . In the process of t a k i n g the temperature d e r i v a ­ t i v e o f the heat generation f u n c t i o n of Eq. 1 the product E'/XQ 1/eXG a r i s e s . Because t h i s a n a l y s i s could not be a p p l i e c to c o p o l y m e r i z a t i o n , an a l t e r n a t e means was r e q u i r e d . The R A parameter 'a' i s more than a mere by-product o f a Semenov ap­ proach. I t i s the r a t i o of i n i t i a l values o f the temperature de­ r i v a t i v e o f the heat removal and generation f u n c t i o n s o f Eq. 1 . Expressed i n terms o f time constants t h i s r a t i o i s X j/XR, and thus the i n t e r p r e t a t i o n o f X | as the i n i t i a l temperature d e r i v a ­ t i v e o f the heat generation f u n c t i o n serves t o d e f i n e an analog, ^ad f o r copolymer i z a t ion. By making use o f A j i n combination w i t h other o v e r a l l time c o n s t a n t s , a s e t o f R A parameters f o r c o p o l y m e r i z a t i o n corresponding to i t s homopolymerization 1

Q

1

M

ac

=

ac

ac

a c

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

15.

SEBASTIAN AND

BiESENBERGER

Chain Addition Copolymerization

175

counterpart ( 0 , was d e f i n e d . The parameters are given i n Table I I . I t i s important t o note that the homopolymerization c r i t e r i a evolved from combined s e n i - a n a l y t i c a l and numerical s o l u t i o n s t o s p e c i f i c k i n e t i c equations. In t h i s work, p h y s i c a l s i g n i f i c a n c e has been attached t o each parameter i n a manner that permits ex­ tension o f the RA a n a l y s i s , independently o f the k i n e t i c form. The u t i l i t y o f the runaway and s e n s i t i v i t y parameters a,B, and b has been demonstrated through both numerical s i m u l a t i o n and experimentation (3,^0· Numerical s i m u l a t i o n s employed l i t e r a t u r e values f o r the k i n e t i c constants f o r the monomer p a i r s o f StyreneMethyl Methacrylate (SMMA), S t y r e n e - A c r y l o n i t r i l e (SAN) and, Acrylonîtrile-Methyl Methacrylate (ANMMA). P h i - f a c t o r k i n e t i c s were g e n e r a l l y used, however both geometric mean and r e c e n t l y advanced penultimate e f f e c t k i n e t i c (6) tested well Ex periments were confine system, however, the f u l rang composition e x t e n s i v e i n i t i a l r a t e study was performed on t h i s system to de­ velop the k i n e t i c constants needed t o evaluate the runaway para­ meters ( 4 , 5 ) . A convenient way t o i l l u s t r a t e the e f f e c t o f the RA para­ meters i s through the use o f RA boundaries. K i n e t i c constants as­ s o c i a t e d w i t h real polymer systems l i m i t the values o f Β t o a narrow range ( g e n e r a l l y 30 - 60) and t h i s i s above the region where monomer s e n s i t i v i t y e f f e c t s become important. Furthermore, i n i t i a t o r consumption w i t h i t s stronger temperature dependence plays a f a r greater r o l e i n reducing s e n s i t i v i t y than monomer con­ sumption does. T o t a l l y u n r e a l i s t i c values o f i n i t i a t o r concentra­ t i o n (on the order o f 100 m/1) are needed i f monomer s e n s i t i v i t y l i m i t a t i o n s are t o be e x h i b i t e d in the absence o f i n i t i a t o r l i m i ­ t a t i o n s . Thus the most meaningful way t o represent runaway bound­ a r i e s i s t o show acr vs b w i t h other dimensionless groups as con­ stant parameters. D e t a i l e d s t u d i e s o f homopolymerization have i l l u s t r a t e d t h i s dependence (2). What i s noteworthy i s that the copolymer systems f o l l o w the same q u a n t i t a t i v e behavior. Figure 1 shows dimensionless runaway boundaries f o r several copolymer sys­ tems shown along w i t h the a s s o c i a t e d homopolymerization boundary. A l l boundaries are not p e r f e c t l y c o i n c i d e n t due t o the e f f e c t s o f composition d r i f t in the c o p o l y m e r i z a t i o n s . The d e v i a t i o n s are rather small although the d r i f t a s s o c i a t e d w i t h SAN and ANMMA sys­ tems f o r Β = 41 i s s i g n i f i c a n t . In Table III values f o r RA parameters a t the t r a n s i t i o n p o i n t are presented f o r v a r i o u s comonomer-initiator systems. Note that RA parameter 'a c o n s i s t e n t l y takes on values near the expected value o f two when RA occurs. As i n homopolymerizations, the c r i t i c a l value o f 'a' becomes depressed as 'b decreases. This e f f e c t i s a by-product o f the decreasing s e n s i t i v i t y o f the cop o l y m e r i z a t i o n c o r r e c t l y c h a r a c t e r i z e d by the d e c l i n i n g value o f 'b'. Figures 2 and 3 i l l u s t r a t e i n i t i a t o r - l i m i t e d s e n s i t i v i t y more c l e a r l y . At a value o f b = 195 there i s a s h a r p l y defined t r a n s i t i o n from non-runaway t o runaway behavior, and t h i s i s 1

1

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION

176

TABLE

ENGINEERING—HOUSTO

I

RATE FUNCTIONS AND BALANCES FOR COPOLYMER IZATI ON

Balance Ini

equations

tiator

dim ] 7^

=

dt

Κ >L

d

ο

J

Co-monorners

dim J —dt

-

R

dt

p

pl2

d

d M dt

Thermal

P

C

m

i

]

d

[

m

2 dt

dt

]

energy

P£

= Σ Σ

(

i

j

"

[ -

"

where

C

p22

I

a

H

Û H

n

k

-

Δ

p n

k

k

22 p22

( u / t ) ( T

ν ν ι -

l

p Z l h

k

2

"

(

H

' .2

+

4

2

p l

-

ν

H

21

t

2t'"2l ]

m

)

k

k

p 2 p21

[

I

o

]

'»" /2

m

,

H

m

2

)

(U/t)(T

"V

= y/A w

Rate

functions for

propagation 1/2

Rp-11 ii =

R

pl2

"

k

ii

k

pll

o» U ^

p21 \

k

t

2

k

n

t

2

I K ] [ m J°

^ 1 2 ^ 2 l / r ^ til

1 / 2

1

2 /

[m^tm^tmj

H

1

/

2

H

-

R

p 2 1

t22^ 1/2

V 2

-

%n^2k-T-) ^ tl! k

WV » 2

k

t22j

and H is :

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

SÉBASTIAN

for

Copolymerization

g e o m e t r i c mean (GM) model

k

[ m

p21 l

(k for

Chain Addition

BiESENBERGER

AND

phi f a c t o r

t22

3

p!2

)T72

l

J

2 ΓΪ72

~tir

(PF) model

_,2 (k )

2\-1/2 k

2φ

Ï72

p2^Pl2

penultimate

(k

effect

k

[

p21 "l

(k

(22

m

l

]

[

m

2

k

] +

172

t M

for

[

k

t22 tl1

[m

p12 2

]

(kt l T J / 2

]

(PE) model

]

) 1/2

J

k

[m

r

3

pl2 2 T72

1/2

2 U [m

fei « [m

+

r [m J 2

2

]

+ [m^

TABLE II

E

(E

Bi

i l T l l 12T12 Y

+

E

*J_ ad A

VT21 * 2 2 W ~ i f j

E

+

E

-1 -1 -1 -1 3H -1 îl GU + 12G12 * 12621 + 22622* * W G -1 < mll ml2 m21 m22 > X

E

j -1 r il Gll E

X

X

+

E

+

X

+

X

E

X

+

X

A

X

-1 -1 -1 12G12 * 12G21 22G22

E

X

E

X

+

E

X

)

3H +

-1 -1 * h 6U * J2G12 * 12G21 * 22G22 H -1 -1 -1 -1 G11 G12 G21 G22 E

"ad

+

Y

X

bi

-1

DIMENSIONLESS RUNAWAY PARAMETERS

ad

X

E

A

X

E

X

X

E

A

X

X

~

Λ

-1 ) Gj1 X

m

3Τ·

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

178

Δ "

Δ 5

ο

ο

ο Br 41 e=0.025 Δ .26 S A N

10

2

10

3

10

4

10

5

b Figure 1.

Simulated RA boundary for two copolymer systems

TABLE

πι

SIMULATION RESULTS Τ

System

ο

Β

u/t

Wo

Ε'

b

a

RA

c a l / c e s e c °K

mol/1

°K 1.57 x Ι Ο " 1.55

5

45

28.6

300

2.025 1.998

No Yes

1.61 χ Ι Ο " 1.60

2

45

23.5

300

1.998 1.985

No Yes

8.99 χ Ι Ο " 8.88

6

45

31.3

300

2.075 2.05

No Yes

ϊ.54 χ ΙΟ" 1.52

6

45

33.5

300

2.05 2.026

No Yes

.05

1.04 χ ί ο " 1.03

2

36

30

400

1.985 1.975

No Yes

.025

4.86 χ Ι Ο " 4.82

3

136

1.915 1.90

No Yes

.01

3.01 χ Ι Ο 2.97

86

1.875 1.85

No Yes

.10

3.55 χ ί ο " 3.49

2

42

1.77 1.74

No Yes

.05

2.37 χ Ι Ο " 2.34

2

30

1.67 1.65

No Yes

1

.2

322

.8

378

.2

318

1.21 χ 10"

.8

306

7.44 χ ίο"**

S/AN/DTBP

.7

403

S/AN/BP

.7

373

AN/MMA/BP

S/MMA/BP

S/AN/AIBN

.7

373

1.33 x ίο" »

• 119

3

1

3

36.0

28.0

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

SÉBASTIAN A N D

1

BiESENBERGER

3

Figure 2.

Chain Addition Copolymerization

5 •Med

7

9

RA transition, b = 195

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

180

CHEMICAL REACTION ENGINEERING—HOUSTON

c a u s e d by a 0 . 3 % change i n ' a . When b i s d e c r e a s e d t o 30 t h e RA p o i n t i s not c l e a r l y d e f i n e d . A continuous spectrum of p r o f i l e s f i l l s the t r a n s i t i o n r e g i o n . Changes i n p a r a m e t e r ' a a r e an o r d e r o f magnitude g r e a t e r than i n the p r e v i o u s case t o b r i n g a b o u t s i m i l a r changes i n t h e t h e r m a l h i s t o r i e s . In a d d i t i o n , t h e v a l u e o f 'a' i n t h e r e g i o n o f t r a n s i t i o n has been s i g n i f i c a n t l y d e c r e a s e d f r o m t h e n o m i n a l v a l u e o f two. 1

1

The

Copolymer

Approximate

Form

(CPAF)

The f a c t t h a t c o p o l y m e r and homopolymer runaway e n v e l o p s a g r e e d b o t h q u a l i t a t i v e l y and q u a n t i t a t i v e l y s u g g e s t s t h a t perhaps c o m p l e x c o p o l y m e r i z a t i o n k i n e t i c s m i g h t be s u c c e s s f u l l y a p p r o x i ­ mated by s i m p l e r k i n e t i c s , s i m i l a r t o t h e homopolymer f o r m . I t is p r o p o s e d t h a t be r e p l a c i n parameter i t h homopolyme balance by t h e i r c o p o l y m e r a n a l o g s AQ, and ε = A J / A Q r e s p e c t i v e l y them we w i l l o b t a i n c o n v e r s i o n and t h e r m a l h i s t o r i e s t h a t match the h i s t o r i e s o f t h e e x a c t k i n e t i c f o r m . I n d e e d , t h i s was t h e case. Thus Eq. 2 w o u l d be a p p r o x i m a t e d by t h e f a r s i m p l e r f o r m : 3C

dT« ^

-1 = A

G

Ε'

1/2

Λ

mm

o

Τ'

exp

1 -

^

, , (Τ τ

τ

,ν

T ) R

(3)

I n d e e d , i t c a n be shown t h a t i f c o n c e n t r a t i o n changes a r e n o t con­ s i d e r e d , the r e m a i n i n g t e m p e r a t u r e dependent p o r t i o n o f Eqs. 2 and 3 a r e n u m e r i c a l l y e q u i v a l e n t . Under i s o t h e r m a l c o n d i t i o n s th< c o n v e r s i o n h i s t o r i e s match p r o v i d e d t h a t one o f t h e comonomers i s not exhausted p r i o r t o the c o m p l e t i o n o f the r e a c t i o n . Under noni s o t h e r m a l c o n d i t i o n s , c o m p o s i t i o n d r i f t i n f l u e n c e s the agreement between t h e two f o r m s . When d r i f t i s t o w a r d s t h e more r e a c t i v e comonomer, t h e a p p r o x i m a t e f o r m u n d e r e s t i m a t e s t h e t h e r m a l t r a j e c ­ t o r y (See F i g . 4 ) . C o n v e r s e l y , when d r i f t i s t o w a r d s t h e l e s s re­ a c t i v e o f the p a i r , the approximate form o v e r e s t i m a t e s the t r a j e c ­ tory. S i m i l a r b e h a v i o r i s n o t e d i n t h e RA b o u n d a r i e s o f F i g . 1. P o i n t s f o r t h e SAN s y s t e m l i e a b o v e t h e homopolymer b o u n d a r y , and d r i f t i s t o w a r d s h i g h AN c o n t e n t c o m p o s i t i o n s . P o i n t s f o r t h e ANMMA b o u n d a r y l i e b e l o w t h e homopolymer b o u n d a r y , and d r i f t i s t o w a r d s t h e l e s s r e a c t i v e o f t h e p a i r , MMA. As c o n d i t i o n s become e i t h e r more a d i a b a t i c o r more i s o t h e r m , s p r e a d between t h e forms narrows. The p o o r e s t a g r e e m e n t o f t h e forms o c c u r s a t t h e p a r a m e t r i c a l l y s e n s i t i v e p o i n t o f t h e RA t r a n s i t i o n . E x p e r i m e n t a l T e s t s o f t h e Runaway

Parameters

The SAN c o p o l y m e r s y s t e m was c h o s e n f o r e x p e r i m e n t a l s t u d y due t o i t s g r o w i n g i n d u s t r i a l i m p o r t a n c e . T h e r e i s a l a c k o f pub­ l i s h e d r a t e d a t a f o r t h i s s y s t e m , as w e l l as b r o a d d i s a g r e e m e n t among t h e d a t a r e p o r t e d f o r h o m o p o l y m e r i z a t i o n o f AN. Without k i n e t i c d a t a t h e r e w o u l d be no way t o e v a l u a t e t h e d i m e n s i o n l e s s parameters a s s o c i a t e d w i t h experimental runs. T h e r e f o r e c o p o l y m e r i z a t i o n k i n e t i c s t u d i e s were conducted v i a the t e c h n i q u e o f D i f f e r e n t i a l S c a n n i n g C a l o r i m e t r y , w h i c h had p r e v i o u s l y been used

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

15.

SEBASTIAN A N D

BiESENBERGER

Chain Addition Copolymerization

181

by o t h e r s f o r homopolymerîzation s t u d i e s . The c o p o l y m e r a p p r o x i ­ mate k i n e t i c f o r m (CPAF) p r o v i d e d t h e means f o r s e p a r a t i n g r e ­ a c t i o n r a t e f r o m h e a t o f r e a c t i o n r e q u i r e d by t h e u s e o f t h i s technique. I t s h o u l d be n o t e d t h a t under i n i t i a l c o n d i t i o n s t h e e x a c t and a p p r o x i m a t e k i n e t i c forms a r e n u m e r i c a l l y e q u i v a l e n t , t h u s t h e r e i s no e r r o r i n v o l v e d i n a p p l y i n g t h e a p p r o x i m a t e f o r m to i n i t i a l r a t e s t u d i e s . The i n i t i a l r a t e s f o r SAN s y s t e m s w i t h s t y r e n e c o n t e n t o f t e n to n i n e t y mole p e r c e n t were d e t e r m i n e d w i t h b o t h b e n z o y l p e r o x i d e and azo-bîs-îsobutyronîtrîle i n i t i a t o r s . T h e s e r a t e s were used t o c a l c u l a t e t h e t e r m i n a t i o n p a r a m e t e r s f o r b o t h PF and PE models o f c o p o l y m e r t e r m i n a t i o n . No s i n g l e , c o m p o s i t i o n - i n d e p e n d e n t value of t h e PF a d e q u a t e l y f i t t h e i n i t i a l r a t e d a t a . The PE model p r o ­ v i d e d f a i r a g r e e m e n t . H i g h s t y r e n e c o n t e n t c o p o l y m e r s showed t h e widest scatter i n the average value o f the P q u a l i t a t i v e l y h i g h e r r a t e s t h a n t h e PE m o d e l . E x p e r i m e n t a l s t u d i e s o f t h e r m a l runaway i n t h e homopolymerîz a t i o n o f s t y r e n e have been c o n d u c t e d i n t h e s e l a b o r a t o r i e s . The Thermal I g n i t i o n P o i n t A p p a r a t u s (TIPA) d e v e l o p e d f o r t h i s work (7) was u s e d f o r t h e e x p e r i m e n t a l s t u d y o f runaway i n SAN c o p o l y ­ merization. The c o m p o s i t i o n s o f 90, 80, 70, 60, 40, and 20% s t y r e n e were p r o v o k e d f r o m non-runaway t o runaway c o n d i t i o n s a t t h e f e e d t e m p e r a t u r e o f 373°K by m a n i p u l a t i n g t h e i n i t i a l c o n c e n ­ t r a t i o n o f i n i t i a t o r a z o - b i s . The 90, 80, and 70% c o m p o s i t i o n s were a l s o t e s t e d a t 363°K and t h e 70% c o m p o s i t i o n was t e s t e d w i t h benzoyl peroxide as i n i t i a t o r . ( F u r t h e r m o r e , an i g n i t i o n e n v e b p e o f T v s [ l ] was c o n s t r u c t e d f o r t h e 70% SAN s y s t e m i n i t i a t e d by b e n z o y l p e r o x i d e ) (k). V a l u e s o f t h e runaway p a r a m e t e r s a,B, and b f o r t h e e x p e r i ­ m e n t a l RA t r a n s i t i o n s u s i n g e a c h o f t h e t h r e e p o p u l a r t e r m i n a t i o n mechanisms, a r e p r e s e n t e d i n T a b l e IV. They r e f l e c t t h e t r e n d s ob­ s e r v e d i n t h e b e h a v i o r o f t h e e x p e r i m e n t a l r u n s . A l l RA's were o f t h e t y p e c l a s s i f i e d a s n o n - s e n s i t i v e . The v a l u e s o f p a r a m e t e r b c l e a r l y a r e i n agreement w i t h t h i s o b s e r v a t i o n . L o w e r i n g f e e d t e m p e r a t u r e r e s u l t e d i n h e i g h t e n e d s e n s i t i v i t y , and a g a i n an i n ­ c r e a s e d v a l u e o f b i s i n agreement w i t h t h i s o b s e r v a t i o n . Figjres 5 and 6 i l l u s t r a t e t h i s b e h a v i o r f o r 80% SAN a t 363°K and 373°K respectively. They a r e c o m p u t e r g r a p h s o f e x p e r i m e n t a l d a t a w h i c h are not c u r v e - f i t t e d , but r a t h e r a r e p o i n t - t o - p o i n t connect ions o f t h e d a t a . The c u r v e s i n b o t h f i g u r e s a p p e a r v e r y s i m i l a r t o t h e n o n - s e n s i t i v e t r a n s i t i o n i n F i g . 3 o b t a i n e d from n u m e r i c a l s i m u ­ lation. The p a r a m e t e r s i n T a b l e IV r e f l e c t t h e d e c r e a s e i n s e n ­ s i t i v i t y c a u s e d by i n c r e a s e d t e m p e r a t u r e . As c h a r a c t e r i z e d by *b' t h e e f f e c t o f t e m p e r a t u r e on t h e r a t e o f i n i t i a t i o n îs r e s p o n s i b l e f o r t h e d e c r e a s e d s e n s i t i v i t y a s i n i t i a l t e m p e r a t u r e r i s e s (4). A t a c o n s t a n t i n i t i a t o r l e v e l , runaway c a n be c a u s e d by m a n i ­ p u l a t i n g t h e i n i t i a l s t y r e n e c o n t e n t . With i n i t i a l i n i t i a t o r con­ c e n t r a t i o n f i x e d a t 0.03 m/1 and i n i t i a l t e m p e r a t u r e T = 373°K, r u n n i n g t h e r a n g e o f c o m p o s i t i o n s from 90 t o 20% c a u s e s t h e o n s e t 0

0

Q

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

182

CHEMICAL

REACTION

ENGINEERING—HOUSTON

S A N BP (*,)o

[ilç τ .0734 383 β* 35.6 26.7 β

0.60 b

195

exact —

1

5

3

Figure 4.

7

TABLE

IV

PARAMETERS FOR EXPERIMENTAL RUNS

GM Τ ο .9

SAN/AIBN

363 373

.8

SAN/AIBN

363 373

.7

SAN/AIBN

363 373

.6 .4 .2

SAN/AIBN

SAN/A IBN

SAN/AIBN

373 373 373

9

Exact and Cpaf nonisothermal histories, 60% SAN

DIMENSI0NLESS

System

approx

PF

PE

a

Β

b

a

B

b

a

B

b

Typ

0.87 0.79

35 35

34

0.94 0.86

36 36

31 32

0 98 0 89

34 34

30

N R

0.71 0,58

33 33

16

.05

0.75 0.62

34 34

15 16

0 79 0 65

32 32

.05 .06

0.80 0.76

36 36

30 34

0.94

38 38

26 29

0 99 0 94

34 34

24

0.89

27

N R

.015 .02

0.80 0.64

35 35

12

0.91 0.73

36 36

10 11

1 00 0 80

33 33

9 10

N R

.0425 .05

1.03 0.87

39 39

44

1.37 1.Ί4

42 42

33 35

1 41

N

1 19

36 36

32

45

33

R

.015 .0175

0.95 0.57

36 36

11 16

0.85 0.71

38 38

12

33 33

10 11

N

13

0 95 0 78

.0075 .01

0.72

12 14

0.98

42 42

9 11

1 .12 0 .97

34 34

8

0.63

39 39

N R

.0035 .005

0.71 0.69

44 44

12 16

1.19 1.18

49

7 9

1 .44 1 .39

34 34

6 8

N

49

.0035 .005

0.55 0.39

51 51

17 19

1.32 0.92

57 57

7 8

1 .99 1 .44

27 27

4

N

5

R

Mo .09

.04

35 17

13

0.85

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

31 14 15

9

N R

R

R

SÉBASTIAN A N D

BiESENBERGER

Chain Addition Copolymerization

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

184

CHEMICAL REACTION ENGINEERING—HOUSTON

o f RA a t t h e 80% l e v e l . I t s h o u l d be n o t e d t h a t t h e v a l u e s o f 'a' a s s o c i a t e d w i t h e x p e r i m e n t a l RA t r a n s i t i o n s a r e somewhat l o w . The e x t r e m e l y i n ­ s e n s i t i v e n a t u r e o f t h e r e a c t i o n s would depress t h e v a l u e o f a consîderably. S c a t t e r i n t h e d a t a used t o d e t e r m i n e t h e p a r a ­ m e t e r s f o r t e r m i n a t i o n was s u f f i c i e n t t h a t i n o r d e r t o f i t t h e e n t i r e r a n g e o f c o m p o s i t i o n s w i t h a s i n g l e m o d e l , e r r o r was i n ­ troduced i n the r a t e s . The c r i t i c a l v a l u e s o f ' a ' s h o u l d l i e more i n t h e v i c i n i t y o f 1.4 t h a n 1.0. A l t h o u g h t h e r e i s an o f f ­ s e t i t i s important t o note t h a t t h e e x p e r i m e n t a l systems respond i n t h e same manner as t h e p a r a m e t e r s p r e d i c t . When e x p e r i m e n t s i n d i c a t e d e c r e a s i n g s e n s i t i v i t y t h e p a r a m e t e r s change i n t h e same direction. When t h e e x p e r i m e n t s show t h e r m a l t r a j e c t o r i e s be­ coming i n c r e a s i n g l y more non-îsothermal t h e parameter 'a' de creases accordingly. The p a r a m e t e r s see i s o b s e r v e d , and t h u s RA t r a n s i t i o n w o u l d be p r e d i c t e d a t l o w e r values of T f o r a given [ l ] . C e r t a i n l y , the results using the k i n e t i c constants developed s a t i s f y t h e engineering accuracy ex­ p e c t e d o f them. The s t r o n g q u a l i t a t i v e agreement s u g g e s t s t h a t more p r e c i s e d e t e r m i n a t i o n s w o u l d c a u s e p r e d i c t i o n s and e x p e r i m e n ­ t a t i o n t o merge. F u r t h e r m o r e , t h e c r i t e r i a w e r e f o r m u l a t e d i n such a way t h a t s h o u l d a more a p p r o p r i a t e t e r m i n a t i o n mechanism be d e t e r m i n e d o r s h o u l d t h e h e t e r o g e n e o u s k i n e t i c mechanism o f a c r y l o n i t r i l e p o l y m e r i z a t i o n and acrylonitrîle - r i c h c o p o l y m e r i z a t i o n be s u c c e s s f u l l y m o d e l l e d , t h e r e s u l t i n g p a r a m e t e r s c o u l d be e a s i l y adapted. c

Q

r

Q

Symbol s a

=

b,B

=

Cp Ε E

= = =

ε jk

= =

f H AHjk

= = =

I k I

= = =

1

E

m. J

=

R-A p a r a m e t e r d e f i n e d i n r e f e r e n c e 1 f o r h o m o p o l y m e r i z a t i o n s and T a b l e M l f o r c o p o l y m e r î z a t i o n s IG p a r a m e t e r s d e f i n e d i n r e f e r e n c e 1 f o r h o m o p o l y m e r i z a t i o n s and T a b l e M l f o r copolymerîzatîons s p e c i f i c heat a c t i v a t i o n energy (with a p p r o p r i a t e s u b s c r i p t ) E/RgT = d i m e n s i o n l e s s a c t i v a t i o n e n e r g y ( w i t h a p p r o ­ priate subscript) Ι/Ε' ( p j k ' Epiu) 1/2 ( E " E - j - E ) = Ekj f o r copoly­ mer ιzation initiator efficiency factor a f u n c t i o n defined i n Table I h e a t o f r e a c t i o n between f r e e r a d i c a l w i t h end u n i t j and monomer k free-radical initiator reaction rate constant heat t r a n s f e r l e n g t h = V/A , r e a c t o r volume/wetted heat t r a n s f e r area comonomer j o r d i m e n s i o n l e s s c o n c e n t r a t i o n o f comonomer j , [mj]/[mj] Q

E

+

d

tJ

TN

w

0

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

15.

SEBASTIAN A N D

m

=

Chain Addition Copolymerization

BiESENBERGER

185

I n i t i a t i n g species or dimensionless concentration of i n i t i a t i n g s p e c i e s , [ m ] / [ m ] ; for i n i t i a t o r s used i n t h i s s t u d y , I -*· 2m r e a c t i o n r a t e p o i n t f u n c t i o n w i t h u n i t s moles/volume/time (and w i t h a p p r o p r i a t e s u b s c r i p t s ) u n i v e r s a l gas c o n s t a n t t e m p e r a t u r e (K) ( Τ - To)/To time o v e r a l l heat t r a n s f e r c o e f f i c i e n t mole f r a c t i o n o f comonomer j time c o n s t a n t s o r c h a r a c t e r i s t i c times ( w i t h a p p r o p r i a t e subscr i pts) 2 2 ^ ^ Εj / X 0

0

0

Q

R

=

Rg Τ Τ* t U xj λ,Λ

= = = = = =

=

ad

k

j = l k=l λ

1II pC Τ /(-ΔΗ)(k ) [m] [m ] f o r homopolymerization p o a p o o o o pC Τ / ( - A H . , ) ( R .. ) f o r c o p o l y m e r i z a t i o n ρ ο jk pjk ο

=

0

G λ... Gjk

=

2

^G

=

^2 ^2 ^ ^ G j k ^ j = l k=l

λ. J X

l/(k

mjk

ρ [ Y

-1

2

=

Κ

]

=

o r

c

°P°Wmer izat ion 1 / 2

..) [ f ( k . ) / ( k , . . ) pjj ο d o / t j jο ο /

(

Κ

1

[m ] ο ο

/

2

ρ ] ^ ο

j = l k=l density molar c o n c e n t r a t i o n

= ] =

Tyk

^

X

A

Gjk R

Subscr i pts ap d G i j,k

= = = = =

£

=

m ο ρ R t

= = = = =

a p p a r e n t o r lumped decomposition o f i n i t i a t o r g e n e r a t i o n o f heat initiator depletion or initiation comonomer o r r e p e a t u n i t o f t y p e j o r k, where j = 1 , 2 and k = 1,2 i n d e x w h i c h t a k e s on v a l u e s I = 1,2 b u t a l w a y s such that £ = j monomer d e p l e t i o n feed c o n d i t i o n s (except i n m ) propagation r e s e r v o i r ( t h e r m a l ) o r removal o f h e a t termination Q

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

186 Acknowledgment

T h i s work was s u p p o r t e d i n p a r t by a G r a n t f r o m t h e N a t i o n a l S c i e n c e F o u n d a t i o n (ENG-7605053). The a u t h o r s a l s o w i s h t o t h a n k U n i o n C a r b i d e f o r s u p p l y i n g t h e s t y r e n e monomer a t no c o s t .

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

Biesenberger, J . Α., Capinpin, R . , and Sebastian, D . , Appl. Polymer Symp. (1975), 26, 211. Biesenberger, J. Α., Capinpin, R., and Yang, J., Polymer Eng. Sci., (1976), 16, 101. Sebastian, D. H. and Biesenberger, J. Α., submitted to J. Appl. Polym. Sci. Sebastian, D. H., Ph.D. Thesis, Stevens Institute of Tech­ nology (1977). Sebastian, D. H. an Polymer S c i . Russo, S., Munari, S., J. Macromol. Sci-Chem., (1967), A-1,5, 2159. Sebastian, D. H. and Biesenberger, J. Α., Polymer Eng. Sci., (1976), 16, 117.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

16 Comparison of Different Determination Methods for Effective Thermal Conductivity of Porous Catalysts U . H O F F M A N N , G . E M I G , and H. H O F M A N N Institut fur Technische Chemie I, University of Erlangen—Nuremberg, 8520 Erlangen, West Germany

For the design and analysis of fixed-bed c a t a l y t i c reactors as well as the determination of c a t a l y s t ef­ f i c i e n c y under nonisothermal conditions, the e f f e c t i v e thermal conductivity of the porous p e l l e t must be known. A c o l l e c t i o n of thermal conductivity data of s o l i d s pub­ l i s h e d by the Thermophysical Properties Research Centre at Purdue University [1] shows "a d i s p a r i t y i n data probably greater than that of any other p h y s i c a l prop­ erty". Some of these differences n a t u r a l l y can be ex­ plained, as no two samples of s o l i d s , e s p e c i a l l y porous c a t a l y s t s , can be made completely i d e n t i c a l . However, the main reason i s that the assumed boundary conditions for the Fourier heat conduction equation

never can be met experimentally exactly. On the other hand, the magnitude of values predicted by pore s t r u c ­ ture models d i f f e r up to 40 % [2] and there i s there­ fore a need for experimental measurement. In order to come as close as possible to the required boundary con­ d i t i o n s , d i f f e r e n t authors have developed d i f f e r e n t s t a t i c and dynamic methods for the experimental deter­ mination of the thermal conductivity of s o l i d s . A r e ­ view of these methods has been given recently by J.E. Parrot and A . D . Stuckes [2]. For porous p a r t i c l e s i n p a r t i c u l a r much less information i s a v a i l a b l e [ 3 , 4 , 5 , 6 , 7,8,9,10,11]. The aim of t h i s paper i s to compare r e s u l t s from d i f f e r e n t experimental methods for several types of c a t a l y s t s i n order to explore t h e i r advantages and d i s ­ advantages . ©

0-8412-0401-2/78/47-065-189$05.00/0

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

190

CHEMICAL

REACTION

ENGINEERING—HOUSTON

E x p e r i m e n t a l Methods Among t h e s t a t i c methods t h e l i n e a r heat f l u x me­ thods seem t o be most commonly used f o r porous p a r t i ­ c l e s . In t h i s case, i t i s assumed t h a t the t r a n s p o r t o f h e a t t h r o u g h t h e specimen i s m a i n l y i n one d i r e c t i o n thus t h e F o u r i e r law g i v e n by Eqn. (1) becomes one d i ­ m e n s i o n a l and can be c a l c u l a t e d a c c o r d i n g t o \

L ^ _L » A(T--T ) A R 12 ρ To g e t c o r r e c t v a l u e s o f X from t h i s e q u a t i o n , t h e heat l o s s e s from th n e g l i g i b l e . This conditio e x t e n t i n t h e so c a l l e d conductometer, o r i g i n a l l y de v e l o p e d by J . Schroder [12] and now c o m m e r c i a l l y a v a i l ­ a b l e t h r o u g h C o l o r a MeBtechnik GmbH. The p r i n c i p l e o f t h e q u i c k and s i m p l e , y e t e l e g a n t and a c c u r a t e method ( l a i n T a b l e 3) c o n s i s t s i n c o n t a c t i n g a c y l i n d r i c a l sample w i t h two b o i l i n g l i q u i d s L- and L o f d i f f e r e n t boiling points and T (ΔΤ=10 t o 20 K ) . F i g u r e 1 shows t h a t t h e l i q u i d or h i g h e r b o i l i n g p o i n t i s con­ t a i n e d i n t h e lower v e s s e l Β , t h e o t h e r i n the upper one B . The c o n t a c t between t h e sample Ρ and t h e v e s ­ sels i s p r o v i d e d by two s i l v e r s t o p p e r s a t t h e t o p o f t h e lower S- and t h e bottom o f t h e upper v e s s e l S to a v o i d r a d i a l temperature g r a d i e n t s . The heat f l o w from t h e lower v e s s e l t h r o u g h t h e sample causes the l i q u i d i n B t o b o i l a t a c o n s t a n t r a t e under s t a t i o n a r y con­ d i t i o n s . A c o n s t a n t temperature d i f f e r e n c e T ^ - T i s r e a c h e d between t h e two s i l v e r p l a t e s . The vapor from the upper v e s s e l i s condensed i n a condenser C and t h e condensate i s c o l l e c t e d i n a measuring b u r e t t e B. The time t needed f o r t h e e v a p o r a t i o n of a c e r t a i n amount o f l i q u i d i s measured. The e f f e c t i v e t h e r m a l c o n d u c t i v i t y o f t h e sample t h e n can be c a l c u l a t e d a c c o r d i n g t o Eqn. (2) w i t h t h e known s p e c i f i c heat o f v a p o r i s a t i o n ( - A H ) by s e t t i n g A

=

=

(:

K Z }

p

0

2

2

2

2

2

2

v

f

=

V

2

£

2

2

(3)

To a v o i d s y s t e m a t i c e r r o r s , e.g. caused by r a d i a l h e a t l o s s e s , a r e l a t i v e measurement i n s t e a d o f an ab­ s o l u t e d e t e r m i n a t i o n i s recommended i n which t h e t h e r ­ mal c o n d u c t i v i t y o f t h e sample i s compared w i t h t h a t o f a r e f e r e n c e m a t e r i a l . In a d d i t i o n , t h i s e l i m i n a t e s

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

16.

HOFFMANN ET AL.

Thermal

Conductivity

Determination

Methods

191

the n e c e s s i t y o f knowing the e x a c t v a l u e o f (-ΔΗ )~ and the b o i l i n g temperature o f the lower b o i l i n g l i q u i a . High p u r i t y copper, Armco i r o n , n i c k e l a l l o y s and p a r ­ t i c u l a r g l a s s e s are commonly used as r e f e r e n c e m a t e r i a l . The method i s g e n e r a l l y s u i t a b l e f o r ( i ) the whole tem­ p e r a t u r e range f o r which one can f i n d s t a b l e l i q u i d s w i t h w e l l d e f i n e d b o i l i n g p o i n t s , and ( i i ) n e a r l y a l l s o l i d s w i t h the e x c e p t i o n o f t h o s e w i t h v e r y h i g h t h e r ­ mal c o n d u c t i v i t y l i k e copper and s i l v e r , because i n t h i s case heat l o s s e s («xl/L) a r e too g r e a t or measuring times (o % ^ (f) . (9) a ζ On the b a s i s o f e x p e r i m e n t a l r e s u l t s i t has been demonstrated f u r t h e r m o r e [16] t h a t w i t h c y l i n d r i c a l par­ t i c l e s , h a v i n g a l e n g t h t o d i a m e t e r r a t i o o f 1, t h e lim­ i t i n g temperature d i f f e r e n c e r e a c h e d i s 1.203 times l a r g e r than t h a t f o r s p h e r i c a l p a r t i c l e s , which means that A m A

T

lim

=

1.203 — 6 i

C

,cL 2>

2

(

χ ( l o )

The a d d i t i o n a l i n f o r m a t i o n ( d e n s i t y and heat c a p a c i t y of t h e p e l l e t ) , needed i n o r d e r t o c a l c u l a t e the t h e r ­ mal c o n d u c t i v i t y from a, can be g a i n e d by s t a n d a r d r o u t i n e methods. Experimental Results T a b l e 1 shows the p r o p e r t i e s o f t h e c a t a l y s t s used i n t h i s study. V a l u e s o f t h e t h e r m a l c o n d u c t i v i t y i n W/m,K of d i f f e r e n t nonporous r e f e r e n c e and embedding m a t e r i a l s are g i v e n i n T a b l e 2. Values of the e f f e c t i v e thermal c o n d u c t i v i t y i n W/m,K, d e t e r m i n e d a c c o r d i n g t o t h e d e s c r i b e d methods a r e g i v e n i n T a b l e 3. 1

^Methods w i t h a p e r i o d i c v a r i a t i o n of temperature a r e not d i s c u s s e d h e r e . In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

[JL4]

196

CHEMICAL

REACTION

ENGINEERING—HOUSTON

thermostat bath with programmed heating rate catalyst particle with central and periphered thermocouple thermocouple line recorder indicating linear increasing bath temperature and Δ Τ between center and periphery e programmer for heating rate f circulation pump

Figure 5.

Principle of the apparatus for the dynamic method

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

16.

HOFFMANN ET

AL.

Thermal Conductivity Determination Methods

197

D i s c u s s i o n and C o n c l u s i o n The d a t a g i v e n i n T a b l e 1 show t h a t i n t h i s s t u d y a b r o a d spectrum o f c a t a l y s t p r o p e r t i e s has been cove r e d . A l l o f t h e c a t a l y s t s a r e o f t e c h n i c a l importance. The r e s u l t s g i v e n i n T a b l e 3 and t h e e x p e r i e n c e g a i n e d d u r i n g the i n v e s t i g a t i o n p e r m i t t h e f o l l o w i n g s t a t e ments : 1) For the d e t e r m i n a t i o n o f t h e e f f e c t i v e t h e r m a l c o n d u c t i v i t y o f porous c a t a l y s t p e l l e t s no s t a n d a r d i z e d method e x i s t s and p r o b a b l y w i l l never be d e v e l o p e d . On the c o n t r a r y , t h e most s u i t a b l e method depends s t r o n g l y on the p r o p e r t i e s o f the c a t a l y s t . In t h i s c o n n e c t i o n s i z e and form o f th ture, i t s s o l u b i l i t y t i v i t y o f t h e s o l i d m a t e r i a l and r e a c t i o n m i x t u r e a r e most i m p o r t a n t . As a g e n e r a l r u l e , t h a t method s h o u l d be p r e f e r e d i n which the c a t a l y s t can be a p p l i e d as used i n t h e r e a c t o r . T h i s i s not always p o s s i b l e . O f t e n the c a t a l y s t must be s p e c i a l l y p r e p a r e d f o r t h e measurement by g r i n d i n g and r e p e l l e t i z i n g , c o a t i n g , embedd i n g , e t c . , i n o r d e r t o produce a more o r l e s s s u i t a b l e sample. The i n f l u e n c e o f t h e c a t a l y s t p r e p a r a t i o n i s seen most c l e a r l y from the v a l u e s f o r c a t a l y s t A i n T a b l e 3. The c a t a l y s t was used i n i t s o r i g i n a l form o n l y i n methods l b and I I I . 2) Among t h e c o m m e r c i a l l y a v a i l a b l e u n i t s , the Col o r a conductometer seems t e c h n i c a l l y f u l l y d e v e l o p e d and can be r e a d i l y adapted f o r c o n d u c t i v i t y measurements on c a t a l y s t p e l l e t s . The d e s i g n m i n i m i z e s t h e unc o n t r o l l a b l e heat l o s s and a s s u r e s n e a r l y c o n s t a n t temp e r a t u r e i n any h o r i z o n t a l p l a n e t h r o u g h the sample. The time n e c e s s a r y f o r one measurement i s about 3 h o u r s . I f the r e f e r e n c e method i s used, no a d d i t i o n a l i n f o r m a t i o n i s needed f o r the d e t e r m i n a t i o n o f the e f f e c t i v e thermal c o n d u c t i v i t y . Other c o m m e r c i a l l y a v a i l a b l e u n i t s , m a i n l y des i g n e d f o r d e t e r m i n a t i o n o f the t h e r m a l c o n d u c t i v i t y o f b u i l d i n g m a t e r i a l s i n t h e form o f p l a t e s , l i k e t h e L i n s e i s L91 u n i t , s u f f e r from the s h o r t c o m i n g t h a t i n o r d e r t o minimize heat l o s s e s , the sample d i a m e t e r i s 80 t o 120mm. T h i s l a r g e d i a m e t e r makes i t d i f f i c u l t t o o b t a i n good c o n t a c t between the h e a t e r s and the c a t a l y s t sample. Furthermore, w i t h e l e c t r i c h e a t e r s i t i s d i f f i c u l t t o r e a l i z e a c o n s t a n t temperature a c r o s s the e n t i r e c r o s s s e c t i o n o f t h e probe. F i n a l l y t h e sample s i z e demands a r a t h e r l a r g e amount o f c a t a l y s t . The dynamic method ( I I I ) used i n t h i s study has the advantage o f a s h o r t measuring time (0.5 h o u r s ) ,

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

198

CHEMICAL

Table 1

Sample

catalyst

REACTION ENGINEERING—HOUSTOÎ

1

Properties

specific density s p e c i f i c pellet s u r f a c e a r e a (kg/m ) h e a t porosity (mVka) (kJ/kg,K) 56900 1950 1.07 0.468 3

A.

25%Ni on A1 0 2

3

Β

Ca/Niphosphate

C

Fe/Mo-oxid

D

Zeolite

Ε

6%Zn-acet a t e on ac­ t i v e carbon

145000

1350

1.98

0.570

7500

2260

0.66

0.448

253000

1040

2.15

0.490

3310

Table 2 P r o p e r t i e s meth­ od la Ha lie III

o f R e f e r e n c e and Embedding M a t e r i a l s

a c r y l i c Hostaform T e c h n o v i t Re1opal glass C 9021 GK 4071 0.21 0.24 0.15 0.18 — 0.42 0.20

T a b l e 3 E f f e c t i v e Thermal C o n d u c t i v i t i e s o f Porous C a t a l y s t s , Determined by D i f f e r e n t Methods meth­ mean meas­ od u r i n g tem­ p e r a t u r e (K)

367

Ic

III

D

C

0.18

0.30

0.22

0.67 0.52

1.60

0.19

0.63

D.82

0.26

0.68

0.40

-

333-353

1.19

Ε

Β

0.37

313

lib lie

A 0.57

la lb

catalysts

-

0.51 0.24

3 ]

0.29

l)ground a . r e p e l l e t i z e d , 2) broken p e l l e t s , i z e d under h i g h p r e s s u r e

0.22

0.63

3) p e l l e t -

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

16.

HOFFMANN

ET

AL.

Thermal Conductivity Determination Methods

199

p r o v i d e d a p r o p e r b a l a n c e between p e l l e t diameter, h e a t ­ i n g r a t e and t h e r m a l d i f f u s i t y o f t h e p e l l e t can be reached.. In t h i s study p e l l e t d i a m e t e r s o f 6 t o 20mm and h e a t i n g r a t e s between 100 and 300 K/h had been found s u i t a b l e . The a p p a r a t u s f o r t h i s method i s easy t o b u i l d u s i n g s t a n d a r d l a b o r a t o r y equipment. I f a v a i l ­ a b l e , a DTA u n i t c o u l d a l s o be used f o r t h i s s p e c i a l purpose. 3) The embedding o f c a t a l y s t p a r t i c l e s i n q u i c k h a r d e n i n g p l a s t i c T e c h n o v i t 4071 ( K o l z e r ) causes no problems, p r o v i d e d t h e p e l l e t s have a c o n s t a n t c r o s s s e c t i o n a l a r e a a c r o s s t h e sample h e i g h t L. With i r r e g u ­ l a r shaped p a r t i c l e s t h e d e t e r m i n a t i o n o f t h e d e n s i t i e s needed i n E q u a t i o n 5 sample l e a d t o u n c e r t a i l a r g e sample d i a m e t e r (method l i a ) i t i s d i f f i c u l t t o obtain a p e r f e c t l y plane contact s u r f a c e . C o a t i n g o f r e g u l a r shaped p e l l e t s w i t h a s u i t a b l e two component p o l y u r e t h e n e v a r n i s h (Fliigger u. Boecking K.G.) caused no problems i f a methanol-water o r g l y c e r i n e - w a ­ t e r m i x t u r e i s used as i n method l i e . I f carbon t e t r a ­ c h l o r i d e must be used t o r e a c h a low enough v a l u e f o r the t h e r m a l c o n d u c t i v i t y , a n o t h e r c o a t i n g system has t o be found. I r r e g u l a r shaped p a r t i c l e s c o u l d n o t be c o a t ­ ed s a t i s f a c t o r i l l y i n t h i s study as no way was found t o make t h e v a r n i s h f i l m t h i n enough. To suppress t h e t h e r m a l c o n v e c t i o n o f t h e l i q u i d m i x t u r e i n t h e v o i d s between t h e p e l l e t s (as another s o u r c e o f e r r o r ) t h e c o a t e d p a r t i c l e s s h o u l d be as s m a l l as p o s s i b l e and f i l l up t h e measuring chamber com­ pletely. 4) The s t a n d a r d d e v i a t i o n o f t h e measurement de­ t e r m i n e d f o r c a t a l y s t C w i t h method l a was 0.013 f o r a mean v a l u e o f 0.30 which i s v e r y s a t i s f a c t o r y as t h i s value i n c l u d e s both the v a r i a t i o n i n the c a t a l y s t pre­ p a r a t i o n as w e l l as t h e e x p e r i m e n t a l e r r o r s . Symbols 2 A c r o s s - s e c t i o n a l area (m ) a=X/$ c thermal d i f f u s i v i t y o f the c a t a l y s t p e l l e t (m /s) C Ρ Bemperature gradient i n the ambient f l u i d (K/s) c s p e c i f i c heat (kJ/kg K) D probe diameter (m) d p e l l e t diameter (m) f f r a c t i o n a l area (m /m t o t a l ) (-ΔίΟ heat o f evaporation (kJ/kg) L d i s t a n c e (m) R thermal r e s i s t a n c e (K/W) R e l e c t r i c a l r e s i s t a n c e (V/A) P

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

200

CHEMICAL REACTION ENGINEERING—HOUSTON

Τ temperature (K) ^ • l i m l i m i t i n g temperature d i f f e r e n c e (K) t time ( s ) U v o l t a g e (v) V volume o f L condensed (m^) w weight f r a c t i o n (kg/kg t o t a l ) λ thermal c o n d u c t i v i t y (W/mK) S d e n s i t y (kg/m ) φ heat flow r a t e (W) Indices f fm ρ m t

fluid l i q u i d mixture pellet p l a s t i c matrix total

Literature

[1] Touloukian,Y.S. (Ed.), 1970, Thermophysical Properties of Ma­ ter. The Thermophysical Properties Research Centre Data Se­ r i e s , Volumes 1 und 2 (IFI/Plenum Press, New York) [2] P a r r o t , J . E . and Stuckes,A.D., Thermal Conductivity of Solids Pion Limited, 207 Brondsbury Park, London NW2 5JN [3] Sharma,C.S. and Hughes,R., Can.J.Chem.Engng. 54 (1976)538-36 [4] Sehr,R.A., Chem.Engng.Sci 9 (1958) 145 [5] S a t t e r f i e l d , C . N . , Mass Transfer i n Heterogeneous Catalysis, M.I.T. Press, Cambridge, Mass./USA, 1970 [6] Butt, J.B., Α . I . C h . E . J . 11 (1965) 106 [7] Masamune,S. and Smith,J.M., J.Chem.Engng.Data 8 (1963) 54 [8] Cunningham, R . S . , Carberry, J.J. and Smith,J.Μ., Α . I . C h . E . J . 11 (1965) 636 [9] H a r r i o t t , P . , Chem.Engng.J., 10 (1975) 65-71 [10] Sharma,C.S., H a r r i o t t , P . and Hughes,R., ibid., 10 (1975) 7380 [11] Saegusa,T., Kamata,K., Iida,Y. and Wakao,N., Int.Chem.Engng. 14 (1974) 169-173 [12] S c h r ö d e r , J . , Review of S c i e n t i f i c Instruments, 34 (1963) 615-621 [13] Ritter,J., Helm,Ε. and F ü r s t , H . , Chem.Techn. 28 (1976) 232-621 [14] Gunn,D.J. and De Souza,J.F.C., CES 29 (1974) 1363-1371 [15] Carslaw,H.S. and Jaeger,J.C., Conduction of Heat i n Solids, Oxford, Clarendon Press, 1959 [16] Jirátová,K. and Horák,J., Chem.Techn. 28 (1976) 550-553

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

17 Interpretation of Catalyst Deactivation by Fouling from Interactions of Pore Structure and Foulant Deposit Geometries C. C. H U G H E S and R E G I N A L D

MANN

Department of Chemical Engineering, University of Manchester Institute of Science and Technology, Manchester, England

Deactivation is a encompasses several d i s t i n c t processes, that give r i s e to a lowering of catalyst a c t i v i t y . Poisoning, ageing, sintering and fouling are particular examples of deactivation and these terms ought in principle to clearly indicate and discriminate the mechanisms involved. In practice, probably due to the potential complexity if these processes take place simultaneously, there is often some overlap and confusion i n their use. Levenspiel 1 has referred to fouling as being primarily rapid, accompanied by deposition and a physical blocking of surface. He then defines poisoning as a slow modification of a c t i v i t y by chemisorption on the active s i t e s , the poison being characterised by difficulty of removal. It i s our view that rate of loss of a c t i v i t y is not a sufficiently meaningful discriminant. Instead, we propose that poisoning should refer to active site deactivation by monolayer type adsorption at the site, and thereafter no further poison adsorption takes place at that location. In this way, a very great loss of a c t i v i t y can take place with the adsorption of very small amounts of poison. I f , however, successive adsorption on the surface can take place, such that significant amounts of material accumulate, then t h i s represents fouling of the catalyst. The c l a s s i c a l treatments of a c t i v i t y loss by poisoning by Thiele 2 and Wheeler 3t support the above d i s t i n c t i o n s , since the poison was not considered to have any influence upon the pore geometry or effective d i f f u s i v i t y . Uniform, non-uniform and anti-selective poisoning do give r i s e to a wide spectrum of deactivation behaviour, but the non-comprehensive capability of a theory of poisoning to explain deactivation when significant accumulation takes place, requires that new approaches be made. This is confirmed by several more recent observations. Thus, Butt's 4 measurements of a very non-uniform coke p r o f i l e , indicate that ultimate penetration of a coke type foulant into a catalyst p a r t i c l e i s very quickly attained, and sybsequent deposition occurs entirely within an outer s h e l l . ©

0-8412-0401-2/78/47-065-201$05.00/0

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

202

CHEMICAL

REACTION

ENGINEERING—HOUSTOI

There remains an uncoked c e n t r a l c o r e , apparently never contactée by r e a c t a n t . The work o f Rostrup-Nielsen 5 and L e v i n t n e r 6 a l s o suggests t h a t pore mouth c l o s u r e by coke plugs may be t h e o r e t i ­ c a l l y r e q u i r e d , and a s i m p l i f i e d theory has been r e c e n t l y proposed by Newson 7· There i s t h e r e f o r e a good d e a l o f evidence t o support t h e i d e a t h a t the e f f e c t o f f o u l a n t d e p o s i t s on a c t i v i t y , s e l e c t i v i t y and p e l l e t macroscopic p r o p e r t i e s i s s e n s i t i v e t o both the pore s t r u c t u r e and the f o u l a n t deposit s t r u c t u r e . Such an approach should improve upon the more e m p i r i c a l l y based methods used by Voorhies 8 and Wojciechowski 9» which have t r a d i t i o n a l l y attemptedTto describe d e a c t i v a t i o n when f o u l i n g occurs. O u t l i n e o f the Theory The nature o f the i n t e r a c t i o n o f the pore s t r u c t u r e and f o u l a n t deposit geometries i s determined from two b a s i c assumptions. F i r s t l y , t h a t t h e pore s t r u c t u r e may be represente( by a set o f i d e a l i s e d p a r a l l e l s i d e d non i n t e r s e c t i n g pores o f v a r i a b l e r a d i u s , but each o f a c e r t a i n l e n g t h L. This i s the so c a l l e d ' p a r a l l e l bundle' model. Secondly, t h a t the f o u l a n t accumulates by simultaneous p e n e t r a t i o n and t h i c k e n i n g , g i v i n g r i s e t o successive l a y i n g down o f f o u l a n t . We c a l l t h i s t h e 'wedge l a y e r i n g ' model o f f o u l a n t d e p o s i t i o n . The q u a l i t a t i v e f e a t u r e s o f the subsequent i n t e r a c t i o n are depicted i n F i g . 1. The s m a l l e s t pore A b l o c k s f i r s t as t h i c k e n i n g proceeds and t h e r e a f t e r the remaining surface w i t h i n pore A i s rendered i n a c c e s s i b l e and thus c a t a l y t i c a l l y i n a c t i v e . I f the d e s i r e d n o n - f o u l i n g r e a c t i o n i s t a k i n g place without d i f f u s i o n i n f l u e n c e , the l o s s i n a c t i v i t y i s equal t o t h i s l o s s o f area i n pore A. T h i s i s shown i n F i g . 2 . As p e n e t r a t i o n and t h i c k e n i n g continue a t the same r e l a t i v e r a t e , a d d i t i o n a l l o s s e s i n a c t i v i t y take p l a c e , as the remaining l a r g e r pores become plugged. I t i s c l e a r t h a t i n the absence o f a theory o f p l u g g i n g , the a c t i v i t y l o s s would be erroneously i n t e r p r e t e d as being caused by p o i s o n i n g w i t h d i f f u s i o n a l r e s i s t a n c e . T o t a l f o u l a n t content as a f u n c t i o n o f p e l l e t a c t i v i t y i s perhaps the most important c h a r a c t e r i s t i c i n a n a l y s i n g f o u l i n g behaviour, s i n c e i t i s f a i r l y simply observed by experiment. F i g . 3 shows some q u a l i t a t i v e aspects. I t i s c l e a r t h a t a t any given f o u l a n t content two p o s s i b i l i t i e s e x i s t f o r t h e d i s t r i b u t i o n o f f o u l a n t t h a t g i v e r i s e t o the same a c t i v i t y . Thj i s i l l u s t r a t e d i n F i g s . 3 ( a ) , ( c ) . I f the f o u l a n t has a s m a l l t h i c k n e s s and l a r g e p e n e t r a t i o n as i n ( a ) , t h i s can be viewed as a p o i s o n i n g mode o f d e a c t i v a t i o n . On the other hand, the same amount o f f o u l a n t could be present as a l a r g e t h i c k n e s s s m a l l p e n e t r a t i o n wedge as i n F i g . 3 ( c ) , and t h i s would be a pore mouth plugging mode o f d e a c t i v a t i o n . A f u r t h e r o b s e r v a t i o n i s t h a t a t a c e r t a i n l e v e l o f the parameter β defined by β = rate o f foulant thickening/rate o f foulant penetration

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

17.

HUGHES

AND M A N N

Catalyst Deactivation by Fouling

Figure 1. Fouling by "wedge layering" in a parallel bundle pore structure model

0-6 h

PORE Ap*

FOULANT PENETRATION

Figure 2. Activity hsses as foulant penetrates and accumulates

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

203

204

CHEMICAL

Figure 3.

REACTION

ENGINEERING—HOUSTON

Illustration of differing modes of deactivation

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

17.

HUGHES

Catalyst Deactivation by Fouling

AND MANN

205

which i s here assumed t o be a constant i r r e s p e c t i v e o f degree o f p e n e t r a t i o n o r t h i c k e n i n g , a pore o f a g i v e n s i z e reaches a maximum f o u l a n t content as β i n c r e a s e s from zero (pure poisoning) to i n f i n i t y (pure pore mouth p l u g g i n g ) . T h i s i s i n d i c a t e d i n F i g s . Ma) and ( b ) . T h i s c h a r a c t e r i s t i c o f maximum f o u l a n t accumulation a t some c r i t i c a l value β has been deduced w i t h respect t o pores o f a s i n g l e s i z e . lS order f o r the theory t o f i n d general a p p l i c a b i l i t y , i t requires extension t o p e l l e t s with d i s t r i b u t e d pore s i z e s . For a u n i t mass o f c a t a l y s t , i f f ( r ) d r i s the surface area contained i n pores o f s i z e between* r and r+dr, then r

00

ίο

f (r)dr 8

(1)

a S *

where S i s the s p e c i f i pore moith p o i s o n i n g were t o take p l a c e under n o n - d i f f u s i o n i n f l u e n c e d c o n d i t i o n s , the reduced a c t i v i t y a t a g i v e n p e n e t r a t i o n χ i s g i v e n by (-co

(1 - τ)

Ι f (r)dr/S = 1 - f (2) Jo where L i s the l e n g t h dimension o f the p a r a l l e l pore bundle. Now, i f f o u l i n g takes p l a c e by wedge l a y e r i n g such t h a t β = h/x, pores w i l l remain unplugged, and t h e i r i n t e r i o r surface w i l l be a c c e s s i b l e and c a t a l y t i c a l l y a c t i v e , provided t h a t r>h. Therefore the reduced a c t i v i t y a t a g i v e n p e n e t r a t i o n χ w i l l be g i v e n by w

S

δ

L

-00

(1 - £) Γ Jh

(3)

f (r)dr/S 6

The dimensionless a c t i v i t y i s t h e r e f o r e i d e n t i f i e d w i t h nonf o u l e d pore surface t h a t succeeds i n remaining a c c e s s i b l e . As mentioned p r e v i o u s l y , t h i s e f f e c t due t o mouth p l u g g i n g can be s p u r i o u s l y i d e n t i f i e d as pore d i f f u s i o n a l r e s i s t a n c e accompanying p o i s o n i n g . In c a l c u l a t i n g the corresponding volume o r mass o f accumulated f o u l a n t , those pores which have a l r e a d y become sealed have t o be d i s t i n g u i s h e d from those t h a t y e t remain t o be plugged. For unplugged pores, i f f ( r ) d r i s the number f r a c t i o n o f pores s i z e d between r and r+dr, the f o u l a n t volume i n t h i s category o f pores at a p o t e n t i a l mouth t h i c k n e s s h i s g i v e n by -co V£(h) = J

£ττ(

2 Γ

2

2

- β χ )χΝί (Γ)ά Ν

Γ

W

where Ν i s the t o t a l number o f pores c o n s t i t u t i n g the p a r a l l e l bundle w i t h i n a u n i t mass o f c a t a l y s t . For the category o f plugged pores, a pore becomes plugged and t h e r e a f t e r remains plugged a t the i n s t a n t when h = βχ = r , and hence a l l the pores between 0 and h are blocked o f f f o r a

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

206

CHEMICAL REACTION ENGINEERING—HOUSTON

FOULANT CONTENT (a) FOR 0)

A special case which has received much attention (1-2, 4-6) is the plug flow model, resulting from Eqn (7) in the limit Pe ~*»: a

09

Λ"*

5.

B i

2

-4a z

Data Analysis The models were subjected to two stages of analysis:

(A) Overall.Analysis A stringent test of the models i s provided by f i t t i n g them simultaneously to data measured at several bed depths. In the axial dispersion model, the parameters Pe , Pe and Bi were est ated by minimising the sum of squares of residuals on the 32 be exit temperatures: a

Ν F

=;

32 ;

r

9

(texp.0 - W o )

o°

where Ν is the number of bed depths; t ] p is calculated from either Eqn. (7) or (8), depending upon which boundary condition is adopted at the bed exit, at the appropriate radial measuring points for z=L. c a

Ç j

(B) Depth_bY_Degth_AnalYsis The a b i l i t y of the models to f i t the data at individual bed depths (N=l) was next examined in order to detect any trend in t parameters with bed depth. The non-linear function minimisations of Eqn.(10) and i t s simpler cases were carried out by the Marquardt search algorithm

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

20.

DIXON

ETAL.

Heat Transfer in Packed Beds

243

(Fortran sub-routine E04 FBF NAG library, NAG Ltd., Oxford). A preliminary grid search was made to check for irregularities in the sum of squares surface and provide a starting point for the search. Previous analysis of experimental errors (8) substantiated the validity of the unweighted least squares criterion (]0) for estimation of the model parameters. 6.

Evaluation of Models Results of Depth by Depth Analysis

Neither model showed significant lack of f i t to the data at the 95% confidence level th plu flo model were found to decrease systematicall Fig. (3) shows this effect quite clearly in the case of the effect ive radial conductivity. No such effect was observed with the axial dispersion model, as i s apparent from Fig. (4). DeWasch and Froment (6) also noted the dependence of the plug flow model parameters with bed depth. They therefore only correlated their data obtained on the longest beds hoping to minimize axial dispersion effects. However, i f Figs. (3) and (4) are superimposed, the estimates of k obtained from the axial dispersion model are significantly greater than those obtained on the longest bed using the plug flow model, even at the quite large Reynolds numbers of industrial practice. The two sets of estimates ultimately merge at large Reynolds numbers. No doubt the differences would have been even greater had a larger bed been used. r

This behaviour of the plug flow model may be a significant factor in explaining some of the scatter in literature correlations obtained on beds of different length. Results of Overall Analysis When a l l the bed depths were analysed simultaneously, the plug flow model was clearly rejected for a]J[ the different particles and Reynolds numbers considered. The ratio Fcalc/Fo.05 found to be between 1.5 and 8, where F ] is the estimated F ratio from analysis of variance and FQ.05 is the appropriate s t a t i s t i c at the 5% significance level. w

c a

a

s

c

For a l l the beads the axial dispersion model (Eqn. 7) showed no significant lack of f i t at any Reynolds number, F Ç ^ C / F Q lying between 0.4 and 0.9. Fig. (5) shows a typical t i t of this model. Fig. (5), however, i s unusual in that the calculated and experimental entrance profiles (z=0) agree well. In the majority of cases this was not so, which we attribute in part to unsatisfactory measurements at the entrance.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

244

CHEMICAL

SL5mmcERAMic

à

too

Figure 3.

ENGINEERING—HOUSTON*

SPHERES

—ièo Ν

REACTION

RE

ώο -

Correlation of k with bed depth for the plug flow model r

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

1

20.

DIXON

ET AL.

Heat Transfer in Packed Beds

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

245

Figure 5. Fit of axial dispersion model to angular smoothed radial temperature profiles

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

DIXON E T

20.

Heat Transfer in Packed Beds

AL.

247

Incorporation of the f i n i t e bed boundary condition into the model (Eqn. 8) generally led to a poorer f i t , in many cases leading to a significant lack of f i t . Its main effect was to increase estimates of Pe by some 10-20%, the other parameters Pe and Bi remaining virtually unaffected. a

r

It was observed that, in general, the model f i t is worst at low Reynolds number and improves progressively as the Reynolds number increases. This is probably due to the d i f f i c u l t y of measuring the development of the radial temperature profile, since at low Reynolds number the bed attains the wall temperature within a few particle diameters of the entrance (z=0). A typical cross-section of the parameter cross correlations is shown in Table 2. Table 2:

Typical Parameter Cross-Correlations: Ceramic Beads: Bed Depth 17.5 cms.

'Re

Vw -0.72 -0.77 -0.82 -0.91

535 430 290 140

r* a

Vw

-0.10 -0.05 +0.06 +0.34

-0.11 -0.07 -0.07 -0.26

k

h

12.7 ntn

h

k

Estimates of (k ,k ) and (k »h ) are virtually uncorrected except possibly at low Reynolds number; those for (k hw) strongly correlated at a l l Reynolds numbers. While k i s not a conductivity in the true sense, i t nevertheless has a sound theoretical basis, as proposed by Argo and Smith (9_); h on the other hand is perhaps no more than an empirical parameter needed in the model to account for a decreasing k near the wall. r

a

a

w

a r e

rJ

r

w

r

7.

Correlation of Heat Transfer Data

Analysis of the data revealed that the radial conductivity (k ) is of particular importance. It would be desirable, therefore, to develop a model which gives a priori prediction of this parameter in terms of flow rate, particle diameter and conductivity and compare the predictions with our experimental data. r

7.1

A Model for Prediction of the Radial Conductivities

Starting along the lines of Argo and Smith (9J, the radial conductivity is given by k

r

= k

q

+ k, , + k . td series American Chemical Society Library

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; 1155 16th St.» M.W. ACS Symposium Series; American Chemical Society: Washington, DC, 1978. Washington, O.C. 20036

(11)

CHEMICAL REACTION ENGINEERING—HOUSTON

248

where k , k j and k · represent the molecular conductivity of the f l u i d , the turbulent conductivity and the effective conductivi­ ty of the solid, a l l based on unit of void + non-void area. g

tc

$

s

The turbulent conductivity k^d i s given in terms of the Rey­ nolds, Prandtl and Peel et numbers by td m = Re Pr rm < ) where k is the molecular conductivity of the f l u i d . From turbuleni mixing data (10), Pe = 10 for N R > 4 0 , and for a i r Np =0.72. Thus, Eqn. (12) simplifies to / k

k

N

N

/ P e

12

m

rm

td'

k

k

=

m

g

°-

0 7 2

N

f

N

Re

( Re

> 4

13

°)

Heat transfer betwee occur by a static proces gas f i l l e t s at the point of contact, and a dynamic process involv­ ing a series mechanism of solid conduction, film convection and turbulent mixing,as in Fig. (6). The static and dynamic processes occur in p a r a l l e l , thus k

series

=

k

st

+

k

( 1 4 )

dyn

The static contribution can be measured experimentally (Y\J or estimated from the model of Kunii and Smith ( 1 2 ) . The dynamic term is obtained by f i r s t integrating the heat flux over the hemispher­ ical surface between e=0 and θ=90° in Fig. (6). After some algebra, the total heat flow is given by 0 Q

P td - φ )

2 π

-

T

"

R

k

β

{

_J_ Vl

1 η β

.

/dL ' dH

1 }

1 Π β

, }

(

Π5) f l u i d

( , b )

where B=hk / k V j (h+k /R ) and (dT/dr) -j 4 is the temperature gradient in tne f l u i d in the direction of heat flow (assumed linear). Eqn. (15) enables an effective conductivity k^yn to be defined, based on solid projected area i T R p , f

U

d

2

'dyn

•

k

T^frtFr"*-"

(,6

»

For a packed bed, Eqn. (16) must be modified to account for the bed voidage and for the number of contacts (n) a pellet makes with i t s neighbours, corrected for the cross-sectional areas norma to the direction of heat flow and for the frequency of the orient­ ations. Assuming an actual bed is a composite of loose and close packings then, according to Kunii and Smith (12), n-2 for beds of voidage ε=0.44 to 0.46, as measured in our studies. Thus,

dyn = ^ t d T F i j i F T ^ -

k

1

1

}

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

( 1 7 )

20.

DIXON E T A L .

Heat

Transfer

in

Packed

249

Beds

Eqns. (11), (13), (14) and (17) permit a priori prediction of k in terms of the underlying heat transfer processes. No adjustable parameters are involved. A comparison of this model with our data is shown in Fig. (7). Static conductivities were measured separate­ ly using Sehr's electrical heating method (Vl_) and the correlation of DeAcetis and Thodos (13J was used to estimate h. r

The results show an encouraging agreement over a wide range of flow rate,particle size and conductivity. In particular, i t is found that (a) k increases linearly with N for N >40 but does not extra­ polate linearly to the static results. (b) k is virtually independent of pellet diameter. (c) k„ is only weakly dependen 100-fold increase i r

Re

Re

r

Also shown in Fig. (7), for comparison, is the contribution to k due to turbulent conduction (k^d). It is apparent that heat transfer through the solid forms a significant, i f not dominant, fraction of the total radial heat transfer within the Reynolds number range of interest. r

7.2

The_Wall_Biot_Number

If the data are plotted as (Bi) χ (d /dL)^vs. N then the results for different particle sizes and conductivity are brought together on a single curve, at least to within the scatter of the data. The results show that the Biot number decreases with Reynolds number, according to (see Fig. 8). ι r Q κι -0.262 ,„ (Bi) (dp/d )J = · * (18) Re

ΛΧ

5

3

t

R e

which correlates the data to within 15% in the range 100

l i g h t gases, N H

Oils (

V

H S, ?

naphtha, furnace and heavy f u e l o i l s , e t c .

etc.)

CD

This mechanism i s c o n s i s t e n t w i t h our understanding of the low s e v e r i t y c a t a l y t i c l i q u e f a c t i o n process. More complex r e a c t i o n mechanisms which i n c l u d e hydrocracking ( i . e . , degeneration of high­ er b o i l i n g hydrocarbons i n t o lower b o i l i n g components) and hydroger donor r e a c t i o n s may be important under high s e v e r i t y thermal process. Gas and s l u r r y flow c o c u r r e n t l y upwards through the open spaces between the c a t a l y s t tubes. The gas flow i s the primary cause o f backmixing i n the s l u r r y phase. L i t e r a t u r e on hydroprocessing operations i n d i c a t e s t h a t the mass t r a n s f e r r e s i s t a n c e f o r the t r a n s f e r o f hydrogen from the gas to the l i q u i d phase can be neglected. Furthermore, very high s o l u b i l i t y of hydrogen i n c o a l l i q u i d s d i c t a t e s t h a t , f o r a l l p r a c t i c a l purposes, the mass t r a n s f e r r e s i s t a n c e of hydrogen at the g a s - l i q u i d i n t e r f a c e can be neglected. This does not mean, however, that the r a t e of d i f f u s i o n o f hydrogen through the l i q u i d i s n e g l i g i b l e compared with the r a t e at which hydrogen i s consumed at the c a t a l y s t surface. However, because of the reasons mentioned l a t e r , i t i s

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

25.

Catalytic Liquefaction of Coal

SHAH E T A L .

307

assumed t h a t the hydrogen c o n c e n t r a t i o n i s i n excess and constant for a l l pertinent reactions. The c o a l depolymerizes, d i s s o l v e s i n the l i q u i d , and forms v a r i o u s gaseous and l i q u i d products. The s i m p l i f i e d mechanism assumes t h a t both gaseous and l i q u i d products are d i r e c t l y formed from c o a l . The c a t a l y s t w i t h i n the c a t a l y s t tubes con­ t i n u o u s l y s u p p l i e s hydrogen-rich solvent f o r hydrogen t r a n s f e r r e a c t i o n s . The s o l v a t i o n o f c o a l i s undoubtedly accompanied by some hydrocracking r e a c t i o n s (degeneration o f higher b o i l i n g hydrocarbons i n t o lower b o i l i n g components), but these appear t o be r e l a t i v e l y unimportant, and i n the present study, they were not i n c l u d e d i n the mechanism. The r e a c t o r feed i n c l u d e s a moisture- and ash-free coal component designated "C." d c a r r i e solvent d hydroge and f l u s h o i l are incluàe The product stream i s composed o f a p f r a c t i o n ( l i g h t gases H 0 , CO, C 0 , H S, NH ), a "C" f r a c t i o n (unconverted moisture- and ash-free c o a l ) , and an f r a c t i o n (coal l i q u i d s p l u s s o l v e n t , i . e . , C^+). The concentrations o f the above-defined feed and product components are expressed i n terms o f dimensionless weight f r a c ­ t i o n s ; m a t e r i a l balance feed and product q u a n t i t i e s have been normalized w i t h respect t o feed moisture- and ash-free c o a l ; i . e . , ρ = Ρ / C , c = C /C. , and £ = L /C. , where Ρ , e t c . , * o ο 1* O 0 1* Ο 0 1* ο . ' are the c o n c e n t r a t i o n s by weight o f components p, e t c . , i n the product, and C. i s the c o n c e n t r a t i o n o f the maf c o a l a t the reactor i n l e t . D i f f e r e n t i a l mass balances based on the standard a x i a l d i s p e r s i o n model can be expressed a s : 2

2

( R dx

• R )

2

3

r

- ± Pe dx

_i_£i-dR Pe dx dx

Pe dx

+

R

2

C =

0

c = 0

dx

The independent v a r i a b l e "x" i s the dimensionless r e a c t o r l e n g t h , i . e . , χ = ζ/ξ, where ζ i s the d i s t a n c e from the r e a c t o r i n l e t and ξ i s the t o t a l r e a c t o r l e n g t h . and R2 are the dimensionless r a t e constants. They can be expressed as: R^

—

k^f,

(3) R2 — ^2^*

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

308

where k and k a r e i n t r i n s i c r a t e constants which i n c l u d e c a t a l y s t v o i d t r a c t i o n and d i l u t i o n e f f e c t s . The q u a n t i t y Γ i s defined as the r e c i p r o c a l o f s l u r r y space v e l o c i t y (g s l u r r y / g c a t / h r ) , i . e . , s l u r r y space time. Pe i s the P e c l e t number d e f i n e d as ϋξ/ϋ , where U i s the s u p e r f i c i a l v e l o c i t y o f l i q u i d s l u r r y and D the a x i a l d i s p e r s i o n c o e f f i c i e n t measured i n a g l a s s model under the present r e a c t o r c o n f i g u r a t i o n (14). Equation (2) assumes t h a t the P e c l e t numbers f o r a l l species are equal. The magnitude o f the P e c l e t number c h a r a c t e r i z e s the extent o f backmixing w i t h i n the r e a c t o r . At the l i m i t i n g condi­ t i o n s , an i n f i n i t e P e c l e t number means plug flow, while a P e c l e t number o f zero means completely backmixed flow, i . e . , the r e a c t o r operates j u s t l i k e a continuous s t i r r e d tank r e a c t o r . Equation (2) i s subjecte tions: ?

α

C

1 dc " P e dx -±J&

0 = ρ . P

Pe dx

ι

(4)

Pe dx

and dc dp dil dx = dx = c E =

^

Λ 0

ι χ = 1-

, (5) r c

Equation (2) assumes that t h e feed contains only c o a l and s o l v e n t . An a n a l y t i c a l s o l u t i o n t o Equations (2)-(5) can be obtained i n a s t r a i g h t f o r w a r d manner. The s o l u t i o n f o r the coal concen­ tration i s

c =

V

T-

^

x

- ae

Ψ

2

^

x

6

where

q = / 4 (R R ) / 1 + k: — Pe +

α

' α

2

= +

U q)

- (1-q) e

F e q

il^I -Peq (i+q) ι e

2

S i m i l a r s o l u t i o n s f o r "p" and

can be obtained.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

(7)

25.

SHAH E T A L .

Catalytic Liquefaction of Coal

309

Results and D i s c u s s i o n The best values o f the r a t e constants were obtained by non­ l i n e a r l e a s t square f i t t i n g o f the data t o the a n a l y t i c a l equations (16). Experimental c o a l s o l v a t i o n s and the y i e l d s o f gases and o i l s are compared w i t h model p r e d i c t i o n s i n Figure 2. As shown by t h i s f i g u r e , the model c o r r e l a t e s the experimental data q u i t e w e l l . From the experimental data, r a t e constants f o r two r e a c t i o n s were obtained a t three temperature l e v e l s . The Arrehenius p l o t s f o r the r a t e constants are shown i n Figure 3. I n t e r e s t i n g l y , the a c t i v a t i o n energies f o r a l l the r e a c t i o n s were found t o be c o n s i d e r a b l y higher than normally encountered i n f i r s t order c a t a l y t i c r e a c t i o n s This o f f e r s f u r t h e r evidence that the c a t a l y s t i s no reaction. The major d i f f e r e n c e between the k i n e t i c model presented i n t h i s study and those presented i n the l i t e r a t u r e i s t h a t , here, c o a l l i q u e f a c t i o n i s assumed t o occur i n a p a r a l l e l r e a c t i o n mechanism. A l l the products, l i g h t o r heavy, are assumed t o be formed d i r e c t l y from c o a l . The models proposed i n the l i t e r a t u r e assume a s e r i e s r e a c t i o n mechanism, wherein only heavy components ( i . e . , high b o i l i n g o i l f r a c t i o n s ) are formed d i r e c t l y from c o a l , and the l i g h t e r components ( i . e . , low b o i l i n g o i l f r a c t i o n s ) and the gases are produced by the c r a c k i n g o f the heavy compon­ ents. The present model a l s o assumes that the c a t a l y s t provides an excess o f hydrogen donor solvent r e q u i r e d f o r the c o a l l i q u e ­ f a c t i o n . A more r i g o r o u s model (which would a l s o take c a t a l y s t aging e f f e c t s i n t o account) should i n c l u d e the r o l e o f hydrogen donor s o l v e n t . Separate measurements o f water, l i g h t gases (C^-C^) and by­ products as f u n c t i o n s o f space time and temperature were a l s o carried out. These data were c o r r e l a t e d by a k i n e t i c model which assumes t h a t water, l i g h t gas and by-products a l l are produced d i r e c t l y from c o a l by f i r s t - o r d e r i r r e v e r s i b l e r e a c t i o n s . This type of'shooting star" mechanism c o r r e l a t e d the separate data f o r water, l i g h t gases and by-products as f u n c t i o n s o f space time as w e l l as the data f o r the t o t a l gas shown i n Figure 2. Further­ more, the a c t i v a t i o n energies f o r the r e a c t i o n s c o a l --> water, c o a l --> by-product and c o a l --> l i g h t gases were found to be 53,500, 63,500 and 85,200 c a l / g mole. In a backmixed r e a c t o r , the gas flow r a t e should have a s i g n i f i c a n t e f f e c t on the product d i s t r i b u t i o n . High gas flow i s important f o r e l i m i n a t i n g p o s s i b l e r e s i s t a n c e s t o the t r a n s f e r o f hydrogen from the gas phase t o the c a t a l y s t surface. Two important r e s i s t a n c e s i n the present case are the g a s - l i q u i d i n t e r f a c e r e s i s t a n c e and the i n t e r - p a r t i c l e d i f f u s i o n a l r e s i s t a n c e w i t h i n the c a t a l y s t tube. A l a r g e gas flow would, however, a l s o give s i g n i f i c a n t backmixing i n the open p o r t i o n o f the r e a c t o r , 1

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

310

1.0 α

CD

Ζ

ional

«-* Φ

duct/

>

0.8


-CH-CH

3

+

CH

4>-CH-CH3

->

4>-CH=CH2

+

Η

->

-CH-CH3

+

H

->

Φ"ΟΗ

2

(4)

H

+ 4>-CH -CH

(5)

H

+

3

+

(6) (7)

CH

2

3

4>-CH2 CH

2φ-ΟΗ

3

->

C

2

H

4

2

3

6

φ—CH CH 2

2

-Φ

E t h y l b e n z e n e i s d i s i n t e g r a t e d i n t h e well-known i n i t i a t i o n r e a c t i o n (1). Methyl i n i t i a t e s the r e a c t i o n c h a i n i n which s t y r e n e and hydrogen a r e formed. T o l ­ uene i s formed i n t h e t r a n s f e r r e a c t i o n ( 5 ) , w h i l e i n t h e two r e a c t i o n s (6) and (7) r e c o m b i n a t i o n o f r a d i c a l s occurs. K i n e t i c p a r a m e t e r s ( p r e e x p o n e n t i a l f a c t o r s and a c t i v a t i o n e n e r g i e s ) have been a l l o c a t e d t o t h e p a r ­ t i c u l a r r e a c t i o n s t e p s . F o r r e a c t i o n (1),(2) and (6) the v a l u e s were t a k e n from t h e l i t e r a t u r e , f o r t h e o t h e r r e a c t i o n s v a l u e s have been e s t i m a t e d from ana­ l o g o u s a p p r o x i m a t i o n s (2)-(£). These a r e l i s t e d i n T a b l e I . C a l c u l a t i o n s o F t h e r e a c t i o n based on t h e scheme were made and t h e r e s u l t s compared w i t h t h e e x p e r i m e n t a l r e s u l t s o b t a i n e d from t h e r u n s c a r r i e d o u t i n t h e NPA. Good agreement was o b t a i n e d f o r t h e d e c r e a s e i n e t h y l b e n z e n e and t h e i n c r e a s e i n s t y r e n e and hydrogen c o n c e n t r a t i o n s . I n t h e NPA e x p e r i m e n t s r e l a t i v e l y l a r g e amounts o f e t h y l e n e and benzene were formed a t temperatures below 760°C. To t a k e

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

26.

EBERT E T A L .

Models for Complex

Gas Phase

Reactions

317

Figure 1. Low pressure apparatus. (1) inlet, (2) vacuum pump, (3) manometer, (4) ion source of mass spectrometer.

Figure 2. Normal pres­ sure apparatus. (1) inlet argon carrier, (2) inlet ethylbenzene, (3) inlet ar­ gon quench, (4) silit heater housing, (5) mixing cham­ ber, (6) sampling line to GC, (7) outlet, (8) ther­ mocouple, (9) reaction zone.

601

I

92$ 777

I

1091

1118

I 1122 I

1031

1209

1177

1254

I 1231 I

1288

1321

1273

Ι

I

.

;

13M

„

K

1349

1 ι 1ι 1 ι 1 ι 1ι I ι 1 ι ι ι Γ V

1 5 - METHYL

»

1 6 - METHANE

-

·

26-

ACETYLENE

28-

ETHYLENE

3 9 - C3H3

.

.

.

.

.

.

*

.

·

»

»

»

·

·

.

·

•

•

•

•

•

·

•

·

·

·

»

t

a

t

t

•

•·· ·

»

•

• •

·

•

·

·

·

>

»

*

·

•

•

·

·

» •

M -

PROPANE

50-

DιACETYLENE

78-

BENZENE

65- C5H5

89- C7H5

79- C H 6

90-

9 1 - BENZYL 9 2 - TOLUENE 1 0 2 - PHENYLACETYLENE 1 0 4 - STYRENE 105-

•

•

•

•

•

a

t

7

PHENYLCARBEN

ETHYLBENZYL

1 0 6 - ETHYLBENZENE 1 2 8 - NAPHTHALENE

.

.

1 8 2 - DIBENZYL

Figure 3. Survey pattern of LP A experiments. Abun­ dances of various species at different temperatures.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

318

CHEMICAL REACTION ENGINEERING—HOUSTON

t h e s e two s p e c i e s i n t o account t h e f o l l o w i n g s t e p s were s e t up and have been added t o t h e r e a c t i o n scheme : (3a) (3b)

-CH-CH

-> ->

3

C H 6

(4a)

5

+

-CH -CH

H

+

φ—CH2 "*CH 3

2

(4b)

C

(4c)

3

H

+

6

C H 6

5

+

C H

+

φ-CH

+

C2H4

+

C2H4

2

6

4

C Hn 8

8H11

C H 6

7

>

C H

(4d)

C H

4 3

D i s i n t e g r a t i o n of the e t h y l b e n z y l leads t o the f o r ­ mation o f p h e n y l and e t h y l e n e , t h e former s t r i p p i n g a hydrogen atom from e t h y l b e n z e n e t o form benzene and e t h y l b e n z y l . S i n c e , as t h e temperature g e t s h i g h e r , t h e p r o ­ d u c t i o n o f e t h y l e n e by f a r exceeds t h a t o f benzene r e a c t i o n s (4a-4d) a r e p r o p o s e d , i n which t h e a r o m a t i c r i n g i s d e s t r o y e d and two m o l e c u l e s o f e t h y l e n e a r e produced. B i a c e t y l e n e as w e l l as t h e t h r e e r a d i c a l s 8 n / CeH , ^ 4 3 have been d e t e c t e d i n t h e low p r e s s u r e e x p e r i m e n t s . A g a i n , k i n e t i c parameters have been e s t i m a t e d and a l l o c a t e d t o t h e v a r i o u s r e a c t i o n steps (Table I ) . F o r v e r i f i c a t i o n o f t h e c a l c u l a t i o n s o f t h e exc

a n c

H

C

H

7

ER

NO

(1) da) (2) (2a) (3) (3a) (3b) (4)

1 0

log A

Ε

ER No

lolog A

Ε

15.3 16.0 7.82 13.0 14.85 14.85 11 .0 10.5

305.4 347.3 29 .3 125.5 125.5 182 31 .4 21 .0

(4a) (4b) (4c) (4d) (5) (6) (7)

11 .0 13.0 13.0 13.0 11 .0 10.34 11 .9

46 105 105 105 0 0 0

T a b l e I . K i n e t i c ( A r r h e n i u s ) parameters f o r a l l r e a c ­ t i o n s t e p s ER o f t h e comprehensive r e a c t i o n mechanism. P r e e x p o n e n t i a l F a c t o r A i n s e c . " o r (1/mol-sec) r e s p . , A c t i v a t i o n Energy i n ( k J / m o l ) . 1

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

26.

EBERT ET

AL.

Models for Complex Gas Phase Reactions

319

tended r e a c t i o n scheme a r a t h e r l a r g e v a r i e t y of exp e r i m e n t a l d a t a were a v a i l a b l e from the NPA r u n s . Two s e t s o f experiments were performed, one up t o temperat u r e s o f 720°C and c o n v e r s i o n s o f e t h y l b e n z e n e t o 13% and t h e second up t o temperatures as h i g h as 830°C a c c o r d i n g t o c o n v e r s i o n s o f approx. 75%.The f l o w o f the r e a c t i o n gas was c o n s t a n t i n a l l t h e s e experiments the r e a c t i o n time v a r i e d , due t o d i f f e r e n t temperat u r e s , between 2 and 3 msec. Good agreement was obt a i n e d w i t h the e x p e r i m e n t a l d a t a f o r the experiments c o v e r i n g the temperatures up t o 750°C. T h i s i s shown i n F i g u r e s 4-7, i n which f o r e t h y l b e n z e n e , s t y r e n e , benzene and e t h y l e n e c o n v e r s i o n s a t s p e c i f i c r e a c t i o n times a r e p l o t t e d a g a i n s t the r e a c t i o n temperature The d o t t e d l i n e s r e p r e s e n extended r e a c t i o n scheme t a i n e d f o r the p r o d u c t i o n of methane and t o l u e n e where l a r g e r amounts were o b t a i n e d i n the experiments than r e s u l t e d from the c a l c u l a t i o n s . However i t s h o u l d be noted t h a t the a b s o l u t e amounts o f b o t h s u b s t a n c e s were r e l a t i v e l y low i n t h i s temperature range. For f u r t h e r t e s t i n g o f the r e a c t i o n scheme we c a l c u l a t e d c e r t a i n q u o t i e n t s of molar q u a n t i t i e s o f s p e c i e s and compared them w i t h the e x p e r i m e n t a l d a t a . Some o f them are shown i n F i g u r e s 8-10. The hydrogen-styrene r a t i o s h o u l d be u n i t y as b o t h s p e c i e s are produced i n the same r e a c t i o n c h a i n e x c l u s i v e l y , which i s conf i r m e d by the e x p e r i m e n t a l r e s u l t s o v e r the whole temperature range, as shown i n F i g u r e 8. F i g u r e 9 shows the b r a n c h i n g o f r e a c t i o n s (3) and ( 3 a ) . A g a i n good agreement i s o b t a i n e d between the c a l c u l a t i o n s and the e x p e r i m e n t s . As the tempera t u r e i n c r e a s e s , the c h a i n r e a c t i o n s (3) and (4) d e c r e a s e i n terms o f r e l a t i v e c o n v e r s i o n s . The second b r a n c h i n g w i t h i n the r e a c t i o n scheme i s the c o n c u r r i n g r e a c t i o n s (4) and (4a), which can be e x p r e s s e d by the e t h y l e n e s t y r e n e r a t i o . In F i g u r e 10 the e x p e r i m e n t a l v a l u e s a r e compared w i t h t h e c a l c u l a t i o n s . The a g r e e ment i s a g a i n v e r y s a t i s f a c t o r y which means t h a t the a r o m a t i c r i n g i s d e s t r o y e d even a t r e l a t i v e l y low temperatures. F o r t h e methane and t o l u e n e f o r m a t i o n s the c a l c u l a t e d v a l u e s were t o o s m a l l compared w i t h the c a l c u l a t i o n s , and i t seems t h a t t h i s has t o be taken i n t o account by the a d d i t i o n of f u r t h e r r e a c t i o n s t e p s . P r o b a b l y the two s u b s t a n c e s a r e formed i n a c a t a l y t i c p r o c e s s on the r e a c t o r w a l l s , which needs a more c o m p l i c a t e d mechanism. As shown i n F i g u r e 4 the c a l c u l a t i o n o f the o v e r a l l r e a c t i o n r a t e s w i t h the extended scheme agrees

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

320

CHEMICAL

1.00

REACTION

ENGINEERING—HOUSTON

0.50

t

\

t c

t/

r

0.80 h

t\ 0.60

•

030

t

-

t •

0 40

-

/ .-r

- 1

600

800 °C

700

600

800 °C

700

Figure 5. Styrene

Figure 4. Ethylbenzene

1

0.50

•

tr

1

1

020

·/ mi I I

1 1 1

c

•

1

/

/

0.30

/

! /·/·

!

010

1

•i

•

/* **

010

•

/ 0.00

/ ' -»''

600

700

Figure 6. Benzene

800 °C

600

!

.

700

800 °C

Figure 7. Ethylene

Figures 4-7. Comparison of the decomposition of ethylbenzene and yields of different products or ratios of them in relative molar concentrations at various temperatures in the NPA ( · A experiments at different runs) with calcuhtions of the extended (· · -) and comprehensive ( ) reaction schemes

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

EBERT E T

Models for Complex Gas Phase Reactions

AL.

10.00 r

4.00

aoo 3.00

600

2.00 4.00 h

1.00

Ι ι ·

A

k

A

ι I·• a

I

600

Figure 8.

I

800 °C

600

Hydrogen/styrene

Figure 9.

700

700

800 °C

Styrene/benzene

1 50

1

oo Ι­

ο 50 h

îi

1

800 °C

Figure 10.

Ethylene/styrene

Figures 8-10. Comparison of the decomposition of ethylbenzene and yields of different products or ratios of them in relative molar concentrations at various temperatures in the NPA ( · A experiments at different runs) with calculations of the extended (· · · ) and comprehensive ( ) reaction schemes

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

322

CHEMICAL

REACTION

ENGINEERING—HOUSTON

w e l l w i t h the experiments c o v e r i n g temperatures up t o 750°C. Above t h i s temperature the e x p e r i m e n t a l r a t e s a r e a p p r e c i a b l y h i g h e r and accompanied by an i n c r e a s e i n benzene and e t h y l e n e c o n c e n t r a t i o n s . To account f o r t h i s we i n t r o d u c e d a second i n i t i a t i o n r e a c t i o n : (1a)

-CH CH 2

3

+

C H 6

5

+

C H 2

5

i n which e t h y l b e n z e n e i s s p l i t i n the a - p o s i t i o n . P h e n y l undergoes r e a c t i o n (3a) and e t h y l d i s i n t e g r a t e s as f o l l o w s : (2a)

C H 2

5

+

C H 2

4

+

H

Both r e a c t i o n s hav (see T a b l e I) and adde scheme. As shown i n F i g u r e s 4 and 5 c a l c u l a t i o n s now f i t t e d i n much b e t t e r w i t h the e x p e r i m e n t a l d a t a up t o temperatures o f 825°C. Benzene and e t h y l e n e p r o d u c t i o n g i v e s v e r y good agreement w i t h the c a l c u l a t i o n as can be seen from F i g u r e s 6 and 7. In a s e r i e s o f p r e l i m i n a r y experiments i n the NPA c o n v e r s i o n - t i m e runs have been performed a t 675°C s i m p l y by changing t h e f l o w r a t e . S p e c i a l c a r e has been t a k e t o keep the temperature c o n s t a n t . D e v i a t i o n s c o u l d not be p r e v e n t e d a t low f l o w r a t e s , i . e . h i g h c o n v e r s i o n s . The r e s u l t s are shown i n F i g u r e s 11-13. D e v i a t i o n s a t h i g h e r c o n v e r s i o n s may be due t o a d e c r e a s e i n temperature o r i n h i b i t i o n r e a c t i o n s . The agreement a t s h o r t r e a c t i o n times i s remarkably good, and i n d u c t i o n p e r i o d s were i n a l l c a s e s o f t h e same shape i n b o t h the c a l c u l a t i o n s and the e x p e r i ments . Summarising and C o n c l u d i n g

Remarks

For the p y r o l y s i s of ethylbenzene a r e a c t i o n scheme c o u l d be s e t up by f i r s t l y s e l e c t i n g the most s i m p l e r e a c t i o n scheme, t a k i n g i n t o account t h e main p r o d u c t s o f the r e a c t i o n a t low t e m p e r a t u r e s . Secondl y , on r a i s i n g the temperature and the c o n v e r s i o n the number o f s p e c i e s i n the r e a c t i o n m i x t u r e g e t s more abundant, t h e r e a c t i o n scheme was improved by a d d i n g new r e a c t i o n s f o r which e x p e r i m e n t a l e v i d e n c e c o u l d be o b t a i n e d from the LPA e x p e r i m e n t s . Then a l l r e a c t i o n s t e p s were a l l o c a t e d k i n e t i c c o n s t a n t s , which e i t h e r were t a k e n from the l i t e r a t u r e o r e s t i m a t e d from analogous r e a c t i o n s . Minor a l t e r a t i o n s o f some of the k i n e t i c c o n s t a n t s were made f o r b e t t e r a g r e e ment w i t h the e x p e r i m e n t a l d a t a . In t h i s way, g r a d -

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

EBERT

Models for Complex Gas Phase Reactions

ET AL.

015

0.10 h

0.05 Κ

β

m» 8

Figure 11. Ethylbenzene

t_J

Ο

1

l 2

1 3

l 4

L_J 5 6

Figure 13. Benzene

3

4

5

6

7ms 8

Figure 12. Styrene

ί7ms 8

7 ms 8

Figure 14. Ethylene

Figures 11-14. Comparison of relative molar concentrations against time of different species at 675°C with calculations of the comprehensive mechanism

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

324

CHEMICAL

REACTION

ENGINEERING—HOUSTON

u a l l y , the r e a c t i o n mechanism, which f i n a l l y c o n s i s t s o f 15 r e a c t i o n s t e p s , has been d e v e l o p e d up t o r e a c ­ t i o n temperatures of 825°C and c o n v e r s i o n s o f n e a r l y 80%. Care was taken t o ensure t h a t each r a d i c a l c o u l d r e a c t w i t h i n a t e r m i n a t i o n r e a c t i o n . T h e r e f o r e some more t e r m i n a t i o n r e a c t i o n s than those f o r m u l a t e d above were o r i g i n a l l y i n t r o d u c e d i n t o the c a l c u l a t i o n s . Some o f them c o u l d l a t e r be dropped, when i t was found t h a t they were o f o n l y minor importance t o the calculation. For the r e a c t i o n chosen the agreement o f the c a l c u l a t i o n s and e x p e r i m e n t a l r e s u l t s was good. The d i s t r i b u t i o n of a l l main p r o d u c t s c o u l d be c a l c u l a t e d within a r e l a t i v e l The method o u t l i n e a p p l i c a b l e t o c o m p l i c a t e d r e a c t i o n s and p r o v i d e s k i n e t i c r e s u l t s o f good q u a l i t y , i n v o l v i n g an e f f o r t which i s j u s t i f i a b l e i n many c a s e s . A l s o i t g i v e s an i n s i g h t i n t o the c o u r s e o f a r e a c t i o n , showing how the i n d i v i d u a l elementary r e a c t i o n s c o n t r i b u t e t o the p r o c e s s . Furthermore the r e a c t i o n mechanism can be compressed by d r o p p i n g c e r t a i n r e a c t i o n s t e p s which a r e o f minor i n t e r e s t , o r by combining s e v e r a l s t e p s i n t o one e q u a t i o n w i t h a p p r o p i a t e c o n s t a n t s , which may be h e l p save computer time. I n t h i s way i t seems p o s s i b l e t o modify a r e a c t i o n mechanism t o s u i t a s p e c i a l problem w i t h o u t s a c r i f i c i n g a c c u r a c y o f the r e s u l t s obtained. Literature

Cited

(1) Gear W.C., "Numerical Initial V a l u e Problems i n Ordinary Differential Equations" P r e n t i c e - H a l l I n c . , New York, 1972. (2) Benson S.W., "Thermochemical Kinetics", John W i l e y , New York, 1968 (3) Benson S.W., O'Neal H.E., " K i n e t i c Data on Gas Phase M i n i m o l e c u l a r R e a c t i o n s " NSRDS-Nat.Bur.of S t a n d a r d s 21, Washington, 1970 (4) K e r r J.Α., Parsonage M.J., " E v a l u a t e d K i n e t i c Data on Gas Phase Hydrogen T r a n s f e r R e a c t i o n s o f M e t h y l R a d i c a l s " B u t t e r w o r t h , London, 1976 (5) K e r r J.Α., Parsonage M.J., " R e a c t i o n s o f Atoms and R a d i c a l s w i t h A l k e n e s , A l k y n e s and A r o m a t i c Compounds" B u t t e r w o r t h , London, 1972 (6) K o n d r a t i e v V.N., "Rate C o n s t a n t s o f Gas Phase R e a c t i o n s " NSRDS-Nat.Bur.of S t a n d a r d s , Washington, 1972

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

27 Aromatic Sulfonation in a Cyclone Reactor, a Stirred Cell, and a Cocurrent Tube Reactor; Influence of Mass Transfer on Selectivity A N T O N I E A. C. M . B E E N A C K E R S Department of Chemical Engineering, Twente University of Technology, Enschede, P.O. Box 217, The Netherlands For mass transfer, followed by a

Van de Vusse [1] pointed out that selectivity with respect to I increases with an increase of the mass transfer coefficient (k ). In light of this observation, we have developed a new reactor of cyclonic type in which, due to strong centripetal forces on the gas bubbles, a very high k is realized [2]. This paper deals with the selectivities obtained in sulfonation of benzene with sulfur trioxide. Both neat benzene and benzene diluted with 1,2-dichloroethane were used. This re­ action was selected as a model reaction for industrially important aromatic sulfation (e.g. deter­ gents). We studied the reaction in three reactor types that greatly differ in mass transfer charac­ teristics, i.e. in a stirred cell reactor (low k ), a co-current gas-liquid tube reactor (intermediate k ) and in the cyclone reactor(highk ). L

L

L

L

L

Reaction Kinetics; Regime of Mass Transfer with Chemical Reaction We have discussed reaction mechanism and kinetics of sulfonation of benzene (B) with SO (A) in aprotic media [3] and have concluded that the reaction proceeds according to Van de Vusse kinetics (1-3), with k (25°C) >9.4 m /kmol s and z = / . Pyrosuifonic acid (I) and Ar S O H (I') are both unstable and react with benzene to give the desired product benzenesulfonic acid (P) and the unwanted product diphenyl sulfone (X), respectively 3

3

1

x

2

3

9

Reaction (4) is slow with respect to mass transfer and thus of negligible influence on absorption rate. Reaction (5) consumes only minor amounts of benzene (all experimentally observed selec­ tivities are (often much) above 70%based on benzene). Therefore this reaction also does not influence absorption rate appreciably. For reaction sequence (1-3), the relation between mass transfer parameters and conversion rate is — in general — complex. However, as long as observed selectivity η is high, the influence of reaction (3) on SO absorption rate is an effect that may be neglected in the first, rough estimation of the regime of absorption with reaction [4] which characterizes the system. Which regime occurs, mainly depends on the numerical values of the dimensionless groups Ha, E^and mk E/k . Due to uncertainties in the kinetic rate constant, in local liquid viscosity in the interface diffusion zone (to be discussed later), and in S0 -solubility, a prediction of the regime characterizing sulfonation of benzene, solved in 1,2-dichloroethane, is not free of speculation. In case of no liquid viscosity increase at the interface during reaction, Table I gives numerical estimations of the relevant parameters for atmospheric sulfonation at 3

L

Q

3

©

0-8412-0401-2/78/47-065-327$05.00/0

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

328

2 0 ° C with a mixture of S 0 % benzene

k

by

Ha

G

1 + zD m(c )

volume

A

A

mk

G

L

taining 10 mol % S 0

3

3

and nitrogen con­

(typical for our experi­

ments in cyclone and tube reactor) in a conven­ tional bubble c o l u m n . In our stirred cell sulfona­

> 4

5.6

0.7

30

> 2.2

2.4

0.7

tion experiments, k

10

> 1.3

1.4

0.7

10 lower than the value 1.2 10"

5

> 0.9

1.2

0.7

calculating Table I. Therefore Ha »

100

/zD m(c ) A

T a b l e I.

Estimated mass transfer parameters for

sulfonation of

benzene, solved in

1,2-dichloroet­

hane with gaseous sulfur trioxide (10 m o l

A

Q

L

was found to be a factor of 4

[m/s] used in 1 +

D c B

B

in the stirred cell. This means that

the reaction is instantaneous with respect to mass transfer in that reactor.

% in ni­

r

trogen) at 2 0 C and 1 0 Pa in a conventional bub0.7 10

ble c o n t a c t o r with μ

s Pa and k i t h e m i -

Influence of Mass Transfer on Selectivity

n i m u m value of 9.4 m ^ / k m o l s. F o r h y d r o d y n a m i cal

and physical constants applied, see reference

No

[3].

plies Ha > 0.5 and not much smaller than

A s first pointed out by V a n de Vusse [1 ] the ob­

[5]. Some experimental results are available for

chlorination [1,6-9]. A numerical analysis [10], an analog simulation [1 ] and trial and error pro­ cedures [6,8,10] by which approximate solutions can be obtained, have been presented. A s in our sulfonation experiments, there is often much doubt about the exact values of the relevant parameters (c, m, ρ, μ , D, T) at the interface, mainly because local interface conditions differ from bulk conditions. Because of this difficulty, explicit rough approximate relations for 1? are sophisticated enough to discuss experimental results and are therefore very useful. Harriott [5] derived such a simple model for the intermediate regime between fast and instantaneous re­ action. Our experiments are mainly in the instantaneous regime. Based on film theory, we deriv­ ed for this regime [3]

k D 2

(1

[D c /D, +

A

B

c,]

(6) 2z

for (1

B

-η')=k

L

2 E

~

2

- τ ? ' ) « 1 .

Equation (6) shows the manner in which the selectivity is favoured in the instantaneous regime by a high value of k , provided that the selectivity is not much smaller than one. T h e latter con­ L

dition is always fulfilled in our experiments.

Experimental The stirred cell reactor was of the Danckwerts type [4, page 180]. The reactor was filled with de­ gassed (diluted) benzene and kept under its own vapour pressure. T h e experiment was then start­ ed by connecting the space above the liquid to a thermostrated ( 3 0 ° C ) container, filled with de­ gassed stabilized liquid sulfurtrioxide, which was also under its own vapour pressure. Due to the difference in partial pressure of reaction mixture and liquid S 0 , the latter evaporated and flow­ 3

ed via a flow controller and a rotameter to the cell reactor where it absorbed into the liquid. Figure 1 is a sketch of the cyclone reactor. The liquid is fed tangentially into it (A). A gas mixture of S 0 The

3

and N

2

is introduced into the reactor via a porous section of the cylindrical wall.

liquid phase is the continuous phase in the reactor, except near the cyclone-axis. Here, a

gaseous core is f o u n d , due to a strong centripetal field, generated by the rotating liquid. This field causes gas bubbles to spiral from the wall to the cyclone-axis. Gas leaves the reactor via the upper outlet which is known as the vortex. Liquid leaves the reactor via the bottom outlet which

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

27.

329

Aromatic Sulfonation and Mass Transfer

BEENACKERS

is referred t o as the apex. Cone Ε prevents gas entrainment with the liquid. Liquid entrainment through the vortex varied between 12 and 2 0 % depending o n gas and liquid velocities. L i q u i d conversion per pass through the reactor was small. Therefore the system was operated batch wise with respect to the liquid, b y recycling reaction mixture over the reactor. Absorption efficiency of S 0

was ^ 100%.

3

3

The diameter o f the cocurrent gas-liquid tube reactor was 8 1 C T m . Gas and liquid were in­ troduced via a T-piece of the same diameter.

Results and Discussion Mass Transfer in Absorption without Reaction. We measured k 0

2

- H

0 system (figure 2). Forced convection k

2

L

in the stirred cell with an

L

in the reaction mixtures was calculated from

this result according t o [11] n

Sh~

Re Sc

l / 3

(7

with η = 1.1. Reaction effects wer ments, as will be explained in a later section, a local increase of viscosity at the interface caused by pyrosulfonic acid accumulation, produced a lower k We measured k

L

L

than calculated this way.

in a cyclone reactor with simultaneous absorption of C 0

droxide solution [2]. Figure 3 gives results. T h e figure shows that k

L

2

and 0

2

in a hy­

reaches extremely high

4

values in this reactor ( k is o n the order of 10" m/s in conventional reactors as the stirred tank L

[13], the bubble column [14], the bubble cap plate [15] and the packed column [ 1 6 , 1 7 ] . Slugflow is obtained in the tube reactor in the range of gas and liquid velocities, we applied in sulfonation [18, Figure 10.3]. k

L

values realized in this flow regime have been reported b y

Gregory and Scott [19]. F r o m this reference we calculated [3] k

L

in our tube reactor (see Figure

3). Mass Transfer in Stirred Cell Reactor during Sulfonation. T h e actual k

L

during sulfonation

follows experimentally from

k

(8)

L=C

Ai

E

As derived earlier, sulfonation of benzene is instantaneous in a stirred cell reactor. Therefore [4]: 2D c B

c

E

A i

a

s

° A i

+

B

- S —

Because o f uncertainties in c

(

A

j

, only an approximate k

L

9

)

during sulfonation can be obtained this

way. Experiments were carried out with both neat and diluted benzene (5.3 and 3 0 vol% benzene initial

Τ

reaction

J

(1 -n)

[ ° C ] [10 " k m o l / m ^ 3

mixture

k

L

c

Ii

-0.5

=1

= 4.1

= 1.5

= 3.75

0 187

= 2.2

0 25

= 1.5

0.15

0 031

=2

30 vol%

25

0.092

0 107

35

0.13

0 137

45

0.23

28

0.35

T

i

t°c]

= 3.6

35

T a b l e II.

x

3

_5

5.3 vol%

100% Β

Ii"5I

C10 m/s] [kmol/m J

2

k 2DA 5 2 [m /kmol s ]

51

3.0 Ι Ο "

= 0.7

44

0.67 Ι Ο "

= 0 .6

53

1.9 1 0 " 1 1

= 4.25

= 0.8

67

4.2 1 0 " 1 1

= 8.75

= 1

78

14 1 0 " 1 1

1 1

1 1

E s t i m a t e d values f o r gas-liquid interface p y r o s u l f o n i c acid c o n c e n t r a t i o n rise ( C j j - C j ) , s u r f a c e tempera­

ture rise (Tj-T) a n d reaction rate constant ^ D / ^ ) '

ns t

i

r r e

d

c

e

" reactor sulfonation experiments.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION

330

ENGINEERING—HOUSTON

26

33

Figure 1. Cyclone reactor. Unit of length: J 0 " m. ( A) liquid inlet (4 J O " m), (B) gas outlet (vortex) (3 JO" m), (C) liquid outlet (apex) (8.66 J O " m ), (D) gas inlet, (E) cone (120°C), (PI) pressure indicator, (a)8°C. 3

3

3

6

2

Figure 2. k in stirred cell reactor. (O), ( ) our measurements (O in H 0at25°C);( ) Jhaveri and Sharma [12]; (- · -) SOs in both 1,2dichloroethane and benzene, with Equation 7. L

s

2

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

27.

Aromatic Sulfonation and Mass Transfer

B E E NA C K E R S

in 1,2-dichloroethane

331

respectively). Stirrer speed (N) varied between 0 and 2 r e v / s . k ^ showed

to be independent of Ν and t o be appreciably lower than without reaction. T h e average values of k

L

are summarized in Table II. Table II also shows that both the interface pyrosulfonic acid

concentration ( c ) and the interface temperature M

(T.) are much higher than in the bulk of the

liquid. T h e first quantity (c .) has been approximated with (

1

c .-c = / r?J/k |

j

2

T h e second quantity

(10)

L

(T.) has been estimated from the simple film model according to Danck-

werts [4]

Τ. —Τ = J D ι

R

Β

(ΔΗ

a

+ ΔΗ ) / r

ΧΛ.

(11)

S L

T h e influence o f pyrosulfonic acid concentratio because o f the

instability

viscosit

i

neithe

know

measurabl

o f thi

mixture at 2 3 . 5 ° C as a function o is:

Ιη(μ(χ )/μ(ο))=8.85χ ρ

Without

(12)

ρ

measurements, our best possible assumption is that pyrosylfonic acid has the same

influence on viscosity as sulfonic acid. Recalling from eqn. (7) that

k ~(D/M)

2 / 3

L

and applying the Stokes-Einstein equation results in

k

It

L

~M"

4

/

3

(13)

follows from x

( j

(Table

II) and eqns (12,13) that k

L

is appreciably lowered by viscosity

effects that occur during reaction. In practice this tendency is counteracted by both the inter­ face temperature

rise and free convection, driven by density and/or surface tension gradients.

Both effects lower the extent of interface viscosity increase. T h u s , a k

L

is obtained which is

independent of stirrer speed and lower than that for forced convection in the absence of inter­ face viscosity effects as given in Figure 2. Selectivity in Stirred Cell Reactor.

Observed 1 -

η is always «

1. Therefore eqn. (6)

is expected t o be applicable though its accuracy is probably low due to the discussed interface viscosity increase. F r o m eqn. (6)

1-T?~1/k

2

(14)

L

Figure 4 shows (1— η)

t o be nearly independent o f N . Even the abcense o f stirring does not

lower selectivity significantly. This fact is in agreement with, and additional argument for, our preceding conclusion that k

L

is independent of stirrer speed.

Figure 4 shows that by-product formation Taking as a first approximation D

Q

= D , c, « (

increases with initial benzene concentration. δ

β

and 1 - η = 1 - i? (allowed for f «

1)

we obtain from eqn. (6) with ζ = % :

1-T?^k D 2

A

c

B

/(k EJ

2

L

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

(15)

CHEMICAL REACTION ENGINEERING—HOUSTON

332

Figure 3. k as f(U ) for C0 in 2.07M NaOH solution in a cyclone reactor with Vi = 5.97 m/s (1) and 9.15 m/s (2) and in tube reactor for U = I m/s (3) and 1.75 m/s (4) L

s

2

L

30-

1-η[·/.] *

t

; 20-

υ-, 0

, 066

,

,

,

1

133

2

•

N[s-1]

Figure 4. By-product formation in sulfonation of benzene with gaseous sulfur trioxide in a stirred-cell reactor in rehtion to initial benzene concentration and stirrer speed. (A) 5.3 vol % benzene in dichloroethane, T ss 35°C, ζ = 0.8; (Ο) 30 vol % benzene in dichloroethane, T ss 25°C, ζ 0.09; (Ο) 30 vol % benzene in dichlo­ roethane, Τ ss 35°C, ζ Ξ* 0.1; (A) 100 vol % benzene in dichloroethane, Τ as 28°C, ζ ss 0.005.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

27.

333

Aromatic Sulfomtion and Mass Transfer

BEENACKERS

Combining with equation (8) gives k D = * ( 1 - T?) J / ( c c 2

2

A

B

2 A j

)

(16)

ι/Vith this equation, the value of k D 2

II). Figure 5 shows log k D 2

k D 2

A

=k

0

0

D

A

e-

A

E

/

R

T

A

has been estimated from the experimental results (Table

as a function of 1/T.. Fitting the experimental data to

A

i

(17)

esults in

k

and

oo

D

5

=4.5 m /kmol s

A

2

6

Δ Ε = 3 0 . 7 10 J/kmol

The obtained value for Δ Ε is likel approximate same value for Δ Ε in a chemically, very similar reaction in sulfonation of chloroberizene. Assuming at the interface: D 2

l 0

A

2

s 1 0 " m / s , it follows from eqn. (17) that k

2

(25°C) =

3

1.7 10" m / k m o l s. Reaction rate constant for the first reaction (eqn. (2)) has been shown to be 3]: 3

k ( 2 5 ° C ) > 9 . 4 m /kmols 1

Hence, in homogeneous sulfonation, no diphenyl sulfone will be obtained. Selectivity in the Cyclone and in the Tube Reactor. Differential selectivity (τ?') was measued as a function o f f . A b o u t 25 experimental runs were carried o u t . Table III shows the range between τ

Initial

vol %

f

A

ς

benzene i n liquid

40

ved η

on

[m/s]

20

the operation

depended mainly o n ini­

tial benzene concentration and

phase

[°cl

which

parameters were varied. Obser­

10

0 02 - 0.04

3.5 - 6.8 0 09 - 0 1 1 0 1 3 - 0 46

30

0 01 - 0.38

3.3 - 7.9 0 06 - 0 13

0 07 - 0 42

100

0 01 - 0.21

2.8 - 6.6 0 08 - 0 13

0 01 - 0 05

30

0 01 - 0.08

2.7 - 7.9 0 09 - 0 12

0 04 - 0 51

100

0 01 - 0.02

2.4 - 7.6 0 11 - 0 12

0 01 - 0 05

are

s

summarized

Figure

6

in Figure 6.

also

shows

results

from tube reactor experiments (1 < U
1. For t h i s case a zero-order d e s c r i p t i o n i n Ο i s v a l i d . 2 When F Q < 1, a l l 0 -consuming r e a c t i o n s were m u l t i p l i e d by the f a c t o r F Q 2 . This means that i n t h i s case a f i r s t - o r d e r r e a c t i o n i n 0^ 2 i s assumed. The example shown i n F i g . 2 serves to i l l u s t r a t e to what extent the l a b o r a t o r y experiments are covered by the model. 2

3. MODEL OF THE GAS-LIQUID REACTOR With regard t o the g a s - l i q u i d r e a c t o r the f o l l o w i n g assumptions have been made : - the l i q u i d phase and the gas phase are p e r f e c t l y mixed, - the i s s u i n g gas stream i s i n p h y s i c a l e q u i l i b r i u m w i t h the i s s u i n g l i q u i d stream, - the r e a c t o r operates a d i a b a t i c a l l y , - the compositions, f l o w r a t e s , temperatures and pressures o f the feed streams are known. In c a l c u l a t i n g the p h y s i c a l e q u i l i b r i u m , we made use o f gasl i q u i d e q u i l i b r i u m constants, which are defined as (z)

6

L

d

L

G

-

GO

S

(1 +

OC)

—

(1-x

)

Ο

=

L ^L

=

k

quan­

( Π )

H

{ l Z )

(13)

L

(14) 6

St.

0

l+0t(l-z)

= U

Pe

^

following dimensionless

£

Γ

L

—2-

(15) S L Here p r e s e n t s t h e 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 , L t h e e n t i r e c o l u m n l e n g t h , R t h e gas constant, Τ t h e t e m p e r a t u r e , and u the s u p e r f i c i a l l i q u i d v e l o city . The i n i t i a l c o n d i t i o n f o r eqn (10) i s T

U

χ(Ο) The b o u n d a r y of c o c u r r e n t

= χ

(16)

ο

c o n d i t i o n s f o r eqn f l o w (a = -1) :

(11)

are

f o r the

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

case

30.

DECKWER

ET

r

L dz

365

CO Inter phase Mass Transfer

AL.

+

Va Pe,

dp

(Ο)

T

L

dz

(17)

( 1 )

=

(18)

Ο

for countercurrent

flow

(a

= +1) :

dp (0) L

(19)

~"dz

P (1) L

dz

Pe,

Li

The i n d e x i r e f e r s t o i n l e t c o n d i t i o n s . The d i f f e r e n t i a l e q n s (10) and (11) w e r e s o l v e d n u m e r i ­ c a l l y by t h e m e t h o d o f Lee (_14_) w h i c h i s w e l l s u i t e d t o s o l v e n o n - l i n e a r boundary v a l u e problems w i t h non-con­ s t a n t c o e f f i c i e n t s . H o w e v e r , as w i l l be d i s c u s s e d l a t e r i t was n o t p o s s i b l e t o o b t a i n c o n v e r g e n c e f o r c e r t a i n parameter combinations, p a r t i c u l a r l y at high values of k . I t i s a s s u m e d t h a t t h i s h a s t o be a t t r i b u t e d t o s t i f f n e s s of the system of d i f f e r e n t i a l e q u a t i o n s . Since d e p e n d s on g a s v e l o c i t y ( s e e eqn ( 7 ) ) and t h i s v a r i e s c o n s i d e r a b l y a l o n g the column p r e l i m i n a r y computations were c a r r i e d o u t w i t h d i f f e r e n t v a l u e s o f calculated from u and u ^ (gas v e l o c i t y a t o u t l e t ) / r e s p e c t i v e l y . These c a l c u l a t i o n s r e v e a l e d t h a t computed gas p h a s e p r o f i l e s a r e p r a c t i c a l l y n o t e f f e c t e d by f o r the p o s s i b l e range of v a r i a t i o n . T h e r e f o r e D was calcula­ t e d f r o m eqn (7) w i t h t h e mean gas v e l o c i t y w h i c h i s def i n e d by G o

1

u

G

( ζ ) dz

(21)

w h e r e t h e l o c a l v a l u e s o f u ( z ) a r e o b t a i n e d f r o m eqn (9) by c o n s i d e r a t i o n o f eqn (6) and t h e m e a s u r e d g a s p h a s e p r o f i l e . The 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 now t h e o n l y q u a n t i t y w h i c h i s u n k n o w n . I t was t h o u g h t t h a t t h e s e k - v a l u e s c a n s i m p l y be determined by f i t t i n g m o d e l p r e d i c t i o n s t o e x p e r i m e n t a l g a s p h a s e p r o f i l e s . No s p e c i a l o p t i m i z a t i o n p r o c e d u r e was a p p l i e d . S i n c e o n l y one p a r a m e t e r h a d t o be d e t e r m i n e d and t h e c o m p u t a t i o n s were f a s t enough a t r i a l - a n d - e r r o r method was sufficient. G

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL

366 Description

of Measured

REACTION

ENGINEERING—HOUSTON

Profiles

When u s i n g c o n s t a n t v a l u e s o f k the model equa­ t i o n s c o u l d not d e s c r i b e r e a s o n a b l y the e x p e r i m e n t a l p r o f i l e s . T h i s i s shown i n f i g . 2 f o r d e s o r p t i o n mea­ s u r e m e n t s . The c u r v e s f o r f = 1 r e f e r to k -values w h i c h a r e c o n s t a n t o v e r t h e e n t i r e c o l u m n . T h o u g h ex­ p e r i m e n t a l and t h e o r e t i c a l r e s u l t s c a n be b r o u g h t i n agreement nearby the top of the column, the c a l c u l a t e d mole f r a c t i o n s a r e a l w a y s c o n s i d e r a b l y t o o low c l o s e t o the bottom. F u r t h e r i n c r e a s e of k d i d not improve the agreement but l e d u s u a l l y to s t i f f n e s s s i n c e convergence c o u l d n o t be o b t a i n e d any m o r e . As t h e t h e o r e t i c a l p r o ­ f i l e s indicate that transfe i to small merel n e a r t h e gas d i s t r i b u t o applied there. Favorabl r u n s c o u l d be o b t a i n e d i f t h e c o n s t a n t mass t r a n s f e r c o e f f i c i e n t was r e p l a c e d by a p r o f i l e w h i c h i s shown i n f i g . 3. F o r r e a s o n s o f s i m p l i f i c a t i o n i n t e g e r v a l u e s of f were t a k e n o n l y : 2 ^ f < 4 ( s e e t a b l e 1 ) . Thus a s t r i k i n g a g r e e m e n t b e t w e e n t h e m e a s u r e d d a t a and t h e m o d e l p r e d i c t i o n s ( f u l l d r a w n c u r v e s ) i s o b t a i n e d as c a n be s e e n f r o m f i g . 1. F i g . 4 and 5 p r e s e n t C 0 pro­ f i l e s o f t h e g a s and l i q u i d p h a s e , r e s p e c t i v e l y , f o r the case of a b s o r p t i o n runs at c o u n t e r c u r r e n t f l o w . Once a g a i n a s u f f i c i e n t a g r e e m e n t i s o b s e r v e d . I t i s i n t e r e s t i n g t o n o t e t h a t t h e gas p h a s e c o n ­ c e n t r a t i o n c a n r u n t h r o u g h a minimum v a l u e . T h o u g h t h i s minimum i s v e r y f l a t i t i s r e p r o d u c i b l e and was a l s o f o u n d f o r o t h e r r u n s . S u c h e x t r e m e v a l u e s i n gas c o n c e n t r a t i o n were not o b s e r v e d e x p e r i m e n t a l l y b e f o r e , however, t h e y were a l r e a d y p r e d i c t e d t h e o r e t i c a l l y from n u m e r i c a l s t u d i e s f o r t h e c a s e o f c o c u r r e n t f l o w (4_) . For the c o u n t e r c u r r e n t a b s o r p t i o n run presented i n f i g . 4 t h e minimum r e s u l t s f r o m t h e r a t h e r h i g h i n l e t c o n ­ c e n t r a t i o n o f CO^ i n t h e l i q u i d p h a s e , s e e f i g . 5. Due to the h y d r o s t a t i c head the c o n c e n t r a t i o n of C 0 i n the g a s p h a s e d e c r e a s e s t o a l o w e r v a l u e t h a n t h a t one w h i c h corresponds to the i n l e t p a r t i a l p r e s s u r e i n the l i q u i d p h a s e . T h e r e f o r e a t column t o p s m a l l amounts o f C 0 desorb from the l i q u i d phase which i s s u p e r s a t u r a t e d a g a i n s t gas p h a s e . T h o u g h t h e o b s e r v e d m i n i m a a r e i r r e ­ l e v a n t f o r any t e c h n i c a l a p p l i c a t i o n t h e y p r e s e n t a j u s t i f i c a t i o n of the a p p l i e d model s i n c e s i m p l e r models are not a b l e to d e s c r i b e the measured p r o f i l e s . I f c o n s t a n t v a l u e s o f t h e h o l d - u p and t h e i n t e r f a c i a l a r e a (^ (z) = 1) w e r e a p p l i e d i n t h e c a l c u l a t i o n s a r e a s o n a b l e f i t t i n g of the measured p r o f i l e s c o u l d not be o b t a i n e d . T h i s i s shown i n f i g . 6 w h e r e t h e d o t t e d l i n e s i n d i c a t e t h e o r e t i c a l p r o f i l e s w i t h the s m a l l e s t B

2

2

2

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

30.

DECKWER

ET AL.

χ

367

CO ^-Interphase Mass Transfer

0,6

0

OA

0,2

0,6

0.8

1.0

—

2

Figure 2. Measured and calculated gas phase mole fraction of C0 for different values ofi 2

B

Figure 3. Applied profile of liquid phase mass transfer coefficient

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL

368

χ

REACTION

ENGINEERING—HOUSTON

0.8

0 Figure 4.

0.2

0,4

0.6

0.8

1,0

Measured and calculated gas profiles at countercurrent absorption

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

30.

DECKWER

ET AL.

CO -Interphase Mass Transfer 2

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

369

370

CHEMICAL

REACTION

ENGINEERING—HOUSTON

a t t a i n a b l e d e v i a t i o n ( k = 0.0235 cm/s and f = 2 for r u n 12, = 0.0133 and f = 3 f o r run 14). This obser­ v a t i o n l e a d s t o the c o n c l u s i o n t h a t the proposed model i s a b l e to d e s c r i b e the measured p r o f i l e s o n l y because *f (z) i s known w i t h s u f f i c i e n t a c c u r a c y t o o . The k - and f - v a l u e s d e t e r m i n e d f r o m m a t c h i n g t h e o r e t i c a l p r e d i c t i o n s to experimental r e s u l t s are g i v e n i n t a b l e 1. S i n c e t h e i m p o r t a n t h y d r o d y n a m i c p r o ­ p e r t i e s are l o c a l l y dependent i t i s understood t h a t the mass t r a n s f e r c o e f f i c i e n t i s a l s o a f u n c t i o n o f z. The o b t a i n e d k ~ d a t a are i n the r e a s o n a b l e range. However, c o n t r a r y t o p r e v i o u s f i n d i n g s a t l o w i n t e r p h a s e mass t r a n s f e r (6_) t h e y d i f f e r l a r g e l y f o r a b s o r p t i o n and desorption runs. Furthermor t desorptio yield s u r p r i s i n g l y higher value The d e p e n d e n c y o f k operating p a r t i c u l a r l y on t h e f r e q u e n c y f a c t o r s o f b u b b l e c o a l e s ­ c e n c e and b r e a k up (8_) w i l l be d i s c u s s e d t o g e t h e r w i t h f u r t h e r m e a s u r e m e n t s i n a f o l l o w i n g p a p e r (_1_5) · L

L

Conclusion The f i n d i n g s o f t h i s s t u d y on a b u b b l e c o l u m n o f i n d u s t r i a l l e n g t h and a d i a m e t e r s u f f i c i e n t l y l a r g e n o t to i n v o l v e w a l l e f f e c t s c o n f i r m s the s i g n i f i c a n c e of the a p p l i e d model which a c c o u n t s f o r the h y d r o s t a t i c h e a d and gas f l o w v a r i a t i o n s . H o w e v e r , t h e e x c e l l e n t a g r e e m e n t b e t w e e n e x p e r i m e n t a l and t h e o r e t i c a l r e s u l t s c o u l d o n l y be o b t a i n e d w i t h c o n s i d e r a t i o n o f d e t a i l e d i n f o r m a t i o n on t h e h y d r o d y n a m i c p a r a m e t e r s . Unfortunate­ l y s u c h e x a c t k n o w l e d g e on h y d r o d y n a m i c p r o p e r t i e s i s seldom a v a i l a b l e . T h i s f a c t w i l l c e r t a i n l y not p e r m i t the w i d e s p r e a d a p p l i c a t i o n o f the proposed model i n i n ­ d u s t r y at the p r e s e n t t i m e . T h e r e f o r e f u r t h e r s t u d i e s at o p e r a t i n g 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 y a r e nee­ ded w h i c h a r e f o c u s e d on m e a s u r e m e n t s i n s i d e t h e e q u i p ­ ment and w h i c h a r e e v a l u a t e d on t h e b a s e o f r e a l i s t i c m o d e l s . I t c a n be e x p e c t e d t h a t o n l y f r o m s u c h s t u d i e s r e a s o n a b l e g u i d e l i n e s may be d e v e l o p e d w h i c h p r o v i d e for a r e l i a b l e d e s i g n of bubble columns. Acknowledgement The a u t h o r s g r a t e f u l l y a c k n o w l e d g e s u p p o r t f r o m Deutsche Forschungsgemeinschaft and S t i f t u n g V o l k s w a g e n we r k .

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

30.

DECKWER

ET

AL.

CO -lnterphase Mass Transfer

371

2

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Pavlica,

R.T.,

Olson,J.H.,

I n d . E n g . C h e m . (1970)

62 45

(2) (3)

M h a s k a r , R . D . , C h e m . E n g n g . S c i . ( 1 9 7 4 ) 2 9 897 Szeri,A., Shah,Y.T., Madgavkar,A., Chem.Engng.Sci.

(4) (5) (6)

Deckwer,W.-D., C h e m . E n g n g . S c i . (1976) 31 309 Deckwer,W.-D., C h e m . E n g n g . S c i . (1977) 32 51 D e c k w e r , W.-D., Burckhart,R., Zoll,G., Chem.Engng.

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(9)

(1974)

29

2177

D e c k w e r , W.-D., Zaidi,A., Adler,I., Chem.-Ing.T e c h n . (1976) 48 1075 Deckwer,W.-D., Zaidi,A., Adler,I., Preprints Eur Congr.: Transfer Nuremberg,Germany, , y lerus B a i r d , H . M . I . , R i c e , R . G . , Chem.Engng.J. (1975) 9 171

(10) S u b r a m a n i a n , G . ,

Tien,C.,

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(1975)

53 611

(11) T o w e l l , G . D . , A c k e r m a n , G . H . , P r o c . ISCRE 2, B 3 - 1 , A m s t e r d a m 1972 (12) S e r p e m e n , Y . , Deckwer,W.-D., I n d . E n g . C h e m . F u n d a m . (1974) 13 399

(13) Göhler,P., D r . - I n g . thesis, TU Berlin, 1973 (14) L e e , E . S . : "Quasilinearisation a n d Invariant Im­ bedding" A c a d e m i c Press, New York, 1968 (15) Deckwer,W.-D., Zaidi,A., Adler,I., Chem.Engng.J., in preparation

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

31 Determination of Fluid Dynamic Parameters in Bubble Column Design T H . P I L H O F E R , H . F . B A C H , and K. H. M A N G A R T Z Lehrstuhl A für Verfahrenstechnik, Technische Universität München, West Germany

Bubble columns are applied employed in the sam also in waste water cleaning (2). Quite recently, their use for microbial processes has become increas­ ingly important (3). In spite of the variety of these applications and the number of known experimental studies, the design and scale-up of a bubble column is still a difficult task. In this paper, results of ex­ periments are presented, which are concerned with the determination of fluiddynamic parameters for column design. The description of a process, taking place in a bubble column, requires the selection of a suitable model. In most cases the application of the one-dimen­ sional dispersion model has proven satisfactory. When a differential mass balance is made around a differen­ tial segment of the column, disregarding radial depen­ dencies, the following equations result for the case of counter-current:

The l i n e a r velocities o f the c o n t i n o u s and d i s p e r s e phase, u and u , can be a d j u s t e d arbitrarily, whereas the mass t r a n s f e r coefficient k depends first o f all on the system's p h y s i c a l p r o p e r t i e s . On the o t h e r hand the f l u i d d y n a m i c parameters like interfacial a r e a a, gas holdup ε and the d i s p e r s i o n coefficients and are i n f l u e n c e d s t r o n g l y by the phases throughputs. I t is t h e r e f o r e n e c e s s a r y to p r e p a r e a p p r o p r i a t e correlC

D

L

©

0-8412-0401-2/78/47-065-372$05.00/0

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

31.

PILHOFER

Parameters in Bubble Column Design

ET AL.

373

ations f o r the c a l c u l a t i o n o f these parameters i n o r ­ der to solve equation ( l ) a n d ( 2 ) . The f o l l o w i n g state­ ments a r e concerned w i t h t h i s problem. F i r s t of a l l , the l a y - o u t of the gas d i s t r i b u t o r l l be treated. I t s t a s k i s t o g e n e r a t e swarms o f bbles. I f a sieve t r a y i s used, one should be aware the fact, that a l l the holes must be i n o p e r a t i o n . h e r w i s e , u n d e s i r e d c i r c u l a t i o n s come i n t o existence. rthermore, weeping must be a v o i d e d when u s i n g large enings. This i s most i m p o r t a n t , i f the l i q u i d tends incrustate o r s o l i d i f y . These phenomena a r e caused b y t h e mechanism o f t h e p a r t i c l e formation on the sieve t r a y . The openings work i n the j e t t i n g r e g i o n and n o t i n the b u b b l i n g r e g i o n (k). Therefore, to o b t a i so much a g a s t h r o u g h p u t h a s t o b e p r e s e n t e d , that a l l openings work at least at the beginning o f the j e t t i n g region. The minimum gas l o a d r e l a t i v e tqjeach h o l e c a n be d e t e r m i n e d b y t h e f o l l o w i n g e q u a t i o n s (k): Small hole diameters:

w i bu of Ot Fu op to

We.

=

w

L

Large

hole

,

d

L ' P p

=

2

(3)

a

L

diameters:

Fr^

= _ ί ί _ . ( _ 2 _ ) d -g ΔΡ

(4)

=0,37

T

The v a l i d i t y o f f o l l o w i n g value

d These

Q

=

Li both equations i s separated o f the hole diameter:

2,32 · ( a / p -

equations

D

a r e v a l i d

5

g

)°' · ( ρ / Δ ρ )

5

by the

/

(5)

8

0

f o r g a s / l i q u i d

systems

w e l l

as

as f o r l i q u i d / l i q u i d systems (k)· The swarms o f b u b b l e s p r o d u c e d b y t h e d i s t r i b u t o r moves upward t h r o u g h t h e l i q u i d . Now, the nature o f the bubble motion i s most important f o r t h e develop­ ment o f t h e p r o c e s s i n the column. A t l o w gas v e l o c i ­ t i e s the bubble h a r d l y hinder each other and the swarm r i s e s u p w a r d i n a r e g u l a t e d manner. This i s c a l l ­ ed t h e "bubbly f l o w regime (5.). P r e s u m i n g a constant bubble s i z e , there i s a maximum v a l u e o f gas t h r o u g h ­ put w i t h i n t h i s bubbly f l o w regime, that can be deter­ mined by f l o o d i n g p o i n t c a l c u l a t i o n s (6). I f the throughputs a r e increased beyond t h i s p o i n t , a f l o w a l t e r a t i o n takes place. I n order to reach higher buoy­ ancy forces f o r gas transport, bubble c l u s t e r s o r plugs a r e formed. This i s c a l l e d the "churn turbulent regime" ( 5 ) · 1 1

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

374

CHEMICAL

REACTION

ENGINEERING—HOUSTON

F o r t h e s e two f l o w r e g i m e s f i g u r e 1 shows s c h e m a ­ t i c a l l y t y p i c a l c u r v e s f o r the dependency o f the gas h o l d u p on t h e gas v e l o c i t y . D u r i n g b u b b l y f l o w t h e gas h o l d u p i n c r e a s e s s u p e r p r o p o r t i o n a l l y w i t h t h e gas throughput. With the b e g i n n i n g f o r m a t i o n of bubble c l u s t e r s , these curves are s h i f t e d to the r i g h t because of the c o n t i n u o u s l y i n c r e a s i n g bubble s i z e . This r e ­ s u l t s i n a s u b p r o p o r t i o n a l r i s e o f t h e gas h o l d u p w i t h gas t h r o u g h p u t . I t i s t h e r e f o r e n e c e s s a r y t o d i s t i n ­ g u i s h b e t w e e n t h e s e two f l o w r e g i o n s . A t t h e moment i t i s n o t p o s s i b l e t o s p e c i f y t h e l i m i t s of both regimes. For a rough approximation the f o l l o w i n g c a l c u l a t i o n may be c a r r i e d o u t : W a l l i s recommends t h e f o l l o w i n equatio f o th motio f swarm o f b u b b l e s i n (6 )

= ( ι - ε ) Using a batch-type l i q u i d , f o r the r e l a t i v e the f o l l o w i n g h o l d s : w = u / R

The

flooding

D

velocity

ε

(7)

condition i s : du

D

/ άε

=

0

F r o m e q u a t i o n (6) a n d (7) we g e t a t t h e f l o o d i n g a g a s h o l d u p o f 0,5 and the r e l a t i o n s h i p : u

D

=

0,25-Woo

(8) point (9)

F o r a u s u a l r i s e v e l o c i t y o f a s i n g l e b u b b l e o f 23 cm/s, f r o m e q u a t i o n (9) a maximum l i n e a r g a s v e l o c i t y o f 5i7 cm/s a r i s e s . A t h i g h e r g a s v e l o c i t i e s o n l y t h e c h u r n t u r b u l e n t r e g i m e e x i s t s . Y e t , e x p e r i m e n t s show, t h a t f l o w a l t e r a t i o n may a l r e a d y o c c u r a t l o w e r g a s t h r o u g h p u t s. A t hi^te moment e q u a t i o n (6) may be r e c o m m e n d e d f o r t h e c a l c u l a t i o n o f t h e gas h o l d u p i n t h e b u b b l y f l o w r e g i m e . A b e t t e r c o r r e l a t i o n can be o b t a i n e d , i f equations f o r the motion of s o l i d s are m o d i f i e d i n a c o n v e n i e n t way. T h i s h a s a l r e a d y b e e n a c h i e v e d f o r t h e m o t i o n o f d r o p l e t swarms ( 7 ) · T h o u g h t h e c h u r n t u r b u l e n t r e g i m e i s t h e more s i g n i f i c a n t r e g i o n , t h e r e a r e no e q u a t i o n s g e n e r a l l y a p p l i c a b l e t o d e t e r m i n e the gas h o l d u p . Beyond t h i s , most e x p e r i m e n t s have been c a r r i e d out w i t h a i r / w a t e r s y s t e m s . I n o u r e x p e r i m e n t s p r e f e r e n c e was t h e r e f o r e given to the v a r i a t i o n of the system's p h y s i c a l pro­ p e r t i e s . F o u r l i q u i d s w e r e u s e d u n d e r d i f f e r e n t tem­ p e r a t u r e s ; experiments under pressure are s t i l l going on b u t n o t y e t e v a l u a t e d . F o r e x a m p l e , i n f i g u r e 2 measurements o f t h e gas h o l d u p a t d i f f e r e n t l i n e a r gas

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

PILHOFER

Parameters in Bubble Column Design

ET AL.

bubbly

flow

Figure 1. Dependency of the gas holdup on the linear gas velocity for different flow regions

0.3-

C O O C ο ο c

»

Q ο

α

α · ο

ο·

δ

ο

t%

*

• Ί ° * *

°· „

·

ο ° . \ ο

°. ν

η α

• 0 ι °· ο

»*

•

8

ο

3

liquid

ndo

butane diol

29.5 6,8

ethylene glycol octanol

11.7

•

3.2

tetrabromo eth 0

5

10

1.7

15 cm/s

gas phase linear velocity u

20

0

Figure 2. Measured gas holdup values for four different liquids as a function of gas linear velocity

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

376

CHEMICAL

REACTION

ENGINEERING—HOUSTON

v e l o c i t i e s w i t h d i f f e r e n t l i q u i d s are p l o t t e d . E v a l u a t i n g o u r own m e a s u r e m e n t s a n d c o n s i d e r i n g t h e r e s u l t s o f K u s t e r s (£0 a n d Hammer/Rahse (9.) , u s i n g c o l u m n s w i t h t h e same d i m e n s i o n s , t h e f o l l o w i n g e q u a ­ t i o n f o r the dependency o f the gas h o l d u p f r o m the l i n e a r gas v e l o c i t y and t h e p h y s i c a l p r o p e r t i e s h o l d s : ——

= 0,115

( u

3

/

( v . g - A p /p c

))

c

0 , 2 3

do)

E q u a t i o n (10) i s v a l i d f o r a c o l u m n w i t h a n i n n e r d i a ­ m e t e r o f 100 mm a n d a c l e a r l i q u i d h e i g h t g r e a t e r t h a n 1200 mm. I n a f u r t h e r s t e p we t h e r e f o r e e x a m i n e d , wèther g a s h o l d u p i s i n f l u e n c e d b y t h e c o l u m n d i m e n ­ sions. In f i g u r e 3 S holdup measurements are p l o t t e d v e r s u s gas l i n e a r v e l o c i t y ed o u t i n c o l u m n s w i t 150 mm a n d c l e a r l i q u i d h e i g h t s h i g h e r t h a n 1000 mm. F u r t h e r m o r e , t h e e m p l o y e d gas d i s t r i b u t o r s c a u s e d a c h u r n t u r b u l e n t f l o w a l r e a d y a t l o w gas throughputs. I t c a n be s e e n , t h a t a l l t h e v a l u e s a r e d e s c r i b e d b y one r e g r e s s i o n l i n e j w i t h s a t i s f a c t o r y a c c u r a c y . C o n s e ­ q u e n t l y , t h e r e i s no d e p e n d e n c y o f g a s h o l d u p f r o m column d i m e n s i o n s . Because of the agreement of the e x p o n e n t o f t h e gas l i n e a r v e l o c i t y i n e q u a t i o n (10) w i t h t h e r e s u l t s o f f i g u r e 3, e q u a t i o n (10) c a n be r e ­ commended f o r g a s h o l d u p c a l c u l a t i o n s . I t i s p o s s i b l e , t h a t t h e c o n s t a n t v a l u e o f 0,115 m u s t be c o r r e c t e d i n ­ s i g n i f i c a n t l y , a s e q u a t i o n (10) has been d e r i v e d f o r a column o f 100 mm i n n e r d i a m e t e r w h e r e a s f i g u r e 3 f e r s to columns w i t h a d i a m e t e r equal or g r e a t e r than 150 mm. The m e n t i o n e d d e p e n d e n c i e s c o m p l y w e l l w i t h t h e r e s u l t s o f R i q u a r t s ' s c o n s i d e r a t i o n s ( 10 ) f o r . f l u i d i z e d beds. An a d d i t i o n a l f l u i d d y n a m i c p a r a m e t e r t o be d e t e r ­ m i n e d i s t h e i n t e r f a c i a l a r e a a: a s

r e

a

=

6·ε

/ d

3 2

(11)

I n e q u a t i o n (11) t h e g a s h o l d u p c a n be d e t e r m i n e d by e q u a t i o n (10) o r r e s p . (6). Further informations are n e e d e d w i t h r e g a r d t o t h e medium b u b b l e s i z e d . U n f o r t u n a t e l y t h e r e i s n o t much e x p e r i m e n t a l data on b u b b l e s i z e s r e s p . b u b b l e s i z e d i s t r i b u t i o n s due t o the c o m p l i c a t e d m e a s u r i n g methods. For our measurements a new e l e c t r i c m e a s u r i n g d e v i c e (11 ) ,(12 ) was u s e d . A p a r t i a l stream of the d i s p e r s e f l u i d two-phase system i s s u c k e d o f f by a v e r t i c a l f u n n e l c o n n e c t e d w i t h a g l a s s c a p i l l a r y . The c a p i l l a r y d i a m e t e r i s c h o s e n s o , t h a t most o f t h e b u b b l e s a r e d e f o r m e d t o p l u g s . These a r e d e t e c t e d t w i c e b y a s u i t a b l e l i g h t s e n s i n g means t h a t i n f o r m s on t h e l e n g t h o f t h e p l u g s . I f t h e p l u g

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

31.

PILHOFER

ET AL.

Parameters in Bubble Column Design

377

c r o s s - s e c t i o n i s determined by a d d i t i o n a l c a l i b r a t i o n p r o c e d u r e s , the volume o f each p a r t i c l e c a n be c a l c u ­ l a t e d ^ i t i s a n advatage o f t h i s m e a s u r i n g method t o enable high measuring f r e q u e n c i e s . I n f i g u r e 4 m e a s u r e d mean b u b b l e s i z e s a r e shown f o r the a e r a t i o n o f x y l e n e and propanol by n i t r o g e n . The m e a s u r e m e n t s t o o k p l a c e i n a c o l u m n o f 225 mm d i a ­ m e t e r . The m e a s u r i n g h e i g h t w a s 850 mm a b o v e t h e g a s d i s t r i b u t o r , w h i c h was f o r m e d a s a s i e v e t r a y w i t h d i f f e r e n t h o l e d i a m e t e r s . I t can be seen, t h a t t h e s a u t e r mean d i a m e t e r d i s almost independent o f t h e g a s t h r o u g h p u t . K u s t e r s (8^) g o t s i m i l a r r e s u l t s . More d e t a i l e d i n f o r m a t i o n r e s u l t s f r o m a n a n a l y s i s of bubble s i z e d i s t r i b u t i o n s Thes hav bee approxi mated by a l o g a r i t h m i value o f thesauter b e f o r e . The c e n t r a l v a l u e s d and the standard d e v i a ­ t i o n s 0£, c a l c u l a t e d i n t h e way m e n t i o n e d b e f o r e , a r e p l o t t e d i n f i g u r e 5- The d e p e n d e n c y o f t h e c e n t r a l v a l u e s o f t h e g a s t h r o u g h p u t i s b a s i c a l l y t h e same a s on s i n g l e h o l e s . A f t e r t h e t r a n s i t i o n o f a l l h o l e s i n t h e j e t t i n g r e g i o n ( u » l cm/s ) a s t r o n g d e c r e a s e o f d_ appears, which f l a t t e n s w i t h higher gas through­ p u t s . Y e t , i t must be c o n s i d e r e d , t h a t t h e s t a n d a r d d e v i a t i o n s a t f i r s t i n c r e a s e stroPgly w i t h gas holdup, before reaching a constant value. With respect t o t h e p a r a l l e l s t o s i n g l e o r i f i c e s , a f u r t h e r a s p e c t must be n o t e d : t h e b u b b l e s , e m e r g i n g f r o m t h e s i e v e p l a t e , s h o u l d b e n o t l a r g e r t h a n a c e r t a i n maximum v a l u e ; o t h e r w i s e t h e y a r e no l o n g e r s t a b l e a n d d e v i d e i n t o s m a l l e r p a r t i c l e s . A c c o r d i n g t o M e r s m a n n (13)> t h e maximum s t a b l e p a r t i c l e d i a m e t e r r e s u l t s f r o m t h e r e ­ lation : n

Q

d

(12)

P · g

max Taking a l l experiments i n t o account, i f p a r t i c l e s c o l l a p s e , a churn t u r b u l e n t f l o w r e g i o n a l r e a d y appears at lower gas throughputs. I n sieve p l a t e design, t h i s a s p e c t h a s t o be checked a d d i t i o n a l l y . F o r the d e t e r ­ m i n a t i o n o f t h e s i z e o f t h eemerging bubbles, w e l l - known methods l i k e t h a t o f R u f f ( l4) c a n be u s e d . I n d e t e r m i n i n g mean b u b b l e s i z e s i n c o l u m n s , t h e r e i s s t i l l a l a c k o f s u i t a b l e c o r r e l a t i o n s . Even o u r r e s u l t s do n o t e n a b l e m o r e p r e c i s e s t a t e m e n t s . T h e r e ­ f o r e we r e c o m m e n d t o d e t e r m i n e mean b u b b l e s i z e s f r o m e q u a t i o n (12). A c c o r d i n g t o o u r c a l c u l a t i o n s t h e r e i s a n a c c u r a c y o f +_ JO % w i t h r e s p e c t t o m e a s u r e d v a l u e s , i f t h e l i q u i d v i s c o s i t y i s l o w e r t h a n 10 c P . F i n a l l y , the d e t e r m i n a t i o n o f the d i s p e r s i o n c o e f f i c i e n t s i n b o t h p h a s e s i s t o b e t r e a t e d . The


Π0 3

°- 3

atr/water nitrogen /n-proponol atr/glycol 30

40

50

60

relative velocity wR

70 cm/s

Figure 7. Gas phase dispersion coefficient as a function of the relative velocity be­ tween gas and liquid

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL

382 N o m e n c l a2 t u r3e : a m /m c kmol/kmol c* / m d_p m dg m d Q m Fr g-" D m /g g m/s HQ m m/s t s u m/s w m/s We χ m ε m /m η |g/ms V m / s ρ kg/m^ Δρ »/" Cf N/m 11

lf

1

subscripts : C D F G L co

REACTION ENGINEERING—HOUSTON

i n t e r f a c i a l area concentration equilibrium concentration hole diameter s a u t e r mean d i a m e t e r column diameter central value d i m e n s i o n l e s s mod, F r o u d e - n u m b e r dispersion coefficient gravitational acceleration clear l i q u i d height mass t r a n s f e r c o e f f i c i e n t tim linea velocity d i m e n s i o n l e s s Weber-number length gas holdup dynamic v i s c o s i t y kinematic v i s c o s i t y density density difference surface tension standard d e v i a t i o n

continuous phase d i s p e r s e phase liquid gas hole referring to single

bubbles

Literature cited: (1) Mashelkar R.A., Brit. Chem. Eng, (1970),15,1297 (2) Ploos v. Amstel J.J.Α., Rietema Κ . , Chem.Ing. Techn.,(1970),42,981 (3) Todt J., Lücke J., Schügerl Κ., Renken A., Chem. Engng.Sci.,(1977),32,369 (4)RuffΚ., Pilhofer T h . , Mersmann Α., Chem.Ing. Techn.,(1976),48,759 (5) Wallis G . B . , ASME Int.Dev.Heat Trans.,(1962),319 (6) Lapidus L., Elgin J.C., AIChE J.,(1957),3,63 (7) Pilhofer T h . , Chem.Ing.Techn.,(1976),48,273 (8) K ü s t e r s W., Ph.D.Diss. TH Aachen Germany 1976 (9) Hammer H., Rähse W.,Chem.Ing.Techn.,(1973),45,968 (10) Riquarts H . P . , Verfahrenstechnik,(1977),11,164 (11) Pilhofer T h . , Jekat Η . , Miller H . D . , M ü l l e r J.H., Chem.Ing.Techn.,(1974),46,913

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

31. piLHOFER ET AL. (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26)

Parameters in Bubble Column Design

US Pat. 3.818.200 Mersmann Α . , Verfahrenstechnik,(1976),10,641 Ruff Κ . , Chem.Ing.Techn.,(1972),44,1360 Ohki Υ . , Inoue Η . , Chem.Engng,Sci.,(1970),25,1 Badura R . , Deckwer W.D., Warnecke H.J., Lange­ mann Η . , Chem.Ing.Techn.,(1974),46,399 Hikita Η . , Kikukawa Η., Chem.Eng.J.,(1974),8,191 Towell G.D., Ackermann G.H., 2.Int.Symp.Chem. React.Eng., Amsterdam 1972, Preprints B3 Kastanek F., Nyvlt V., Rylek Μ., Coll.Czech.Chem. Comm.,(1974),39,528 Deckwer W.D., Burckhart R . , Zoll G., Chem.Engng. Sci.,(1974),29,2177 Freedman W., Davidso J.F., Trans.Instn.Chem Engrs.,(1969),47,25 Akita Κ . , Yoshida F., Ind.Eng.Chem.Proc.Des.Dev. (1973),12,76 Reith T., Chem.Engng.Sci.,(1968),23,619 Towell G.D., Strand C.P., Ackermann G.H., AIChE - I.Chem.E.Symp.Ser.,(1965),10,97 F a i r J.R., Ind.Eng.Chem.Proc.Des.Dev.,(1962),1,33 Jekat Η . , Ph.D.Diss. TU München Germany 1976

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

383

32 Catalyst Effectiveness Factor in Trickle-Bed Reactors M . P.

DUDUKOVIĆ

and P. L . M I L L S

Chemical Reaction Engineering Laboratory, Department of Chemical Engineering, Washington University, St. Louis, MO 63130

Observed rates in a in hydrodesulfurization cate that they operate in the regime free of major gas-liquid mass transfer limitations (1,2,3,4,5). Due to the fact that often the liquid reactants are nonvolatile or dilute at the operating condi­ tions used the reaction is frequently liquid reactant limited and confined to the catalyst effectively wetted by liquid. Since po­ rous packing, typically 1/32" to 1/8" (0.08 cm to 0.318 cm) extru­ dates is most often employed it is clear that reaction rates may be affected both by internal pore fill-up with liquid and by inter­ nal diffusional limitations. Catalyst effectiveness factors from 0.5 to 0.85 have been generally reported (1,3,5,6,7,8,). In order to interpret or predict trickle-bed performance at­ tempts have been made to account for liquid maldistribution, devia­ tion from plug flow and for incomplete wetting of catalyst parti­ cles (4,9,10,11,12). It has been shown that liquid phase d e v i a ­ t i o n from plug flow does not have significant e f f e c t s on conver­ s i o n in commercial and pilot s c a l e t r i c k l e - b e d r e a c t o r s (13). A p p l i c a t i o n of Mears' (14) criterion confirms the i n s i g n i f i c a n c e of d i s p e r s i o n e f f e c t s . Incomplete c a t a l y s t w e t t i n g ( i . e . con­ t a c t i n g e f f i c i e n c y , c a t a l y s t u t i l i z a t i o n ) as a f f e c t e d by the hydrodynamic regime i n the bed was s i n g l e d out as the most important parameter which determines r e a c t o r performance (12). One may d i s ­ t i n g u i s h between r e a c t o r s c a l e incomplete contacting caused p r i ­ m a r i l y by flow m a l d i s t r i b u t i o n and g l o b a l hydrodynamic e f f e c t s , and p a r t i c l e s c a l e incomplete c o n t a c t i n g which i s determined by l o c a l v i s c o u s , i n e r t i a and surface f o r c e s . When transport e f f e c t s c o n t r o l the o v e r a l l r e a c t i o n r a t e r e a c t o r hydrodynamics has a dom­ inant e f f e c t on r e a c t o r performance. When k i n e t i c s masked by i n ­ t e r n a l d i f f u s i o n c o n t r o l s the r a t e s i n g l e p a r t i c l e phenomena deter­ mine r e a c t o r performance to a great degree. The purpose of t h i s paper i s t o summarize previous i n t e r p r e t a ­ t i o n s of the e f f e c t of incomplete c a t a l y s t w e t t i n g on t r i c k l e - b e d performance and to develop a model f o r the e f f e c t i v e n e s s f a c t o r f o r p a r t i a l l y wetted c a t a l y s t p e l l e t s . I n the case of a r e a c t i o n ©

0-8412-0401-2/78/47-065-387$05.00/0

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL

388

REACTION

ENGINEERING-HOUSTON

confined to the wetted p o r t i o n of the c a t a l y s t only the wetted volume of the p e l l e t c o n t r i b u t e s to r e a c t i o n and the supply of l i q u i d r e a c t a n t occurs only across the wetted, e x t e r n a l surface of the p e l l e t . Under these c o n d i t i o n s the 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 i s a f u n c t i o n of the r a t i o of the maximal k i n e t i c r a t e and maximal r a t e of i n t e r n a l d i f f u s i o n , of the 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 and of i n t e r n a l pore f i l l - u p . An approximate equation d e s c r i b i n g t h i s r e l a t i o n s h i p and based on the work of A r i s (15) can be incorporated i n the t r i c k l e - b e d r e a c t o r performance equa­ t i o n . S o l u t i o n s to more r i g o r o u s models r e p r e s e n t i n g the e f f e c ­ t i v e n e s s of p a r t i a l l y wetted p e l l e t s were sought a l s o i n order to assess the v a l i d i t y of the approximate models. Review of Previous Models Most of the p r e v i o u s l y expression p l e t e c a t a l y s t w e t t i n g i n t r i c k l e - b e d s are summarized i n Table I . A l l of these, w i t h the exception of the l a s t one, are based on the assumptions of a) plug flow of l i q u i d , b) no e x 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 , c) i s o t h e r m a l c o n d i t i o n s , d) f i r s t order i r r e v e r s ­ i b l e r e a c t i o n w i t h respect to the l i q u i d r e a c t a n t , e) n o n v o l a t i l e l i q u i d r e a c t a n t , f ) no n o n c a t a l y t i c homogeneous l i q u i d phase reac­ tion. S a t t e r f i e l d (5) suggested comparing the apparent r a t e constant. k , obtained from t r i c k l e bed data to the r a t e constant, k , de­ termined i n p e r f e c t l y mixed s l u r r y r e a c t o r s , as a measure of t r i c k ­ l e bed e f f e c t i v e n e s s . The r a t i o k / k t c l e s s than u n i t y was i n t e r ­ preted on the b a s i s of l i q u i d d e v i a t i o n s from p l u g flow (10) and of incomplete c a t a l y s t w e t t i n g (8,16). Ross (12) i n t r e a t i n g the data from commercial and p i l o t p l a n t h y d r o d e s u l f u r i z a t i o n r e a c t o r s assumed that l i q u i d space time i s the b a s i c parameter i n r e a c t o r performance. This a s s e r t s that performance and the apparent r a t e constant are p r o p o r t i o n a l to l i q u i d holdup as shown i n equation (1). Bondi (17) developed an e m p i r i c a l expression (2a) i n i n t e r p r e t i n g data f o r the h y d r o d e s u l f u r i z a t i o n of heavy gas o i l . This expres­ s i o n r e l a t e s the space time r e q u i r e d to achieve 50% conversion, τ^, to the analogous space time at complete w e t t i n g , τ^°, and to 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 , U L « This can a l s o be w r i t t e n as equation (2b) i n terms of p r e v i o u s l y defined constants. Henry and G i l b e r t (11) extended Ross (12) formula by i n c o r p o r a t i n g i n t o i t an a v a i l ­ able c o r r e l a t i o n f o r l i q u i d holdup which r e s u l t e d i n expression (3). F i n a l l y , Mears (4) hypothesized that the apparent r a t e constant, k , i s p r o p o r t i o n a l to the true r a t e constant on completely wetted c a t a l y s t , k^ to the 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 , η^, and to the c o n t a c t i n g e f f i c i e n c y , riçE> i . e . to the f r a c t i o n of the e x t e r ­ n a l c a t a l y s t area contacted by l i q u i d . By i n c o r p o r a t i n g the c o r r e ­ l a t i o n of Puranik and Vogelpohl (18), which was developed f o r i n ­ complete c o n t a c t i n g i n absorbers packed w i t h d i f f e r e n t packing s i z e and shape, Mears (4) a r r i v e d to expression (4). S y l v e s t e r and P i t a y a g u l s a r n (19) reproduced the model of Suzuki and Smith v

t c

v

1

v

C9

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

32.

DUDUKovic A N D

Catalyst Effectiveness in Trickle-Bed Reactors 389

MILLS

Table I Suggested Performance Equations f o r T r i c k l e - B e d Reactors -

k

1

H

tc TL

-

7"^ν

= T-^-

(2a)

5

+

ν

^

+

; 0.5 < b < 0.7

tc

,

n

(2b)

U L

1 in

krs.. L 1/3 tt cc m m /o (LHSV)2/ _ 0.32, L (LHSV) m AJ

Œ

:-

1-X 1 In -r-rr 1-X

œ

—

TtlotrN

/o\

d

ρ

(

c

τ

Τ

in J L = Λ ω

(5)

3

where

χτ

Λ

Β = -f-

3

[1 + 4 Λ / Ν 2

- 1]

β

(5a)

Ο Λ

( 5 b )

2 = 1/Α + 1/Ν , 1 st Ί

Λ

ι

=

Ί

[

V

o

t

h

φ

τ ~

1 1

( 5 c )

(20) f o r gas s o l i d c a t a l y t i c r e a c t i o n s and a p p l i e d i t t o three phase systems i n t r i c k l e beds. Incomplete w e t t i n g was accounted f o r by assuming only a p o r t i o n of the r e a c t o r , i . e . an e f f e c t i v e l y smaller volume, to be c o n t r i b u t i n g t o r e a c t a n t conversion. This i s again e q u i v a l e n t t o assuming t h a t a primary parameter i s l i q u i d space time. When the e x 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 a x i a l d i s p e r s i o n e f f e c t s are neglected the model expressed by equations (5) i s reduced to Ross (12) expression (1) m u l t i p l i e d w i t h c a t a ­ l y s t effectiveness factor. Recently (21) another approximate model f o r the c a t a l y s t s e f f e c t i v e n e s s f a c t o r i n t r i c k l e bed r e a c t o r has been proposed. I n t h i s model the e f f e c t i v e n e s s f a c t o r f o r a p a r t i a l l y wetted c a t a l y s t p e l l e t i n a t r i c k l e - b e d r e a c t o r f o r a r e a c t i o n o c c u r r i n g only i n the l i q u i d f i l l e d pore r e g i o n of the p e l l e t i s defined by: 1

η TB

= ( a c t u a l r a t e on a p a r t i a l l y wetted p e l l e t ) / i d e a l maximum r a t e a t bulk c o n d i t i o n s \ Ion a completely wetted p e l l e t J

=

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING-HOUSTON

390

= ( a c t u a l r a t e per u n i t volume of p a r t i a l l y wetted p e l l e t ) i d e a l maximum r a t e per u n i t volume of completely \ wetted p e l l e t )

χ

(

( f r a c t i o n of p e l l e t a c t u a l l y i n t e r n a l l y wetted) f

Using A r i s (15) d e f i n i t i o n f o r the modulus of i r r e g u l a r the f o l l o w i n g modified modulus was obtained: n Φ

particles

i

=

ΤΒ

(6)

( 7 )

*T

which r e s u l t s i n the expression f o r the e f f e c t i v e n e s s f a c t o r given below: . , , tanh ( — η

=

\B

n

(8)

CE

Expression (8) reduces t o the product of η^ η , as used by Mears (4) under two c o n d i t i o n s . Ε

n Φ

Τ

>

>

1 ;

η

ΤΒ

~

CE 0Ε Τ

=

η

η

τ

( 9 a )

In t h i s case the i n t e r n a l pore d i f f u s i o n a l l i m i t a t i o n s a r e severe and thus r e a c t i o n occurs only i n a narrow zone ( s h e l l ) c l o s e t o the e x t e r i o r s u r f a c e . The u t i l i z a t i o n of the p e l l e t i s d i r e c t l y p r o p o r t i o n a l t o the s i z e of t h i s zone which i n t u r n i s d i r e c t l y r e l a t e d t o the f r a c t i o n of e x t e r n a l area wetted.

n./n

CE

= l;

= n

(9b)

CE

The second case i m p l i e s t h a t the pores i n the c a t a l y s t p e l l e t s a r e not interconnected and that the f r a c t i o n of i n t e r n a l w e t t i n g c o r ­ responds d i r e c t l y t o e x t e r n a l w e t t i n g . This i n general i s not the case when d e a l i n g w i t h r e a l c a t a l y s i s and hydrocarbon feeds which r e a d i l y wet i n t e r n a l pore s t r u c t u r e s (22). For s m a l l m o d u l i i i . e . very slow r e a c t i o n s such as t y p i c a l of h y d r o d e s u l f u r i z e r s expression (12) reduces t o : ^TB

*\

t

1

" i

2s

ls+

A

o

- • 2A.+3s

+ A

2s+

3+

s

(7) s'+A. Is

f

-> 2A +3s

surface oxidation and reduction

3

•s +A

?

Intrinsic Rate Expressions Model 2

Model 1

Equil: θ (χ ,χ ) = K x ( l - x ) / ( l + K x )

(1) Equil: θ ^ , χ ^ =

R

(2) Equil: θ (χ χ ) = K 'C (l-x )/(l+K

1

=

2 k C 2

R

=k

2/F

C

1

2

1

1

2

1

1

[(l-x )/(l+K x )] 2

x

x

£

1

M

x

1

2

(3) R = k c

)

3 3 l F l 2 3( ' 2 R = k 9 (x ,x )x f (u,x )

3

3

ρ

ljF

(l-x )/(1+K^) 2

2

x e 1

2

2 F

2

(χ ,χ )

2

1

2

>

4

4

1

1

2

2

4

(4) R

2

R = 0 5

(

R = 0

5) R

4

= k e (x x )9 (x ,x ) 4

p

χ

θ

2

χ

1

2

χ

5 = ^Ρ 1 2( 1» 2)

(6) R = k 9 ( x , x ) 6 ( x , x )

6

6

R = 0

(7) R

?

where χ = C /0 χ

x

1

2

2

=

θ

6

1

1

2

2

1

= k [9 (x ,x )] x

2

v

?

7

1

1

2

2

where x^ = C^/C^ ρ

χp

2 Equations Model 1

Model 2 Balance on total CO:

Balance on total CO: dx-i

2τ

dx-,

C

ST • i " * !

1,F Balance on chemisorbed 0 dx ax ?

l

c -d

• c^

3 model l a where m = { 4 model lb

err

- V

: 2

Balance on oxidized sites: dx τι. 2

1,F where m = {3 4 5 6

model 2a model 2b model 2a model 2b

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

]L

490

CHEMICAL REACTION ENGINEERING—HOUSTON

(This model i s a s p e c i a l v e r s i o n of a more general model described i n Table k of reference 1.) The main r e s u l t o f our a n a l y s i s o f model 1 i s that i f the functions f ^ and f ^ (see r a t e expressions R3 and R^ f o r model 1 i n Table l ) i n models l a and l b r e s p e c t i v e l y are assumed to be u n i t y , then n e i t h e r case can y i e l d o s c i l l a t o r y s t a t e s according to the c r i t e r i o n s t a t e d e a r l i e r . This i s some­ what s u r p r i s i n g at f i r s t glance because model l b , which i n c l u d e s r e a c t i o n U, gives a p o s i t i v e feedback e f f e c t due to CO i n h i b i t i o n by chemisorption on a c t i v e s i t e s . However, t h i s p o s i t i v e e f f e c t i s o f f s e t by the negative feedback e f f e c t of the chemisorption o f oxygen. We found f u r t h e r that i f a k i n e t i c model i s formulated so as to account f o r a p o s i t i v e feedback e f f e c t of chemisorbed oxygen by t a k i n g and f ^ t o be the quantity ( l - x ) , then the value of μ must be at l e a s t 2 f o r o s c i l l a t o r y s t a t e s t o be p o s s i ­ ble. An i n h i b i t i o n e f f e c p l a u s i b l e unless i t i s (-μχ2), wherein the chemisorbed oxygen has the e f f e c t of i n c r e a s ­ i n g the a c t i v a t i o n energy f o r the r a t e o f formation of CO2. Such dependencies of a c t i v a t i o n energies on surface coverage are sup­ ported from t h e o r e t i c a l c o n s i d e r a t i o n s and have been observed experimentally. I f t h i s a c t i v a t i o n energy dependence on X2 i s incorporated i n t o the k i n e t i c model i n e i t h e r of the two subcases, the c o n d i t i o n that aF /3x2 > 0 r e q u i r e s that the f o l l o w i n g i n e q u a l i t y be s a t i s f i e d : y

2

2

-

(k - m)

- (1 - x ) / x 2

2

+ μ (1 - x ) 2

> 0

(2)

where m has the value 3 i n model l a and k i n model l b . As i n e q u a l i t y (2) i n d i c a t e s , o s c i l l a t i o n s are p o s s i b l e f o r model 1 i f μ i s greater than some c r i t i c a l value. We c a l c u l a t e d the c r i t i c a l values to be k and 1 f o r models l a and l b r e s p e c t i v e ­ ly. Thus r e a c t i o n h i s more l i k e l y t o l e a d t o o s c i l l a t o r y s t a t e s than i s r e a c t i o n 3, according to t h i s model The magnitudes o f the c r i t i c a l values appear t o be quite reasonable. The a n a l y s i s of other v a r i a t i o n s o f t h i s model are described i n reference 1 and some computer simulations of o s c i l l a t o r y s t a t e s are presented l a t e r i n t h i s paper. Important items o f information obtainable through a more extensive a n a l y s i s are t h a t ( l ) the model admits m u l t i p l e steady s t a t e s (2) the added i n c l u s i o n o f a surface cov­ erage-dependent chemisorption e q u i l i b r i u m constant for CO, to account f o r a decrease i n the enthalpy o f CO adsorption with oxygen coverage, enhances the p o s s i b i l i t y o f o s c i l l a t o r y s t a t e s and (3) the assumption o f a d i s s o c i a t e d form o f chemisorbed oxygen decreases the l i k e l i h o o d o f s a t i s f y i n g i n e q u a l i t y (2). I t should be noted here that although t h i s model with the a c t i v a t i o n energy dependence on oxygen surface ocverage permits o s c i l l a t o r y s t a t e s , i t i s not capable o f d e s c r i b i n g a l l o f the experimentally observed features of o s c i l l a t o r y behavior ( 1_). Therefore, no c l a i m i s made that t h i s model i s g e n e r a l l y s a t i s f a c t o r y . The main c o n c l u s i o n t o be drawn i s that i f one i s t o base a mathematical d e s c r i p t i o n of

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

40.

SHEiNTucH AND SCHMITZ

Oscillatory

Catalytic

Reactors

491

CO o x i d a t i o n on the r e a c t i o n steps and r a t e expressions underlying t h i s model, as i s t h e c u r r e n t l y popular approach, then t h e i n c o r ­ p o r a t i o n o f an a c t i v a t i o n energy dependence on surface coverage seems reasonable as does t h e assumption o f more than one r a t e determining step — a t l e a s t over c e r t a i n ranges o f c o n d i t i o n s . In model 2 the o x i d a t i o n and r e d u c t i o n o f surface s i t e s , as represented by r e a c t i o n s 5, 6 and 7 i n Table I , are taken i n t o account. I n order t o r e t a i n a second-order d i f f e r e n t i a l model, •we invoke the assumption t h a t both chemisorption steps ( r e a c t i o n s 1 and 2) are i n e q u i l i b r i u m . We f u r t h e r assume t h a t t h e i n h i b i ­ t i o n e f f e c t o f chemisorbed oxygen i s n e g l i g i b l e . The r a t e - d e t e r ­ mining s t e p s , t h e r e f o r e , are r e a c t i o n s 3 through 7 t h e r a t e expression f o r which are l i s t e d i n Table I . Here x-^ i s t h e reduced gas-phase c o n c e n t r a t i o n o f CO as i n the previous model and X2 i s t h e f r a c t i o n assumed t o be i n a c t i v e expressions Rcj and Rg are assumed t o be p r o p o r t i o n a l t o t h e 0 0 formation r a t e s i n expressions R 3 and R^ r e s p e c t i v e l y . This assumption was prompted by the r e s u l t s o f o x i d a t i o n s t u d i e s reported by Ostermaier e t a l . (k). Notice a l s o t h a t t h e r e a c t i o n order ν i n the expression f o r Rj i s u n s p e c i f i e d . I n the a n a l y s i s o f t h i s model, we are i n t e r e s t e d i n the c r i t i c a l value o f ν beyond which o s c i l l a t o r y s t a t e s are p o s s i b l e . Again we consider two subcases. I n the f i r s t o f t h e s e , model 2a, r e a c t i o n s k and 6 do not occur, and i n the second, model 2b, r e a c t i o n s 3 and 5 do not take p l a c e . Both subcases l e a d t o mathematical d e s c r i p t i o n s o f the form given i n equation ( l ) , and the c r i t e r i o n f o r o s c i l l a t i o n s s t a t e d e a r l i e r i s r e a d i l y a p p l i e d . Our a n a l y s i s by t h i s approach l e d t o c r i t i c a l values o f ν o f 2 and 3 f o r models 2a and 2b r e s p e c t i v e l y . That i s t o say t h a t ν must have values g r e a t e r than these i n order f o r o s c i l l a t o r y s t a t e s t o be p o s s i b l e . From a fun­ damental viewpoint, t h e r e q u i r e d high order o f the surface r e ­ duction step i s bothersome. The important p o i n t , however, i s that t h e o x i d a t i o n and r e d u c t i o n o f c a t a l y t i c s i t e s during reac­ t i o n can indeed l e a d t o o s c i l l a t i o n s . A l t e r n a t e r a t e expressions or r e a c t i o n s t e p s , perhaps more r e a l i s t i c ones which account f o r the m i g r a t i o n o f o x i d i z e d s i t e s i n t o the b u l k o f the m e t a l , would l e a d t o more p l a u s i b l e explanations o f o s c i l l a t i o n s . We are con­ d u c t i n g f u r t h e r i n v e s t i g a t i o n s i n t o the e f f e c t s o f v a r i a t i o n s o f t h i s model. 5

2

A c o n c l u s i o n t o be drawn from the r e s u l t s o f a n a l y s i s o f t h e two models described here i s t h a t some accounting f o r i n s i d i o u s mechanistic d e t a i l s i n c a t a l y t i c r e a c t i o n s , more than i s u s u a l l y necessary f o r r e a c t i o n engineering purposes, i s apparently neces­ sary i n order t o describe o s c i l l a t o r y behavior. The models each possessed mechanisms o f p o s i t i v e feedback r e s u l t i n g from the r o l e of a surface species — as was shown t o be necessary from the d i r e c t a p p l i c a t i o n o f well-known theorems.

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

4b>Z

CHEMICAL REACTION ENGINEERING—HOUSTON

Some Experimental

Observations

and Computed R e s u l t s

Due to space l i m i t a t i o n s , we do not present an extensive a r r a y o f computed and experimental r e s u l t s , but i n s t e a d show a s u f f i c i e n t sample t o give an a p p r e c i a t i o n o f key f e a t u r e s . F i g u r e 1 shows l i m i t c y c l e s computed from model l a w i t h ί3(μ,Χ2) = exp ( - μ χ 2 ) . (Our computations f o r model l a are f a r more e x t e n s i v e than f o r other models, but r e s u l t s f o r the others do not seem t o be 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 model l a . ) N o t i c e t h a t the axes o f the phase plane are CO c o n c e n t r a t i o n and the r a t e of CO conversion. We used t h i s r a t e on the v e r t i c a l a x i s because i t s instantaneous values could be computed i n exper­ iments d i r e c t l y from s t r i p chart data o f CO2 c o n c e n t r a t i o n versus time. As the value o f τ proach a r e l a x a t i o n c y c l e bottom p o r t i o n o f the c y c l e f o r τ = 20 sec. c l o s e l y f o l l o w the branches of the steady r a t e curve (dashed curve i n F i g u r e l ) f o r CO conversion. (Notice t h a t the steady r a t e curve, computed from the s t e a d y - s t a t e equation f o r t h i s model i s m u l t i v a l u e d at lower CO c o n c e n t r a t i o n s and t h a t the upper branch shows a decreasing r a t e w i t h i n c r e a s i n g CO c o n c e n t r a t i o n . The decreasing r a t e has been w e l l e s t a b l i s h e d through recent y e a r s , but the mul­ t i v a l u e d geometric n a t u r e , caused by the form of ^^{\i,X2) employed, has not been s u b s t a n t i a t e d . Steady s t a t e s o l u t i o n s , according t o the steady species balance f o r CO, would be the p o i n t s o f i n t e r ­ s e c t i o n o f the r a t e curve w i t h s t r a i g h t l i n e s of negative slope — the supply l i n e s . ) Decreasing the capacitance f a c t o r , £ has the same q u a l i t a ­ t i v e e f f e c t on model p r e d i c t i o n s o f l i m i t c y c l e s as i n c r e a s i n g τ. Experimental l i m i t s c y c l e s i n the r a t e - c o n c e n t r a t i o n plane are shown i n F i g u r e 2 . The important p o i n t s r e g a r d i n g t h i s f i g u r e are: ( l ) the amplitude of the o s c i l l a t o r y s t a t e s were found t o i n c r e a s e as τ i s decreased — i n c o n f l i c t w i t h the t h e o r e t i c a l curves o f F i g u r e 1 ; ( 2 ) s t a b l e n o n o s c i l l a t o r y s t a t e s were obtained at residence times below ^9 sec. and above 130 s e c ; (3) multipeak c y c l e s were observed at lower residence times as the b i f u r c a t i o n to s t a b l e s t a t e s was approached. (See the i n s e r t i n F i g u r e 2 and the time t r a c e i n F i g u r e 3 . ) Multipeak c y c l e s r e q u i r e a higher dimensional space f o r t h e i r r e p r e s e n t a t i o n and are i n d i c a t i v e t h a t more than two r a t e - d e t e r m i n i n g r e a c t i o n steps are i n v o l v e d under some c o n d i t i o n s . c

F i g u r e k presents an example o f another experimental obser­ v a t i o n — t h a t o f a m u l t i p l i c i t y of l i m i t c y c l e s — which has not p r e v i o u s l y been r e p o r t e d and i s not p r e d i c t e d by the models d e s c r i b e d e a r l i e r . When such m u l t i p l i c i t y was encountered, we were able t o reach e i t h e r o f the two p e r i o d i c r e a c t o r s t a t e s by means of a p p r o p r i a t e feed c o n c e n t r a t i o n changes. I t i s i n t e r e s t i n g t o note t h a t the p e r i o d of the single-peak c y c l e (curve b i n F i g u r e k) i s very n e a r l y h a l f t h a t o f the complex c y c l e , curve

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

40.

SHEiNTucH AND scHMiTz

Oscillatory

Catalytic

Reactors

Figure 1. Simulated limit cycles for model la with ΐ (μ>^2) = exp (—μχ ). Parameter values: μ = 8; l = 0.08; K = 10; a^k-j = 0,01 sec' , aJksCjg,*' = 0.12 sec' . 3

2

2

c

1

1

CO Concentration in Reactor,vol % Figure 2. Experimental limit cycles for reactor temperature of 217°C; feed composition: 1.95% CO, 19% 0 ,and 79% N (by vol). Insert shows a magnification of multipeak cycle at the high concen­ tration extreme for τ = 58 sec. 2

2

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

493

CHEMICAL REACTION ENGINEERING—HOUSTON

494

Ο

95Γ

Figure 3. One period of a three-peak cycle for τ = 49 sec with experimental conditions given in Fig­ ure 2

T i m e , min

T i m e , min

Figure 4. Multiplicity of periodic states—(a) multipeak cycle and (b) simple cycle—at reactor tem­ perature of 217°C, residence time of 82.6 sec and feed state: 2.15% CO, 12.9% 0 ,85% N 2

2

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

40. SHEiNTucH AND scHMiTz

Oscillatory Catalytic Reactors

495

( a ) , -which contains two l a r g e peaks. Even a more i n t r i g u i n g type of behavior was observed i n one s i n g l e run at a r e a c t o r temperature o f 2T1°C and a feed composi­ t i o n o f 1.9935 CO, 19.3% 0 , and 19.1% Ν · In t h i s run our data gave strong evidence t h a t " c h a o t i c " s t a t e s e x i s t e d at residence times below 29 sec. Such s t a t e s are c h a r a c t e r i z e d by s u s t a i n e d time-dependent but nonperiodic behavior. P r i o r t h e o r e t i c a l work suggests t h a t such behavior may be i n t r i n s i c i n d i f f e r e n t i a l systems o f order three and h i g h e r (5.) and might g e n e r a l l y be accompanied by such phenomena as multipeak c y c l e s and m u l t i p l e p e r i o d i c s t a t e s (6.). There a r e , o f course, competing explanations f o r c h a o t i c outputs, i n c l u d i n g the simple one t h a t the r e a c t o r s t a t e under c e r t a i n c o n d i t i o n s i s very s e n s i t i v e t o s m a l l e x t r i n ­ s i c d i s t u r b a n c e s . We are s t r o n g l y i n c l i n e d toward a c c e p t i n g the existence o f i n t r i n s i c chaoti matter r e q u i r e s c o n s i d e r a b l imentation than we have given i t thus f a r . In c o n c l u s i o n we should comment f u r t h e r on two p o i n t s . ( l ) T h e o r e t i c a l and experimental r e s u l t s are not i n agreement. Models which we have examined here serve mainly t o exclude c e r t a i n mechanisms and r a t e expressions. S t i l l the p r i n c i p a l f e a t u r e s i n c o r p o r a t e d s e p a r a t e l y t o account f o r o s c i l l a t o r y behavior, namely an a c t i v a t i o n energy dependence on surface coverage and metal o x i d a t i o n and r e d u c t i o n c e r t a i n l y are r e a l i s t i c f e a t u r e s . We f e e l t h a t some a l t e r n a t e method o f d e s c r i b i n g them or o f i n ­ c l u d i n g both e f f e c t s simultaneously (or perhaps i n c l u d i n g other r a t e processes) t o o b t a i n q u a l i t a t i v e agreement w i t h experimental i n f o r m a t i o n w i l l l i k e l y shed new l i g h t on the k i n e t i c s o f CO o x i ­ d a t i o n and perhaps on c a t a l y t i c o x i d a t i o n r e a c t i o n s i n general. (2) As i s n e a r l y always the case w i t h c a t a l y t i c r e a c t i o n e x p e r i ­ ments, we f a c e d , i n our l a b o r a t o r y work, the problem o f a chang­ i n g and nonreproducible c a t a l y t i c a c t i v i t y . The i n f o r m a t i o n shown i n Figures 2 and 3 was obtained during a r e l a t i v e l y s t a b l e a c t i v ­ i t y p e r i o d and could be reproduced q u i t e a c c u r a t e l y over a p e r i o d of a few days. A f t e r regeneration o f the c a t a l y s t , the q u a l i t a ­ t i v e features shown and d e s c r i b e d f o r those f i g u r e s were u s u a l l y preserved, but a l l q u a n t i t a t i v e i n f o r m a t i o n was a l t e r e d . The changing a c t i v i t y makes i t p a r t i c u l a r l y d i f f i c u l t t o s t a t e c o n c l u ­ s i v e l y t h a t such phenomena as the m u l t i p l e l i m i t c y c l e s shown i n Figure 3 and the c h a o t i c behavior (which i n c i d e n t a l l y was observed on only one occassion — on the t h i r d day f o l l o w i n g c a t a l y s t r e ­ generation) d e s c r i b e d above are t r u l y b e h a v i o r a l t r a i t s and not simply the e f f e c t o f t r a n s i e n t a c t i v i t y l e v e l s . Unfortunately t h e o r e t i c a l and experimental s t u d i e s and the understanding o f the causes and e f f e c t s o f i n s i d i o u s a c t i v i t y changes have not yet reached t o the p o i n t a t which questions r e l a t i n g t o such matters can be answered w i t h assurance. 2

2

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

496 Nomenclature Α^,Α^,Α^

chemical components CO, the gas phase

^ls'A"2s

chemisorbed

0^, and CO^

respectively, in

components CO and 0^ r e s p e c t i v e l y

c a t a l y s t area per u n i t v o i d volume gas phase c o n c e n t r a t i o n o f CO i n the r e a c t o r C

C

l

F' 2

F^jF^

concentrations o f CO and 0^ i n the feed stream functions o f μ and χ used i n r a t e expressions R^ f o r model 1 elements i n the v e c t o r F

Ε J

vector of function Jacobian matri

Κ

F

dimensionless chemisorption e q u i l i b r i u m constant, K

Κ

and 5

?

Κ

*1 ' ·2

Ι

V 1,F C

chemisorption e q u i l i b r i u m constants f o r CO and

0^

k. _J Ε

r e a c t i o n v e l o c i t y constant f o r the j t h r e a c t i o n matrix o f capacitance f a c t o r s

&

surface chemisorption c a p a c i t y f a c t o r f o r CO, JV^a^/C^ ^

c

m M

index d e f i n e d where used concentration of active s i t e s

s

η q R. J s s t V χ χ-^,χ^ f

(moles/area)

index d e f i n e d where used volumetric flow r a t e at r e a c t o r temperature r a t e expression f o r the j t h r e a c t i o n i n Table I a c t i v e surface s i t e oxidized (inactive) surface s i t e dimensionless time, time/τ v o i d r e a c t o r volume general v e c t o r o f s t a t e v a r i a b l e s dimensionless s t a t e v a r i a b l e s d e f i n e d i n Table I f o r s p e c i f i c models

Greek L e t t e r s θ

^1' 2 θ . s μ ν τ

f r a c t i o n o f s i t e s occupied by chemisorbed respectively f r a c t i o n o f s i t e s i n the o x i d i z e d s t a t e

CO and

0^

parameter used as r e a c t i o n order or as c o e f f i c i e n t i n exponent i n r e a c t i o n s 3 and k o f model 1 order o f r e a c t i o n 7 with respect o f CO coverage i n model 2 residence time, V/q

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

40. SHEiNTucH AND scHMiTz

Oscilhtory Catalytic Reactors

497

Ac knowle dgment This work was supported by grants from the N a t i o n a l Science Foundation and the G u l f O i l Corporation.

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

Sheintuch, M. and Schmitz, R. Α . , Cat. Rev.-Sci. & Eng. (1977) 15, 107. Plichta, R. T. and Schmitz, R. A. (in press). Sheintuch, Μ., Ph.D. Thesis, Univ. of Ill., Urbana (1977). Ostermaier, J . J.; Katzer, J. R. and Manogue, W. H . , J. Cat. (1976) 41, 277. Rössler, O. Ε . , Z. Naturforsch. (1976) 3la 259 May, R. M., J. Theor

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

41 Theoretical and Experimental Study of Self-Sustained Oscillations in a Stirred Tank Reactor P. H U G O and H.-P. W I R G E S * Institut für Technische Chemie, Technische Universität Berlin Strasse des 17. Juni 135, 1000 Berlin 12, West Germany

1. Mathematical model The dynamics of temperatur continuous-flow stirre the material and energy balances. For a simple first order chemical reaction they are in a dimensionless form dudө=- u

+ Da (l-u)exp

(la)

0

1 b d v d ө = - µ * v + Da (l-u)exp

[v1

0

+

εV]

(lb)

where u, ν , Θ are the dimensionless conversion, temperature difference and time, respectively, defined by 2 (T - T ) a

u = 1 - cc ; v = ERT E

0

0

nd ө = tT

T is the stationary temperature of the cooled reactor in the absence of a chemical reaction 0

T = T +µTk1+µ (3) with µ = k FMC 0

E

W

p

as a dimensionless heat transfer coefficient. The type of reaction and the reaction conditions are re­ presented by four dimensionless parameters B = E(-ΔH) c R E

p

c T p

p

2

*

; ε = RT E ; µ = 1+µB ;Da = 0

0

* Present address: Bayer AG, Werk Urdingen, 4150 Krefeld.

©

0-8412-0401-2/78/47-065-498$05.00/0

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

41.

HUGO AND wraGEs

Oscillations in Stirred Tank Reactor

499

This choice of the dimensionless parameters is useful for a mathematical description of stability. 2. Steady state and stability At a steady state the solutions of Eq. (1) are: Da u

s

=

TT1£Ç

u

v

6a

s = ** s

< >'
ο; i n s t a b i l i t i e s of the type 3 < ο correspond to multiplicity phenomena [1]. For 3 > ο and α > ο oscillatory i n s t a b i l i t i e s can be observed i f +

( 1 + ;

1

—lu—

6

>-

75

) 2 J

9

μ Such sustained oscillations (limit cycles) of the temperature and the conversion are mostly due to a unique steady state solution of Eq. (1) which is unstable to small perturbations. The region of parameter space for which i n s t a b i l i t i e s occur can be plotted into a so-called s t a b i l i t y diagram. Fig. 1 gives μ* versus u^ with Da as a fixed parameter. The curves α = ο and 3 = o calculated from Eqs. (7) and (8) are drawn into this diagram. It will be used here to present the results for a l o t of numerical calculations concerning limit cycles in the region α > o, 3 > o. 0

3. Numerical calculations Several attempts have been made [ 3 , 5 - 8 ] to describe limit cycles by approximate solutions of the balance equations (1).

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

500

CHEMICAL REACTION

ENGINEERING—HOUSTON

However the range of v a l i d i t y of such approximate solutions is small. The application i s either limited to comparatively small B-values or to the neighbourhood of the borderline α = o. To find out a better description of limit cycles, extensive numerical calculations were carried out for B-values from 10 to 30 and ε = ο to 0.02075. Details of these calculations are pre­ sented in [9]. As an example Fig.2 shows a temperature oscillation computed under rather extreme conditions. Typical for the temperature oscillations i s the asymmetry of the oscillation due to the law of Arrhenius. From the numerical calculations the computed frequency is obtained by ω com

=

(10)

ΔΟ i s the dimensionless time difference between two succeeding maxima of temperature. From the maxima and minima of the temperature oscillations a modified amplitude A can be calculated A

'

1

ν max 7 1 + v , max e

m

v

ν · min 1 + ev . min

(11)

m

Further a time averaged conversion u was calculated: 2π/ω / Ο

ÏÏ = £

u d 0

(12)

In the subsequent sections these results will be compared with approximate solutions and empirical correlations. 4. Frequency of limit cycle For fixed values Β, ε and by varying μ* and Da several frequen­ cies were computed. From these data pairs of parameters μ*, Da were selected which gave the same frequency. Fig. 3 and 4 show the result for ε = 0.02075 and Β = 15 and 30. The values a)omp were compared with approximate solutions. The linearized theory [1] gives 0

C

u>

L

=

/β - α

(13)

ζ

This approximation i s useful for small α-values but f a i l s in the center of the region α > o. We found empirically that the simple e q U a t i 0

"

ω

1 ο

=

ΓΓ

gives in most cases a sufficient approximation. A better f i t of the data of the computer simulation was obtained by the regression equation

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

(14)

41.

HUGO AND WIRGES

Oscillations in Stirred Tank Reactor

501

Figure 1. Stability diagram (B = 20,£ = 0) 12

w . 10 10

|l

10 50

1090

1 'I 1130

11,70

!

1210

1

12,50

i

12,90

13,30

Θ • Figure 2. Typical temperature oscillation from computer simuhtion (B = 30, e = 0 02075, * = 0,44505, u = 0,65) μ

8

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

502

CHEMICAL REACTION ENGINEERING—HOUSTON

Figure 3. Stability diagram with curves of equal frequency (B = 15, c = 0,02075)

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

HUGO AND WIRGES

41.

Oscillations in Stirred Tank Reactor

u> = 9 . 6 - 3 5 . 7 u

+ 23.9 u

D

s

K

< 0.95

$

K

5.

J

x

s

+ 10.6 u e

(15)

s

and

ο ο < u

+ 2 0 . 5 y V - 0 . 2 By*

2

s + 0.23

0.40

c

503

10

< Β < 30

0.2

< μ*
)/ a ) , was + 1 0 % . comp R " comp D

A m n

Comparison of some r e p r e s e n t a t i v e f r e q u e n c i e s .

Amplitude of temperature o s c i l l a t i o n s

A l o t of more severe d i f f i c u l t i e temperature i s to be p r e d i c t e d . Several proposed approximations [ 3 ] , [ 5 ] [ 6 ] , Γ 7 ] are only useful i n a small range, namely in the neighbourhood of the b o r d e r l i n e α = ο and f o r comparatively small B-values. The asymmetric behavior of the temperature o s c i l l a t i o n s can approximately be accounted f o r by s e t t i n g 5

Δν a

ν - v

=

$

=

-

In ( 1 - a cos ω Θ) where

(16) (17)

= tanh (A)

F i g . 5 and 6 show curves of equal a-values f o r ε = 0 . 0 2 0 7 5 and Β = 1 5 and Β = 3 0 . These diagrams i l l u s t r a t e that small tempera­ ture amplitudes are r e s t r i c t e d to a very small zone near the b o r d e r l i n e α = o. A l l a n a l y t i c a l approximations must f a i l in the main part of the region α > ο , β > ο where the a-values are very near to 1 . A r e g r e s s i o n method was a p p l i e d s e l e c t i n g about 5 0 0 r e p r e ­ s e n t a t i v e data from the computer s i m u l a t i o n . The best f i t t i n g was found by A

*

= - 1 1 . 5 - 5 4 . 4 μ* + 5 7 . 2 u. + 0 . 7 6 Β - 5 7 . 2 ε

D

"»|^ -

-

1i ·J

-

-

56.5 u

Jt.t μ

$

2

Τ

- 0.012Β

\JI.L·

2

+ 5 1 . 1 *u P

$

(18)

which i s v a l i d i n the same range of the parameters as E q . ( 1 5 ) . As f a r as A < 5 the maximum percentage e r r o r (A - A R ) / A was about + 3 0 % . To our own s u r p r i s e a comparatively simple semi-empirical approximation works q u i t e well in the range of high temperature amplitudes. From Eq. ( 1 ) a c o u p l i n g equation can be obtained by e l i m i n a t i o n the dimensionless r e a c t i o n r a t e

£ 0

+ 0

* =

ν

;

Υ = Β υ _ ^ By* - 1

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

(

1

9

)

CHEMICAL REACTION ENGINEERING—HOUSTON

504

Table I: Comparison of some representative frequencies ω comp Eq.dO)

parameters

ω

Eq.(13)

Ι_ο Eq.(14)

Eq.(15)

B=10 ε=0

u =0 80 μ*=0 280

2,406

2,449

2,451

2,210

B=10 ε=0

u =0 80 μ*=0 2509

1,917

2,118

2,132

1,800

B=10 ε=0

u =0 60 μ*=0 261

0,938

0,561

0,717

0,868

B=30 ε=0 02075

u =0 80 μ*=0 311

B=30 ε=0,02075

u =0,75 μ*=0 310

4,325

2,060

4,100

4,511

B=30 ε=0 02075

u =0 60 μ*=0 3038

3,159

imagin.

2,485

2,981

B=30 ε=0,02075

u =0 55 μ*=0 2716

2,394

imagin.

1,705

2,580

s

9

9

s

9

9

s

9

9

9

9

s

9

9

s

9

s

9

9

s

9

9

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

41. HUGO AND WIRGES

Oscillations in Stirred Tank Reactor

505

From several numerical calculations we found that the oscillations of y are considerably smaller than those of v. This effect i s demonstrated for a typical limit cycle with a high temperature amplitude in Fig. 7. So we tested the approximation Y ( v ) = v where the e x t r

$

corresponding conversion u i s obtained from Eq. (lb) by setting %

= o. One gets (Bu* - l ) v - Β - v s

D a

D a

extr = o

e x

-

e x t r

·v

(20)

e x t r

extr 1 +

P

(21)

The f i r s t and the third intersection of the curve f ( v , ) with the line Ψ = v (see Fig. 7) yield approximate values for v - j and v which are used to calculate A from Eq. (11). e J

t r

s

m

n

m a x

Table II: Comparison of some representative amplitudes of temperature 6. Time averaged conversion A short comment should be made to the time-averaged conversion. By an approximate solution [ 9 J we obtained

and

II

> u

$

for

v" < 2

U

< u

s

for "v > 2

From our numerical calculations we found that this rule i s valid even at high B-values.__From the practical point of view the i n ­ crease of conversion (u - u ) in the range ν < 2 is comparatively small. The severe problems of a reactor with self-sustained oscillation makes i t unrealistic to use this way for increase of conversion. s

7. Experimental results In the experimental part of this study the catalytic decomposition of hydrogen peroxide by Fe(No3)3 * ^ 2 ° ' t r i c acid solution was used as a model reaction. This reaction has the advantage ob being f i r s t order [10, 11]. The concentrations of Fe^ and H remain constant during the reaction. The following rate expression was obtained by kinetic experiments: H

i n

a

m

+

1 8

C

3

* - ι 6.in Fe * " ^ 'c + 0,01 r

1

0

H +

. 14620, H 0 ' P(- - T - >

n c

ex

2

2

g-mole l i t r e - sec

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

+

. < )

/ 9 9

22

CHEMICAL REACTION ENGINEERING—HOUSTON

506

μ* οβ

Γ

Figure 6. Stability diagram with curves of equal temperature amplitude (B = 30, c = 0,02075)

ψ(ν)

26

'

1

ι

·

ι

·

1

'

1

B»30 C «002075 u *Qf5 μ* > OUSI s

22 ....

-

ψ|ν) ^) φ ( ν

20

-

\/ I

Figure 7.

.

I

.

I

.

I

.

I

.

ι

Limit cycle φ(ν) for Β = 30, e — 0, 02075, μ* = 0, 445pnd u = 0,65 s

In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

41.

HUGO AND WIRGES

Oscillations in Stirred Tank Reactor

507

The values of the activation energy (E = 121,5 kJ/g-mole) and of the reaction enthalpy (-ΔΗ = 94,8 kJ/g-mole) are high enough to f u l f i l Eq.(9) so that the oscillatory behaviour of temperature and conversion in the CSTR can be observed for a wide range of operating conditions (see Table III). The acid/hydrogen peroxide solution and the catalyst were pumped in two feed streams via rotameters into the reactor. The liquid phase volume (V = 500 ml) was kept constant with an outlet valve. The extent of the reaction was followed by titration of hydrogen peroxide and by sensing the temperature with a thermo­ couple. Table III Range of experimental conditions 800 ml/h

< v