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.
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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.
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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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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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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.
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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.
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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.
60
CHEMICAL REACTION
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.
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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) <3y ζ q w =
1
2
B
w
β
The f i r s t d e r i v a t i v e of the c o n c e n t r a t i o n i n the y - d i r e c t i o n can now be computed by s u b s t i t u t i n g C = C^ i n eq (10), provided that the c o n c e n t r a t i o n at the r e a c t o r w a l l , C , i s known. We have w assumed that i t i s equal t o 0 t o a f i r s t approximation, i n other words that the c a t a l y s t l a y e r i s so t h i c k that complete conversion of C 0 e n t e r i n g i t i s obtained. This appeared j u s t i f i e d on the b a s i s of numerical c a l c u l a t i o n s a t the c o n d i t i o n s a p p l i e d i n our experiments as w e l l as the c a l c u l a t i o n s reported here. Equation (11) then represents the mass transport i n t o the c a t a l y s t bed: 2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
6.
BRUIJN ET
AL.
Methanation in a Parallel Passage Reactor
2A = Β e f f • ~T (
y-y. k
67
i ( B C
k
"
l n
0
+
B C
k
) ) 2
(Π)
This means that boundary c o n d i t i o n (5) i s now known and t h a t the mass balance i n the z - d i r e c t i o n can be s o l v e d , i n a way s i m i l a r to the c a l c u l a t i o n s on the c a t a l y t i c p a r a l l e l p l a t e r e a c t o r (7_) . In t h i s f i r s t phase of the work the e x p l i c i t f i n i t e d i f f e r e n c e s method of Binder-Schmidt was a p p l i e d ( 8 ) ; other methods being examined are the method of Dufort and F r a n k e l (9.) and orthogonal c o l l o c a t i o n (10). R e s u l t s and d i s c u s s i o n Before making runs w i t h the r e a c t o r f i l l e d w i t h c a t a l y s t , ex periments were made w i t conversions were noted, to c a t a l y t i c a c t i v i t y of the s t a i n l e s s s t e e l wire screen. A f t e r replacement by an i r o n screen no conversion i n the empty r e a c t o r was found. Experimental r e s u l t s are shown i n f i g u r e s 4, 5 and 6 f o r three temperatures, i n the form of p l o t s of the conversion against the space v e l o c i t y at s e v e r a l concentrations of C0 i n hydrogen. At high space v e l o c i t i e s , i . e . at low residence times, the r a t i o of mass t r a n s p o r t by flow through the channel to the mass t r a n s p o r t by d i f f u s i o n i n t o the c a t a l y s t bed i s r e l a t i v e l y h i g h , r e s u l t i n g i n low C0 conversion. As the f l o w r a t e of the gas i n the channel i s decreased, the above r a t i o diminishes and a l a r g e r p r o p o r t i o n of C0 i s then converted. At very low space v e l o c i t i e s the r e s i dence time apparently i s long enough to give complete conversion. The f i g u r e s a l s o i n d i c a t e a number of e n c i r c l e d conversion p o i n t s c a l c u l a t e d by means of the simple model outliied p r e v b u s l y . l t i s found that the c a l c u l a t e d r e s u l t s agree reasonably w e l l w i t h the experimental data at the higher two temperatures ( f i g u r e s 4 and 5 ) ; at 208 °C ( f i g u r e 6 ) , the lowest of the three temperatures, the c a l c u l a t e d conversions are i n v a r i a b l y higher than the measured v a l u e s . This i s presumably due to the low r a t e of chemical r e a c t i o n i n the bed at t h i s temperature, which causes the c o n c e n t r a t i o n of C0 at the r e a c t o r w a l l , C , to have a f i n i t e value. I t i s concluded that the model should be improved to i n c o r p o r a t e a numerical c a l c u l a t i o n of the c o n c e n t r a t i o n p r o f i l e i n the c a t a l y s t bed. S t i l l , i t was thought p o s s i b l e to make a small e x t r a p o l a t i o n to assess the e f f e c t of o p e r a t i n g at a higher pressure, at other wise unchanged c o n d i t i o n s . E x p l o r a t o r y c a l c u l a t i o n s i n d i c a t e that when r a i s i n g the pressure from 1 to 4 atm at 224 °C and a C0 c o n c e n t r a t i o n of 0.58 v o l % , the space v e l o c i t y can be increased from about 4000 to about 11000 h~* to o b t a i n the same conversion, 81%, i n the two cases. Thus, o p e r a t i o n at pressures higher than atmospheric gives improved r e a c t o r performance. F u r t h e r work, both experimental and by improved model c a l c u l a t i o n , i s i n progress to evaluate the performance of the r e a c t o r f o r methanation purposes 2
2
2
2
2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—]
gas wire catalyst channel screen bed Κ
> y Figure 3. Concentration changes caused by reaction and mass transport to the catalyst bed
Figure 4.
Plot of conversion against the space velocity at Τ = 515°K
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
BRUIJN ET AL.
Methanation in a Parallel Passage Reactor
Τ =497 Κ * *0.19 /β(Χ>2 ©calculated
100
β
90
ο «0.58·/·0θ2 ©
£(·/·)) '
e
ο «2.56 /.CC2 ©
»
80 70605040 ® 30-
β
2010 0
4000 0.1
8000 0.2
12000
16000 0.4
0.3
20000
GHSV
0.5 <)> (m3/h) v
Figure 5. Plot of conversion against the space velocity at Τ = 497°K
Τ = 4 8 1 °K ο * 0.58 % CO2 e
* = 1.75 /eC02
β calculated ®
ο . Z56%C02
0.4 0.5 • <J> (mVh) v
Figure 6. Plot of conversion against the space velocity at Τ = 481°K
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
70
more f u l l y . I f the p a r a l l e l passage r e a c t o r i s a p p l i e d i n an i n d u s t r i a l methanation o p e r a t i o n , i t w i l l most probably be followed by a small fixed-bed a d i a b a t i c methanator, to enable o p e r a t i o n at a c e r t a i n small c o n c e n t r a t i o n of carbon oxides i n the product gas of the p a r a l l e l passage r e a c t o r . Moreover, the r a t i o of the r e a c t o r length to the bed depth can be taken much higher i n such a p p l i c a t i o n s ; an i n d u s t r i a l r e a c t o r would operate at much higher l i n e a r v e l o c i t i e s i n the gas channel than our model r e a c t o r . This i m p l i e s not only that mass t r a n s f e r from the channel to the bed may be much f a s t e r , p a r t i c u l a r l y when the flow i n the channel i s t u r b u l e n t , but a l s o that the average C0 c o n c e n t r a t i o n i n the f r o n t end of channel as w e l l as i n the bed w i l l be r a t h e r higher. Thus, c a t a l y s t u t i l i z a t ion i s a l s o expected to be higher. An advantage of th p l a t e or coated tube r e a c t o r w i l l most probably have l e s s e f f e c t because i t contains a r e l a t i v e l y t h i c k c a t a l y s t l a y e r . Model c a l c u l a t i o n s are i n progress to assess the e f f e c t s of poisoning more f u l l y . On the b a s i s of the encouraging r e s u l t s obtained so f a r we are now c o n s t r u c t i n g a r e a c t o r system f o r operation at higher temperatures and pressures i n which r e c y c l e i s p o s s i b l e , i n order to study methanation i n the p a r a l l e l passage r e a c t o r at c o n d i t i o n s more r e p r e s e n t a t i v e of i n d u s t r i a l SNG operations. 2
Acknowled gement s The authors thank the K o n i n k l i j k e / S h e l l Laboratorium, Amsterdam, f o r t h e i r generous help i n the c o n s t r u c t i o n of our experimental r e a c t o r , and mrs.J.S.van Regteren f o r a s s i s t a n c e i n c a r r y i n g out measurements and model c a l c u l a t i o n s . Summary Exothermic g a s / s o l i d r e a c t i o n s i n v o l v i n g l a r g e q u a n t i t i e s of gas, such as carbon oxide methanation w i t h r e c y c l e of c o l d product gas f o r temperature c o n t r o l , can be c a r r i e d out i n a p a r a l l e l pas sage r e a c t o r i n which the reactants flow through narrow empty chan n e l s between shallow beds of s o l i d reactant or c a t a l y s t . A model r e a c t o r has been b u i l t and studied using the methanat ion of carbon d i o x i d e as the t e s t r e a c t i o n . C a l c u l a t i o n r e s u l t s of a simple mathematical model agree w e l l w i t h the experimental data except at low temperatures. The conversions obtained are s u f f i c i e n t l y promising to warrant f u r t h e r e x p l o r a t i o n of the p a r a l l e l passage r e a c t o r as a t o o l i n SNG production, the more so because e x p l o r a t o ry c a l c u l a t i o n s show that o p e r a t i o n at higher pressures r e s u l t s i n much improved performance.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
6.
BRuijN E T A L .
Methanation in a Parallel Passage Reactor
L i s t of symbols a A
d i s t a n c e between wire screens p K RTexp(-E /RT)]D defined by eq. 10 bed
Β
oo
Κ
ρ Λ
a
RT
m
eff
"
,!
"
"
LU ry
. 3 concentration mole/m i n l e t concentration " c o n c e n t r a t i o n i n c a t a l y s t bed a t w i r e screen concentration at reactor w a l l " 2 diffusion coefficient m /s i n wire screen " " i n c a t a l y s t bed reaction rate mole/k
C C
11
C w I) D r
11
r n
11
11
2 ν y^
gas v e l o c i t y m/s running v a r i a b l e p e r p e n d i c u l a r t o d i r e c t i o n m of flow y^ y behind wire screen m y^ y at reactor w a l l m ζ running v a r i a b l e i n f l o w d i r e c t i o n m ^ ρ, , d e n s i t y of c a t a l y s t bed kg/m References 1. Haynes, W.P., Schehl, R.R., Weber, J.K., Forney, A.J. Ind.Eng.Chem.Process Des.Dev. 16(1) 113 (1977) 2. R a l s t o n , R.D., Haynes, W.P., Forney, A . J . , Schehl, R.R. Bur.of Mines, Rep. of I n v e s t . 7941 (1974) 3. Helden, H.J.A.van US patent 3.501.897 March 1970 Versluis, R. US patent 3.747.308 J u l y 1973 4. Herwijnen, T.van, Doesburg, H.van, Jong, W.A.de J.Cat 28 391 (1973) 5. Doesburg, H.van Transient behaviour of an a d i a b a t i c fixed-bed r e a c t o r . D o c t o r a l t h e s i s , D e l f t U n i v e r s i t y of Technology, 1974 6. Hoogschagen, J. Ind.and Eng.Chem 47 906 (1955) 7. S o l b r i g , C.W., Gidaspow, D. Ind.Chim. Beige 32 392 (1967) 8. F o r s y t h , G.E., Wasow, W.R. Finite d i f f e r e n c e methods f o r partial differential equations John Wiley & Sons, Inc. 4th ed. 1967 9. Dufort, E.C., F r a n k e l , S.P. Math.Tables Aids Comput. 7 135 (1953) 10. F i n l a y s o n , B.A. Cat.Rev. - Sci.Eng. 10 (1) 69 (1974)
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
7 Experimental and Theoretical Study of the Simultaneous Development of the Velocity and Concentration Profiles in the Entrance Region of a Monolithic Convertor M. A. M. BOERSMA,* W. H. M. TIELEN, and H. S. VAN DER BAAN University of Technology, Departmen Eindhoven, The Netherlands
In c a t a l y t i c afterburning of waste gases the monolithic or ac tive wall reactor is becoming increasingly important. Most experi mental and theoretical studies on this reactor that have been pu blished so far consider the velocity field i n the separate channels of the monolith either undeveloped, i . e . plug flow (1-3), or fully developed, i.e. laminar flow (4-7). In r e a l i t y , however, the velo city p r o f i l e , which can be assumed to be more or less uniform at the entrance of the channel, will develop into a laminar P o i s e u i l l e p r o f i l e downstream the tube. This implies that the experimental measured conversions will not correspond to the theoretically calcu lated concentration profiles for either plug flow or laminar flow, i.e. concentration profiles calculated for a uniform v e l o c i t y pro file will result i n a conversion which is higher than the actual conversion, while a fully developed p r o f i l e gives r i s e to a con version lower than the actual one. Therefore, to get a more accu rate description of the phenomena taking place i n the entrance re gion of the active wall reactor we studied the simultaneous devel opment of the velocity and concentration profiles by numerical ana l y s i s of the governing steady state d i f f e r e n t i a l equations, i . e . the Navier-Stokes equation of motion and the diffusion equation for incompressible flow of a Newtonian f l u i d . Some work in this f i e l d has been performed e a r l i e r by Ulrichson and Schmitz (8). These i n vestigators used the approximate solution of Langhaar (9) for the entrance velocity profiles to provide the velocity data for nume rical solution of the component material balance. The calculations apply to an isothermal reactor, a condition which generally is satisfied i n case of low concentration of the waste gas. Further it is assumed that the kinetics of the chemical reaction taking place at the tube wall can be described by Γ
=
, η * HC,wall C
* Present address: Koninklijke/Shell-Laboratorium (Shell Research B.V.) Amsterdam, The Netherlands © 0-8412-0401-2/78/47-065-072$05.00/0 In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
7.
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Velocity and Concentration Profiles
ET AL.
73
η being the order o f the r e a c t i o n . This r a t e expression a p p l i e s t o the o x i d a t i o n of s m a l l concentrations hydrocarbon i n an excess of air. To check the c a l c u l a t e d c o n c e n t r a t i o n p r o f i l e s i n p r a c t i c e we s t u d i e d the combustion of low concentrations of ethylene and i s o butene i n a commercial m o n o l i t h i c convertor s p e c i a l made f o r us by Kali-Chemie Engelhard K a t a l y s a t o r e n GmbH. Theoretical Part At f i r s t we t r i e d to s o l v e the problem i n study by a s i m u l t a neous numerical a n a l y s i s of the Navier-Stokes equations and the mass t r a n s p o r t equation. Since by t h i s method s e r i o u s numerical i n s t a b i l i t i e s were encountered we choose an a l t e r n a t i v e procedure. This c o n s i s t s of c a l c u l a t i n the a x i a l and r a d i a l v e l o c i t i e s to s o l v e the mass t r a n s p o r t equation. I n s o l v i n g t h i s equation ca re i s taken that the g r i d used i s i d e n t i c a l to that f o r s o l v i n g the velocity field. The Entrance V e l o c i t y F i e l d For an i s o t h e r m a l , steady s t a t e , incompressible flow of a Newtonian f l u i d being symmetrical i n the azimuthal d i r e c t i o n , the governing equations are the Navier-Stokes equations and the steady s t a t e c o n t i n u i t y equation. I n dimensionl e s s form the equations are:
The pressure dependent terms i n equations (1) and (2) can be remo ved by d i f f e r e n t i a t i n g equations (1) and (2) w i t h respect t o ζ and r , r e s p e c t i v e l y , and s u b t r a c t i n g the r e s u l t a n t equations from each other ( L Q , U ) . According t o the method o u t l i n e d by Vrentas et. a l . ( 1 1) now a stream f u n c t i o n Ψ i s introduced which i s d e f i n e d as: u
—
V r3r
-
^
t
r3z
(4)
We f u r t h e r r e c a l l t h a t the only non zero component of the v o r t i c i t y v e c t o r i s the azimuthal p h y s i c a l component, which i s given by: ω
=
3 l • 3Ϊ
( 5 )
With the a i d of equations (4) and (5) we f i n a l l y get the f o l l o w i n g
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
74 equations: _ω 3Ψ 2 3z r
J_ 3Ψ 3ω _ j_ 3Ψ 3ω r 3z 3r r 3r 3z
2
2_ Re L 2
1 3ω _ ω_ r 3r 2 r
3jo\ I
^2
w
2
8Ψ 3 Ψ _ J_ 3Ψ . 2 * 2 r 3? 9z dr
(7)
When i n these equations the second p a r t i a l d e r i v a t i v e s of Ψ and ω w i t h respect to ζ are neglected,which i s j u s t i f i e d because i n the m o n o l i t h i c convertor the convective t r a n s p o r t of v o r t i c i t y i n the a x i a l d i r e c t i o n i s greater than the a x i a l d i f f u s i v e t r a n s p o r t , the e l l i p t i c d i f f e r e n t i a l equations change i n t o p a r a b o l i c equations. S o l u t i o n of the equations i s c a r r i e d out w i t h the f o l l o w i n g i n i t i a l and boundary c o n d i t i o n s r = 0, ζ > 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 + !
25) the term 3 C/3z may be neglected. The i n i t i a l and boundary c o n d i t i o n s are then given by: 2 9 u c
+
n
K
a
n
}
a
2
3C
Λ
ι · 3C r-0
3 C 3 r
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
/1
o\
7.
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Velocity and Concentration Profiles
ET AL.
0 < r < 1, ζ = 0: C = 1 KRc r
- l , > 0: υ z
-
75 (13)
η-1 ο D
DaC
(14)
As the r a d i a l c o n c e n t r a t i o n gradient a t the tube w a l l determines the mass f l u x s u p p l i e d by d i f f u s i o n a good approximation of t h i s gradient i s necessary to o b t a i n an accurate d e s c r i p t i o n o f the con c e n t r a t i o n p r o f i l e s i n the tube. I n the numerical a n a l y s i s t h i s i s e f f e c t e d by r e d u c t i o n of the r a d i a l step width near the tube w a l l . During the c a l c u l a t i o n s i t turned out, however, that a non e q u i d i s tant r a d i a l g r i d r e s u l t e d i n p e r s i s t e n t numerical i n s t a b i l i t i e s . We, t h e r e f o r e , used an e q u i d i s t a n t g r i d , which was i d e n t i c a l to that a p p l i e d f o r the v o l o c i t y p r o f i l e . For a f u l l y develope the r a d i a l v e l o c i t y i s independen so the r a d i a l v e l o c i t y may be neglected. Equation (11) then reduces to 2 (d C 2
W
pe
2
I
3c\
v
ra
(15)
Equation (11) and (15) have been solved n u m e r i c a l l y together w i t h c o n d i t i o n s (12)-(14) f o r v a r i o u s values of the r e a c t i o n order (η), Damkohler number (Da) and Schmidt number ( S c ) * . F i g u r e 2 shows f o r a f i r s t order r e a c t i o n and Da = 1.28 the average and tube w a l l con c e n t r a t i o n s obtained n u m e r i c a l l y f o r three flow c o n d i t i o n s , i . e . undeveloped, developing and f u l l y developed flow. We see that i n deed the average c o n c e n t r a t i o n f o r developing flow l i e s between that f o r f u l l y developed and undeveloped flow. S i m i l a r p i c t u r e s were obtained f o r other combinations of n, Sc and Da. Experimental Part Methods The r e a c t i o n system used f o r the o x i d a t i o n e x p e r i ments c o n s i s t s of a gas mixing p a r t , a r e a c t o r and an a n a l y s i s sy stem. I n the gas mixing p a r t mixtures of a i r and the hydrocarbon t o be o x i d i z e d can be prepared i n a l l d e s i r e d compositions. A f t e r l e a v i n g the mixing room, the feed gas enters a preheater. Both the mix ing room and the preheater are f i l l e d with g l a s s Raschig r i n g s . The r e a c t o r s h e l l , which i s made from g l a s s , has a hexagonal cross s e c t i o n , i n which the commercial honeycombs f i t snugly. I t c o n s i s t s of a preheating s e c t i o n , about 15 cm i n l e n g t h , which i s f i l l e d w i t h packing m a t e r i a l , and a r e a c t i o n zone c o n t a i n i n g the monolith. The temperature o f both s e c t i o n s can be c o n t r o l l e d sepa r a t e l y w i t h Éurotherm T h y r i s t o r c o n t r o l l e r s . Temperature o f the gas stream e n t e r i n g and l e a v i n g the monolith i s measured by means of chrome1-alumel thermocouples. To determine the i n l e t and o u t l e t hydrocarbon c o n c e n t r a t i o n s , gas samples are taken j u s t before and a f t e r the r e a c t i o n zone by means of an eight way Becker gas sampling v a l v e . For hydrocarbon a n a l y s i s we use a Pye s e r i e s 104 gas chromatograph w i t h flame i o n i zation detector. * D e t a i l s o f the numerical s o l u t i o n procedure are given elswhere (12) In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
76
CHEMICAL REACTION ENGINEERING—HOUSTON
Figure 2. Numerical solutions of equations 11 - 15 for afirstorder reaction with Da = 1.28 and Sc = 1.09
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
7.
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ET
AL.
Velocity and Concentration Profiles
77
The experiments have been executed p a r t l y w i t h a commercial (WK 220, s u p p l i e d by Kali-Chemie Engelhard K a t a l y s a t o r e n GmbH, Han nover) honeycomb r e a c t o r , and p a r t l y w i t h a h i g h l y a c t i v e honeycomb, e s p e c i a l l y made f o r us by Kali-Chemie Engelhard. The WK 220 honey comb i s 10 cm i n length and contains 169 tubes each of which are 2.4 mm i n diameter. I n both monoliths the a c t i v e component was p l a tinum. Results When we assume that the c a t a l y z e d w a l l r e a c t i o n takes p l a c e homogeneously and can be d e s c r i b e d as b e i n g f i r s t order i n the hydrocarbon c o n c e n t r a t i o n , w h i l e the gas f l o w through the tubes i s supposed to be i d e a l p l u g f l o w , an impression of the magnitude of the r a t e constant can be obtained by u s i n g the r e l a t i o n : c In — = - kT (16 c ο Since the dimension of k i n t h i s equation does not correspond to that of K, f i g u r i n g i n equation ( 1 4 ) , the experimental measured r a te constant, k, has to be transformed i n the w a l l r a t e constant, K, by the r e l a t i o n : Κ = (|)· k
(17)
Determination of Κ by r e l a t i o n (17) assumes that the tube w a l l con c e n t r a t i o n equals the cup mix c o n c e n t r a t i o n . Since i t i s expected that c o n c e n t r a t i o n g r a d i e n t s are present i n the tubes of the mono l i t h the r a t e constant from equation (17) w i l l always be lower than i t s r e a l value. The k i n e t i c s of the ethylene combustion (c = 200 - 300 ppm) was s t u d i e d i n the commercial honeycomb r e a c t o r . The temperatures of the gas e n t e r i n g and l e a v i n g the r e a c t o r were almost equal ( w i t h i n 1-2 C). The o x i d a t i o n appeared to be f i r s t order i n e t h y l e n e . Changing the temperature gave the r e s u l t shown i n f i g u r e 3. Below 500 Κ the o x i d a t i o n takes p l a c e i n the r e a c t i o n c o n t r o l l e d r e g i o n . The a c t i v a t i o n energy then amounts to 42 kJ/mol. Above t h i s tempe r a t u r e , however, a t r a n s i t i o n to the f i l m d i f f u s i o n l i m i t a t i o n r e gion occurs. The a c t i v a t i o n energy now amounts to only 8 kJ/mole. The e x i s t e n c e of the d i f f u s i o n l i m i t a t i o n r e g i o n i s a l s o i l l u s t r a ted by the e x c e l l e n t agreement between the temperature dependence of the d i f f u s i o n c o e f f i c i e n t of ethylene i n a i r , as determined by the Lennard-Jones e x p r e s s i o n , and the temperature dependence of the r a t e constant i n t h i s r e g i o n . F i g u r e 4 shows f o r the v a r i o u s temperatures the r e l a t i o n between the o u t l e t c o n c e n t r a t i o n and reac tor length. We see that the p o s i t i o n of the curves r e l a t i v e to each other i s determined by the Da number. I n the r e a c t i o n l i m i t e d r e gion (< 500 K) the Da number increases w i t h temperature. I n the f i l m d i f f u s i o n l i m i t e d r e g i o n , however, the Da number decreases w i t h i n c r e a s i n g temperature due to the s l i g h t temperature dependen ce of Κ i n t h i s r e g i o n . I n the f i l m d i f f u s i o n r e g i o n a modified form of the Leveque equation holds ( 1 3 ) , i . e . Q
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
78
100
Ί
1.4
1.6
1.8
2.0 —
2.2 2.4 1QQQ -1)
2.6
(K
Figure 3. Arrhenius plot for the oxidation of ethylene in the commercial honeycomb reactor (WK 220)
Figure 4.
Oxidation of ethylene in commercial (WK honeycomb reactor
220)
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
7.
BOERSMA ET AL.
Velocity and Concentration Profiles
79
2/3 F (conversion) = constant
08) R
/ J
I t appears that f o r the experiments at 666 Κ t h i s equation gives a good d e s c r i p t i o n o f the measurements up to F = 80 - 90%. H e r e a f t e r we s t u d i e d the entrance e f f e c t by using a honeycomb converter which c o n s i s t e d of a non-impregnated and an impregnated ( h i g h l y a c t i v e ) p a r t , both about 5 cm i n length. When the feed gas enters the non-impregnated p a r t f i r s t l y , the v e l o c i t y p r o f i l e w i l l be f u l l y developed when e n t e r i n g the impregnated p a r t . By t u r n i n g around the convertor 180° i n the r e a c t o r we have the s i t u a t i o n of developing flow combined w i t h chemical r e a c t i o n at the tube w a l l . This procedure allows to measure the entrance e f f e c t experimental l y . The r e s u l t s of the measurements are shown i n f i g u r e 5. I t turns out that indeed the conversio for f u l l y developed flow rements w i t h a Κ value from equation (17) amounts t o 1.28. The c a l c u l a t e d p r o f i l e f o r f u l l y developed flow w i t h t h i s Da number, how ever, does not correspond w i t h the experimental p o i n t s f o r t h i s flow c o n d i t i o n , i n d i c a t i n g that indeed the average c o n c e n t r a t i o n does not equal the tube w a l l c o n c e n t r a t i o n . With Da = 2.7, however, the agreement between the t h e o r e t i c a l p r o f i l e s f o r f u l l y developed flow and the experimental measured conversions f o r t h i s flow condi t i o n i s e x c e l l e n t . This i n d i c a t e s that the tube w a l l c o n c e n t r a t i o n i s roughly two times as low as the average c o n c e n t r a t i o n . The agree ment between the t h e o r e t i c a l p r o f i l e f o r developing flow (Da = 2.7) and the experimental p o i n t s i s somewhat worse than f o r f u l l y d e v e l oped f l o w , i n d i c a t i n g that f o r developing flow the Da number w i l l be somewhat lower. With the h i g h l y a c t i v e convertor used f o r studying the entran ce e f f e c t a l l experiments i n the temperature range 400-680 Κ are run i n the f i l m d i f f u s i o n r e g i o n . This allows to study the v a l i d i ty of the Leveque equation i n more d e t a i l . From f i g u r e 6 we may conclude that a t a l l three i n v e s t i g a t e d temperatures the Leveque equation gives a good d e s c r i p t i o n of the experiments up to F = 80 - 90%. Besides the o x i d a t i o n of ethylene we a l s o p a i d a t t e n t i o n to the combustion of 1-butene. This r e a c t i o n was found t o be 1.3 order i n 1-butene and has an a c t i v a t i o n energy of 6.7 kJ/mole (500-713K), i n d i c a t i n g that the r e a c t i o n runs a l s o i n the f i l m d i f f u s i o n l i m i t a t i o n r e g i o n . L i k e i n the case o f ethylene o x i d a t i o n the r e l a t i v e s i t u a t i o n o f the curves i n the c/c vs L/RPe plane i s s o l e l y d e t e r mined by the value of Da. A l s o here the Leveque equation proves to be a good d e s c r i p t i o n of the experimental r e s u l t s . Discussion From the preceding paragraph i t has become c l e a r that the ex perimental determined r a t e constant, K, always w i l l be l e s s than i t s r e a l value. Therefore, i t looks appropriate t o d e a l more spe c i f i c w i t h the r a t i o between the tube w a l l and cup mix concentra t i o n , since t h i s r a t i o determines how f a r the r a t e constant K, as
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—]
10
j^
: theoretical profile, fully developed flow : theoretical profile, developing flow : theoretical profile, undeveloped flow • \
\
experimental, developing flow; Da « 1.28, Se m 1.09
ο experimental, fully developed flow, Da * 1.28, Sc « 1.09 1 : Da = 1.28, Sc 1.09 B
2,3,4 : Da = 2.7, Se s 1.09
0".2
OA ~L/(Pe*R)
Figure 5.
Entrance effect in highly active monolith. Oxidation of ethylene (C = 300-350 ppm) at 40ŒK. 0
1·5η 4/3
ο • ft
F*R ^2/3
(D*i)
1-0H
0.5H
400 K Sc.1.09 508 Κ Sc.1.00
5
2
5
2
D.2.31 10" m / s D 3.82 10" m /s e
5
2
680 Κ Sc=0.91 D«6.74 10~ m /s
0.5
Figure 6.
0.6
0.7
0.8
0.9
1.0
Verification of the Leveque equation for the oxidation of ethylene in the diffusion limitation region
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
7.
BOERSMA ET AL.
Velocity and Concentration Profiles
81
determined from a homogeneous d e s c r i p t i o n o f the w a l l r e a c t i o n , de v i a t e s from the r e a l r a t e constant. Table I gives f o r three flow c o n d i t i o n s , i . e . f u l l y developed, developing and undeveloped f l o w , t h i s r a t i o as a f u n c t i o n of the a x i a l d i s t a n c e , r e a c t i o n order, Da number and Sc number. Developing
Undeveloped
Fully developed
No L / (Pe * R) 1 2 3 4 5
Da=1.7; Sc = 0.97; n = 1 Da=2,7; Sc = 1.09; n = 1 Da=5.5; Sc = 1,19; η = 1.3 Da=10; Sc = 1; n = 1 Da=10; Sc = 1; n=2
0.1 0.68
0.2
0.3
0.675 0.673
0.564 0.557 0.557
0.1 0.57
0.2
0.3
0.545 0.544
0.1 0.564
0.2
0.3
0.557 0.565
0.442 0.424 0.423
0.438 0.432 0.432
0.459 0.516 0.578
0.447 0.506 0.572
0.48 0.23 0.56
0.635 0.722
Table I R a t i o between tube w a l l and cup mix c o n c e n t r a t i o n f o r v a rious conditions. We see that the r a t i o between tube w a l l c o n c e n t r a t i o n and cup mix c o n c e n t r a t i o n i s highest f o r undeveloped flow and lowest f o r a f u l l y developed v e l o c i t y p r o f i l e . I t f u r t h e r f o l l o w s that under our experimental c o n d i t i o n s (no 1, 2, 3 Table I ) f o r a l l three flow c o n d i t i o n s the average c o n c e n t r a t i o n i s roughly two times as high as the w a l l c o n c e n t r a t i o n . This i m p l i e s that a l s o the r a t e constant roughly spoken has to be two times as high as the experimental v a l u e . I n the preceeding paragraph we saw that f o r the f u l l y developed v e l o c i t y f i e l d t h i s indeed i s the case. The c a l c u l a t i o n s f u r t h e r have shown that the c o n c e n t r a t i o n pro f i l e s f o r developing flow agree b e t t e r w i t h the f u l l y developed ve l o c i t y f i e l d than w i t h the undeveloped flow c o n d i t i o n . This agree ment becomes even b e t t e r w i t h i n c r e a s i n g Da number. Therefore, i n p r a c t i c e one should use the P o i s e u i l l e p r o f i l e f o r c a l c u l a t i n g the conversion i n the monolith r e a c t o r . F i n a l l y , i t has become c l e a r that as a r e s u l t of d i f f u s i o n l i m i t a t i o n Da values greater than 10 are h a r d l y r e a l i s t i c i n a c t i v e w a l l r e a c t o r s i n which the reactants are i n the gas phase. Acknowledgement I t i s a pleasure t o thank Kali-Chemie Engelhard K a t a l y s a t o r e n GmbH, Hannover, Germany, f o r supplying the monoliths used i n t h i s study. We a l s o want t o thank Dr.G.J. V i s s e r of the Computer Centre f o r h i s v a l u a b l e advice during the computational work. Notation C c cο fi
dimensionless c o n c e n t r a t i o n exit concentration i n l e t concentration
ρ μ τ
density dynamic v i s c o s i t y residence time
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
82 d D F k Κ L η Ρ r R U U V ζ
diameter tube Ψ molecular d i f f u s i o n c o e f f i cient ζ r e l a t i v e conversion r a t e constant homogeneous ω reaction r a t e constant f o r w a l l reaction length of tube Da r e a c t i o n order pressure Pe r a d i a l d i s t a n c e / r a d i u s of t u be Re r a d i u s of tube velocity axial directio a x i a l v e l o c i t y at r velocity radial direction a x i a l d i s t a n c e / r a d i u s of tube
dimensionless stream function dimensionless a x i a l co o r d i n a t e (= 2 z/Re) dimensionless azimuthal com ponent of the v o r t i c i t y vec tor . Damkohler number
g
Péclet number j ~ Reynolds number £uiL y
Literature Cited 1. Baron, Th., Manning, W.R., and Johnstone, H.F., Chem. Eng. Prog., (1952), 48, 125. 2. Johnstone, H.F., Houvouras, E.T., and Schowalter, W.R., Ind. Eng. Chem., (1954), 46, 702. 3. Brauer, Η., and Schlüter, Η., Chemie-Ing.-Techn., (1966), 38, 279. 4. Bräuer, H.W., and Fetting, F., Chemie-Ing.-Techn., (1966), 38, 30. 5. Seifert, Α., and Schmidt, Η., Chemie-Ing.-Techn., (1967), 39, 593. 6. Koch, Η., and K i r c h n e r , Κ., Dechema Monografiën, (1973), 75, 145. 7. Young, L.C., and F i n l a y s o n , B.A., Adv. Chem. S e r . , (1974), 133, 629. 8. U l r i c h s o n , D.L., and Schmitz, R.A., Ind. Eng. Chem., Fundam., (1965), 1, 1. 9. Langhaar, H.L., J . Appl. Mech., (1942), 9, A-55. 10. Wang, Y.L., and Longwell, P.Α., Α.I.Ch.Ε. J o u r n a l , (1964), 10, 323. 11. Vrentas, J.S., Duda, J.L., and Bargeron, K.G., A.I.Ch.E. J o u r n a l , (1966), 12, 837. 12. T i e l e n , W.H.M., "An experimental and theoritical study of the a c t i v e w a l l r e a c t o r " , MSc-Thesis, Eindhoven, The Netherlands, (1976). 13. Cowherd, C., and Hoelscher, H.E., Ind. Eng. Chem, Fundam., (1965), 4, 150.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
8 Monolithic Reactor-Heat Exchanger T. F . D E G N A N , JR. and J. W E I University of Delaware, Newark, DE 19711
A novel monolithic reactor-heat exchanger has been constructed an Experiments were conducte bon monoxide over copper chromite p e l l e t e d c a t a l y s t s . The experimental temperatures of reactants and c o o l ants, and concentrations agree with computations with a cell model. V i r t u a l l y f l a t temperature p r o f i l e s can be obtained i n the co-current mode. Equipment A novel chemical reactor has been constructed of four crossflow monoliths arranged i n series to act as reactor-heat exchangers. Every second pass of each crossflow i s packed with a p e l l e t e d c a t a l y s t or has c a t a l y s t deposited on the monolith w a l l s . The remain ing passes are empty to f a c i l i t a t e the flow of heat exchange medium. A p e l l e t e d crossflow monolith i s shown i n F i g . 1, and its dimensions are shown i n Table I. For the coated monolith, the heights of the two passes are the same. Note the large heat transfer area to volume r a t i o achieved i n the cross flow design, which leads to a high number of trans ference units for heat exchange. Arranging the crossflows i n series approximates true cocurrent or countercurrent flow. Mathematical analyses of simple heat transfer were published on cocurrent or countercurrent behavior for a series of crossflows (1,2). This paper deals with the mathe matical modeling and experiments for simultaneous reaction and heat transfer. The oxidation of carbon monoxide over a base metal c a t a l y s t was selected because i t i s a highly exothermic reaction whose rate has an approximate f i r s t order dependence on the concentration of ©
0-8412-0401-2/78/47-065-083$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
84
Table I P h y s i c a l Dimensions o f C r o s s f l o w M o n o l i t h s P e l l e t F i l l e d Monoliths R e a c t i o n Pass C o o l a n t Pass Cross S e c t i o n a l of
Flow, A
Area
x
2.326 i n
Heat T r a n s f e r A r e a , A
86.2
H e i g h t Between F l a t s , b
in
2
0.867 i n
2
6 7.82
0.315 i n
in
2
2
0.125 i n
Thickness of F l a t s Volume o f Pass, V H y d r a u l i c Radius,
4.652 i n r
3
1.735 i n
0.054 i n
3
0.026 i n
Heat T r a n s f e r A r e a t o Volume R a t i o , a 18.49 in" 39.10 i n " CO Q/i,,^) ; p e l l e t e d copper chrome "aero ban" c a t a l y s t p r o v i d e d by American Cyanamid Co. was c h a r a c t e r i z e d , u s i n g a 1.25 cm OD i n t e g r a l r e a c t o r i n a c o n s t a n t temperature sand b a t h . F i r s t o r d e r k i n e t i c s were o b t a i n e d i n the range o f 425 t o 1000°F. The f o l l o w i n g k i n e t i c parameters were o b t a i n e d : 1
I
= 6,300 °R1
1
1
1
k = 1.194x1ο * s e c " . oo
The p e l l e t e d copper chrome c a t a l y s t was metered i n t o each o f the l a r g e s i n u s o i d a l d u c t s o f the r e a c t i o n pass o f each o f the f o u r m o n o l i t h s c o m p r i s i n g the r e a c t o r - h e a t exchanger. A h" l a y e r o f q u a r t z c h i p s a t each o f t h e r e a c t i o n pass f a c e s o f t h e c r o s s f l o w s guaranteed t h a t the r e a c t i o n was c o n f i n e d t o the volume o f the m o n o l i t h where h e a t exchange c o u l d take p l a c e . In a s e p a r a t e s e t o f f o u r c r o s s f l o w m o n o l i t h s , a c a t a l y s t o f s i m i l a r c o m p o s i t i o n (1.442% Cu and 0.966% Cr) and d e n s i t y was c o a t e d e x c l u s i v e l y on the w a l l s o f the r e a c t i o n p a s s . No attempt was made t o keep the c a t a l y s t from a d h e r i n g t o the s e c t i o n o f w a l l a d j a c e n t t o which no h e a t t r a n s f e r medium f l o w e d . In b o t h c a s e s , the f o u r c o r d i e r i t e m o n o l i t h s were p o s i t i o n e d i n a s t e e l m a n i f o l d shown i n F i g . 2.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
70.10 inches
Figure 2. Top view of MRHE
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
86
CHEMICAL REACTION ENGINEERING—HOUSTON
F i f t y - s e v e n chromel-alumel thermocouples measured the temperatures w i t h i n the r e a c t o r . A D o r i c m u l t i p o i n t d i g i t a l r e c o r d e r m o n i t o r e d the thermocouple r e a d i n g s and p r i n t e d these r e a d i n g s on paper tape. A c o n v e r s i o n p r o f i l e a l o n g the r e a c t i o n pass was o b t a i n e d by measuring the c o m p o s i t i o n i n each o f the t r i a n g u l a r shaped empty volumes between the m o n o l i t h s . F i f t e e n centimeters long pieces of s t a i n l e s s s t e e l were welded i n t o the c e n t e r o f each o f the t e n t r i a n g u l a r shaped volumes f o r use as gas sample p o r t s . Sample a n a l y s i s was performed u s i n g a gas chromatograph. Cocurrent,
Countercurrent
and A u t o t h e r m a l
Operation
By f e e d i n g the i n t o s e p a r a t e p o r t s o f the r e a c t o r , i t was p o s s i b l e to a c h i e v e f i v e d i f f e r e n t flow schemes, shown i n F i g . 3. An a d i a b a t i c r e a c t o r was s i m u l a t e d by f e e d i n g a stream o f p r e h e a t e d a i r and CO to the c a t a l y s t c o n t a i n i n g r e a c t i o n pass and by s e a l i n g o f f the c o o l a n t p a s s . S i m i l a r l y , the c o c u r r e n t and c o u n t e r c u r r e n t schemes were approximated by f l o w i n g c o o l a n t and r e a c t a n t streams e i t h e r i n t o a d j a c e n t p o r t s o r i n t o p o r t s which l i e a t o p p o s i t e ends o f the r e a c t o r - h e a t exchanger r e s p e c t i v e l y . F i n a l l y , a u t o t h e r m a l c o c u r r e n t and c o u n t e r c u r r e n t schemes were approximated by f e e d i n g a c o o l stream o f CO i n a i r i n t o the c o o l a n t pass and f e e d i n g the h e a t e d stream l e a v i n g t h i s pass t o the c a t a l y s t c o n t a i n i n g r e a c t i o n pass. F o r the a u t o t h e r m a l c o u n t e r c u r r e n t r u n , the p a r t i t i o n between p o r t s G and H was removed, the p o r t s were s e a l e d , and the CO c o n t a i n i n g s t r e a m was f e d t o p o r t E. F o r the a u t o t h e r m a l c o c u r r e n t c a s e t h i s p a r t i t i o n was r e s t o r e d , and the m i x t u r e o f CO i n a i r was f e d i n t o P o r t G. An i n s u l a t e d s t a i n l e s s s t e e l f l e x hose was used t o c a r r y the gas stream from p o r t Ε t o p o r t H. The r e a c t e d stream e x i t e d a t p o r t F. M a t h e m a t i c a l Models The c e l l model (6., 7) i s p a r t i c u l a r l y w e l l s u i t e d to d e s c r i b i n g the two d i m e n s i o n a l temperature and con centration p r o f i l e s i n crossflow, including a x i a l d i s p e r s i o n i n these s h o r t p a s s e s (L/Dp<25 f o r the mono l i t h s and c a t a l y s t used i n t h i s s t u d y ) . After n e g l e c t i n g the r a d i a l and i n t e r p h a s e c o n c e n t r a t i o n and temperature g r a d i e n t s , we can w r i t e the m o d e l l i n g equations f o r a f i r s t order r e a c t i o n with simultaneous
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
DEGNAN AND WEI
Monolithic Reactor-Heat Exchanger
Reactant Counlercuirent
Coolant"* Reactant
3Q>4» Coolant
Aufethermol
Figure 3.
Cocurr*nl
Five MRHE flow modes
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
88
h e a t t r a n s f e r and h e a t l o s s i n a s i n g l e c r o s s f l o w a s : R e
R
i,j- i-i,j = W ^ e * .-θ^.,.^^κ
am
e
1
}
r J
+βΥ.
, βχρ(-α/θ? . ) . ) fJ fJ l»J . , = NTU (6 .-θ? . J - N T U ^ i e ? .-θ* *) -"-/J Ji»3 i f ] i f ] 1
C
θ9 i/j Y
(1)
1
i , j-Vl,
R
1
(2)
j - " ^ i , j « P < - a / e J j) (e?/6f ·) #
(3)
f
An e x p l a n a t i o n o f t h e terms used i n t h e above e q u a t i o n s can be found i n t h e nomenclature. These e q u a t i o n s a r e a p p l i c a b l e f o r i>2 and j>2. The f i r s t s e t o f p o i n t s i n each d i r e c t i o n , i . e . j=l, i = l , 2, ...M a r boundary c o n d i t i o n s . The boundary c o n d i t i o n s a r e thus Y
i,j
= Y.
j
= 2,3,.., . .N
(4) = θ§ j = 2,3,... . .N If J eC . = eÇ i = 2,3,.,. . .N if 1 where N - l i s t h e number o f c e l l s i n t h e j - d i r e c t i o n and M - l i s t h e number o f c e l l s i n t h e i - d i r e c t i o n . To s o l v e f o r t h e d i m e n s i o n l e s s temperatures 9 , and 6 and the f r a c t i o n r e m a i n i n g Y over t h e e n t i r e g r i d , a marching method i s used i n which t h e NewtonRaphson a l g o r i t h m s o l v e s f o r 6 Ç j , 9Ç j and Y i j a t each p o i n t u n t i l t h e g r i d i s c o m p l e t e l y s p e c i f i e d . E x t e n s i o n o f the proposed c e l l model f o r one c r o s s f l o w m o n o l i t h t o any number o f c r o s s f l o w s i s r e l a t i v e l y straightforward. Each m o n o l i t h i s a s s i g n e d an NXM g r i d w h i l e t h e t r i a n g u l a r shaped chambers between t h e m o n o l i t h s a r e t r e a t e d as c o n t i n u o u s s t i r r e d volumes. The stream e n t e r i n g each o f t h e chambers has a temperature and c o m p o s i t i o n t h a t a r e the average o f t h e streams l e a v i n g t h e c r o s s f l o w s . To o b t a i n the i n l e t temperatures t o t h e n e x t m o n o l i t h i n t h e d i r e c t i o n o f f l o w , a h e a t b a l a n c e must be drawn around the chambers t o a c c o u n t f o r h e a t l o s s . Heat t r a n s f e r c o e f f i c i e n t s needed t o o b t a i n NTU , NTU , NTU C, N T U , N T U and N T U a r e o b t a i n e d from a n a l y s i s o f s t e a d y s t a t e and s t o p f l o w h e a t t r a n s f e r data. By a l t e r n a t e l y s o l v i n g t h e s e t o f e q u a t i o n s desc r i b i n g t h e NXM g r i d and t h e h e a t b a l a n c e s around t h e chambers, i t i s p o s s i b l e t o compute t h e temperature and c o n c e n t r a t i o n p r o f i l e s o v e r t h e e n t i r e r e a c t o r . C
R
f
f
C
R
A
A R
C R
C R
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
8.
DEGNAN AND WEI
Monolithic Reactor-Heat Exchanger
89
The c o u n t e r c u r r e n t , a u t o t h e r m a l c o c u r r e n t , and a u t o t h e r m a l c o u n t e r c u r r e n t schemes r e q u i r e an i t e r a t i v e approach s i n c e the boundary c o n d i t i o n s a r e s p l i t i n each o f t h e s e c a s e s . The hydrodynamic e n t r a n c e e f f e c t i s i m p o r t a n t on the h e a t t r a n s f e r c o e f f i c i e n t i n the c o o l a n t pass o f each c r o s s f l o w . Under the e x p e r i m e n t a l c o n d i t i o n s , the e n t r a n c e e f f e c t may p e n e t r a t e more than halfway i n t o the c r o s s f l o w . A p p r o x i m a t i o n s t o the G r a e t z problem f o r f l o w e n t e r i n g a s i n u s o i d a l d u c t a r e a v a i l a b l e (8) a l t h o u g h many o f t h e s e a r e i n the form o f i n f i n i t e series. Hawthorn (j^) has proposed an ana l y t i c a l a p p r o x i m a t i o n t o the G r a e t z problem o f the form, | | = B(l+0.078(dRePr/x) where d i s the h y d r a u l i c d i a m e t e r , χ i s the d i s t a n c e , and Β i s the a s y m p t o t i c n u s s e l t number (NU=2.12) f o r flow i n a s i n u s o i d a l duct. Results E x p e r i m e n t a l a n a l y s e s o f the h e a t t r a n s f e r c h a r a c t e r i s t i c s o f the m o n o l i t h i c r e a c t o r - h e a t exchanger were c a r r i e d o u t i n the absence o f r e a c t i o n t o d e f i n e the NTU v a l u e s i n e q u a t i o n s ( 1 ) , ( 2 ) , and ( 3 ) . Experiments were performed i n which the c o o l a n t pass flow r a t e was v a r i e d i n d e p e n d e n t l y o f the r e a c t i o n pass f l o w r a t e , t o produce j - f a c t o r s vs Reynolds number, i n good agreement w i t h b o t h the G r a e t z s o l u t i o n and d a t a from an e x p e r i m e n t a l study by Kays e t a l (10) o f a c r o s s f l o w o f s i m i l a r d e s i g n . Heat t r a n s f e r c o e f f i c i e n t s o f the r e a c t i o n pass i n which the p e l l e t e d c a t a l y s t f i l l e d the s i n u s o i d a l volume was s a t i s f a c t o r i l y d e s c r i b e d by the c o r r e l a t i o n proposed by Leva (1950) f o r l a r g e ratios: jl| =
0.125
(dp
Ρ
v 0.75
?
}
(
g
)
The NTU v a l u e s i n e q u a t i o n s (1) and (2) d e s c r i b i n g the h e a t loss* from the m o n o l i t h i c r e a c t o r - h e a t exchanger chambers and c r o s s f l o w shapes were e v a l u a t e d using data obtained i n stop flow experiments. Overall h e a t t r a n s f e r c o e f f i c i e n t s based on the chamber w a l l a r e a v a r i e d from 0.3 BTU/hr. f t ° F t o 0.55 BTU/hr. f t F depending on the p o s i t i o n i n the r e a c t o r . The m o n o l i t h i c r e a c t o r - h e a t exchanger was run s u c c e s s i v e l y as an a d i a b a t i c r e a c t o r , a c o u n t e r c u r r e n t r e a c t o r - h e a t exchanger and a c o c u r r e n t r e a c t o r - h e a t 2
2 o
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
exchanger. Measured temperature and c o n v e r s i o n d a t a a r e shown as p o i n t s i n F i g . 4 , 5 and 6. Each o f these runs was made u s i n g i d e n t i c a l i n l e t c o n d i t i o n s . T a b l e I I l i s t s these r u n n i n g c o n d i t i o n s and p r o v i d e s comparison o f t h e maximum and minimum temperatures and c o n v e r s i o n measured i n t h e t h r e e i n d i v i d u a l r u n s . The v e r t i c a l l i n e s through t h e d a t a p o i n t s i n d i c a t e the range o f temperatures measured i n each o f t h e b l o c k s and chambers (up t o 9 thermocouples) p e r b l o c k . In the c o c u r r e n t and c o u n t e r c u r r e n t r u n s , t h e l a r g e s t s p r e a d i n temperatures o c c u r s i n the b l o c k t h a t t h e r e a c t i o n stream f i r s t e n t e r s s i n c e the r e a c t i o n r a t e is greatest at this point. The a d i a b a t i c r u n has a s m a l l d i s t r i b u t i o n o f temperatures i n each o f t h e f o u r b l o c k s because t h e s i o n a l with only a smal a t t r i b u t a b l e t o h e a t l o s s from t h e r e a c t o r . The c o c u r r e n t r u n has t h e f l a t t e s t r e a c t i o n pass temperature p r o f i l e o f the t h r e e shown. Indeed, i t i s p o s s i b l e t o o b t a i n an a b s o l u t e l y f l a t r e a c t i o n pass temperature p r o f i l e i n a r e a c t o r - h e a t exchanger i n which the r e a c t a n t and c o o l a n t streams flow c o c u r r e n t l y (11) . T h e o r e t i c a l p r o f i l e s c a l c u l a t e d by t h e c e l l model d e s c r i b e d p r e v i o u s l y a r e a l s o shown i n F i g . 4 through 6. The s o l i d l i n e s a r e o b t a i n e d w i t h a p l u g f l o w model, and the d o t t e d l i n e s a r e o b t a i n e d w i t h a c e l l model. The s i m u l a t e d p r o f i l e s f i t t h e average v a l u e s o f t h e temperature and c o n v e r s i o n s c a l c u l a t e d f o r each m o n o l i t h and chamber. A seven χ seven g r i d used t o s i m u l a t e t h e two d i m e n s i o n a l p r o f i l e s i n t h e c o c u r r e n t and c o u n t e r c u r r e n t runs produced t h e b e s t agreement between e x p e r i m e n t and t h e o r y . To s i m u l a t e t h e a d i a b a t i c r u n shown i n F i g . 4 , e q u a t i o n s (1) and (3) were s o l v e d s i m u l t a n e o u s l y . The same seven g r i d p o i n t ( i . e . , s i x c e l l ) model was used t o c a l c u l a t e the r e a c t i o n and c o o l a n t pass p r o f i l e s so t h a t t h e e f f e c t o f t h e a x i a l p e l l e t number on the temperature and c o n c e n t r a t i o n d i s t r i b u t i o n s c o u l d be e v a l u a t e d . A one d i m e n s i o n a l p l u g f l o w model of the a d i a b a t i c r e a c t o r was then f o r m u l a t e d and s o l v e d u s i n g a f o u r t h o r d e r Runge-Mutta t e c h n i q u e . A comparison o f t h e two models, shown i n F i g . 4 , i n d i c a t e s t h a t the e f f e c t o f a x i a l d i s p e r s i o n on t h e c o n v e r s i o n o r temperature o b t a i n e d i s n o t s i g n i f i c a n t . A u t o t h e r m a l c o c u r r e n t and c o u n t e r c u r r e n t runs f o r the p e l l e t f i l l e d r e a c t o r - h e a t exchanger were a l s o made and were c o r r e l a t e d w i t h t h e o r y . As i n t h e above t h r e e cases t h e r e s u l t s showed good agreement w i t h theory. A more d e t a i l e d d e s c r i p t i o n o f t h e a u t o t h e r m a l
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
Figure 4. Adiabatic run; reactant flows from left to right
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
92
CHEMICAL
Figure 5.
REACTION
ENGINEERING—HOUSTON
Counter-current run; reactantflowsfrom left, coolant from right
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
8.
DEGNAN
AND WEI
Monolithic Reactor-Heat Exchanger
Figure 6. Cocurrent run; both streamsflowfrom left
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
94
Table I I R e a c t i o n Run Data a) Reactor
Run C o n d i t i o n s
Mass Flow Rate R e a c t i o n Pass Mass Flow Rate C o o l a n t Pass Gas Composition
21.38 lbm/hr. 5.67 lbm/hr.
Reactio
I n l e t R e a c t i o n Pass Temperature
403°F 75°F
I n l e t C o o l a n t Pass Temperature b) Run Comparison
Maximum R e a c t i o n Temperature
Pass
Minimum R e a c t i o n Temperature
Pass
Maximum C o o l a n t Temperature R e a c t i o n Pass Temperature C o o l a n t Pass Temperature
Adiabatic
CounterCurrent
CoCurrent
69 3°F
673°F
504°F
403°F
304°F
403°F
607°F
496°F
304°F
497°F
535°F
500°F
0.880
0.864
0.731
R-4
R-2
R-4
Pass
Exit 691°F Exit
Conversion P o s i t i o n o f Maximum R e a c t i o n Pass Temperature
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
8.
DEGNAN
AND WEI
Monolithic Reactor-Heat Exchanger
95
r e a c t i o n schemes and the m u l t i p l i c i t y o f steady s t a t e s encountered i n these schemes can be found i n a p r e v i o u s r e f e r e n c e (11). S e v e r a l runs were a l s o made u s i n g m o n o l i t h s t h a t had r e a c t i o n pass w a l l s coated w i t h copper chrome catalyst. The c a t a l y s t coated m o n o l i t h s have much h i g h e r o v e r a l l h e a t t r a n s f e r c o e f f i c i e n t s / so t h a t t h e r e i s e q u a l i z a t i o n o f the c o o l a n t and r e a c t a n t temperatures i n t h r e e o u t o f f o u r m o n o l i t h s . Conclusions A novel reactor, consisting o f a series o f crossf l o w m o n o l i t h s f o r a c o o l a n t stream and a r e a c t a n t stream, has been d e s i g n e thermic f i r s t order exchanger i s v e r s a t i l e and can be run i n f i v e modes: (1) as an a d i a b a t i c r e a c t o r , (2) w i t h c o o l a n t and r e a c t i n g schemes f l o w i n g c o c u r r e n t l y , (3) w i t h c o o l a n t and r e a c t i n g streams f l o w i n g c o u n t e r c u r r e n t l y , (4) w i t h a u t o t h e r m a l c o c u r r e n t flow and (5) w i t h a u t o t h e r m a l c o u n t e r c u r r e n t flow. Temperature and c o n c e n t r a t i o n p r o f i l e s from a d i a b a t i c , c o c u r r e n t and c o u n t e r c u r r e n t runs compare f a v o r a b l y w i t h a c e l l model used t o s i m u l a t e the c r o s s flows i n s e r i e s d e s i g n . Acknowledgemen t s The a u t h o r s would l i k e to thank the Minnesota M i n i n g and M a n u f a c t u r i n g Company f o r s u p p o r t i n g t h i s i n v e s t i g a t i o n and s u p p l y i n g the c e r a m i c c r o s s f l o w monoliths. The American Cyanamid Company s u p p l i e d the c a t a l y s t . Nomenclature
A A Afr a a x
1
b C
Roman. Heat t r a n s f e r a r e a o f c r o s s f l o w m o n o l i t h C r o s s s e c t i o n a l area o f c r o s s f l o w m o n o l i t h F a c i a l area o f c r o s s f l o w m o n o l i t h A r e a t o volume r a t i o T h i c k n e s s o f ceramic f l a t s D i s t a n c e between c r o s s f l o w f l a t s Concentration Heat c a p a c i t y H y d r a u l i c diameter E f f e c t i v e diameter o f p a r t i c l e A c t i v a t i o n energy F i l m heat t r a n s f e r c o e f f i c i e n t
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
96
CHEMICAL REACTION ENGINEERING—HOUSTON
kg koo NTU
Thermal c o n d u c t i v i t y o f gas Catalyst preexponential factor Number o f t r a n s f e r u n i t s =
R r U V ν χ Y
α
θ
Greek. Activity
T
p
coefficien /Ε) Ρ P ) V -ΔΗ Co' C
(
R e a c t i o n parameter (=kooT) Enthalpy of reaction R a t i o o f f r e e flow a r e a i n m o n o l i t h t o f r o n t a l area D i m e n s i o n l e s s temperature 1
μ ρ τ
a
Gas c o n s t a n t Hydraulic radius 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 M o n o l i t h volume Gas v e l o c i t y Denotes a x i a l p o s i t i o n i n the d u c t F r a c t i o n remaining
= β ΔΗ σ
U
LC
-ΔΗ
Co'
Viscosity Density Space time based on s u p e r f i c i a l
Dimensionless
velocity
Groups
Re Reynolds number (pdv/y) Pr P r a n d t l number (C u/kg) j-factor (h/vAXCp) (Cpu/kgV' p
3
S u b s c r i p t s and S u p e r s c r i p t s AC AM AR C CC CR C-L Η 0 R R-K
Denotes a m b i e n t - c o o l a n t pass r e l a t i o n s h i p Ambient Denotes a m b i e n t - r e a c t i o n pass r e l a t i o n s h i p C o o l a n t pass Denotes chamber-coolant pass r e l a t i o n s h i p Denotes chamber-reaction pass r e l a t i o n s h i p Chamber d e s i g n a t i o n ( c o o l a n t pass) Hot pass ( n o n c a t a l y t i c ) Inlet condition R e a c t i o n pass Chamber d e s i g n a t i o n ( r e a c t i o n pass)
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
8.
DEGNAN AND
WEI
Monolithic Reactor-Heat Exchanger
L i t e r a t u r e Cited 1. Nusselt, W., Tech. Mech. Thermod. (1930), 1, 417. 2. Stevens, R. A., Fernandez, J. and Woolf, J . R . , Trans. ASME (1957), 79, 287. 3. Harned, J. L., paper presented at Soc. Auto. Eng., SAE paper No. 720520, D e t r o i t , May, 1973. 4. H e r t l , W. and Farrauto, R. J., J. C a t a l . (1973), 28, 352. 5. Yu-Yao, Y., J. C a t a l . (1975), 39, 104. 6. Deans, H. A. and Lapidus, L., AIChE J. (1960), 6, 663. 7. Kuo, J. C. W., Morgan paper presente D e t r o i t , SAE paper No. 710289 (1971). 8. Shah, R. K. and London, A. L., Tech. Report #75, Dept. Mech. Eng. Stanford University (1971). 9. Hawthorn, R. D . , paper presented at AIChE National Meeting (1972). 10. Kays, W. Μ., London, A. L. and Johnson, D. W., ASME P u b l i c a t i o n , New York, A p r i l 1951. 11. Degnan, T. and Wei, J., to be published
(1978).
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
9 Hysteresis and Multiplicity in Wall-Catalyzed Reactors BRUCE A. FINLAYSON Department of Chemical Engineering, University of Washington, Seattle, WA 98195
A mathematical mode elucidate the effects o geometry of the duct, and a x i a l conduction on the hysteresis, m u l t i p l i c i t y and parametric s e n s i t i v i t y . The monolith reactor for carbon monoxide oxidation is the prototype considered, with wall catalyst being platinum on alumina on a ceramic substrate. Previous models have dealt with only a single tube of the monolith. Two adjacent ducts are examined to see the effect of heat exchange between them when the velocity i n each is different. 1. Hysteresis The term hysteresis refers to a m u l t i p l i c i t y of steady states, and the actual steady state depends on the past history of operation of the reactor. In p a r t i c u l a r , different outlet conversions are obtained for the same i n l e t temperature depending on whether the device starts out hot or cold. This effect i s i l l u s t r a t e d i n Figure 1, which was obtained experimentally by Hlaváček and Votruba (1) and Mostercky, et al. (2) i n the follow ing manner. Beginning with a cold reactor, desired i n l e t condi tions are maintained at a low temperature u n t i l steady state has been reached, giving one data point on the top part of the curve. Then the i n l e t temperature is raised, and the experiment again proceeds to steady state, giving another data point. This procedure i s followed giving the curve denoted by . At the i g n i t i o n temperature l i g h t off occurs and the concentra tion of carbon monoxide out of the reactor decreases d r a s t i c a l l y . Almost complete conversion i s obtained for any higher i n l e t temperature. Then the i n l e t temperature i s lowered, step by step, giving r i s e to the curve marked*-. At the extinction temperature the exit concentration suddenly increases and l i t t l e reaction takes place. For a given temperature between the extinction and i g n i t i o n temperatures i t i s possible to have two different outlet conditions; thus there i s a m u l t i p l i c i t y of steady states. When the i n l e t temperature i s near the extinction or i g n i t i o n temperature, a small change i n operating conditions - i n l e t concentration or temperature or v e l o c i t y - can cause a large ©
0-8412-0401-2/78/47-065-098$05.00/0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
9. FiNLAYsoN
Wall-Catalyzed Reactor Hysteresis and Multiplicity
99
change i n the o u t l e t c o n d i t i o n s . This phenomena i s parametric s e n s i t i v i t y . The h y s t e r e s i s curve i l l u s t r a t e d i n F i g u r e 1 thus i n c l u d e s i n f o r m a t i o n about the m u l t i p l i c i t y o f steady s t a t e s o l u t i o n s and the regions o f parametric s e n s i t i v i t y . What i t does not show, however, i s whether the two steady s t a t e s shown a r e s t a b l e , and i f there are any other steady s t a t e s between those shown (probably unstable ones). Judging from s t u d i e s o f packed beds (3) i t i s probable t h a t both the steady s t a t e s shown a r e s t a b l e , and any other ones are u n s t a b l e . A model developed e a r l i e r (4,_5) used the c o l l o c a t i o n method to s o l v e the equations f o r heat, mass and momentum t r a n s f e r i n a s i n g l e , a d i a b a t i c channel o f the monolith. The b a s i c model i s the one described as Model II-A(5) : a square du^ct w i t h a x i a l conduction o f heat l o n g i t u d i n a l l y i n the s o l i d w a l l s , but w i t h i n f i n i t e l y f a s t conductio i n c l u d i n g the d i f f u s i o n i n the f l u i d (See 5^ f o r a d i s c u s s i o n o f the importance o f i n c l u d i n g t h i s e f f e c . ) N u s s e l t and Sherwood numbers are not assigned a. p r i o r i , but are d e r i v e d from the s o l u t i o n . The r e a c t i o n r a t e e x p r e s s i o n P2 i n (5) w i t h a b a s i c form
k ( E + y)y Q
rate (1 + a y )
2
This i s the expression d e r i v e d by V o l t z , _et a l . t o f i t t h e i r data (6). Here however, we a l l o w d i f f u s i o n l i m i t a t i o n s i n the very t h i n c a t a l y t i c l a y e r . The temperature i s assumed constant w i t h i n the l a y e r s i n c e the primary heat t r a n s f e r r e s i s t a n c e occurs i n the f l u i d . The e f f e c t i v e n e s s f a c t o r curve i s generated u s i n g a one-term c o l l o c a t i o n method f o r s m a l l T h i e l e modulus and the asymptotic s o l u t i o n f o r l a r g e T h i e l e modulus ( 7 ) . The base case, unless otherwise noted, i s f o r a Reynolds number 160, 3^0* i n l e t 0.04, P2 k i n e t i c s , square geometry, k / k = 0.04, D /D = 20. =
f
g
f
g
Other parameters a r e given elsewhere (4,5), and the parameters a r e c h a r a c t e r i s t i c o f an Englehard PTX-4 converter. The t h e o r e t i c a l h y s t e r e s i s curve i s shown i n F i g u r e 2 f o r three d i f f e r e n t i n l e t CO mole f r a c t i o n s . The c o r r e c t q u a l i t a t i v e trends a r e exhibted: the h y s t e r e s i s i s wider ( g r e a t e r d i f f e r e n c e between the i g n i t i o n and e x t i n c t i o n temperatures) f o r l a r g e r concentrations o f carbon monoxide. Other c a l c u l a t i o n s (J) i n d i c a t e the i n g n i t i o n and e x t i n c t i o n temperatures depend on f l o w r a t e , too, r e f l e c t i n g the experimental o b s e r v a t i o n s : the h y s t e r e s i s i s wider f o r the lower flow r a t e s . As i n the case o f packed beds, the higher v e l o c i t i e s tend t o blow the r e a c t i o n zone out the downstream end o f the duct, whereas lower v e l o c i t i e s l e a d t o i g n i t i o n t h a t moves upstream towards the i n l e t . The e f f e c t o f geometry i s examined i n Ref. 8^ and ducts
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
100 0.05
1
1 — 1
1
π
1
1
Y =0.04 in
^ ο
0.04 IGNITIOT)
EXTINCTION
« ο Ε
0.031
ο ο
Y =0.02 in
0.02
3 °
0.01
50
1 100
1
1 200
:.i ; . ι 300
e
INLET TEMPERATURE ( F) Figure 1.
Experimental hysteresis curve, Re = 152, Refs. 1,2
Figure 2.
Theoretical hysteresis curves, Re = 160
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
400
9.
FiNLAYSON
Wall-Catalyzed Reactor Hysteresis and Multiplicity
101
w i t h four d i f f e r e n t shapes (square, c i r c l e , t r a p e z o i d , rectangle) have almost i d e n t i c a l h y s t e r e s i s p r o p e r t i e s . Consequently i t i s p o s s i b l e t o do c a l c u l a t i o n s w i t h the geometry that leads t o the most convenient computations. The most important e f f e c t o f the model i s the a x i a l conduc t i o n o f heat i n the s o l i d tube w a l l . Figure 3 shows the tem perature and mole f r a c t i o n p r o f i l e s f o r d i f f e r e n t values o f the s o l i d thermal c o n d u c t i v i t y . The i n l e t mole f r a c t i o n o f CO i s 0.04 and the i n l e t temperature i s 600°F. Figure 2 i n d i c a t e s that for these c o n d i t i o n s there are m u l t i p l e steady s t a t e s o l u t i o n s , one w i t h e s s e n t i a l l y complete r e a c t i o n , and one w i t h e s s e n t i a l l y no r e a c t i o n . The curves marked A and Β correspond t o the c o n d i t i o n s g i v i n g the p o i n t s A and Β i n the h y s t e r e s i s curves i n Figure 2. The extinguished s t a t e has very l i t t l e r e a c t i o n and the mole f r a c t i o n and w a l the l e n g t h o f the duct a x i a l thermal c o n d u c t i v i t y i s s e t t o zero, i . e . the a x i a l conduction o f heat i s absent, Model I I i n ( 5 ) . The i g n i t e d s t a t e has a sharp r i s e i n temperature i n s i d e the duct a t z/L = 0.65. The o s c i l l a t i o n s i n the s o l u t i o n are due to numerical e r r o r caused by using too few elements, 10, r a t h e r than the 20 used e a r l i e r (5). The importance o f a x i a l conduction o f heat i s emphasized by the other curves i n Figure 3. Shown there are the i g n i t e d s t a t e s for d i f f e r e n t s o l i d thermal c o n d u c t i v i t i e s , and as the s o l i d thermal c o n d u c t i v i t y decreases the i g n i t i o n zone moves t o the end o f the r e a c t o r , and f o r a small enough value only the extinguished s t a t e i s p o s s i b l e . The h y s t e r e s i s i s thus much enhanced by a l a r g e value o f k , o r by t h i c k e r w a l l s . This i s g
f u r t h e r demonstrated i n Table I . Table I . I g n i t i o n and E x t i n c t i o n Temperatures for D i f f e r e n t W a l l Thermal C o n d u c t i v i t i e s (from 7) k-/k f s 0.04 1.0 100.
Τ (°F) ex
T. (°F) ig
418 560 615
618 619 615
AT(°F) 200 59 0
Since the mechanism f o r h y s t e r e s i s i s due t o the a x i a l conduction of heat i n the w a l l , the h y s t e r e s i s should decrease as k o r the w a l l thickness decrease, as i l l u s t r a t e d by the parameter a f f e c t i n g the r a t e o f a x i a l conduction k
__s_
1h
2ΐ
ι1-ε
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
102
CHEMICAL REACTION ENGINEERING—HOUSTON
1400
~i
Γ
0.04
1.0
1200 JLL
ξ
1001
1000
<
cr LU
2
800
(D
® 600 ^
EXTINGUISHED STATE FOR ALL k , . k,= 0=> MODEL II $
0.04
σ ^
0.03|
Q> Ο S
8
0.02
Lu Ο
< UJ ο.οιh <
Figure 3.
Axial temperature and mole fraction profiles for different thermal conductivities
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
9.
FiNLAYsoN
Wall-Catalyzed Reactor Hysteresis and Multiplicity
103
2. E f f e c t o f M u l t i p l e Channels The c a l c u l a t i o n s reported above were f o r a s i n g l e , a d i a b a t i c channel o f a duct i n a m u l t i - c h a n n e l monolith. I f each channel i s not the same i t i s p o s s i b l e t h a t f u r t h e r c o m p l i c a t i o n s can a r i s e . We i n v e s t i g a t e t h i s p o s s i b i l i t y i n a p r e l i m i n a r y way. Since the m a t e r i a l e n t e r i n g a l l the channels i s the same (coming from the same l a r g e r channel o r i g i n a l l y ) , i t i s l i k e l y t h a t the i n l e t c o n c e n t r a t i o n and temperature a r e i d e n t i c a l i n the adjacent channels. We thus focus on the e f f e c t o f v e l o c i t y d i f f e r e n c e s i n adjacent channels. To s i m p l i f y the computational task we consider only two channels which share the same s o l i d w a l l . We saw above that the behavior o f the h y s t e r e s i s curve was not i n f l u e n c e d by the shape o f duct, and here we use a c i r c u l a r duct f o r computational convenience. The combined geometry i s then a checkerboard e f f e c t , w i t s t i l l assume t h a t ther of heat, so t h a t a t any a x i a l p o s i t i o n the w a l l temperature i s everywhere the same. For t h i s p r e l i m i n a r y s i t u a t i o n we a l s o assume t h a t the a x i a l conduction o f heat i s n e g l i g i b l e , even though we know t h i s i s not the case. However, s i n c e the w a l l temperature i s everywhere the same a t a given a x i a l l o c a t i o n , i t should be p o s s i b l e t o study the e f f e c t o f v e l o c i t y v a r i a t i o n s i n adjacent channels and a x i a l conduction o f heat s e p a r a t e l y , and the r e s u l t s add credence t o t h i s s u p p o s i t i o n . Such a d r a s t i c , but p l a u s i b l e , assumption was made f o r computational convenience. The computations f o r m u l t i p l e channels were made w i t h a r e v i s e d v e r s i o n o f the program REACOLL. This program converts a set of p a r a b o l i c p a r t i a l d i f f e r e n t i a l equations i n t o a l a r g e r s e t of o r d i n a r y d i f f e r e n t i a l equations by u s i n g the orthogonal c o l l o c a t i o n method (9,10). Previous v e r s i o n s o f REACOLL have used a f i f t h order Runge-Kutta v a r i a b l e step s i z e i n t e g r a t i o n r o u t i n e t o i n t e g r a t e i n the a x i a l d i r e c t i o n . We m o d i f i e d the program t o use Gear's a l g o r i t h m (11,12). Gear's a l g o r i t h m i s a c o l l e c t i o n of m u l t i - s t e p methods, w i t h the step and order o f the method a u t o m a t i c a l l y c o n t r o l l e d t o achieve a u s e r - s p e c i f i e d accuracy w i t h i n a minimum computation time. We chose the o p t i o n of an i m p l i c i t method w i t h the n o n l i n e a r a l g e b r a i c equations solved w i t h the Newton-Raphson method, w i t h a numerical generation of the Jacobian a t each Δζ s t e p . The Jacobian i s not reevaluated at each Δζ s t e p , but i s evaluated i f the i t e r a t i o n cannot converge i n three i t e r a t i o n s . I f the i t e r a t i o n s t i l l does not converge, a s m a l l e r Δζ i s chosen and the c a l c u l a t i o n i s repeated. The advantageous f e a t u r e o f the method i s t h a t i t w i l l always work f o r a s m a l l enough Δζ, but the computational c o s t may be h i g h . For these problems comparisons were made w i t h a f i f t h - o r d e r Runge-Kutta i n t e g r a t i o n i n Δζ, too, and Gear's a l g o r i t h m was about twice as f a s t f o r the same u s e r - s p e c i f i e d accuracy.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
104
CHEMICAL REACTION ENGINEERING—HOUSTON
The model equations can be w r i t t e n as
v
(
r
)
!ii
=
α
. _l |_
9c.
w i t h the f i r s t two v a r i a b l e s as the mole f r a c t i o n and temperature i n the f i r s t channel, and the t h i r d and f o u r t h v a r i a b l e being the mole f r a c t i o n and temperature i n the second channel. The c o n d i t i o n s a t the w a l l r e q u i r e that the d i f f u s i o n o f mass towards the w a l l equal the generation of mass by the w a l l - c a t a l y z e d r e a c t i o n , and the same i s true f o r heat. We thus have the boundary conditions 9c. 9r
r=l
i
r
> " W
r=l
9c, 9r
r=l
9r
3 R( 2
C;L
, T) + 3 R ( c , T) 4
3
r=l = Τ at r = l
The mathematical s t r u c t u r e of the problem i s thus a s e t of p a r t i a l d i f f e r e n t i a l equations which a r e coupled w i t h a s e t of n o n l i n e a r a l g e b r a i c equations a t each a x i a l p o s i t i o n . The a l g e b r a i c equations a r e solved u s i n g a Newton-Raphson i t e r a t i o n w i t h the d e r i v a t i v e s c a l c u l a t e d n u m e r i c a l l y . The same r e a c t i o n r a t e expression (P2)was used. The f i r s t case corresponds to a case which has not " l i t o f f . " We note f i r s t that without a x i a l conduction o f heat i n the w a l l the s o l u t i o n has to be unique ( 5 ) , and there i s no h y s t e r e s i s curve. For an i n l e t temperature o f 600°F the w a l l temperature p r o f i l e i s shown i n Figure 4 f o r d i f f e r e n t average v e l o c i t i e s . The three s o l i d curves a r e f o r cases i n which the v e l o c i t y i n each channels i s the same, but the magnitude of the average v e l o c i t y i s d i f f e r e n t . I n a l l cases a p a r a b o l i c v e l o c i t y d i s t r i b u t i o n i s taken as a f u n c t i o n of r a d i u s of the duct, since the flow i s laminar and only the average v e l o c i t y i s changed. The s o l i d curves then represent three separate u n r e l a t e d cases, i n which the average v e l o c i t y i s i n c r e a s e d . The c a l c u l a t i o n f o r m u l t i p l e channels i s made w i t h the v e l o c i t y i n one channel being 0.8 the normal v e l o c i t y ( g i v i n g Re = 128) and the v e l o c i t y i n the other channel being 1.2 times the normal v e l o c i t y ( g i v i n g Re = 192). The m u l t i p l e channel r e s u l t s a r e denoted by the ft i n the Figure 4, and i t i s seen that they a r e very c l o s e t o the r e s u l t s expected from two channels w i t h the same average v e l o c i t y i n each
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
FiNLAYsoN
Wall-Catalyzed Reactor Hysteresis and Multiplicity
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
/ /
/
= 0.8
l\. 2
1.2
WALL TEMPERATURE AVERAGE FLUID TEMPERATURE] •
MULTIPLE CHANNELS
: 0 . 8
LU
l.0\
l.2\
0.01 h «MULTIPLE CHANNELS =l.2 2
0.2
04
0.6
0.8
1.0
LENGTH Figure 5. Wall temperature in multiple channels, = 650°F
T
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
FiNLAYsoN
Wall-Catalyzed Reactor Hysteresis and Multiplicity
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
108
CHEMICAL REACTION
ENGINEERING—HOUSTON
channel. Here the e f f e c t o f d i f f e r e n t v e l o c i t i e s i n d i f f e r e n t channels i s minimal. The e f f e c t o f d i f f e r e n t v e l o c i t i e s may be more pronounced for a case which has " l i t o f f " , and t h i s i s examined i n F i g u r e 5. The nomenclature i s the same as i n F i g u r e 4 and we see that even at l i g h t o f f the m u l t i p l e channel w i t h d i f f e r e n t v e l o c i t i e s gives r e s u l t s which are almost i d e n t i c a l t o the two channels w i t h the same average v e l o c i t y . The temperature p r o f i l e s i n the r a d i a l d i r e c t i o n a r e shown i n F i g u r e 6. For the m u l t i p l e channel case, w i t h d i f f e r e n t v e l o c i t i e s , the f l u i d temperature p r o f i l e s are d i f f e r e n t but w i t h the same w a l l temperature ( s i n c e that i s shared); d e s p i t e that discrepancy the o v e r a l l e f f e c t s a r e very s i m i l a r t o the average case shown a t the r i g h t . We thus conclude that the e f f e c t o f d i f f e r e n t v e l o c i t i e s i n adjacent channels i s no however, f o r a model whic However, we have made c a l c u l a t i o n s f o r three d i f f e r e n t types of t r a n s v e r s e conduction: d i f f e r e n t geometries o f the duct ( 7 ) , p e r i p h e r a l conduction around the duct ( 5 ) , and now d i f f e r e n t v e l o c i t i e s i n adjacent ducts. I n the f i r s t two cases the i n c l u s i o n o r e x c l u s i o n of a x i a l conduction had l i t t l e e f f e c t on the q u a l i t a t i v e c o n c l u s i o n as t o the importance of the e f f e c t , and there i s no reason t o assume that the m u l t i p l e channel a n a l y s i s w i l l be any d i f f e r e n t . The i n c l u s i o n of a x i a l conduction w i l l have a dramatic e f f e c t on the h y s t e r e s i s but that h y s t e r e s i s should not be g r e a t l y a f f e c t e d by any o f the three t r a n s v e r s e phenomena: d i f f e r e n t geometries, p e r i p h e r i c a l conduction, o r m u l t i p l e channels w i t h d i f f e r e n t v e l o c i t i e s . We thus conclude that a n a l y z i n g a s i n g l e channel s u f f i c e s . 3. Conclusions The h y s t e r e s i s of a w a l l - c a t a l y z e d r e a c t o r f o r o x i d i z i n g carbon monoxide, as i l l u s t r a t e d i n F i g u r e s 1 and 2, i s g r e a t l y a f f e c t e d by a x i a l conduction of heat i n the s o l i d . This can be i n f l u e n c e d by changing e i t h e r the w a l l m a t e r i a l or the w a l l t h i c k n e s s . Having d i f f e r e n t v e l o c i t i e s i n adjacent channels does not change the r e s u l t s : they are very s i m i l a r t o those f o r a s i n g l e channel under the average c o n d i t i o n s . The t h e o r e t i c a l model d i s p l a y s h y s t e r e s i s of the same q u a l i t a t i v e f e a t u r e s as experiments: the h y s t e r e s i s i s enhanced by h i g h e r CO concentra t i o n s , lower v e l o c i t i e s , and h i g h e r s o l i d thermal c o n d u c t i v i t y . The geometry of the duct has minimal impact. 4. Acknowledgments Acknowledgment i s made t o the donors o f the Petroleum Research Fund, administered by the American Chemical S o c i e t y , f o r support of t h i s research under Grant PRF No. 7698-AC7. 5. L i t e r a t u r e C i t e d 1. Hlaváček, V. and Votruba, J., "Chemical R e a c t i o n Engineering-II," pp. 545-558, M.M. Hulburt (ed.), Am. Chem. Soc. Ser. 133 (1974).
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
9.
FINLAYSON
Wall-Catalyzed Reactor Hysteresis and Multiplicity
109
2. Mostecky, J., Hlaváček, V. and Votruba, J., Erdöl and Kohle (1974) 27, 261. 3. Eigenberger, G., Chem. Eng. S c i . (1972) 27, 1909, 1917. 4. Young, L . C . and Finlayson, B . A . , A.I.Ch.E. J . (1976) 22, 331. 5. Young, L . C . and Finlayson, B . A . , A.I.Ch.E. J . (1976) 22, 343. 6. Voltz, S . E . , Morgan, C.R., Liederman, D. and Jacob, S.M., Ind. Eng. Chem. Prod. Res. Devel. (1973) 12, 294. 7. Young, L . C . and Finlayson, B . A . , paper presented at A.I.Ch.E. meeting, Nov. 13-17, 1977. 8. Young, L . C . and Finlayson, B . A . , "Second International Symposium on F i n i t e Element Methods i n Flow Problems," Santa Margherita Ligure, I t a l y , June 14-18, 1976, pp. 623-634. 9. Finlayson, B . A . , Chem. Eng. S c i . (1971) 26, 1081. 10. Finlayson, B . A . , "The Method of Weighted Residuals and Variational P r i n c i p l e s , 11. Gear, C.W. 1971 "Numerica Differential Equations, Prentice-Hall. 12. Hindmarsh, A.C. 1975 "GEARB: Solution of Ordinary Differential Equations Having Banded Jacobian," Report UCID-30059, Rev. 1, Lawrence Livermore Laboratory, U.S. AEC W-7405-Eng-48, March, 1975.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
10 Poisoning in Monolithic Catalysts SHENG-TAI L E E and RUTHERFORD ARIS Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, M N 55455
Almost all c a t a l y t i decay or poisoning of th monolith i s no exception. Indeed this i s notorious i n the auto motive application where the c a t a l y t i c converter must survive 50,000 miles of operation and still perform adequately. Although we s h a l l use the kinetics of carbon monoxide oxidation over a platinum catalyst as an obvious and important example, our main objective i s to develop a model which can handle any catalyst decay question and to point out the differences i n two types of poisoning. Thus our study comes within the t h i r d main d i v i s i o n of the subject as laid out by Butt (1) i n 1972; not the mechanism or rate determination but the effect of deactivation on the operation of the reactor. The pertinent work before 1972 has been reviewed by Butt (1). Since then Hegedus and Petersen (2) have considered various kinet i c alternatives and Hegedus (3) has extended some of these results to include mass transfer effects. Becker and Wei (4) have consid ered the effect of non-uniform catalyst a c t i v i t y i n a sphere and its advantages and disadvantages with respect to poisoning, and there have been several studies of the fixed bed (5,6,7). Wei (8) has discussed deactivation of the catalyst i n the automotive context and with Heck and Katzer (9) has considered the modelling of the monolith following the pioneer work of Finlayson and Young (10). The generally accepted kinetics of the oxidation of CO over a Pt catalyst imply the adsorption of CO and oxygen with reaction between adsorbed species. The rate i s therefore proportional to the square of the active site concentration and leads, when oxygen is i n excess, to a kinetic expression of the form r =k c r
c o
/(l
+
k c )2 a
c o
(1)
By non-selective poisoning we mean (as i n Wei and Becker (2)) that the poison i s deposited randomly on the remaining unpoisoned s i t e s , whether or not these ©
0-8412-9491-2/78/47-065-110$05.00/0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
10.
LEE
AND
Poisoning in Monolithic Catalysts
ARIS
111
be c a t a l y t i c a l l y a c t i v e . Thus c , the t o t a l amount of poison pre cursor deposited, w i l l be governed by w
àc àt
c - tc c (1 -τ^) = k c θ ρ ps ρ ps Λ
w
(2)
v
where L^, i s the t o t a l amount that could be adsorbed a t s a t u r a t i o n , Cp the c o n c e n t r a t i o n of poison precursor i n the gas a t the s u r face and θ the unpoisoned f r a c t i o n . I f f =L/L» i s the c a t a l y t i c a l l y a c t i v e f r a c t i o n o f t o t a l s i t e s then we assume that s i n c e the poison i s n o n - s e l e c t i v e an amount f c ^ i s e f f e c t i v e i n b l o c k i n g a c t i v e s i t e s . A balance of a c t i v e s i t e s i s Î. = CQQ + 8Q + f c + c , where CQQ and CQ are the concentrations of these occupied by CO or 0 and c i s that of the a v a i l a b l e a c t i v e s i t e s . But i f the adsorptions o latter is dissociative C S
w
fl
a
c
= L9/Î1+ ( K c ) ^ + K
fl
0
0 2
c o
c
c o
} ;
(3)
here CQQ and CQ2 are the concentrations i n the gas near the surface and K^Q and KQ a d s o r p t i o n e q u i l i b r i u m constants. The surface r e a c t i o n i s a t a r a t e V C0 0 - \ C O C O C
£
K
C
( K
C
0 0
=Vco^oV* 2
= k e c r
c o
/(
1 +
) % £ 2
a
1 2 θ 2c
k c a
c o
2
co
)
2
/{ 1 +
(
Vo
2
) % + K
co c } c
0
2
(4)
.
which i s of the form (1) w i t h a f a c t o r of θ i f the c o n c e n t r a t i o n of oxygen i s constant. The equation f o r the r a t e of poisoning (2) can be w r i t t e n |=-k«c θ dt ρ ps
(5)
By s e l e c t i v e poisoning we mean t h a t a d s o r p t i o n of the poison takes place only on t o a v a i l a b l e c a t a l y t i c a l l y a c t i v e s i t e s . Thus θ d e c l i n e s a t a r a t e p r o p o r t i o n a l t o c ( r a t h e r than i t s e l f ) and by (3) and the assumed excess of oxygen a
||=-k c p
p s
9/(l
+
k c a
c o
).
(6)
The Assumptions of the Model and i t s Equations I t i s assumed that a t y p i c a l s i n g l e passage of the monolith can be represented as an e q u i v a l e n t c i r c u l a r c y l i n d e r through which
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
112
CHEMICAL REACTION ENGINEERING—HOUSTON
the r e a c t a n t s pass i n a f u l l y developed laminar f l o w . A x i a l con d u c t i o n and d i f f u s i o n a r e ignored but the r a d i a l t r a n s p o r t processes a r e considered. The w a l l of the c y l i n d e r i s coated w i t h a t h i n , porous, c a t a l y t i c a l l y a c t i v e l a y e r which o f f e r s some d i f f u s i o n a l r e s i s t a n c e so t h a t the equations f o r d i f f u s i o n and r e a c t i o n have t o be solved i n i t ; i t i s however s u f f i c i e n t l y t h i n that i t s curvature i s unimportant. Hegedus and Baron (11) observed t h a t poisoning and s i n t e r i n g had opposite e f f e c t s on the d i f f u s i v i t i e s i n the porous l a y e r so that we w i l l assume that they remain constant f o r the l i f e of the c a t a l y s t . I t i s assumed that the d e a c t i v a t i o n i s slow so that g i v e n any d i s t r i b u t i o n o f a c t i v i t y the temperature and c o n c e n t r a t i o n have steady s t a t e behavior. I t i s assumed that the a c t i v e c a t a l y s t l a y e r i s a t the same tem perature as the w a l l and that the r e l a t i v e l y h i g h c o n d u c t i v i t y of the ceramic keeps t h i s unifor s i n c e the l o n g i t u d i n a l d i n a l conduction of heat i n the w a l l s i s considered; r a d i a t i o n i s ignored. Only the dimensionless form of the equations w i l l be g i v e n . A l l symbols are d e f i n e d i n the nomenclature and r e l a t e d t o the p h y s i c a l v a r i a b l e s , here we need only say t h a t u, ν and w r e f e r t o c o n c e n t r a t i o n of CO, temperature and c o n c e n t r a t i o n of poison p r e c u r s o r , t h e s u f f i x e s f and s apply t o f l u i d and s o l i d phases r e s p e c t i v e l y where ξ and ξ a r e the r a d i a l coordinates, ζ i s the a x i a l coordinate and τ the time. Then i n the f l u i d : (7)
(8)
(9) At the entrance u (T,0,?) = v (T,0,§) = 1 , w (T,0,§) = W , f
f
f
Q
(10)
on the a x i s Ô /b§ = bv /b? = bw /b§ = 0 Uf
f
f
(ID
w h i l e a t the w a l l u ( T , C , l ) = u (T,C,0) , f
e
v (T,C,l) = V (T,C,0) , f
s
w (T,C,l) = W ( T , C , 0 ) . f
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
(12)
10.
L E E AND
113
Poisoning in Monolithic Catalysts
ARIS
The other c o n d i t i o n s a t the w a l l s t a t e that the CO which d i f f u s e s t o the w a l l , passes i n t o i t and there r e a c t s , and that the poison i s deposited: 1 ? buf 2 Γ s? 1 &s = Y0 E ( v ) J ϊ (13) ' Δ~δ]Γ (1+(DUJ θ
u
d
§=o
1=1
ÔWf
w
u
2
s
9w d§
& w
1 s _ ' Δ" b |
s
= γ0
?=o
§=1
V(v )f (l+»u.) s
J
(14)
n
where E(v) = exp e ( v - l ) / v , E"(v) = exp e " ( v - l ) / v . I n the c a t a l y s t l a y e r 0 <§ <1
= 0 E(v) δ! b
w
s
2
9 w
2
2
E P
be bT
(1+U)u ) s
0
bf
(15)
8
2
"
(
2 - p "
=
0
E
v
s s>ôi^n
(16)
θ w
( v
s s>a+^7)
(17)
The l a s t e x p r e s s i o n h o l d s f o r s e l e c t i v e poisoning: f o r nonselec t i v e ω i s s e t equal t o zero i n (14), (16) and (17). We note i n passing that m i s a f u n c t i o n o f v . A t f =1, s
b u / b | = bw /bf = 0 .
(18)
s
F i n a l l y , v , the s o l i d temperature, i s governed by the t r a n s p o r t from the f l u i d , t h e l o n g i t u d i n a l conduction and the heat generated by r e a c t i o n and a d s o r p t i o n : s
bvf
2
ib v_
r s u
e 2 d
f
pweaf
(19)
w
Method o f S o l u t i o n The method employed was a development of our e a r l i e r t e c h nique (12) which uses the s e r i e s expansion f o r the s o l u t i o n o f eqns. ( 7 ) - ( 9 ) . I f u^, v ^ and w^ a r e assumed t o be known as func t i o n s of ζ f o r ξ=1, the e i g e n f u n c t i o n expansion i n terms of Kummer s hypergeometric f u n c t i o n a l l o w s us t o c a l c u l a t e the d e r i v a t i v e s needed i n eqns. (13), (14) and (19). Since u = u , e t c . a t f
s
f
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
114
the i n t e r f a c e ξ=1, ξ=0, the same assumed values a l l o w eqns.(15), (16) and (18) t o be solved. Only the f i r s t and t h i r d terms of eqns. (13) and (14) are needed (since the e q u a l i t y of the second and t h i r d i s a consequence of (15) and (16)) so i n eqns.(13), (14) and (19) we have three equations f o r the three assumed f u n c t i o n s . The values of the f u n c t i o n s U f , V f , a n d W f have t o be c a l c u l a t e d at d i s c r e t e points and 10 elements w i t h 6 c o l l o c a t i o n points per element were found t o s u f f i c e . Rather than solve (15) and (16) s e p a r a t e l y i t was found best t o use c o l l o c a t i o n on these a l s o , using f o u r r a d i a l c o l l o c a t i o n p o i n t s . This gives 459 simultaneous n o n l i n e a r a l g e b r a i c equations which were solved by a modified Newton-Raphson i t e r a t i o n . The m o d i f i c a t i o n s were the use of u n d e r - r e l a x a t i o n and l e s s frequent e v a l u a t i o n of the Jacobian. Even so 30-40 seconds of CDC 6600 time were needed f o r the compu t a t i o n of a l l q u a n t i t i e Nusselt numbers and the a c t u a l r e a c t i o n r a t e t o the r a t e at stream c o n d i t i o n s , were a l s o calculated. R e s u l t s and
Conclusions
Values of the parameters were taken to be approximately those that might be a p p l i c a b l e t o lead poisoning of a CO o x i d a t i o n mono l i t h , though i t should be emphasised that the method i s a p p l i c a b l e to any slow poisoning s i t u a t i o n and that our o b j e c t i v e i s to show the p o s s i b i l i t i e s r a t h e r than to match d a t a — m o d e l l i n g r a t h e r than s i m u l a t i o n t o use Smith's d i s t i n c t i o n (13). The values used are g i v e n i n the t a b l e of nomenclature. The r e s u l t s f o r n o n - s e l e c t i v e poisoning are much what one would expect and are shown i n F i g u r e 1. The amount of poison on the c a t a l y s t ( p r o p o r t i o n a l t o 1-Θ) i s seen t o decrease along the monolith and t h i s agrees q u a l i t a t i v e l y w i t h measurements that have been made. Curves f o r l-θ are given f o r the surface of the c a t a l y t i c l a y e r and at depths of 0.2 and 0.8 of the t h i c k n e s s of the l a y e r . The p r o f i l e s of the poisoning w i t h depth (shown at the r i g h t ) suggest that something l i k e pore mouth poisoning i s the order of the day. Curves are only given f o r one value of time, s i n c e the r e s u l t s f o r other times showed that over the range considered θ was approximately l i n e a r w i t h time. The r e s u l t s f o r s e l e c t i v e poisoning are presented using 9(0,Q) the f r a c t i o n of a c t i v e s i t e s at the f l u i d - w a l l i n t e r f a c e f o r v a r i o u s times (Figure 2 ) . In c o n t r a s t t o n o n - s e l e c t i v e p o i soning f o r which θ would increase monotonically (1 - θ decreased), the s i t e s are v i r t u a l l y u n t a i n t e d a t the i n l e t of the bed and the poison b u i l d s up only a f t e r the r e a c t i o n l i g h t - o f f zone when the CO i s v i r t u a l l y a l l o x i d i z e d . Figure 3 shows that θ does not vary much w i t h depth i n t o the c a t a l y s t so that the surface value i s t y p i c a l and we do not have pore mouth poisoning under these c o n d i t i o n s . The top three curves apply t o a point (ζ=.491) at the head of the l i g h t - o f f zone, the other curves being f o r a point beyond the zone (ζ=.625) and at the e x i t . The p r o f i l e of w a l l
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
LEE AND
Poisoning in Monolithic Catalysts
ARIS
.2
.4
.6
.8
_.6
.2
1.0
Figure 1. Axial and radial distributions of poison deposition. Nonselective poisoning, c =19.4, c" = 27.7, φ = 4, φ = 1, ω = 2.62 exp (1.48/v ), corresponding to T = 377°C, τ = (O c o,o)/ ρ
8
pe
0
C
-
\
θ(0 ζ)
r . , .
„
9
_
1 11 .2 .4
fc
.6
1.0
.8
Figure 2. Axial distribution of fractional active sites at fluidr-solid interface, θ(τ,ζ,Ο). Selective poisoning, φ = 2.0, φ = 0.2, e = 21, c" = 30, ω = 2.62 exp (1.6/v ), corresponding to Ύ - 327°C, τ = (O cco,o)/(LS l ) t. ρ
8
0
pe
y
2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
116
CHEMICAL REACTION ENGINEERING—HOUSTON
Figure 3. Radial distri bution of fractional sites, θ(τ,ζ,ξ). Inlet as in Figure 2.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
10.
L E E A N D ARIS
Poisoning in Monolithic Catalysts
0
.2
.4 „
.6
.8
117
1.0
Figure 5. Axial distributions of emission break through, , and the interface CO concen tration, χχ (τ,ζ,0). ( ) , ( ) u . Inlet conditions as in Figure 2. 8
f
8
Figure 6. Emission breakthrough, , as a function of τ at different axial positions. Inlet conditions as in Figure 2. ;
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
118
CHEMICAL REACTION ENGINEERING—HOUSTON
.1
.3
.5
.7
.9
Figure 7. Effects of solid temperature (V') and CO inhibition (ω) on the axial distribution of θ. ω as in Figure 2 for curve 1; ω = 0 for other curves.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
L E E A N D ARis
10.
Poisoning in Monolithic Catalysts
119
temperature i s shown i n F i g u r e 4 where the e f f e c t of poisoning i s seen t o b r i n g the e x i t temperature down. The CO c o n c e n t r a t i o n s , both < i > the cup-mixing mean i n the flow and the c o n c e n t r a t i o n at the s o l i d - f l u i d i n t e r f a c e are shown i n F i g u r e 5 and the a l l important emission as a f u n c t i o n of τ i n F i g u r e 6. From the l a s t i t i s c l e a r that the o r i g i n a l 99.5% conversion d e t e r i o r a t e s t o 99% by τ =2.5. From these f i g u r e s the reason f o r the s t r i k i n g l y d i f f e r e n t behavior w i t h n o n - s e l e c t i v e poisoning becomes e v i d e n t . A t t h e entrance of the monolith before the l i g h t - o f f zone i s reached the low temperature and h i g h CO c o n c e n t r a t i o n s u f f i c e t o cover the surface so w e l l t h a t the l a y i n g down of the ,poison precursor i s i n h i b i t e d . I t i s only a f t e r the r e a c t i o n i s l a r g e l y spent w i t h the r e s u l t i n g i n c r e a s e i n temperature and decrease of CO t h a t the poison can be a p p r e c i a b l In a s e r i e s of f u r t h e soning near the i n t e r f a c e was found i n the l i g h t - o f f zone. Elsewhere the p e n e t r a t i o n o f the poison was f a i r l y uniform. F i n a l l y the q u e s t i o n of whether temperature or CO i n h i b i t i o n was the more important was r e s o l v e d by the r e s u l t s shown i n Figure 7. The lowest curve i s f o r s e l e c t i v e poisoning as c a l c u l a t e d before w i t h e = 27.7. The curve c l o s e t o i t i s f o r poisoning w i t h no CO i n h i b i t i o n ( i . e . ω = 0) but the same temperature dependence (e = 27.7). I t i s evident t h a t there i s l i t t l e d i f f e r e n c e outside the l i g h t - o f f zone. By reducing the a c t i v a t i o n energy f o r the poisoning through t h e sequence o f curves 3-7 the n o n - s e l e c t i v e poisoning c o n d i t i o n i s a t t a i n e d . f
11
11
Acknowledgement This part of the research on monoliths has not had the bene f i t o f c o n s i s t e n t funding but i t i s i n t e g r a l w i t h the long-term work which has had the support of the NSF (GK 39001 and GP 43923) at v a r i o u s times and we are most g r a t e f u l f o r t h i s . Nomenclature
c
ps
passage r a d i u s , 0.06205 cm c o n c e n t r a t i o n of poison precursor i n the gas near t h e s o l i d s u r f a c e , gmole/cm 2 a v a i l a b l e a c t i v e s i t e s , gmole/cm heat c a p a c i t y a t constant pressure per u n i t mass, cal/gm°K amount of poison precursor deposited, gmole/cm specie molar c o n c e n t r a t i o n , gmole/cm i n l e t CO c o n c e n t r a t i o n , 8.53 χ 1 0 " gmole/cm a t T = 327°C e f f e c t i v e molecular f l u i d d i f f u s i v i t y f o r component i , cm /sec e f f e c t i v e porous s o l i d d i f f u s i v i t y f o r component i , cm /sec, D =O±f/20 dimensionless Arrhenius r a t e constant, e x p e ( v - l ) / v 3
C
P
2
c
2
7
C
C0,0
3
Q
2
D
ie
2
is
E(v)
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
120
CHEMICAL REACTION ENGINEERING—HOUSTON
f
c a t a l y t i c a l l y a c t i v e f r a c t i o n of t o t a l s i t e s , L/L» molar heat of r e a c t i o n , 9 . 0 4 x l 0 cal/(gmole CO + 1/3 gmole H ) Κ adsorption equilibrium c o e f f i c i e n t k r e a c t i o n r a t e constant f o r main r e a c t i o n , 1/sec, d e f i n e d i n eqn. (1) a d s o r p t i o n c o e f f i c i e n t , 1/(gmole/cm ), d e f i n e d i n eqn.(4) kp>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_) (<6) (7_) of characteristic dimension 1. The diffusion time t i s pro portional to l /u. . Let t = l / ( k c ) be the chemical reaction time. As t j / t , t / t or t / t are increased, concentration gradients i n the aggre gates gives rise to p a r t i a l segregation, due to the well-known coupling between reaction and mass transfer. The above ratios are analogous to squared Thiele moduli or Hatta numbers. That rapid reactions may create a variable state of segregation in a given m
D
2
n
R
m
R
D
0
R
R
©
0-8412-0401-2/78/47-065-125$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
126
hydrodynamic p a t t e r n has been demonstrated e x p e r i m e n t a l l y (50 (7_) (8) . However, a l l t h e parameters o f t h e above models {ω±, t ^ , I) remain e s s e n t i a l l y phenomenological. To date, no general c o r r e l a t i o n i s a v a i l a b l e t o p r e d i c t the importance o f micromixing from the o p e r a t i n g parameters o f the r e a c t o r (e.g. s t i r r i n g energy input) and the physicochemical p r o p e r t i e s o f the f l u i d . The aim o f t h i s paper i s t o p r o v i d e w e l l e s t a b l i s h e d e x p e r i mental d a t a , and t o propose a new and t e n t a t i v e i n t e r p r e t a t i o n o f micromixing i n s t i r r e d r e a c t o r s , w i t h the hope o f b r i d g i n g the gap between phenomenological models and c l a s s i c a l r e s u l t s o f t h e theory o f turbulence. With t h i s o b j e c t , we have chosen experimental c o n d i t i o n s i n which micromixing e f f e c t s were expected t o be a maximum i . e . a continuous s t i r r e d r e a c t o d r a p i d l i q u i d phas r e a c t i o c l o s t o zero order w i t h unmixe meters were adjusted t spac t i o n time and the micromixing time was o f the same order o f magni tude, ranging from 1 t o 10 seconds. Micromixing e f f e c t s were thus c l e a r l y and r e l i a b l y observed. Experimental : 3 The s m a l l 196 cm r e a c t o r i s made o f " p l e x i g l a s s " and g l a s s according t o H o l l a n d and Chapman standards (9_) w i t h f o u r b a f f l e s and a s i x blade t u r b i n e . The two i n l e t p o r t s a t the bottom are provided w i t h caps i n order t o break up the incoming j e t s . A t short space times, the k i n e t i c energy o f the e n t e r i n g f l u i d i s not n e g l i g i b l e and i s s u f f i c i e n t t o ensure p e r f e c t macromixing i n the r e a c t o r . The f l u i d flows out o f the r e a c t o r a t the t o p and passes through a spectrophotometer c e l l where product concentra t i o n s are c o n t i n u o u s l y monitored. D e t a i l s o f the c o n s t r u c t i o n and hydrodynamic behaviour o f the r e a c t o r are given elsewhere (10) (U) . P e r f e c t macromixing i s achieved i n the r e a c t o r f o r a l l v i s c o s i t i e s and s t i r r i n g speeds, even without mechanical s t i r r i n g (N=0)ι as can be checked by RTD measurements. A f t e r reviewing many r e a c t i o n s , we f i n a l l y s e l e c t e d the i o d i n a t i o n of acetone. The r e a c t i o n k i n e t i c s were c a r e f u l l y r e d e t e r mined i n batch experiments ( 12_)* The r a t e of i o d i n e consumption g l o b a l l y obeys a Michaëlis-Menten law : k [i] k c o 2ο k + Γι Ί ~ k + c m I 2J m L
1
r
k
U
and k k
are given by the f o l l o w i n g expressions +
ο τη
;
= kfcH_C0CHJ [H 1 = kc c J 3 A H J
H
U
J
L Ji+mirrT1+ακ[ΐ-]
1+Kc k'c — —=°H 1+aKCj TT
(2)
(3)
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
11.
PLASARi E T A L .
Micromixing in Continuous Stirred Reactors
127
As a consequence, k d k can be v a r i e d a t w i l l i n f i x i n g the c o n c e n t r a t i o n o f acetone, H and I " . In p a r t i c u l a r , the r e a c t i o n can be made c l o s e t o zero order (low k ) i n order t o enhance sen s i t i v i t y t o micromixing. Moreover, t h i s r e a c t i o n may c o n v e n i e n t l y be used f o r the s i m u l a t i o n of b i o l o g i c a l or enzymatic r e a c t i o n s . T y p i c a l values of experimental parameters are r e p o r t e d on t a b l e I below. As can be seen, acetone i s i n l a r g e excess and the i o d i n e c o n c e n t r a t i o n i s s m a l l but e a s i l y measured by spectrophotometry. The v i s c o s i t y of the aqueous s o l u t i o n can be v a r i e d by a d d i t i o n of p o l y e t h y l e n e g l y c o l (Emkapol 6000). For each Emkapol concentra t i o n , the v i s c o s i t y μ, the i o d i n e d i f f u s i v i t y D and the k i n e t i c r a t e constants were redetermined. The r e a c t a n t s are fed i n t o the r e a c t o r as two unmixed streams c o n t a i n i n g r e s p e c t i v e l y I2, KI Q
a n
m
+
m
( f l o w r a t e Q±)
and CH3COCH3, H2SO4, K l ( f l o w r a t e Q2) . Concentra
t i o n s i n t a b l e I are expresse Table I : Experimenta Concentration range s : acetone H S0 KI c = 0 space time r e a c t i o n time t = c A o temperature viscosity μ s t i r r i n g speed Ν flowrate r a t i o m = V ( 2 l 2
4
c
R
+
0. 25 - 0.5 M 0. 15 - 0. 3 M 5 X 10-4 M 1. 7 χ 10-5 - 5 χ ΙΟ" Μ 1. 15 - 8 seconds 1. 15 - 10 seconds 2C - 32°C 0. 8 - 6.7 c e n t i p o i s e s 0 - 3000 R.P.M. 0.1 - 0.9 2 ) 5
2
Treatment of experimental data Let y = c / c be the experimental value of reduced i o d i n e con c e n t r a t i o n measured at the r e a c t o r o u t l e t . Set K = k x / c and K3 = k / c . A s t r a i g h t f o r w a r d mass ba lance g i v e s the maximum mixedness o u t l e t c o n c e n t r a t i o n : Q
1
y = M
0
0
m
0
(1 - κ - κ + Λ ι - κ κ ) + 4K )/2 χ
3
Γ
3
2
3
(4)
The feed streams being unmixed, the f u l l y segregated concen t r a t i o n would be y =1. s _ The experimental c o n c e n t r a t i o n l i e s somewhere between y^ and 1, as shown on f i g u r e 1 where t h e o r e t i c a l l i n e s are drawn toge t h e r w i t h some experimental p o i n t s . How can we c a l c u l a t e a micromixing parameter from these o b s e r v a t i o n s ? The s i m p l e s t approach i s t o d e f i n e an e m p i r i c a l segregation index as (50 (8_) : (5)
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
128
CHEMICAL REACTION
1
ENGINEERING—HOUSTON
4 y
0.5
+
Ν =
s
(unmixed)
°\
Ν
X Ν = 50<\ ο Ν = 1000^ Ν = 2000 (premixed) Ν = 3000 • k /C = 0.17 m ο
•
m = 0.5 Figure 1. Residual iodine concentration against Damkohler number according to segregation state. Theoretical lines and experimental points.
μ = 6.6 cp
0.5
1.0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
k τ/C ο ο 1.5
PLASARI ET AL.
11.
Micromixing in Continuous Stirred Reactors
129
A micromixing time may a l s o be c a l c u l a t e d i n a p p l y i n g t h e I . E . M . m o d e l (2) (3) t o e a c h e n t e r i n g s t r e a m . T h i s m o d e l s t a t e s that the iodine concentration decreases i n f l u i d aggregates accor ding to dc dt
k
c-c t m
c
ο
(6)
k +c m
where t i s t h e age o f t h e a g g r e g a t e a n d c t h e mean i o d i n e c o n c e n t r a t i o n a v e r a g e d o v e r t h e w h o l e r e a c t o r c o n t e n t . More p r e c i s e l y , t h e c a l c u l a t i o n h a s t o be made f o r t h e two s t r e a m s , t h e f i r s t one c o n t a i n i n g i n i t i a l l y i o d i n e a n d no a c e t o n e n o r a c i d , a n d t h e s e c o n d one b e i n g i n i t i a l l y f r e e o f i o d i n e b u t c o n t a i n i n g a c i d a n d acetone. Moreover, k and k a r e b o t h dependent on a c i d (c ) and a c e t o n e (c^) c o n c e n t r a t i o n s that k c o u l d be c o n s i d e r e t h e c o u r s e o f t h e r e a c t i o n s o t h a t t h e r a t e o f r e a c t i o n may be w r i t Q
m
H
m
t
e
1
n
_ r
where k
V
A H k + c m
k C
C
o A H k + c m
C
k
= k c ^
Q
y
y
and y
C
U
= c ^ ,
f t
y
H
=
)
c ^ .
A p p l y i n g t h e IEM m o d e l t o a c i d a n d a c e t o n e ( i n l a r g e e x c e s s ) , t h e c o n c e n t r a t i o n s o f t h e s e r e a c t a n t s c a n be c a l c u l a t e d a s a function of θ = t / τ , K = t /x a n d m. S i m i l a r l y , the dimensionless equations f o r i o d i n e are : 2
m
Ϋ-Υ
K
1
Stream 1 : — ^ = — d0 K
-
: —
Υ χ
K
(0)
(1
-
(1
+
(8)
e^W
l*2 K y K
2
= —
ae
l * l
2
Y-y Stream 2
-
v
2
3 +
= 1/m
;
e
y (0) 2
[m
Y l
+
(9)
=0
A v e r a g i n g o v e r a l l ages and b o t h streams
y =
2)
2
(10) :
(l-m)y ]e"" d0 2
(11)
6
Since , K3 a n d m a r e g i v e n , t h e s o l u t i o n o f e q u a t i o n s ( 1 1 ) ( 1 2 ) (13) b y i t e r a t i o n g i v e s y a s a f u n c t i o n o f K = t / x . The m i c r o mixing time t c a n t h u s be o b t a i n e d f o r e a c h e x p e r i m e n t . 2
m
m
Results A f e w e x a m p l e s o f r e s u l t s a r e r e p o r t e d on t a b l e I I b e l o w . T h e w h o l e s e t o f d a t a (142 e x p e r i m e n t s ) c a n be f o u n d e l s e w h e r e (10) .
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL
130
REACTION
ENGINEERING—HOUSTON
Table II - Experimental results n° 1 2 3 4 5 6 7 8 9 10
m 0.5 0.5 0.1 0.9 0.5 0.5 0.5 0.5 0.5 0.5
κ
M 3.2 3.2 3.1 3.1 9.1 4.7 4.7 4.7 4.7 4.7
ι
Κ
3
Emk %
0.55 0.40 0.95 Ο. 90 1.05 1.22 1.22 1.22 1.22 1.22
0.07 0.07 0.12 0.11 0.17 0.23 0.23 0.23 0.23 0.23
0% 0% 0% 0% 15% 5% 5% 5% 5%
Ν m /s 0.88 0.88 0.92 0.95 6.55 2.05 2.05 2.05 2.05
RPM 0 0 0 0 0 0 500 1000 2000
τ sec 2.2 1.6 3.4 3.4 2.9 2.6 2.6 2.6 2.6
t
y 0.58 0.77 0.45 0.40 0.52 0.46 0.43 0.40 0.39
m sec 1.2 2.6 1.0 0.7 2.8 1.1 0.8 0.7 0.6
X
ε
ι m2/s 2.4 6.9 2.0 2.0 1.7 1.9 1.9 1.9 1.9
3
0.14 0.36 0.20 0.01 0.30 0.23 0.17 0.14 0.12
ε
2 m /s 0 0 0 0 0 0 0.07 0.64 6.0 2
3
The importance of segregatio y g the magnitude of t (as compared to τ) or at the segregation i n dex X. Qualitatively, segregation increases with decreasing space time τ (see n° 1,2), with decreasing flowrate ratio m (see n° 3, 4), with increasing viscosity ν (see n° 5,6) and with decreasing stirring speed Ν (see n° 6-10). These last two results are not unexpected. The influence of τ i s much more d i f f i c u l t to under stand. The decrease of t vs τ for aqueous solutions without Emka pol at N=0 RPM leads to : t ^ τ~5/3 ( f i . 2) (12) This experimental result rules out any explanation based on a reaction/diffusion mechanism, in which the diffusion time t varies as £ /D given by the classical expression of CORRSIN (13_) . In effect, i f we assume that the energy input ε i s due to the kinetic energy of jets which varies roughly as τ~3 CORRSIN*S expression leads to an increase of t with τ. An alternative ex planation i s proposed below. m
m
m
g
D
2
m
/
D
The "shrinking aggregate" model (S.A. model) Let us start from Beek and Miller's description of mixing in three successive stages (18) v i z . 1) Distribution of one f l u i d through the other and a uniform average composition without a decrease in local concentration. 2) Reduction of size of the re gions of uniform composition and correlative increase of the areas of contact between regions of different composition. 3) Mixing by molecular diffusion. In experiments with long space times, micromixing occurs mainly during stage 3) and may be explained on the basis of established homogeneous turbulence theory (5_) (14) . Con versely, at short space times with rapid reactions, micromixing is essentially controlled by stage 2) processes. The fresh f l u i d i s assumed to enter into the reactor in the form of aggregates which are gradually "peeled off" and lose their matter toward a maximum mixedness environment. The shrinking aggregates remain f u l l y segregated and the reaction takes place only in the perfect-
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
11. PLASARi E T A L .
Micromixing in Continuous Stirred Reactors
Figure 2. Variation of micromixing time as a function of space time (no mechanical stirring)
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
131
132
CHEMICAL REACTION ENGINEERING—HOUSTON
l y micromixed volume f r a c t i o n . The p e e l i n g o f f process causes the aggregate volume t o de crease a c c o r d i n g t o -dv/dt = hs, o r i n terms o f the s p h e r i c a l aggregate diameter Ζ : dZ/dt = -2h
(13)
h i s a mass t r a n s f e r c o e f f i c i e n t which i s assumed t o be g i v e n by a g e n e r a l c o r r e l a t i o n e s t a b l i s h e d by Calderbank e t a l . (15_) f o r small p a r t i c l e s i n t u r b u l e n t media ; 3
1 / 4
hZ/D = 0.13 l ( ε / ν )
1 / 3
(Se)
(14)
The aggregate diameter i s thus found t o decrease l i n e a r l y w i t h time. The aggregate disappears a f t e r the time : I
t
= — β
2
I
=
2 /
rs
h
0.26 D (ε/ν ) (Se) What i s t h e v a l u e o f the i n i t i a l diameter Z ? The o n l y assumption l e a d i n g t o t h e observed decrease o f segregation w i t h i n c r e a s i n g τ i s t h a t Z v a r i e s as τ " . T h i s h e u r i s t i c assumption i s supported by an o b s e r v a t i o n of Gunkel e t a l . (16) who have found t h a t t h e i n t e g r a l o f t h e a u t o c o r r e l a t i o n f u n c t i o n o f v e l o c i t y f l u c t u a t i o n s i n s t i r r e d r e a c t o r s was a constant independent o f r e a c t o r s i z e and o p e r a t i n g c o n d i t i o n s . T h i s i n t e g r a l i s pro p o r t i o n a l t o Z / u (1_7) . l i s thus p r o p o r t i o n a l t o u , which i n t u r n v a r i e s as τ""1. I n e x p r e s s i o n (15), the e f f e c t i v e energy i n p u t p e r u n i t mass may be expressed as ε = Πιει + η2 2' ε^ and ε a r e t h e j e t k i n e t i c energy and mechanical s t i r r i n g energy d i s s i p a t i o n s , r e s p e c t i v e l y , and n are the corresponding e f f i c i e n c i e s o f these k i n d s o f energies i n the p r o d u c t i o n o f mi cromixing. F i n a l l y , s e t t i n g l = ρ/τ, one o b t a i n s from (17) : q
1
Q
0
Q
0
ε
w
n
e
r
e
2
2
Q
T/t
= (0.26/p) n j
e
where A = (0.26/p) η |
/ 4
/
4
D(
C l
+n
£ 2
)
1 / 4
v"
and G = ϋ ( ε + η ε ) 1
3 / 4
Sc
1 / 3
τ
1 / 4
v"
3 / 4
Sc
2
2
= A.G
(16)
1 / 3
(17)
τ
2
η = ΐΊ/ΐΊι i s the r e l a t i v e e f f i c i e n c y o f the two energies. 2
Assuming t h a t A, i . e . writes : x/t t
e
= B.G
may i n t u r n be a f u n c t i o n o f G, (16)
n
(18)
The segregated volume f r a c t i o n 3 i s e a s i l y c a l c u l a t e d from i n averaging over the aggregate d i s t r i b u t i o n o f ages. t (e V
τ
- e"
t / T
t e ^ 3 dt = ι '(1 - ! _ ) " e e
t / T
dt
(19)
The r e s u l t o f i n t e g r a t i o n i s
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
11.
PLASARI ET AL.
3=1-
Micromixing in Continuous Stirred Reactors
133
3 ( x / t ) + 6 ( T / t ) - 6 ( T / t ) [ l - e " e d t l (20) e e e ·+ 2
3
which i s very c l o s e t o 3 = (1 + 4 x / t ) ~
t
/ T
1
(21)
e
The 3 f r a c t i o n o f the r e a c t o r volume remains f u l l y segrega t e d w h i l e the 1-3 f r a c t i o n r e a c t s i n a s t a t e o f maximum mixedness. A c c o r d i n g l y , 3 i s nothing but the segregation iridex X which f i n d s here i t s p h y s i c a l i n t e r p r e t a t i o n . 3 i s thus known f o r each expe riment, i s deduced from the pressure drop through the r e a c t o r . ε i s e a s i l y c a l c u l a t e d from a c l a s s i c a l c o r r e l a t i o n (ε =φΝ ι>£/ν). The unknown parameters o f the model are Β, η and η. T r e a t i n g f i r s t l y experiments without mechanical s t i r r i n g (ε = Ο ) , para meters Β and n are a j u s t e d by l e a s t square o p t i m a l f i t t i n g on 3 using (17)(18) and (20) The best f i t i s obtained f o r Β = 4000 πΓ /3 s-4/3 an In a second stage, experiment g considered. F i x i n g Β t o i t s Ν = Ο v a l u e , η i s then determined f o r each v a l u e o f the s t i r r i n g speed Ν i n order t o o b t a i n the best grouping o f p o i n t s around the 3 ( x / t ) curve. Figure 3 shows t h i s general c o r r e l a t i o n where a l l experimental p o i n t s have been grouped together. The agreement between the data and the model i s q u i t e s a t i s f a c t o r y . The corresponding values o f η as a f u n c t i o n of Ν are r e p o r t e d on f i g u r e 5. 3
2
2
2
4
e
Equivalence between the SA model and the IEM model The b a s i c i n t e r a c t i o n mechanisms o f the two models are d i f f e r e n t . However, a correspondence may be sought between the m i cromixing parameters t and 3 o r t i n order t o a r r i v e a t s i m i l a r r e p r e s e n t a t i o n s . The equivalence may be e s t a b l i s h e d on t h r e e b a s i s as w i l l be e x p l a i n e d more i n d e t a i l i n a f u r t h e r paper : 1) i n matching the r e l a t i v e amount o f matter l o s t by a nonr e a c t i n g aggregate toward the environment. T h i s leads t o t = t / 4 2) i n matching the v a r i a n c e s o f c o n c e n t r a t i o n d i s t r i b u t i o n s i n the presence o f two unmixed t r a c e r feed-streams (concentrations Ο and 1 ) (2_) (3_) . We o b t a i n t ^ t / 2 . 3) i n matching chemical conversion f o r instantaneous reac t i o n s (unmixed feed, m = 0.5) (2_) (3_) . T h i s leads again t o t ^ t / 4 A c c o r d i n g l y , we may expect the equivalence f o r : Q
m
m
m
e
e
m
2t
m
e
< 4t
m
e
(22)
Coming back t o the i n t e r p r e t a t i o n o f experimental data based on the IEM model, an a l t e r n a t i v e c o r r e l a t i o n may be sought b e t ween t and G i n analogy t o (23). F o l l o w i n g a s i m i l a r procedure as above, the numerical a n a l y s i s o f data shows t h a t experimental r e s u l t s are represented i n an o p t i m a l way by : m
τ/tnj = C . G
4/3
(23)
-4/3 -4/3 w i t h C = 8200 m s . A new set o f η values i s determined
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION
1
1
ι
r
— r -
+
ENGINEERING—HOUSTON
-τ
1
X
N = 0 RPM N = 500
V
N = ÎOOO
1+ IX 1+
•\*
A
• <
V+ x
• 0
\ure 3.
<
1 1
·
7*"— 1 1 2 3
•
χ * +• 1 4
ν
•
5
6
7
τ/t e Segregated volume fraction as a function of r/t . General correlation.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
e
PLASARI E T A L .
Micromixing in Continuous Stirred Reactors
Figure 4. Rehtive micromixing time tm/τ as a function of parameter G. General correlation.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
136
CHEMICAL REACTION ENGINEERING—HOUSTON
Figure 5. Rehtive efficiency of mechanical stirring referred to jet stirring as a function of stirring speed
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
11. PLASARi E T A L .
Micromixing in Continuous Stirred Reactors
137
f o r each s t i r r i n g v e l o c i t y . F i g u r e 4 shows the experimental p o i n t s according t o c o r r e l a t i o n (29). The v a r i a t i o n o f η a g a i n s t Ν i s a l s o r e p o r t e d on f i g u r e 5. Here again, good agreement and c o n s i s tency between model and experiment are obtained. D i s c u s s i o n and c o n c l u s i o n The comparison between (18) and (23) y i e l d s an indépendant e v a l u a t i o n o f the r e l a t i o n s h i p between t and : e
t /t e
m
= C/B = 2.1
(24)
T h i s f a l l s w i t h i n the range p r e d i c t e d i n (22). The i n i t i a l aggregate s i z e may be estimated from (18), (16) and (15) 0.26 „ '
/4
Taking i n t o account the range o f v a r i a t i o n o f G and τ and setting = 1 we f i n d as an upper bound, 50 ym < Z < 500 ym, a reasonable value as compared t o previous e s t i m a t i o n s f o r l a m i nar eddies (3_) and t u r b u l e n t mixing (5_) which l e d t o l 10 to 30 ym. The most i n t e r e s t i n g f e a t u r e i s the dependency o f η = τ^/^ΐ on Ν ( f i g u r e 5 ) . The e x c e l l e n t agreement between η values coming from both SA and IEM models must be n o t i c e d as a check on the c o n s i s t e n c y o f i n t e r p r e t a t i o n , η i s found t o decrease as N"*/ . At low s t i r r i n g speed the e f f i c i e n c y o f mechanical s t i r r i n g i s more than 10 times t h a t o f j e t s t i r r i n g whereas a t h i g h s t i r r i n g speed, the r e l a t i v e e f f i c i e n c y i s c l o s e t o u n i t y . In c o n c l u s i o n , s e v e r a l i n t e r e s t i n g p o i n t s have been e s t a b l i shed i n t h i s paper. 1) A new micromixing ( s h r i n k i n g aggregate)model has been proposed, which d e s c r i b e s the f i r s t stages o f mixing i n s t i r r e d tanks. 2) The equivalence o f t h i s model w i t h the IEM model has been e s t a b l i s h e d , p r o v i d i n g an i n t e r p r e t a t i o n o f the micromixing time ν· 3) Intermediate micromixing parameters have been shown t o depend e s s e n t i a l l y on the group G = D ( e i + y e ) / v ~ 3 / S c / ^ τ . A general c o r r e l a t i o n has been e s t a b l i s h e d and s u c c e s s f u l l y checked w i t h experimental r e s u l t s . 4) The i n i t i a l s i z e o f segregated domains has been estimated. 5) A t low s t i r r i n g speed, mechanical s t i r r i n g i s much more e f f i c i e n t than j e t s t i r r i n g but t h i s r e l a t i v e e f f i c i e n c y s t r o n g l y decreases as s t i r r i n g speed i s increased. These r e s u l t s c o n s t i t u t e a f i r s t attempt a t a comprehensive theory o f micromixing i n s t i r r e d r e a c t o r s based on experimental facts. Q
m
2
1
4
4
1
2
Notation A,B,C
parameters o f the general c o r r e l a t i o n
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
2
138
CHEMICAL REACTION ENGINEERING—HOUSTON
c,c , c ,c ,c c o n c e n t r a t i o n s ( i o d i n e , i n i t i a l , acetone, a c i d , ο A Η I . . iodide) D,EVn molecular d i f f u s i v i t y , t u r b i n e diameter re
+
ε
2
μ /
4
1/3
2
G = g—j Sc τ parameter o f the general c o r r e l a t i o n h mass t r a n s f e r c o e f f i c i e n t k j k Q f k j ^ k , K k i n e t i c parameters i n t h e r a t e law K^,K ,K3 reduced k i n e t i c o r micromixing parameters Z , 2 - , Z aggregate diameter (current, i n i t i a l , f i n a l ) m feedflowrate r a t i o η,α numerical constants Ν s t i r r i n g speed ( r o t a t i o n frequency RPM) ρ parameter Q^,Q feedflowrates r reaction rate s aggregate e x t e r n a Sc = v/D Schmidt number t,tj,t ,t aggregate age, i n t e r a c t i o n time, r e a c t i o n time, d i f f u s i o n time t l i f e d u r a t i o n o f aggregates t micromixing time (IEM model) u i n i t i a l j e t v e l o c i t y (entering streams) v,v aggregate volume, i n i t i a l volume V r e a c t o r volume X segregation index Y'^M'^S' A' H *uced c o n c e n t r a t i o n s ( i o d i n e , maximum mixedness, f u l l y segregated, acetone, acid) β segregated f r a c t i o n o f the r e a c t o r volume ε,ε^,ε^ energy d i s s i p a t i o n p e r u n i t mass ( e f f i c i e n t , from t h e j e t s , from the s t i r r e r ) l' 2' ^f^ *( k i n e t i c energy o f j e t s , mechanical s t i r r i n g , relative) θ = t/τ reduced age μ, ν v i s c o s i t y (dynamic, kinematic) v kinematic v i s c o s i t y = V/(Q +Q ) space time φ power number ω. i n t e r a c t i o n frequency 1
2
0
M
2
R
D
e
m
0
0
y
r ,
r ,
r |
e
y
rec
c :
e n c : i
e s
2
τ
1
2
Acknowledgement : Mathematical treatments o f models on the computer were c a r r i e d out w i t h the h e l p o f Bernard Antoine. H i s v a l u a b l e c o n t r i b u t i o n t o t h i s work i s g r a t e f u l l y acknowledged.
Literature (1) (2) (3) (4)
cited
Ritchie B.W. and Tobgy A.H. Adv. Chem. Series, (1974), 133,376 Villermaux J. and Devillon J . C . 2nd Symp. Chem. React. Eng. B-1-13 (1972) Aubry C. and Villermaux J. Chem. Eng. S c i . (1975), 30, 457 David R. and Villermaux J. Chem. Eng. S c i . (1975), 30, 1309
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
11.
(5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18)
PLASARi E T A L .
Micromixing in Continuous Stirred Reactors
139
Zoulalian A. and Villermaux J. Adv.Chem.Series(1974),133,348 Nauman E.B. Chem. Eng. S c i . (1975), 30, 1135 Nabholz F., Ott R . J . and Rys P. Second European Conference on mixing, Cambridge 1977 Truong K.T. and Methot J . C . The Canad.J.Chem.Eng. (1976), 54, 572 Holland F.A. and Chapman F . S . Liquid mixing and processing i n s t i r r e d tanks. Reinhold Pub. Co. New-York 1966 P l a s a r i E. Thèse de Doctorat ès Sciences, INPL, Nancy 1976 P l a s a r i E., David R. and Villermaux J. Chem. Eng. Sci.,(1977) 32, 1121 P l a s a r i Ε . , David R. and Villermaux J., Nouv. J. de Chimie, (1977), 1, 49 Corrsin S. A.I.Ch.E J. (1964) 10 870 Evangelista J. J., Kat 15, 843 Calderbank P.H. and Moo-Young M.Β.,Chem.Eng.Sci. (1961),16,39 Gunkel A.A. and Weber M.E. A.I.Ch.E. J.(1975),21, 931 Reynolds A.J. Turbulent flows i n engineering, 95, Wiley, New-York, (1974) Beek J. J r and M i l l e r R.S. Chem.Eng.Prog. Symp. Ser. (1959) 55 (25), 33
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
12 Laminar Flow Polymerization of E P D M Polymer J. F. WEHNER E l a s t o m e r C h e m i c a l s D e p a r t m e n t , Ε . I. Du P o n t d e N e m o u r s a n d C o . , I n c . , D e e p w a t e r , N J 08023
The study of polymerizatio simultaneous consideratio and conduction, as well as the kinetics of the polymerization. This work was undertaken to determine the effect of this type of reactor upon the molecular weight distribution of the polymer produced. The system studied was the copolymerization of an elastomer from ethylene, propylene, and 1,4-hexadiene i n solution using Ziegler catalysis. Laminar flow polymerization similar to previously described work involving polymerization of sytrene i n tubular reactors (1, 2, 3, 4) was analyzed, but the numerical techniques are based on unpublished work and appear to be an efficient method i n this application. Model The monomers, dissolved i n hexane and mixed with catalyst, enter a tubular reactor i n parabolic flow. The polymerization releases heat, induces heat transfer by conduction, increases v i s c o s i t y , and depletes monomers. Heat conduction i s considered i n the r a d i a l direction only. Diffusion of both monomers and polymer has been neglected. The solution v i s c o s i t y i s calculated by the following expression (Reference 5). η = 3.58 χ 10-7ο5.7 5^3
3 8 0 / Τ - 8.04) + η 0.811 Hinh = 1.38 χ Ι Ο χ Ç w ^ η
θ χ ρ β ( 2
0
- 4
The reaction rate for a vanadium ion/aluminum a l k y l catalyst of the Ziegler type i s obtained from the kinetic scheme given i n Table I . Various physical properties of the system are tabulated i n Table I I .
©
0-8412-0401-2/78/47-065-140$05.00/0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
12. WEHNER
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Laminar Flow Polymerization
141
TABLE I Reference 7 R
1
B
a
-
a
R2 = - ( 2 1 R
x
a
x
x
(aiixsl + 12 s2 + 1 3 s 3 ) l
a
x s
x
i + a
2 2
x
s 2
)x
2
x
3 = " 31 sl 3
x i s
x
s 2
Lv = x
s l
· xl a i
x
s3 = x l * s
2
£31 x i 13 a
an = k -a i 2
2
a
1 2
= (504/x ) f (T)
a
1 3
= (0.79/X3) f (T)
a
2
a
31 = n / k 3
a
2 i
= 184 f (T)
a
2 2
= kia
k
x
= 0.0489 + 3.8 (x3/x )
k
2
= 20.46 + 32.2 ( x 3 / x i )
k
3
= 0.62 k
i 2
1
,
6
3
2
l e 2 9
2
f (T) = exp (-3220/T + 10.27)/3600
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL
REACTION
ENGINEERING—HOUSTON
TABLE I I
The f o l l o w i n g parameter sumed constant a t Liquid
density:
Propylene Ethylene Hexadiene Hexane Polymer η
0
-
0.52 0.45 0.70 0.66 0.84
g/cc g/cc g/cc g/cc g/cc
- hexane v i s c o s i t y - 0.0005 poise
Heat of r e a c t i o n : Propylene - 488 c a l / g Ethylene - 796 c a l / g Hexadiene - 262 c a l / g 3
L i q u i d heat c a p a c i t y - 0.3 cal/°C-cm
Thermal c o n d u c t i v i t y - 2.4 χ 10"^ cal/sec-cm-°C
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
12.
WEHNER
EPDM
Laminar Flow Polymerization
143
Mathematical A n a l y s i s The flow model was taken from an unpublished r e p o r t described i n the Appendix. The r e a c t o r i s considered t o c o n s i s t of a s e t of a n n u l i each c o n t a i n i n g an equal p o r t i o n of the v o l u m e t r i c flow. The a x i a l d i s t a n c e i s broken i n t o s u b d i v i s i o n s whose s i z e i s dependent upon the s t a b i l i t y a n a l y s i s of the numerical technique. The p h y s i c a l p r o p e r t i e s a t the entrance of each annular s e c t i o n are considered constant i n the r a d i a l d i r e c t i o n . At each a x i a l p o i n t , these p r o p e r t i e s are c a l c u l a t e d and the r a d i a l coordinate i s resubdivided i n t o new ^ n n u l i . The heat balance i s then obtained from the d i f f e r e n t i a l equation i n c y l i n d r i c a l coordinates transformed i n t o a d i f f e r e n c e equation of t r i d i a g o n a l form which was solved by the method of L. H. Thomas (Reference 6 ) . The d i f f e r e n t i a l equatio
i s transformed i n t o t h i s d i f f e r e n c e
equation:
A(J+l)T(N,J)+B(J+l)T(N,J+l)+C(J+l)T(N,J+2) = D(J+1) where A(J+1) = X/ln
r
r(J) (J+l)
B(J+1) - X / l n f g £ C ( J 1 ) - X/ln +
D(J+1)
pC v(r(J)) p
ΔΖ - X/ln
^ggy
^
PCpv('<J>W»-l.J> _ E A H i R i C K N - l . J ) ) ΔΖ i
X = K/(r(J)(r(J)-r(J+l))) S p e c i a l p r o v i s i o n was made f o r J = 0 ( a d i a b a t i c ) and J = JM (symmetrical) ( w a l l and c e n t e r l i n e , r e s p e c t i v e l y ) . Note that the a x i a l s u b s c r i p t i s suppressed f o r the r a d i a l d i s t a n c e although a t each a x i a l i n t e r v a l the r a d i a l s u b d i v i s i o n was changed to g i v e v o l u m e t r i c elements of equal flow. The polymer c o n c e n t r a t i o n and monomer disappearance were incremented by simple t r a p e z o i d a l i n t e g r a t i o n i n the a x i a l direction. The c a l c u l a t i o n s were performed f o r r e a c t o r s broken i n t o 200 or 1000 a n n u l i w i t h up t o 20 a x i a l p o i n t s . The s i z e of the s u b d i v i s i o n s depends on the s t a b i l i t y a n a l y s i s of the Thomas method. The method i s s t a b l e t o round o f f e r r o r s except i n the r e g i o n of the c e n t e r l i n e of the tube where the c o e f f i c i e n t A ( J )
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
144
CHEMICAL REACTION ENGINEERING—HOUSTON
changes s i g n . This s i g n change depends on the a x i a l increment ΔΖ. I f ΔΖ i s too s m a l l , the unstable r e g i o n extends beyond the f i r s t r a d i a l increment from the center. Using increments of equal v o l u m e t r i c flow a d j u s t s the r a d i a l increment so t h a t when the f l o w i s f o r c e d to the center of the tube by the i n c r e a s i n g v i s c o s i t y at the w a l l , the s u b d i v i s i o n i s not too l a r g e at the p o i n t of most r a p i d change. This f e a t u r e minimizes the d i f f i c u l t y w i t h s t a b i l i t y as w e l l as p e r m i t t i n g r e l a t i v e l y l a r g e r r a d i a l increments where they can be t o l e r a t e d . In p r a c t i c e , the i n s t a b i l i t y was observed only f o r the r e a c t o r of l a r g e s t diameter which i s the l e a s t i n t e r e s t i n g p h y s i c a l l y . Results The c a l c u l a t i o n s wer p r a c t i c a l for laborator and f o r p l a n t s c a l e (30 cm). The i n i t i a l v e l o c i t y p r o f i l e i s g r a d u a l l y d i s t o r t e d as p o l y m e r i z a t i o n p r e f e r e n t i a l l y occurs near the w a l l of the r e a c t o r i n c r e a s i n g v i s c o s i t y there. The b u l k of the flow g r a d u a l l y i s f o r c e d to the center of the tube, and beyond a c e r t a i n p o i n t the r e a c t o r i s e f f e c t i v e l y bypassed as f a r as p o l y m e r i z a t i o n i s concerned. By t r i a l and e r r o r i t was found that t h i s occurred when the outermost 10% of the flow occupied about 2/3 of the r e a c t i o n area or the space beyond the r a d i a l p o s i t i o n of 0.6 of the r a d i u s . This s i t u a t i o n i s equiva l e n t to a plugged r e a c t o r and represents the p r a c t i c a l l i m i t of r e a c t o r l e n g t h . The output of the r e a c t o r i s considered to be the product formed up to t h i s p o i n t . The computer program was designed to terminate at t h i s p o i n t and output the r e s u l t s i n the form of polymer c o n c e n t r a t i o n , molecular weight, residence time, v e l o c i t y , and temperature as a f u n c t i o n of r a d i a l coor d i n a t e . Figures 1 to 5 show the v e l o c i t y p r o f i l e s , molecular weight d i s t r i b u t i o n and temperature t r a v e r s e s f o r the v a r i o u s r e a c t o r diameters s t u d i e d . The v e l o c i t y p r o f i l e s f o r a l l three cases were s i m i l a r when superposed so that only one case i s shown i n Figure 1 which shows the i n l e t v e l o c i t y p r o f i l e as w e l l as the e x i t p r o f i l e f o r Case 5. The temperature p r o f i l e s show the e f f e c t of r e a c t o r diameter. For the s m a l l - s c a l e r e a c t o r at any a x i a l d i s t a n c e the temperature gradient i s not severe. The w a l l temperature i s at the most 3°C above the a x i a l temperature. For the l a r g e r diameter there i s a c o n s i d e r a b l e gradient near the w a l l which appears to have the nature of a hot spot i n the 30 cm diameter (20 to 90°C w a l l temperatures are seen w i t h only a degree or two r i s e i n the center of the r e a c t o r ) . Table I I I shows some of the average r e a c t o r r e s u l t s f o r v a r i o u s cases s t u d i e d . As the r e a c t o r increases i n diameter the pluggage s i t u a t i o n s occur f o r a lower average molecular weight. These molecular weights are somewhat lower than that of a p r a c t i c a l polymer although p r a c t i c a l molecular weights could be obtained i n a yet s m a l l e r diameter tube.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
WEHNER
EPDM
Laminar Flow Polymerization
RADIAL
Figure 1.
DISTANCE
Velocity profile
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
146
CHEMICAL
REACTION
ENGINEERING—HOUSTON
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
EPDM
WEHNER
Laminar Flow Polymerization
ι •ι ι I ι ... I ι ι ι ι l ι j ι ι l ι ι ι ι I ι ι ι ι i ι ι ι ι I ι
t 1 t
I
I I I
CONDITION 1
χ ο Œ 1.00D U Lu Ο
0.75-
0.50H
0.25 I ι ι ι ι ι ι ι ι ι ι ι ι ι ι ι ι ι ι ι ι ι ι ι ι I ι ι ι ' I ι ' i ' I 0.00
0.05
0.10
0.15
R A D I A L
Figure 3.
0.20
0.25
D I S T A N C E
0.30
1 1
0.35
1
1
' 1 '' 0.40
0.-45
( R E L A T I V E )
Molecular weight traverse
χ 10"
-JJL
3.5-
CONDITION 5
3.0H 2.5H
5
2.0H < U
Lu
1.5H
1
1
1111
1
11
'l ' ' l ' ' ' ' I i ' I
0.5 0.
0.05
0.10
0.15
R A D I A L
Figure 4.
0.20
D I S T A N C E
1
0.25
0.30
0.35
( R E L A T I V E )
Molecular weight traverse
American Chemical Society Library 16th St., N.W. Weekman, V., et al.; In Chemical Reaction1155 Engineering—Houston; ACS Symposium Series; American Chemical Washington, DC, 1978. Washington, D.C.Society: 20036
0.40
TABLE I I I RESULTS OF LAMINAR FLOW INTEGRATION
1
1
Condition
R cm
(Va " -*") mmol/1
1 2 3 4 5 6 7
0.50 2.5 15.0 0.50 2.5 15.0 15.0
0.035 0.035 0.035 0.01 0.01 0.015 0.07
MW -
V
θ min
77,000 72,300 22,600 126,000 123,000 23,000 11,600
1.97 1.77 0.55 3.30 3.11 0.96 0.28
L m
n
2.1 2.1 3.6 3.5 9.6 67.2 17.9
i n h
1.5 1.42 0.54 2.25 2.2 0.7 0.3
Inlet Condition Τ = 10°C; x
±
= 0.083, x2 = 0.50, X 3 = 0.028
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
MWD 1.27 1.33 1.32 1.29 1.32
12.
WEHNER
EPDM
Laminar Flow Polymerization
149
Discussion As a p p l i e d to copolymerization w i t h Z i e g l e r c a t a l y s i s , t u b u l a r r e a c t o r s are l i m i t e d i n conversion f o r two p r i n c i p a l reasons. The r e a c t i o n i s h i g h l y exothermic and h i g h tempera tures are d e t r i m e n t a l to the c a t a l y s t . In a d d i t i o n , s i n c e the monomers have d i f f e r i n g r e a c t i v i t y , polymer of v a r y i n g composi t i o n i s obtained as the monomers are depleted. U s e f u l EPDM elastomers have a r e s t r i c t e d compositional range. The m a t e r i a l produced i n these s t u d i e s have compositions of 55 to 70% ethylene, 30 to 45% propylene and about 3% hexadiene by weight. An important f e a t u r e of t h i s work i s the l o c a l i z a t i o n of the bulk of the r e a c t i o n near the w a l l of the tube d i s t o r t i n g the v e l o c i t y p r o f i l e . Contrar does not produce a produc r a t i o of weight average d i v i d e d by number average molecular weight i s almost constant at 1.3 f o r a l l the cases s t u d i e d . The above-mentioned compositional v a r i a t i o n near the w a l l l i m i t s molecular weight because of d e p l e t i o n of the most r a p i d l y r e a c t ing species ( e t h y l e n e ) . A previous work (8) w i t h butadiene s o l u t i o n p o l y m e r i z a t i o n i n c l u d e d r e a c t o r s long enough f o r e s s e n t i a l l y complete r e a c t i o n which showed n e a r l y monodisperse polymer at the e x i t of the r e a c t o r . This i s p o s s i b l e a t the expense of a very h i g h temperature and a l a r g e pressure drop when h i g h v i s c o s i t y m a t e r i a l f i l l s the r e a c t o r . Lynn (9) r e c e n t l y published a strong argument a g a i n s t the f e a s i b i l i t y of t u b u l a r r e a c t o r s i n polystyrene p r o d u c t i o n . In Table I I I , i t may be seen that the l a r g e s t diameter r e a c t o r produces the lowest molecular weight. This r e a c t o r s u f f e r s a l s o from an apparent hot spot a t the w a l l (see a l s o Reference 2). A t h i r d l i m i t a t i o n i s that the model f a i l s at t h i s diameter s i n c e the entrance flow i s t u r b u l e n t . I t would not be worth the e f f o r t to develop a model f o r t h i s case s i n c e high molecular weight polymer can only be produced i n s m a l l diameter r e a c t o r s . This paper i s C o n t r i b u t i o n 418 from the Elastomer Chemicals Department. APPENDIX VELOCITY PROFILE ANALYTIC SOLUTION FOR NONUNIFORM VISCOUS FLOW (A Method Derived by R. L. Turner and E. D. Wohlsen) Conceptually, the flo w i s d i v i d e d or lumped i n t o a number of annular streams each r e p r e s e n t i n g a f r a c t i o n of the flow. Equal f r a c t i o n s are most convenient, but the treatment i s general. A l l c o n d i t i o n s w i t h i n an annulus which a f f e c t v i s c o s i t y are assumed to be uniform. (This i s true of shear r a t e a l s o . This means that non-Newtonian f l u i d s cannot be handled d i r e c t l y . In a c t u a l p r a c t i c e , the method has shown i t s e l f to
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
150
be even more h e l p f u l i n non-Newtonian s i t u a t i o n s . I n a l l such cases, the shear r a t e c o n t r i b u t i o n i s c o r r e c t e d a f t e r each "Newtonian" s o l u t i o n and the whole s o l u t i o n scheme repeated u n t i l the v e l o c i t y p r o f i l e i s s t a b i l i z e d . ) Examination of "Newtonian" c o n s i d e r a t i o n s f o r a s i n g l e f l o w annulus between o u t s i d e r a d i u s r j and i n s i d e r a d i u s r j + i c a r r y i n g AQj u n i t s i n a pipe of r a d i u s r shows that the shear s t r e s s a t the mid-point i s w
rj-j-1 + r j 2 The average shear r a t e i n an element i s
[àrjj
The average v e l o c i t y i s
1F(r| - r j n ) The d e f i n i t i o n o f v i s c o s i t y y i e l d s T
J =
dr
U t i l i z i n g these four equations, a r a t h e r lengthy d e r i v a t i o n g i v e s a n a l y t i c a l working equations f o r the v e l o c i t y ( v ) and the r a d i u s ( r ) a t the o u t s i d e o f each annulus. n
n
n-l AQj
n-l
Where :
ΔΟη
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
12.
EPDM
WEHNER
Laminar Flow Polymerization
n-1 Σ
8n -
151
Δ£ Dj
J=l JM
Σ J=I
Λ2
SLj) y
JM = the t o t a l number of a n n u l i T)j = average v i s c o s i t y of the J t h annulus
Nomenclature C η ninh
i s polymer c o n c e n t r a t i o n ( g m / d e c i l i t e r ) i s s o l u t i o n v i s c o s i t y (poise) i s inherent v i s c o s i t y i s v i s c o s i t y of hexane a t r e a c t o r entrance i s weight f r a c t i o n w Mi i s molecular weight i s v i s c o s i t y average molecular weight MWy Q i s r e a c t o r residence time i s the r a t e of r e a c t i o n of the l i t monomer Ri i s the heat of p o l y m e r i z a t i o n f o r t h i s monomer k i s thermal c o n d u c t i v i t y r i s r a d i a l distance i s l i q u i d density Ρ i s l i q u i d heat c a p a c i t y Cp V i s v e l o c i t y i n the Ζ d i r e c t i o n Ζ i s the d i s t a n c e along the a x i s of the r e a c t o r Τ i s temperature (absolute when appropriate) J i s the index f o r the r a d i a l d i s t a n c e Ν i s the index f o r the a x i a l d i s t a n c e >, 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.
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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.
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CHEMICAL
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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.
EUZEN ET AL.
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.
14.
SAWADA ET AL.
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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.
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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.
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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
= V m
+
V
P
=\n
( 1
f
- P
) +
Vp
U
'
)
assuming the a d d i t i v i t y o f p a r a l l e l heat c o n d u c t i v i t i e s and i n v a r i a n t c r o s s s e c t i o n s a l o n g the d i s t a n c e L f o r the two m a t e r i a l s . I f i t i s i m p o s s i b l e t o determine the f r a c t i o n a l s u r f a c e f and f of the two m a t e r i a l s be cause o f the i r r e g u l a r shapS o f the p e l l e t s , t h e s e v a l ues can be approximated by means o f the d e n s i t i e s fnethod Ic i n T a b l e 3) as f
= P
(5) ?p-?m
The ASTM- (or DIN-) s t a n d a r d method f o r low con d u c t i n g s o l i d m a t e r i a l (X
e In the p r e s e n t
i n v e s t i g a t i o n the
L91
L i n s e i s equipment
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
192
Figure 1. Principle of the conductometer
COLORA
[Z * C00
MllflHlllllll I
er
insulation auxiliary heater sample main heater and guard heater sample auxiliary heater
IIMMIIMMIHI
insulation
L Figure 2. Principle of the LP91 LINSEIS conductometer
Q
cooler
_ _ r
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
16.
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193
was used, o p e r a t i n g a c c o r d i n g t o the ASTM method ( l i a i n T a b l e 3 ) , a t l e a s t w i t h the r e f e r e n c e m a t e r i a l . With porous c a t a l y s t p a r t i c l e s , i t i s n o r m a l l y not p o s s i b l e t o produce samples o f 80-12omm d i a m e t e r s . T h e r e f o r e , i n o r d e r t o use t h i s equipment c a t a l y s t p a r t i c l e s were em bedded a l s o i n a q u i c k h a r d e n i n g p l a s t i c (method l i b i n Table 3). In o r d e r t o use t h i s u n i t a l s o f o r c a t a l y s t p a r t i c l e s o f any shape, the s t a n d a r d method was m o d i f i e d (method l i e i n T a b l e 3) i n the same way as d e s c r i b e d f o r the 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 nonporous p l a s t i c powders i n [ 1 3 ] . The concept i s t o compare the t h e r m a l c o n d u c t i v i t y o f t h e c a t a l y s t p e l l e t \ w i t h the c o n d u c t i v i t I f the l i q u i d m i x t u r the same c o n d u c t i v i t y as the p e l l e t , the c o n d u c t i v i t y o f a f l u i d / s o l i d system X (consisting of c a t a l y s t par ticles and the l i q u i d mixture) w i l l be independent of the s o l i d c o n t e n t , and \
= >fm
= *p
( 7 )
'
T h i s e q u a t i o n can be s a t i s f i e d e x p e r i m e n t a l l y by v a r y i n g t h e t h e r m a l c o n d u c t i v i t y o f the b i n a r y l i q u i d mix t u r e s y s t e m a t i c a l l y through v a r y i n g i t s composition. T h i s v a r i a t i o n i s shown i n F i g u r e 3 f o r t h e system methanol/water used i n t h i s s t u d y . F i g u r e 4 shows one of the two probe chambers, f i l l e d w i t h t h e l i q u i d mix t u r e ( l e f t ) and w i t h the added c a t a l y s t ( r i g h t ) . The bottom and the t o p o f t h e chamber c o n s i s t of s t a i n l e s s s t e e l , t h e c y l i n d r i c a l w a l l i s made o f T e f l o n . I f e q u a t i o n (7) h o l d s , t h e n T-=T^ , T = T ' and $ = $'· Method l i e r e q u i r e s t n a t : ( i ) The t h e r m a l conduc t i v i t y o f the c a t a l y s t p e l l e t s be w i t h i n the range of the t h e r m a l c o n d u c t i v i t i e s of the pure l i q u i d compo n e n t s ; ( i i ) t h e t h e r m a l c o n d u c t i v i t y o f the l i q u i d mix t u r e be known as a f u n c t i o n o f i t s c o m p o s i t i o n . T h i s means t h a t c a t a l y s t s w i t h a t h e r m a l c o n d u c t i v i t y g r e a t e r than water can not be t e s t e d i n t h i s way, e.g. c a t a l y s t s A and Ε i n t h i s s t u d y . N a t u r a l l y t h i s method can a l s o be used t o determine t h e t h e r m a l c o n d u c t i v i t y o f s o l i d c a t a l y s t m a t e r i a l i f the p e l l e t s are so f i n e l y ground t h a t t h e l i q u i d can p e n e t r a t e i n t o a l l p o r e s . T h i s v a l u e i s then the b a s i s f o r d e t e r m i n i n g 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 the porous p e l l e t u s i n g known models [_3, 91 . Dynamic methods f o r the d e t e r m i n a t i o n o f 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 n o r m a l l y con s i s t o f experiments i n which a s p h e r i c a l l y o r c y l i n d r i 1
2
2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
194
CHEMICAL
\
{
REACTION
ENGINEERING—HOUSTON
lW/mK]|
0.70
Η
Figure S.
Thermal conductivity of methanol/ water mixtures
- cooling plate binary liquid mixture
mixture catalyst pellets heating plate
τ-/ Figure 4.
M i Sample chambers of the modified plate method
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
16.
HOFFMANN ET
Thermal Conductivity Determination Methods
AL.
195
c a l l y shaped p a r t i c l e , equipped w i t h a c e n t r a l and a p e r i p h e r i c a l thermocouple, i s immersed i n an ambient f l u i d o f c o n s t a n t o r l i n e a r l y changing temperature [4_, 8] . In the f i r s t case one f o l l o w s the temperature r i s e or f a l l i n the c e n t r e o f the p a r t i c l e , i n t h e second case one determines t h e so c a l l e d l i m i t i n g temperature d i f f e r e n c e between the c e n t r e and t h e s u r f a c e of the particle. To compare s t a t i c and dynamic methods, i n t h i s study the second method ( I I I i n T a b l e 3) was a p p l i e d ( F i g u r e 5 ) , u s i n g a gas. A gas o f f e r s t h e advantage t h a t t h e p a r t i c l e s can be used i n t h e i r o r i g i n a l shape and i n t h e a c t u a l r e a c t i o n m i x t u r e (e.g. as a s i n g l e pellet reactor). I t can be show r i c a l p a r t i c l e s 99 % g temperatur ference _2 T
* lim can be
=
fe
Φ
( 8 )
r e a c h e d a t times 2
t > % ^ (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.
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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<^
ACTIVITY LOSS IS POISONING
FOULANT CONTENT (b) FOR βοή\
Figure 4. Activity foulent content be havior during deactivation
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
17.
Catalyst Deactivation by Fouling
HUGHES A N D M A N N
207
p a r t i c u l a r p e n e t r a t i o n x. The volume o f f o u l a n t i n plugged pores i s given by 2
V»(h)
(5)
3
= [ 1ττβ χ Ν f (χ) dx Jo The t o t a l f o u l a n t volume i s obtained from V ( h ) « V£(h)
(6)
+ V»(h)
f
so t h a t P1 2
2
r f>)dr | +
(^|--^)-
S
(7)
which i s now c o n v e n i e n t l y g i v e pelle specifi s u r f a c e , p e l l e t / p o r e l e n g t h dimension and the p e l l e t s u r f a c e area d i s t r i b u t i o n f u n c t i o n . Comparison o f Theory and Experiment f o r a HPS C a t a l y s t The theory can now be a p p l i e d f o r the interprétation o f some experimental r e s u l t s obtained f o r the vapour phase h y d r o d e s u l p h u r i s a t i o n o f thiophene over a commercial alumina supported cobalt-molybdate c a t a l y s t , COMOX 1661 manufactured by Laporte I n d u s t r i e s L t d . , General Chemicals D i v i s i o n , Widnes, U.K., a v a i l a b l e i n the form o f c y l i n d r i c a l extruded p e l l e t s o f dimensions 10 mm χ 1.5 mm. These p e l l e t s were formed i n t o a s m a l l f i x e d bed c o n t a i n i n g 2 gm o f dry oxide c a t a l y s t h e l d i n p l a c e by quartz wool plugs i n a 1.5 cm I.D. g l a s s t u b u l a r r e a c t o r . The r e a c t o r feed was a vapour mixture o f thiophene and hydrogen, formed by b u b b l i n g hydrogen through l i q u i d thiophene kept a t 0 C i n an i c e bath. The r e a c t o r operated a t atmoshperic pressures and was c o n t r o l l e d by an e l e c t r i c furnace a t 300 C. Conversions o f thiophene were determined by o n - l i n e sampling u s i n g a g a s - l i q u i d chromatograph. P r e s u l p h i d i n g o f the c a t a l y s t which i s s u p p l i e d i n the oxide form, was c a r r i e d out i n accordance w i t h procedures recommended by the s u p p l i e r . The conversion - feed r a t e behaviour o f the p r e t r e a t e d unfouled c a t a l y s t i s presented i n F i g . 5· Separate c a t a l y s t samples were then subjected t o f o u l i n g by coke d e p o s i t i o n using a s e q u e n t i a l technique w i t h e t h y l e n e . T h i s coking was c a r r i e d out a t 500 C by passing a mixture o f 50 cm /min o f ethylene and 187.5 cm /min o f oxygen f r e e n i t r o g e n over the 2 gm c a t a l y s t bed, a f t e r p r e s u l p h i d i n g and checking the a c t i v i t y . The extent o f coke d e p o s i t i o n was changed by a l t e r i n g the time o f c o k i n g , using otherwise i d e n t i c a l c o n d i t i o n s f o r each coking run. A f t e r c o k i n g , the conversion o f thiophene hence the r e a c t i o n r a t e , was determined i n the u s u a l way. The complete set o f runs w i t h coking time v a r i e d from 5 t o 120 min i s presented i n F i g . 5· The continuous l i n e s shown are the f i t t i n g o f the k i n e t i c r a t e equation based upon In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
208
CHEMICAL
0
1-0
2-0 ~-
4
x10 gcat
REACTION
3-0 min
g
ENGINEERING—HOUSTON
4-0 mol
1
•A ο Figure 5. Effect of increasing sequential fouling coke deposition time on HDS catalyst activity at 300°C
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
17.
HUGHES A N D M A N N
<--»>
·
1
Catalyst Deactivation by Fouling
%
209
<
8
>
using an assumption o f plug flow i n the r e a c t o r * This kinetic equation i s a reduced form o f a more complete LangmuirHinshelwood e q u a t i o n . The values o f model parameters at 300 C are l i s t e d i n Table I. The negative values o f the apparent a d s o r p t i o n constant Κ i n d i c a t e that the product butanes and hydrogen sulphide are more s t r o n g l y adsorbed than thiophene. TABLE I: The E f f e c t o f Coke D e p o s i t i o n on Apparent Rate Constants
300°c - 1 K
/w coke
gmoles.min / g c a t x10^
0.00 0.70 1.90 2.20 2.50
2.30 1.93 1.67 1.19 0.86 0.25 0.07 0.10
k.26
5.8*f
8Λ7
gmoles /gmole
31.5 30.1** 32.07 30.17 32.00 33.36 35.38 29.69
A n a l y s i s o f d i f f u s i o n and r e a c t i o n f o r g e n e r a l i s e d k i n e t i c s 10, shows that the present r e s u l t s g i v e r e a c t i o n r a t e s i n the n o n - d i f f u s i o n i n f l u e n c e regime 11. Thus, the a c t i v i t y l o s s that i s observed i s érve t o surface area l o s s , and i s not due to 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 . T h i s i s borne out by Table I, where the impact o f f o u l i n g i s seen i n the decrease o f k with being independent o f coke content. The coking procedure that has been used i s a r b i t r a r y , but serves the purpose o f s e p a r a t i n g f o u l i n g mechanism from the a c t i v i t y measurement. P a r a l l e l f o u l i n g by using mixed feeds o f thiophene and ethylene a t 300 C produced no coke d e p o s i t i o n . However, t h i s s e q u e n t i a l technique d i d give uniform coking throughout the c a t a l y s t b e d . The coke contents were determined using burnoff with oxygen on a h o r i z o n t a l thermobalance, and again f u l l d e t a i l s are given i n T1 · The r e a c t i o n r a t e s p r e d i c t e d from the k i n e t i c model a t 10$ conversion increments from 21$ t o 91$ conversion o f thiophene, have been used t o construct Table I I · At each conversion l e v e l the g l o b a l r e a c t i o n r a t e has been normalised t o a f r a c t i o n o f the r e a c t i o n r a t e f o r the unfouled c a t a l y s t . Only r e s u l t s f a l l i n g w i t h i n the experimental range have been i n c l u d e d . The a c t i v i t y f
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
210
r a t i o seems t o be constant over wide ranges o f c o n v e r s i o n f o r a g i v e n coke content. Therefore the average a c t i v i t y a t each coke content i s taken t o represent the e f f e c t o f coke d e p o s i t i o n upon c a t a l y s t a c t i v i t y , and these r e s u l t s form the b a s i s o f comparing theory and experiment. TABLE I I : Experimental Coked C a t a l y s t A c t i v i t i e s
300°C Conversion Level
Coke Content
wt %
2.20
4.26
A
0.00
0.70
21 31 41 51 61 71 81 91
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
-.846
-
.848
.750
Average Activity*
1.00
.850
1.90
-.755
.853 .852
.748 .754
.752
.518 .523 .525 .524
.521
2.50
-
.133 .125
.391 .388 .385 .385
.117
-
0.390
-
.124
5.84 .044
.039
0.042
8.47 .040 .042
0.041
The f i n a l element i n the a n a l y s i s i s the pore s i z e d i s t r i b u t i o n f u n c t i o n o f the experimental c a t a l y s t COMOX 1661. The manufacturers pore s i z e data has been f i t t e d w i t h a l o g normal d i s t r i b u t i o n w i t h r =54 X and σ = 0.30. Using min ~ 2000 A and L = 6.5 x 10 A, a p e l l e t ^ surrace a r e a o f 3?5^*3 m gra" and pore volume o f 0·6θ6 cm gm are p r e d i c t e d . These compare w i t h 300 and 0.60 quoted by t h e manufacturer as t y p i c a l v a l u e s . The consequent comparison o f theory and experiment a s t h e t h i c k e n i n g / p e n e t r a t i o n parameter β i n c r e a s e s from zero t o i n f i n i t y i s presented i n F i g s . 6(a), ( b ) . The experimental r e s u l t s show a c l e a r i n f l e x i o n tendency, and t h e r e f o r e t h e monotone decreasing p r e d i c t i o n f o r p o i s o n i n g dominated f o u l a n t accumulation suggests t h a t t h i s mechanism i s not c o r r e c t . On the other hand, the r e s u l t s do comply w i t h a β value between 3 x 10"^ and 5 x 10 , p l a c i n g the behaviour i n the pore mouth p l u g g i n g dominant regime. I n c o n s t r u c t i n g F i g s . 6(a),(b) a coke d e n s i t y o f 1.0 gm cm has been chosen as i n t e r m e d i a t e between the value o f 0.8 quoted by Beuther and Schraid 12 and 1.7 gm cm~^ use by L e v i t n e r 6. T h i s converts coke volume t o coke wt# i n the p e l l e t . "~ The d i s c r i m i n a t i o n o f the c o r r e c t d e a c t i v a t i n g mechanism i s o f more than academic importance. Thus, i f i n a p a r t i c u l a r case, as here, pore mouth plugging i s the most important d e a c t i v a t i n g mechanism, a t t e n t i o n should be concentrated on changing t h e p h y s i c a l pore s t r u c t u r e o f the c a t a l y s t i n order t o a l l e v i a t e the d e a c t i v a t i o n . The s t r i k i n g o f a c o r r e c t balance between p o i s o n i n g and f o u l i n g pore mouth c l o s u r e when they are both r
1
0
3 1 1 ( 3r
=
1
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
17.
Catalyst Dedctivdtion by Fouling
HUGHES AND M A N N
q
c
wt
%
(a) POISONING DOMINANT REGIME
0
5
10 q
c
wt
%
(b) MOUTH PLUGGING DOMINANT REGIME
Figure 6. Comparison of wedge layering model with experimental results
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
211
CHEMICAL REACTION ENGINEERING—HOUSTON
212
inevitable, by rational design of the pore structure, remains a challenging task for the chemical reaction engineer. Conclusions A new theory of fouling, based upon the way i n which the structure of the pores and the geometric form of the foulant deposit interact together, has been developed, ©lis theory i s comprehensive i n scope and predicts the activity-foulant content behaviour together with the spatial distribution of foulant within the pellet pore structure, and has the potential to predic porosity, permeability and effective d i f f u s i v i t y changes during fouling. Experiments on the activity behaviour of a commercial HDS catalyst i n desulphurising thiophene fouled by a sequential technique using ethylene pore mouth plugging dominate Nomenclature Ρ F
L'
Ν r r S V*(h)
V
χ σ
1
foulant thickening/penetration rate parameter concentration (A=thiophene, H=hydrogen, S=hydrogen sulphide) fractional a c t i v i t y during deactivation molar feed rate of thiophene number-pore radius distribution function surface area-pore radius distribution function volume-pore radius distribution function pore mouth foulant thickness adsorption constant reaction rate constant pellet length dimension number of pores per gm of catalyst pore radius most frequent pore radius pellet specific surface total volume of foulant at a mouth thickness h pore volume of pellet weight of catalyst i n reactor bed conversion of thiophene penetration of foulant variance
Acknowledgement We wish to thank the S.R.C. for provision of a research studentship for CCH. We are also indebted to Laporte Industries Ltd., General Chemicals Div., Widnes, U.K. for the donation of catalyst samples and for many helpful discussions.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
17.
HUGHES A N D M A N N
Catalyst Deactivation by Fouling
213
Literature Cited 1. Levenspiel, O., "Chemical Reaction Engineering", 2nd E d . , Wiley, New York (1972). 2. Thiele, E.W., Ind. Eng. Chem. (1939) 31, 916 3. Wheeler, A . , Adv. in Catalysis (1951) 8, 250 4. Butt. J.B., J. Catalysis (1976) 41, 190 5. Rostrup-Nielsen, J . R . , J. Catalysis (1974) 33, 184 6. Levintner, M . E . , Panchenkov, G.M., Tanaterov, M . A . , Int. Chem. Eng. (1967) 7, 23 7. Newson, Ε . , Ind. Eng. Chem. Proc. Des. Dev. (1975) 14, 27 8. Voorhies, J.R., Ind. Eng. Chem. (1945) 37, 318 9. Wojciechowski, B.W., Cat. Rev. - Sci. Eng. (1974) 9, 79 10. Roberts, G.W., S a t t e r f i e l d C.N Ind Eng Chem (1965) 4, 288 11. Hughes, C . C . , Ph.D , y Institute of Science and Technology (1977) 12. Beuther, H., Schmid, B.K., Proc. 6th World Petroleum Congress (1964) III, 297.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
18 Operational Flexibility Consideration in the Design of Multitubular Reactors C. M c G R E A V Y Department of Chemical Engineering, Leeds University, Leeds, LS2 9JT, England B. R. D U N B O B B I N Union Carbide Corporation, Chemicals and Plastics, Bound Brook, N J 08805
Multitubular reacto that the tube bundle ca are adequate when the operating conditions are remote from regions of high performance, and where maldistribution of the feed to the tubes cannot occur. In other circumstances, s i g n i f i c a n t l y different conditions are found i n the tubes depending on t h e i r position i n the bundle. Moreover, when optimal performance i s being sought, it is often the case that the preferred operating state is i n a region where it is no longer possible to make simplifying assumptions, since it is essential to have r e l i a b l e information on the detailed behaviour of the system. This i s required not only to ensure that adequate flexibilty of operation is possible, but also to be able to evaluate what potential hazardous conditions might a r i s e . To do this, it i s essential to take account o f the multitubular characteristics explicitly and to examine the effects of the coolant flow because s i g n i f i c a n t l y different patterns of behaviour are possible both in respect to s t a b i l i t y as w e l l as having an important bearing on the economic attractiveness of using certain reactor configur ations. At the design stage, the decisions to be taken i n respect of the l a t t e r are obviously of some importance. These considerations will necessarily be influenced by the particular operations, reaction scheme and many other specific factors. Nevertheless, it would be useful to be able to suggest general guide-lines as to how to select initial configurations so as to realise particular operational characteristics. Despite i t s importance, very l i t t l e work has been done i n t h i s area, perhaps because of the considerable amount of inform ation on s h e l l and tube heat exchangers. Unfortunately, t h i s expertise i s not d i r e c t l y applicable. For example, for highly exothermic reactions of the type to be considered here, i t i s better to avoid counter-current flow between coolant and reactants because of operational d i f f i c u l t i e s which can a r i s e . For this reason, i t i s the intention of t h i s work to explore the general operating characteristics o f both co- and counter-current ©
0-8412-0401-2/78/47-065-214$05.00/0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
18.
MCGREAVY
A N D DUNBOBBIN
Flexibility of Multitubular Reactors
215
u n i t s t o enable c r i t e r i a f o r design t o be e s t a b l i s h e d . The i n s i g h t gained from t h i s can be used t o d e v i s e a l t e r n a t i v e arrangements which i s a b l e t o take advantage o f each o f the above modes w h i l e a l l o w i n g adequate f l e x i b i l i t y o f o p e r a t i o n . I n a d d i t i o n , v a l u a b l e i n f o r m a t i o n can be o b t a i n e d as t o how t o deal w i t h c o n t r o l problems. As w i t h the simple heat exchanger systems, the counterc u r r e n t r e a c t o r w i l l g e n e r a l l y r e q u i r e a s m a l l e r heat t r a n s f e r area than a co-current system f o r the same thermal l o a d i n g . In t h i s sense, comparison o f the two systems i s not s t r a i g h t f o r w a r d . But f o r convenience, t h e f o l l o w i n g d i s c u s s i o n w i l l be based on the assumption t h a t a common s h e l l and tube arrangement i s being used and the d i f f e r e n t arrangement obtained b changin connections a t the i n l e As a l r e a d y i n d i c a t e d , th p r i n c i p a y and o p e r a b i l i t y , which would o b v i o u s l y have t o be considered i n relation to capital cost. Although t h i s w i l l not be e x p l o r e d f u r t h e r , i t can be i n c o r p o r a t e d i n t o the procedure o u t l i n e d here, when more d e t a i l e d s t u d i e s are being c a r r i e d out ( O . Model o f the M u l t i t u b u l a r Reactor The f o r m u l a t i o n o f a mathematical d e s c r i p t i o n o f a m u l t i t u b u l a r r e a c t o r poses no s p e c i a l problems, although the comput a t i o n a l e f f o r t needed t o s o l v e the equations can be v e r y c o n s i d e r a b l e , p a r t i c u l a r l y where extreme o p e r a t i n g c o n d i t i o n s are being e x p l o r e d . I t i s under these circumstances t h a t s i g n i f i c a n t i n t e r a c t i o n occurs between the tubes a s a r e s u l t o f the d i s t r i b u t i o n o f the coolant i n the s h e l l . Dunbobbin (J_) and Adderley (2) have shown t h a t u n l e s s these e f f e c t s are accounted f o r i n the heat balances,the r e s u l t s are o f l i m i t e d v a l u e . C l e a r l y , i t would be d e s i r a b l e t o have a general a n a l y t i c a l framework which could be used t o i n d i c a t e when d i f f i c u l t c o n d i t i o n s might a r i s e and how they could be handled. A t the present time, t h i s i s not p o s s i b l e , so a technique must be developed which can demonstrate the broad c h a r a c t e r i s t i c s o f systems and enable the r e l e v a n t i n s i g h t t o be g a i n e d . As a s t e p i n t h i s d i r e c t i o n , a case study o f a r e p r e s e n t a t i v e o f a c l a s s o f important problems o f f e r s a s u i t a b l e compromise, and w i l l be the approach adopted here. The p a r t i c u l a r system to be considered belongs t o the important c l a s s o f c a t a l y t i c p a r t i a l o x i d a t i o n r e a c t i o n s , as represented by the p r o d u c t i o n o f m a l e i c anhydride from benzene. Although these are b a s i c a l l y complex r e a c t i o n schemes, i n t h e i r l i m i t i n g behaviour, where temperature runaway and o t h e r i n s t a b i l i t i e s develop, the k i n e t i c equations approximate a s i n g l e i r r e v e r s i b l e r e a c t i o n t o the complete o x i d a t i o n products. As f a r as heat e f f e c t s are concerned, i t i s then p o s s i b l e t o d i s p l a y a l l t h e important p a t h o l o g i c a l f e a t u r e s . The f o l l o w i n g a n a l y s i s assumes t h a t such an approximation i s acceptable f o r the purposes o f
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
216
i l l u s t r a t i o n , but i n no way r e s t r i c t s the v a l i d i t y o f the procedure. More complex schemes would merely r e q u i r e a much more d e t a i l e d analysis. An approximation which adequately represents a continuum v e r s i o n o f the system shown i n f i g u r e 1 can be obtained by r e p l a c i n g the equation f o r the heat balance on the coolant by a s e r i e s o f m i x i n g c e l l s ( j j , where a volume element o f the c o o l a n t , together w i t h a small group o f r e a c t o r tube s e c t i o n s , i s c o n s i d ered i n one o f the passes. The dimensionless heat balance f o r a t y p i c a l c e l l are g i v e n by the a p p r o p r i a t e equations (1) and (2) below: Co-current flow. Τ
= Τ c
C
(i)
+ (i-D
Counter-current f l o w .
^ Nu
Τ
= Τ c
c
(i)
w
(i-t)
1
(T-T C
G — c J z
)dz (i-D
(2)
2
Figure 1 i n d i c a t e s the nomenclature used i n d e s c r i b i n g the r e a c t o r . The s u b s c r i p t i r e f e r s t o the i t h c e l l , numbered from the c o o l a n t i n l e t (co-current case), or o u t l e t (counter-current). The s o l u t i o n o f the model i s obtained by c o u p l i n g the tubeside r e a c t o r equations w i t h equation (!) o r (2) as a p p r o p r i a t e , and u s i n g a marching procedure to pass through the assembly from c e l l to c e l l , i t e r a t i o n around a guessed o u t l e t coolant temperature being necessary i n the counter-current case. For the r e a c t i o n i n s i d e the tube, the dimensionless mass and energy balances, w i t h the u s u a l assumptions, become (J_, Z) f o r the s i n g l e main r e a c t i o n : Fluid Field. dc
Sî
. +
n G
2
«Φ ;P- - G dz 4
Λ
θ
2
/
_
η
e
(t-T) +
J
- ?
*P
2Nu * ™ -χ G
3
c
=
0
(T-T ) = C
( 3 )
0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
(4)
18.
MCGREAVY
with i n i t i a l
A N D DUNBOBBIN
conditions:
Flexibility of Multitubular Reactors
Τ
c
217
Τ ζ
0
ζ
Ο
c
Reaction on the S o l i d . The r e a c t i o n r a t e on the c a t a l y s t can be e a s i l y c a l c u l a t e d i f t h e p e l l e t i s assumed t o be i s o t h e r m a l ( 1 , 2, 3 ) , a t a temperature g i v e n by: Β Sh
A
(r-g) (5)
t = Τ + (sg + r T h i s equation must be solved i t e r a t i v e l y t o f i n d the temperature and hence the r e a c t i o n r a t e .
solid
D e t a i l s o f the method o f the s o l u t i o n can be found elsewhere (4), but the r e s u l t i n g p r o f i l e s g i v e d e t a i l e d information on t h e coolant temperature and c o n d i t i o n s i n t h e r e a c t o r tubes. It is a l s o p o s s i b l e t o see how heat i s e f f e c t i v e l y passed between tubes and hence which are most v u l n e r a b l e t o the development o f i n s t a b i l ities. Each case requires c a r e f u l scanning o f the r e s u l t s , but the f i n d i n g s can be summarized i n the manner i n d i c a t e d below. N e v e r t h e l e s s , i t should be noted that i t i s not p o s s i b l e i n general t o p r e d i c t , a p r i o r i , which p a r t o f the bundle c o n t a i n s the c r i t i c a l tube. I t w i l l a l s o depend on whether m a l d i s t r i b u t i o n e f f e c t s are present. The number o f c e l l s used w i l l c l e a r l y depend on the nature o f the problem, but f o r the system considered here, and t o c a r r y out a reasonable d e t a i l e d survey, i t i s necessary t o use about 10 c e l l s f o r each o f the c o o l a n t s i d e passes. T y p i c a l r e s u l t s f o r the dimensionless p r o f i l e s f o r tubes a t o p p o s i t e s i d e s o f t h e bundle are shown i n f i g u r e 2 i . e . i d e n t i f i e d as tubes 1 and 50: these are f o r the row o f tubes a c r o s s the d i a m e t e r . The very d i f f e r e n t c o n d i t i o n s i n s i d e the tubes a t these p o s i t i o n s i s apparent. Comparison o f Reactor C o n f i g u r a t i o n s The data i n t a b l e I are f o r the p a r t i a l o x i d a t i o n o f benzene and can be used t o explore how a l t e r n a t i v e mechanical c o n f i g u r a t i o n s a f f e c t the o p e r a t i o n . I n adopting t h i s approach, i t w i l l be appreciated t h a t a number o f d i f f e r e n t bases f o r t h e comparison are p o s s i b l e . For convenience a t t e n t i o n w i l l be confined t o those f a c t o r s a f f e c t i n g the o p e r a b i l i t y o f a g i v e n , f i x e d s i z e reactor u n i t . A l t e r n a t i v e c o n f i g u r a t i o n s are e a s i l y derived from t h i s by a p p r o p r i a t e changes a t the i n l e t and o u t l e t , together w i t h any a s s o c i a t e d r e l o c a t i o n o f the b a f f l e p l a t e s .
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
218
Table I G
2
G
3
G
= 0.0849;
0
= 10°
= 0.84
Β
= 4.602x1 θ"" ;
;
; 5
G
( inlet)
= 76.85 ; A
A
= 500.0 ;
Nu
=
1.0
= 98.25
G
0
4
Sh
Data used i n the case s t u d i e s
c w
= 14.6
;
Τ
= 0.03884 0
T o t a l No. o f tubes = 2,500.
The obvious d i f f e r e n c e between the heat t r a n s f e r mechanism o f the co- and c o u n t e r - c u r r e n t l y cooled r e a c t o r s i s t h a t the former operates w i t h a feed-forwar heat along the r e a c t o r tubes the c o l d c o o l a n t where t h e r e i s a high r e a c t a n t c o n c e n t r a t i o n and heated coolant promotes r e a c t i o n i n the l e a n r e a c t a n t regions towards the tubeside e x i t . Counter-current r e a c t o r s on the o t h e r hand have pre-heated coolant a f f e c t i n g high r e a c t a n t c o n c e n t r a t i o n s and c o l d coolant i n t h e e x i t regions o f the t u b e s i d e . Thus, the r e a c t i o n i s e s s e n t i a l l y r e s t r i c t e d t o the i n i t i a l p o r t i o n s o f t h e bed. A l s o , because o f the h i g h e r coolant temperatures i n t h e r e g i o n o f t h e tube-side h o t s p o t s , the counter-current r e a c t o r g i v e s higher peak temperatures and conversions. However, because o f t h e s m a l l zone a v a i l a b l e f o r high r e a c t i o n , high con v e r s i o n o f t e n r e s u l t s i n temperature runaway on the t u b e s i d e , making the co-current system more a t t r a c t i v e i n many circumstances. Thus, w h i l e counter-current flow may reduce the s i z e o f r e a c t o r to achieve a given conversion, i t has u n d e s i r a b l e f e a t u r e s which can l e a d to d i f f i c u l t o p e r a t i o n . The above o b s e r v a t i o n s suggest an a l t e r n a t i v e c o n f i g u r a t i o n might make i t p o s s i b l e to improve designs. Thus, i f an arrange ment such as t h a t shown i n f i g u r e 3 i s used, i t r e q u i r e s no complex s h e l l - s i d e m o d i f i c a t i o n s and i s achieved very simply by having the coolant e n t e r i n g at pass 2 and l e a v i n g a t passes 1 and 4, a t the c o s t o f a s m a l l amount o f e x t r a p i p i n g . With t h i s scheme the counter-current stream i s heated by coolant pass 2 before e n t e r i n g pass 1, so t h a t the incoming reactant i s contacted by warm c o o l a n t . Since the flowpath i s not as long as i n a conventional counter-current r e a c t o r , the coolant i s not heated as much and so the very l a r g e temperature peaks o f these r e a c t o r s can be avoided. The co-current stream i s a l s o heated and causes r e a c t i o n i n the lower c o n c e n t r a t i o n regions o f the bed. I t there f o r e makes i t p o s s i b l e t o take advantage o f both the co- and counter-current systems, so t h a t the incoming r e a c t a n t s are con t a c t e d by warm c o o l a n t , thus ensuring t h a t a u s e f u l amount o f r e a c t i o n takes place e a r l y i n the bed, and any r e a c t a n t s l e f t i n the l a t t e r h a l f o f the r e a c t o r are a l s o contacted w i t h warmer c o o l a n t , which w i l l thus i n c r e a s e the r e a c t i o n r a t e . In e f f e c t ,
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
18.
MCGREAVY
AND
DUNBOBBIN
Flexibility of Multitubular Reactors
219
COOLANT IN
J
1-
OUT
L
RE ACTA NT
GASES
—I COOLANT PASS 1 TUBE NO.
COOLANT PASS 2
Figure 1. General representation of the reactor indicating the notation used in describing it
0.046i
coolant
velocity 0 . 0 5
m/sec
"
0.1
"
"
0.2
»
0.038!
Figure 2. Typical temperature profiles in reactor tubes at positions 1 and 50 for various flows
COOLANT OUT
C O O L A N T PASS: 1
Figure 3.
Mixed flow reactor
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
220
CHEMICAL
REACTION
ENGINEERING—HOUSTON
t h i s mixed-flow c o n f i g u r a t i o n i n t r o d u c e s the c o l d e s t coolant i n the p o s i t i o n where i t i s most e f f e c t i v e , namely a t the tubeside hotspot, and i t a l s o provides a reasonable degree o f f l e x i b i l i t y . Other methods o f i n c r e a s i n g the heat t r a n s f e r i n the r e g i o n o f t h e hotspot do not tend t o have the same degree o f a d a p t a b i l i t y during operation. P a r i s and Stevens (4) devised a complex s h e l l s i d e arrangement f o r a s i n g l e tube r e a c t o r and s e v e r a l workers (5, 6, 7) have considered u s i n g v a r i o u s s i z e d packings o r i n e r t spheres a t d i f f e r e n t p o i n t s i n the tubes. These methods, w h i l e o f t e n s u c c e s s f u l , assume t h a t design s p e c i f i c a t i o n s can, and w i l l be maintained. An advantage o f the above method i s t h a t i t can be used even w i t h e x i s t i n g tube bundles w i t h very l i t t l e s t r u c t u r a l change. Mixed Flow C o n f i g u r a t i o n To see the inherent advantages o f the mixed f l o w system, i t i s u s e f u l to compare systems f o r each o f the main d i s t r i b u t i o n s i n each l o o p , a t constant t o t a l mass f l o w r a t e o f c o o l a n t . The u n i t s are a l s o taken t o be the same s i z e , the o n l y d i f f e r e n c e being the r o u t i n g o f the c o o l a n t f l o w . T h i s means t h a t although the residence time o f the c o o l a n t i s the same i n the co- and counterc u r r e n t r e a c t o r s , i t w i l l be s m a l l e r i n the mixed flow c o n f i g u r a tion. C o n t r o l can be e x e r c i s e d by a d j u s t i n g the r e l a t i v e flow r a t e s i n the c i r c u i t , and t h i s i s i l l u s t r a t e d by u s i n g the following distributions: 1.
\ the c o o l a n t flow from pass 2 flows c o u n t e r - c u r r e n t l y i n t o pass 1.
2.
% the coolant flow from pass 2 flows c o u n t e r - c u r r e n t l y i n t o pass 1.
3.
% the c o o l a n t f l o w from pass 2 flows c o u n t e r - c u r r e n t l y i n t o pass 1.
The f l o w r a t e through coolant pass 2 i s always the same as i n the co- and counter-current cases. The tubeside temperature p r o f i l e s o f tube 1 f o r the three types o f mixed flow system, together w i t h the p r o f i l e f o r the coand counter-current r e a c t o r s , are g i v e n i n f i g u r e 4. In a l l cases, the tube i n the bundle r e p r e s e n t i n g the 'worst c o n d i t i o n s has been used. An important o b s e r v a t i o n i s t h a t i t i s not always the same one. The lowest, and most s t a b l e , temperature p r o f i l e i s obtained from the co-current r e a c t o r , w i t h the l a r g e s t tempér ature peak being given by the counter-current. The three mixed f l o w p r o f i l e s are intermediate to these, w i t h t h e type 3 g i v i n g the f l a t t e s t p r o f i l e . F i g u r e 5 uses the Τ versus Β s t a b i l i t y p l o t s proposed by McGreavy and Adderley (S) t o examine the co1
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
18.
MCGREAVY
0.05
AND
DUNBOBBIN
Flexibility of Multitubular Reactors
221
r
Figure 4.
The co-current, counter-current, and mixed-flow tubeside tempera ture profiles for tube Una four-coolant pass reactor
0.05r
Figure 5.
Τ vs. Β stability plot comparing the co-current, counter-current, and mixedflow four-coolant pass reactors
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
222
c u r r e n t , counter-current and type 3 mixed f l o w systems a t a constant c o o l a n t f l o w r a t e expressed by the dimensionless parameter GG = 4.0. At t h i s v a l u e , the l a t t e r c o n f i g u r a t i o n i s a t the l i m i t o f s t a b i l i t y w i t h respect t o temperature runaway. To compare performance, i t i s s u f f i c i e n t t o look a t the conversions i n each case which correspond t o the l i m i t o f s t a b i l i t y , since t h i s i n d i c a t e s the most favourable conversions. Making use o f p l o t s s i m i l a r to f i g u r e 5, i t may be shown t h a t f o r the same parameter values and o p e r a t i n g c o n d i t i o n s , the l i m i t o f s t a b i l i t y o f the counter-current r e a c t o r i s GG = 5.0 and the co-current GG = 2.0 (1_). These would correspond w i t h a maximum temperature r i s e o f 25.1 Κ i n t h e mixed f l o w type 3 r e a c t o r a t GG = 4.0. Hence, a t these c o n d i t i o n s , the coolant temperatur r i s i h highe f o the co-current r e a c t o r c u r r e n t system, but w i t same conversion. The co-current r e a c t o r , w i t h i t s low coolant f l o w r a t e (low value o f GG) e x h i b i t s the best behaviour o f a l l the c o n f i g u r a t i o n s . The disadvantage i s the high coolant temperature r i s e (up to 30K). The main advantage o f the mixed flow system i s t h a t , w i t h c o o l a n t f l o w r a t e s lower than those f o r the counter-current system, con v e r s i o n s o f comparable magnitude can be o b t a i n e d , which, though they r e s u l t i n higher c o o l a n t temperature r i s e s , are s t i l l l e s s than those f o r co-current systems. Furthermore, although t h i s study i s i n terms o f a p a r t i c u l a r system, w i t h o n l y adjustment i n the coolant f l o w paths, f u r t h e r f l e x i b i l i t y i s p o s s i b l e by a s u i t a b l e choice o f the p o s i t i o n o f the b a f f l e s , but t h i s must be regarded as a design r a t h e r than an o p e r a t i o n a l v a r i a b l e . The need to i n t r o d u c e some co-current flow f o r the c o o l a n t , d e s p i t e i t s unfavourable e f f e c t on the s i z e o f the r e a c t o r i s to ensure t h a t the r e s u l t i n g a x i a l temperature p r o f i l e i n the tubes i s f l a t t e r , and so cause the thermal l o a d i n g t o be more evenly d i s t r i b u t e d along the l e n g t h . This i s an important advantage o f the mixed flow arrangement. The d e t a i l e d model must be solved to i d e n t i f y the tube which i s s u b j e c t t o the g r e a t e s t r i s k o f damage, however. U n f o r t u n a t e l y , i t i s not always p o s s i b l e t o assume i t w i l l be the same one, as the o p e r a t i n g c o n d i t i o n s change. Once i d e n t i f i e d , the i n f o r m a t i o n can be summarized i n diagrams such as f i g u r e 5. Other p l o t s can a l s o be prepared which g i v e v a l u a b l e i n f o r m a t i o n regarding the i n f l u e n c e o f the coolant flow r a t e parameter, GG ( 0 . Conclusions A comparison o f co- and c o u n t e r - c u r r e n t l y cooled has demonstrated t h a t , although co-current f l o w has some advantages, the temperature r i s e o f the coolant i s g r e a t e r , because o f t h e lower f l o w r a t e s which are p o s s i b l e . There i s a l s o g r e a t e r scope f o r a d j u s t i n g o p e r a t i n g c o n d i t i o n s . Using a mixed f l o w
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
18.
M C G R E A V Y A N D DUNBOBBIN
system, however, i t low coolant pumping temperature r i s e s . d i s t r i b u t i o n can be greater operational
Flexibility of Multitubular Reactors
223
i s p o s s i b l e t o take advantage o f r e l a t i v e l y c o s t s (lower flow rates) w i t h o u t excessive A t the same time, a more even temperature achieved w i t h t h e a d d i t i o n a l b e n e f i t o f flexibility.
Nomenclature A°
= Arrhenius pre-exponential f a c t o r .
Β
=
b C ,
= =
Q
B C
ο radius o f p e l l e t reference concentratio respectively. s p e c i f i c heats o f f l u i d and coolant
C , C = ρ pc D
=
p
Ε e, e h g K
g
L L
c D
D L M c R R r s
=
f l u i d t o p e l l e t mass t r a n s f e r c o e f f i c i e n t ,
=
diameter o f tube bundle,
=
distance between b a f f l e p l a t e s .
= length o f r e a c t o r tube. = mass f l o w r a t e o f coolant, = =
r e a c t o r tube r a d i u s . gas constant.
V(2t))
= 0exp(=
= =
(Sh /2 - 1) P c o o l a n t , f l u i d and p e l l e t respectively. o v e r a l l f l u i d t o coolant heat t r a n s f e r c o e f f i c i e n t , f l u i d a n d coolant i n t e r s t i t i a l v e l o c i t y r e s p e c t i v e l y .
p,
=
d e n s i t y o f f l u i d and coolant
φ
= heat o f r e a c t i o n , = Q exp (-1/(2T)).
t T
effective radial diffusivity within catalyst pellet.
= a c t i v a t i o n energy o f r e a c t i o n . = voidage o f f i x e d bed and tube bundle r e s p e c t i v e l y . = p e l l e t t o f l u i d heat t r a n s f e r c o e f f i c i e n t , = tanh ( r ) . = effective i n t e r s t i t i a l radial conductivity i n f l u i d phase. = thermal c o n d u c t i v i t y o f c o o l a n t .
c
f
k
respectively,
c
9
T
f
9T
A
=
c
U u, u
θ
p
c
T
e
m
e
r
a
t
u
r
e
=
V(A/D ).
=
1.5 S h
o
f
respectively.
p
A
( r - g)/ ( φ
2
(sg + r ) )
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
224
Dimensionless B
Groups D
C R
0
=
("ΔΗ)
C
=
concentration =
p
q
/(2bhE).
g
cVC . Γ
_ G
m
=
ο
C c pc
4nK e f
L
B
GG
= G /G c c reference
G
2
=
(1 - e) L D / ( b ue)
G
3
=
R
G
4
=
(1 - e) 3hL/(bpue C )
Nu w
=
RU/(K^ e ) . f
Nu * w
=
4 Nu / ( 4 + Nu ) w w
9
; G . = 98.25. c reference
2
p
2
up C / ( L
Sh = 2bkg /D A Ρ Τ, T , t = f l u i d , coolant and p e l l e t temperature r e s p e c t i v e l y , T R/E, T R^/E, T R^/E. A
f
ζ
=
c
p
A x i a l position i n reactor.
Literature Cited 1. 2. 3. 4. 5. 6. 7. 8.
Dunbobbin, B.R. Ph.D. Dissertation, University of Leeds (1976). Adderley, C.I. Ph.D. Dissertation, University of Leeds (1973). Thornton, J . M . Ph.D. Dissertation, University of Leeds (1970). Paris, J . R . and Stevens, W.F. Fourth European Symposium on Chemical Reaction Engineering, Brussels (1968), 73, Pergamon Press (1971). Brusset, H. et al, Chem.Eng.Sci. (1972), 27, 1945. Calderbank, P.H. et al. Fourth European Symposium on Chemical Reaction Engineering, Brussels (1968), 93 Pergamon Press (1971). Stewart, W.E. and Sorensen, J . P . F i f t h European/Second International Symposium on Chemical Reaction Engineering, Amsterdam (1972), B8-75. McGreavy, C. and Adderley, C.I., Chem.Eng.Sci. (1973) 28, 577.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
19 Pore Plugging Model for Gas-Solid Reactions J A M E S W . C H R O S T O W S K I and C H R I S T O S G E O R G A K I S Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, M A 02139
In the past few models have been propose account for the interactions between k i n e t i c and d i f f u s i o n a l resistances i n g a s - s o l i d reactions (1-7). Most of the proposed models are categorized as grain models which assume the reactant s o l i d e x i s t s i n the form of small grains dispersed uniformly throughout the volume of the s o l i d p a r t i c l e . In the most general of these models (3,5), three major resistances are taken into account: a) d i f f u s i o n a l resistance through the pores of the p a r t i c l e , b) d i f f u s i o n a l resistance through the s o l i d product and c) k i n e t i c resistance. S o l i d - s o l i d d i f f u s i o n and v a r i a t i o n of grain size and porosity with conversion were allowed i n (6). An important g a s - s o l i d reaction for which porosity decreases with time of exposure to the reactant gas i s the absorption of SO by calcined limestone (CaO) or dolomite (CaO/MgO) to produce calcium sulfate (CaSO or CaSO /MgO), which has a larger molar volume than the reactant s o l i d . If d i f f u s i o n a l l i m i t a t i o n s i n the pores are important, the porosity decrease w i l l be greater near the surface of the s o l i d p a r t i c l e and pores w i l l plug, l i m i t i n g access to part of the reactant s o l i d . As a consequence, conversion w i l l be less than 100 per cent. Hartman and Coughlin (5) extended previous grain models to account for such porosity changes. They were able to predict that the maximum amount of conversion can be less than 100 percent and compared t h e i r model's p r e d i c t i o n with t h e i r experimental data for the reac t i o n of S O with limestone. However, they only account ed for average porosity changes. In order to examine i n more d e t a i l the effect of l o c a l porosity changes and q u a n t i t a t i v e l y account for pore plugging, Georgakis et a l . (8_) and quite indepen dently Ramachandran and Smith (1) focused attention on 2
4
4
2
© 0-8412-0401-2/78/47-065-225$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
226
a s i n g l e pore. In t h e p r e s e n t communication, a b r i e f d e s c r i p t i o n of t h e pore p l u g g i n g model i s p r e s e n t e d and i t s d i f f e r e n c e s w i t h t h a t o f Ramachandran and Smith (7) a r e examined. An a n a l y t i c a l c a l c u l a t i o n o f t h e time r e q u i r e d t o p l u g t h e pore i s p r e s e n t e d . In a d d i t i o n , a p e r t u r b a t i o n s o l u t i o n f o r s m a l l times i s used t o m o t i vate the formulation of a s e m i a n a l y t i c a l v e r s i o n of the c o l l o c a t i o n method f o r two p o i n t boundary v a l u e problems w i t h s t e e p c o n c e n t r a t i o n p r o f i l e s . 1.
Pore P l u g g i n g Model
In o r d e r t o examine t h e i n t e r p l a y between k i n e t i c and d i f f u s i o n a l r e s i s t a n c e r e a c t i o n s when t h e (e.g., CaSC>4) i s l a r g e r than t h e molar volume o f t h e r e a c t a n t s o l i d (e.g., CaO), a t t e n t i o n i s f o c u s e d on a s i m p l e case o f a c y l i n d r i c a l pore o f i n i t i a l r a d i u s and l e n g t h L ( F i g u r e l a ) . As gaseous r e a c t a n t (e.g., SO2) i s absorbed t o form a p r o d u c t l a y e r o f C a S Û 4 , t h e geometry o f t h e pore changes w i t h time ( F i g u r e l b ) . A f t e r some time t h e pore mouth w i l l p l u g and r e a c t i o n w i l l cease. Assuming i s o t h e r m a l c o n d i t i o n s and n e g l e c t i n g b u l k f l o w , r a d i a l c o n c e n t r a t i o n g r a d i e n t s i n t h e pore and e x t e r n a l mass t r a n s f e r r e s i s t a n c e , t h e f o l l o w i n g d i m e n s i o n l e s s form o f t h e pore p l u g g i n g model i s d e r i v e d (13 ). a. Pore D i f f u s i o n
6
ft
(
g
l
c
)
=
fe
1 < 3
1 ^1 ^ D
)
]
+
2 σ α
χ
< '^
(D
where G(x,t)
= g
±
υ
(g
l f
t)
(2)
and w i t h t h e f o l l o w i n g i n i t i a l c(x,0) b.
= 0; c ( l , t )
Product
σ 3t
r 3r
Layer
1
and boundary c o n d i t i o n s
= 1; c ( 0 , t ) = 0
(3)
x
Diffusion (4)
}
dr
with the f o l l o w i n g i n i t i a l
and boundary c o n d i t i o n s
Ô(x,0)=0; c ( g t ) = c ( x , t ) ; - 6 ( g , t ) = K c ( g , t ) 1
r
2
2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
(5)
CHROSTOwsKi A N D GEORGAKis
Pore Plugging Model
CAO
Ό
CAO
-so
2
h a)
Initial Pore Geometry
b)
Pore Geometry after tome reaction has occured (t>0)
Figure 1. Geometric changes of cylindrical pore because of the large molar volume of solid product
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
228 c.
R e a c t i o n F r o n t Change
3g I
= I
6
(g ,t)
with g (x,0) = 1
2
(6)
2
and the f o l l o w i n g e q u a t i o n r e l a t i n g the i n t e r f a c e t o the s o l i d - s o l i d i n t e r f a c e g\ = α +
(l-a)g
gas-solid
(7)
2
D e f i n i t i o n o f a l l symbols i s g i v e n i n the N o t a t i o n section. S i n c e the v a l u e o f β i s u s u a l l y q u i t e s m a l l , the pseudo-steady-state hypothesis i s j u s t i f i e d with r e s pect to t h e ^ d i f f u s i o n a solved f o r c(r,x,t 1 + Kg ln(g /r) c(r,x,t) = c(x,t) χ Kg ln(g / ) 2
2
( 8 )
+
2
Then the o v e r a l l model reduces 3 9x
2 3c ^ l ^ l * ^
2
g i
to g
=
2
σ
Κ
2^ Kg ln(g /
1 +
2
2
w i t h boundary c o n d i t i o n s g i v e n by eq.
3t~ " 2
1 + Kg ln(g / 2
2
g i
)
9
( χ 2
g i
(9)
)
( 3 ) , and
'
0 )
"
1
(10)
Here the d i m e n s i o n l e s s d i f f u s i o n c o e f f i c i e n t D(g^) assumed t o depend on g^ i n the f o l l o w i n g way D(g ) x
= Vg^d
is
(11)
+ Vg ) ±
s i n c e Knudsen d i f f u s i o n i s t a k e n t o be e q u a l l y impor t a n t as m o l e c u l a r d i f f u s i o n . Ramachandran and Smith (7_) r e c e n t l y p r e s e n t e d a s i m i l a r model, but assumed t h a t the d i f f u s i o n c o e f f i c i e n t i s not changing as the geometry o f the pore changes. 2.
A n a l y t i c a l E v a l u a t i o n o f the P l u g g i n g Time
I f a t t e n t i o n i s f o c u s e d on the changes t a k i n g p l a c e a t the mouth o f the pore (x = 1) where the 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 i s u n i t y , eq. (10) l e a d s t o dg (l,t) £ dt 2
=
, ± 2 1+
± Kg ln(g / 2
2
(12) g i
)
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
v ±
;
19. CHROSTowsKi A N D GEORGAKis Eq.
(12)
can be
Pore Plugging Model
integrated to
229
yield 2
g
(g
- i) + f
2
{g
l n
g
2
+
l
n
g
2
l
}
=
t
/
2
( 1 3 )
where g and g imply g , ( l , t ) and g ( l , t ) . A t the t i m e , t p , t n a t the pore mouth w i l l p l u g , g-^ becomes z e r o . L e t t i n g the c o r r e s p o n d i n g v a l u e o f g be denoted by w from eq. (7) i t f o l l o w s t h a t 1
2
2
2
g?
= w
2
( 1 4 )
= -2^.
^2
α - 1
Then eq. (13) t = 2(w
can be - 1)
r e a r r a n g e d so
that
which g i v e s the d i m e n s i o n l e s s time r e q u i r e d t o p l u g the p o r e as a f u n c t i o n o f the d i m e n s i o n l e s s parameter K. 3.
Perturbation
S o l u t i o n f o r S m a l l Times
In o r d e r t o o b t a i n a n a l y t i c a l s o l u t i o n s f o r the n o n l i n e a r model g i v e n i n s e c t i o n 1, v a l i d f o r s m a l l t i m e s , a T a y l o r s e r i e s e x p a n s i o n i s assumed f o r g (x,t): 2
2
g ( x , t ) = 1 + t h ( x ) + t h ( x ) + ... 2
x
I t then f o l l o w s
(16)
2
that
g^Xjt) = 1 +
(1 - o O t h ^ x ) + ...
(17)
and 1 + Kg ln(g / 2
provided
2
g i
t h a t aKt
)
= 1 - aKth.(x) " " " l
<<
1.
A
a
D
By
l
ν
2
= g D(
9 ι
=
assuming
g i
) =
Τ~+Ύ
l
l
S i m i l a r l y i t follows
2
Η( )
u
( 1
+
D
2
that
ή
^
± D
,
(α - 1)
l (
±
l
-
+
D t 2
h l
)
ϋ
that
c(x,t) = c (x) Q
+ tc-^x)
eq. (9) r e s u l t s i n the v a l u e problems
+ ...
(18)
f o l l o w i n g t w o - p o i n t boundary
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
230
d
C
0 —γd 2
2 = φc
°l
2 φ = 2Ko/D
0
2
i;
c (0)=0; c ( l ) = l Q
(19)
0
d
2
h
l
d
c
0
αχ c^(0)=0;
c (l)=0 1
By making s i m i l a r s u b s t i t u t i o n s i n eq. (10) d e s c r i b i n g the r e a c t i o n f r o n t change, i t f o l l o w s t h a t d
2
-[1+th, ( x ) + t h ( x ) 0
which l e a d s t o h^x)
= j c (x); Q
Equations
(19) and
2
h (x)
= |[2 (x)-aKc (x)]
2
(20) can now
CQ(X)
=
c (x)
=8^+6^
(21)
C l
be s o l v e d t o g i v e
cosh<J)x/cosl^
(22)
and 1
coshφx
+ B
2
cosh2x
(23)
with
B
o
=
—'-h:
(1_αΚ)
i
B
=
4 cosh Φ
/ ~ It
~ ^ Ε Φ 1 1 ψ
4 cosh φ
Β, = ( 2 D l - a K ) ° °
5 ΐ ΐ 2 φ
2+
<
2
2 4 )
12 cosh φ By u t i l i z a t i o n
o f eq.
(21) one
writes
g (x,t) = l+|c (x)t+J[2c (x)-aKc (x)h (x)]t 2
0
1
( )
2
(25)
1
and a t χ = 1 g ( l , t ) = 1 + | t - J aKt (26) The above approximate s o l u t i o n s f o r the c o n c e n t r a t i o n p r o f i l e s as w e l l as the v a r i a t i o n o f g i and g w i t h time w i l l be a c c u r a t e when the v a l u e o f Κ i s s m a l l which i m p l i e s t h a t k i n e t i c r e s i s t a n c e i s d o m i n a t i n g . 2
2
2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
19. CHROSTOwsKi A N D GEORGAKis
Pore Plugging Model
231
When k i n e t i c r e s i s t a n c e i s n o t d o m i n a t i n g , t h e f u l l set o f e q u a t i o n s (9) and (10) need be s o l v e d numerically. 4.
Comparison w i t h E x p e r i m e n t a l F u l l y C a l c i n e d Limestone
Data f o r S u l f a t i o n o f
The pore p l u g g i n g model f o r g a s - s o l i d r e a c t i o n s g i v e n by e q s . (9) and (10) i s i n t e g r a t e d n u m e r i c a l l y by t h e use o f o r t h o g o n a l c o l l o c a t i o n s (9). The v a l u e s of c, g]_, g , a r e e v a l u a t e d a t t h e c o l l o c a t i o n p o i n t s as f u n c t i o n s o f time. In o r d e r t o e v a l u a t e c o n v e r s i o n as a f u n c t i o n o f time, an o u t e r r a d i u s , r , i s d e f i n e d so t h a t f o r each pore t h e volume o f t h e a v a i l a b l e s o l i d reactant i s give 2
Q
of
r
i s chosen so t h a t t h e i n i t i a l 2 2
by
e =r /r . 0
Q
solid
Then t h e l o c a l c o n v e r s i o n o f r e a c t a n t
w
i s g i v e n by ο
- r,
y(x,t) =
1
r and
p o r o s i t y i s given
2
( g ( x , t ) - 1)
(27)
- r, w (
t h e o v e r a l l c o n v e r s i o n by
Y(t) =
y ( x , t ) d x =• 2
(γ -ΐ) where γ = 1//ε^.
(
g (x,t)dx-l) 9
(28)
Ramachandran and Smith (1) assumed t h e s u r f a c e a r e a p e r u n i t volume o f t h e pore, g i v e n by ^ Q / 2 , i s e q u a l t o t h a t o f t h e s o l i d p a r t i c l e s from which t h e experimental data are obtained. Furthermore t h e e f f e c t i v e l e n g t h o f t h e p o r e L i s chosen so t h a t t h e T h i e l e modulus a t z e r o time g i v e n by eq. (19) i s e q u a l to t h a t c h a r a c t e r i z i n g r e a c t i o n and d i f f u s i o n i n a sphere o f r a d i u s R w i t h f i r s t o r d e r k i n e t i c s . I t then follows that r
o =
2 v
g
/ s
g
L
=
R / 3 / E
o
( 2 9 )
The a d d i t i o n a l parameters t h a t remain t o be d e f i n e d i n the s i n g l e pore model a r e k and D . The r a t e c o n s t a n t can be e s t i m a t e d from i n i t i a l r e a c t i o n r a t e d a t a and the a p p r o p r i a t e v a l u e o f D determined by matching t h e above model t o a c t u a l e x p e r i m e n t a l d a t a . The pore p l u g g i n g model p r e d i c t i o n s a r e now com pared w i t h e x p e r i m e n t a l d a t a o b t a i n e d by Hartman and C o u g h l i n (6^,10) on t h e s u l f a t i o n o f c a l c i n e d l i m e s t o n e . s
g
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
232
CHEMICAL
REACTION
ENGINEERING—HOUSTON
R e a c t i o n c o n d i t i o n s and p e r t i n e n t stone p r o p e r t i e s a r e l i s t e d below: T=1123°K;
P=l atm;
ε =0.535;
r =l.02xl0" cm;
Λ
0
C =3.147xl0~ gr-mole/cm (0.29%S0 ); 8
3
0
4
0 A
R =2.82x10" Ρ
cm;
a=3.09.
From t h e i n i t i a l r a t e d a t a and e f f e c t i v e pore p r o p e r t i e s , t h e f o l l o w i n g s i n g l e pore parameters a r e estimated. r
=1.39x10
-4
L=l.284x10
cm;
-2
cm;
k=0.10cm/sec
P r e d i c t i o n s o f t h e pore p l u g g i n g mode f o r d i f f e r e n t v a l u e s o f D and k a r e compared w i t h t h e e x p e r i mental d a t a i n F i g u r e s ( 2 ) and ( 3 ) r e s p e c t i v e l y For t h i s p a r t i c u l a t i c a l conversion ( i . e . mated t o be 5 5 p e r c e n t ; t h e maximum c o n v e r s i o n ob t a i n e d e x p e r i m e n t a l l y was o n l y 4 4 p e r c e n t . P r e d i c t i o n s of t h e pore p l u g g i n g model a r e seen t o be m o d e r a t e l y a c c u r a t e e x c e p t f o r t h e upper l i m i t on c o n v e r s i o n . I t s h o u l d be n o t e d t h a t t h e s i n g l e pore model r e s u l t s g i v e n i n (7) compare more f a v o r a b l y w i t h t h e e x p e r i m e n t a l d a t a ; we have n o t been a b l e t o match t h e s e results. Ramachandran and Smith do n o t c o n s i d e r t h e v a r i a t i o n o f t h e pore d i f f u s i o n c o e f f i c i e n t w i t h changing pore r a d i u s ; however, f o r t h e c a s e s p r e s e n t e d i n F i g u r e s ( 2 ) and ( 3 ) , t h i s e f f e c t i s n o t s i g n i f i c a n t because pore d i f f u s i o n i s n o t l i m i t i n g u n t i l about 7 5 p e r c e n t o f t h e pore p l u g time i s r e a c h e d . s
5.
Perturbation —
C o l l o c a t i o n Method o f S o l u t i o n
F o r v a l u e s o f t h e p r o c e s s parameters t h a t y i e l d h i g h v a l u e s o f φ ( φ > 5 ) , t h e pore d i f f u s i o n a l r e s i s t a n c e becomes s i g n i f i c a n t and t h e method o f o r t h o g o n a l c o l l o c a t i o n s r e q u i r e s a v e r y l a r g e number o f c o l l o c a t i o n points i n order t o accurately c a l c u l a t e the r e s u l t i n g s t i f f concentration p r o f i l e s . In s e c t i o n 3, i t was shown t h a t a t time e q u a l t o z e r o t h e i n i t i a l c o n c e n t r a t i o n p r o f i l e was e q u a l t o coshcj)x/cosh(f>. In o r d e r t o improve c a l c u l a t i o n s f o r s t i f f p r o f i l e s f o r a l l times c ( x , t ) i s w r i t t e n as c(x,t) = c (x)u(x,t) where c (x) i s g i v e n by eq. (22) . eq. (23? i n t o eq. ( 9 ) y i e l d s f j χ
+
^ η η φ χ
+
1
(30) Introduction of
- j ^ l f * χ
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
19. CHROSTowsKi A N D GEORGAKis
Pore Plugging Model
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
233
234
CHEMICAL
F(g ) 2 2 + [φ -cf) DΊ H ( ) 2
g i
+
φίβηίιφ Htg,)
8
H
(
REACTION
g
3x
l
ENGINEERING—HOUSTON
}
]u = 0
(31)
w i t h i n i t i a l and boundary c o n d i t i o n s : g (x 0)=g (x 0)=l; 2
/
1
#
u(x,0)=l; u (0,t)=0; x
u(l,t)=l
(32)
In F i g u r e 4, c ( x , t ) p r o f i l e s a r e g i v e n f o r t h e case where φ = 2 K/D.^176 o b t a i n e d through t h e proposed p e r t u r b a t i o n / c o l l a c t i o n method w i t h o n l y 4 c o l l o c a t i o n points. E f f o r t s t o s o l v e e q s . (9) and (10) by t h e r e g u l a r c o l l o c a t i o n method f a i l e d t o g i v e a c c u r a t e r e s u l t s w i t h as many as 10 c o l l o c a t i o n p o i n t s . Accura cy was determined by examining whether n e g a t i v e concen t r a t i o n s , however s m a l l collocation point. 2
6.
Conclusions
A g e n e r a l i z e d g a s - s o l i d r e a c t i o n model f o r a s i n g l e pore was p r e s e n t e d . I t accounted f o r changes i n the pore geometry and d i f f u s i o n c o e f f i c i e n t when t h e molar volume o f t h e s o l i d p r o d u c t i s d i f f e r e n t from t h a t o f t h e s o l i d r e a c t a n t . The change w i t h time o f the r a d i u s o f t h e mouth o f t h e pore and t h e p l u g g i n g time were a n a l y t i c a l l y o b t a i n e d , and a q u a l i t a t i v e agreement w i t h e x p e r i m e n t a l d a t a was o b s e r v e d . A p e r t u r b a t i o n s o l u t i o n f o r s m a l l times was u t i l i z e d i n o r d e r t o i n t r o d u c e a n o v e l approach f o r t h e s o l u t i o n o f two p o i n t boundary v a l u e problem. T h i s new method c a l l e d p e r t u r b a t i o n / c o l l o c a t i o n method was found v e r y s u c c e s s f u l f o r h i g h v a l u e s o f t h e T h i e l e modulus where t h e r e g u l a r c o l l o c a t i o n method was found unsatisfactory. 7.
Notation ( l - e ) r ( w - l ) c V a; cm R
0
( l - e ) r g w l n w / 2 c V a ; cm R
B
R
a b c c c o n c e n t r a t i o n o f gaseous r e a c t a n t i n t h e pore; gr-mole/cm^
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHROSTOwsKi A N D GEORGAKis
Pore Plugging Model
T i m e ( minutes )
Figure 3. Pore plugging model prediction of the % total conversion change with time for different values of k. Same constants as in Figure 2 except k and D . s
0.40
0.50
0.60 Axial
Figure 4.
0.70 Distance,
0.80
0.90
1.00
X - Ζ /L
Steep axial concentration profiles for different times obtained by the perturbation/collocation method
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION
236
c
c o n c e n t r a t i o n o f gaseous r e a c t a n t i n s o l i d p r o d u c t l a y e r ; gr-mole/cm^ b u l k c o n c e n t r a t i o n o f gaseous r e a c t a n t o u t s i d e the p o r e ; gr-mole/cm^
B
D(g ) x
D
* (
ENGINEERING—HOUSTON
f
- i )
D^(f )/D 1
m
=
Vg^d+Vg^
(1/D + 1 / D „ ( f ) ) ~ l o v e r a l l d i f f u s i o n 1
χ
ΙΠ
J\
coefficien
χ 2
i n p o r e ; cm /sec molecular d i f f u s i o n
D m
9 ,
D (f) v
c o e f f i c i e n t of reactant
gas; cm^/sec Knudsen d i f f u s i o n c o e f f i c i e n t = 9700f /T/MW; cm /sec 1
z
W
D
K D
gaseous r e a c t a n s o l i d produc layer D°/D K m r a d i a l distance of the from t h e p o r e c e n t e r ; r a d i a l distance of the from t h e pore c e n t e r ;
g
V
/
f^ ±2
g
f /r
2
2
gas-solid interface cm solid-solid interface cm
0
H(g )
gjD(
k L MW r
r e a c t i o n r a t e c o n s t a n t ; cm/sec l e n g t h o f pore;cm m o l e c u l a r w e i g h t o f d i f f u s i n g gas; gr/gr-mole r*/r
r^
r a d i a l d i s t a n c e from t h e c e n t e r o f t h e pore;cm i n i t i a l pore r a d i u s ; cm
Rp
r a d i u s o f s p h e r i c a l p a r t i c l e ; cm
Τ
outer radius o f the s o l i d reactant a v a i l a b l e t o a g i v e n p o r e ; cm temperature; °K
x
t
g i
)
Q
t , / t
c
t*
time; s e c
t
characteristic
time =
C
t^
pore plugging
(1-ε )r /2kV_c a Κ U Κ 15 Ώ
t
t^/t
molar volume o f s o l i d p r o d u c t ;
V y V
R
n
time; s e c
V
c
A
(dimensionless
pore p l u g g i n g
time)
cm^/gr-mole 3 molar volume o f r e a c t a n t s o l i d ; cm /gr-mole l o c a l conversion o v e r a l l conversion
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
19. CHROSTOwsKi A N D GEORGAKis
Pore Plugging Model
Y χ w
maximum c o n v e r s i o n z/L /α/(α-1)
ζ
d i s t a n c e from t h e end o f t h e p o r e ; cm
237
a t time o f pore b l o c k a g e
Hellenic Letters (l-e )V b/(l-e )V a R
γ
r
w
/ r
p
p
R
0
initial
porosity
£p
microporosit
e
microporosity of reactant
R
Κ
r k/D 0
L 2 D
8.
r
solid
s
D
s/ 0 m
L i t e r a t u r e Cited
(1) Pigford, R.L., S l i g e r , G . , Ind. Eng. Chem. Process Des. Develop. (1973)12, 85. (2) Szekely, J., Evans, J . W . , Chem. Eng. Sci. (1970) 25, 1091. (3) Szekely, J., Evans, J . W . , Chem. Eng. Sci. (1974) 29, 630. (4) Sohn, H . Y . , Szekely, J., Chem. Eng. Sci. (1974) 29, 630. (5) Hartman, M . , Coughlin, R . , AIChE J. (1976) 22, 490. (6) Howard, J.B., Williams, G . C . , Ghazal, F . P . H . , "Mathematical Model of the Reaction Between S u l fur Dioxide and Calcine P a r t i c l e s , " F i n a l Report on Task No. 2 of HEW-NAPCA Services Contract No. CPA-22-69-44, Department of Chemical Engineering, Massachusetts I n s t i t u t e of Technology, September 1971. (7) Ramachandran, P . , Smith, J., AIChE J. (1977)23,353. (8) Georgakis, C. et al., "Modelling of F l u i d i z e d Bed Combustion of Coal" Quarterly Technical Progress Report to ERDA (No. 3) Nov. 1, 1976 Jan. 31, 1977, J . R . L o u i s , P r i n c i p a l Investigator, p. 145-187. (9) Finalyson, B . A . , "The Method of Weighted Residuals and Vanational P r i n c i p l e s " Academic Press, 1972. (10) Hartman, Μ . , Coughlin, R . , Ind. Eng. Chem. Process Des. Develop. (1974) 13, 248.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
20 Heat Transfer in Packed Beds of Low Tube/Particle Diameter Ratio A. G . D I X O N and W . R. P A T E R S O N Department of Chemical Engineering, University of Edinburgh, Edinburgh, Scotland D. L. C R E S S W E L L Systems Engineering Group, E . T . H . Zentrum, CH-8092 Zurich, Switzerland
1.
Introduction
In spite of much researc vant heat transfer parameters in packed beds and their subsequent estimation continue to provide challenging problems, especially so for beds having a small tube to particle diameter r a t i o , where so few experimental data are reported. The aims of this paper are as follows: (1) to rigorously evaluate homogeneous continuum models as applied to heat transfer in beds of low tube to particle diameter ratio (typically d / d - 5 - 1 2 ) . (2) to examine the effect of gas flow rate, particle size and conductivity on the estimated heat transfer parameters. (3) to progress towards a priori prediction of the important para meters by modelling the underlying heat transfer mechanisms. t
2.
p
Experimental Equipment and Procedure
The experimental apparatus is similar to that used by Gunn and Khalid (7), although temperature measurement is different. The bed consisted of two sections of internal diameter 70.8 mms, insulated at the plane z=0 by a sandwich of rubber and PVC gaskets (see fig. 1). Twelve thermocouples were inserted r a d i a l l y through the central PVC gasket to provide duplicate temperature measurements at six radial positions, distant 12,16,23,28,31 and 34 mms. from the central axis. Both sections were packed with similar s o l i d particles to provide a continuous length of packing. The experiments consisted of measuring the temperature distribution in the a i r stream leav ing the top of the packing in the heated section (b) for a range of gas velocities by means of 32 Cr/Al thermocouples (30 SWG) supported at 8 radial positions (r=9,11,13,18,24,29,31 and 33 mms) and at 90° intervals by a brass cross, similar to that used by ©
0-8412-0401-2/78/47-065-238$05.00/0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
20.
DIXON ET AL.
Heat Transfer in Packed Beds
239
deWasch and Froment (6J. The procedure was repeated for a range of bed heights. The temperature uniformity of the a i r stream entering the calming section (a) and of the heated wall (b) was checked by additional thermocouples. Altogether, 107 separate experiments were performed (plus several repeats) covering the range of variables shown in. Table 1.
Table 1 : Ranges of Experimental Variables
d
p
(mms)
12.,7 9..5 6..4 9.5
d /d t
p
^
(
i
f
ceramic beads k<-=0.23 w/m °K 5.6 5-35 35-535 5-25 7.5 65-375 3-25 11.2 45-275 mild steel spheres k~ = 38 w/m OK 7.5 75-470 5 - 25
3.
Some Important Overall Observations
Fig.
Typical measured radial temperature profiles are shown in 2. These show two particularly interesting features:
(1) There is a significant,but apparently random,variation of temperature with angular position. In some instances, this variation is comparable to the total radial temperature change. (2) There i s a reproducible "hump" in the radial temperature prof i l e roughly 0.5 dp from the wall. The hump i s particularly noticeable in shallow beds, but tends to be smoothed out with increasing depth. De Wasch and Froment (6J also observed a hump, although at a somewhat greater distance from the wall. N e i t h e r of these phenomena are accounted f o r by e x i s t i n g model s. 4.
Homogeneous Continuum Heat Transfer Models
We shall confine our study to homogeneous continuum models of heat transfer, since these have been the most widely used in practice. (A) The Axially Dispersed Plug Flow Model In this model the gross heat transfer behaviour is characterized by effective thermal conductivities k and k for heat transfer a
r
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTO
240
t=t
0
(unheated)
z<0
t=t
|z=0
w
(steam heated)
z>0
Figure 1.
Schematic description of test column
Figure 2.
Typical observed temperature profiles
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
DIXON ET
20.
Heat Transfer in Packed Beds
AL.
241
in the axial and radial directions,and a wall heat transfer coefficient hw,introduced to account for the increased thermal resistance of the wall region. Heat balances are required on both sections of the column and boundary conditions are needed at both ends and at the adjoining plane z=0. For the heated section, the heat balance takes the form of an e l l i p t i c P.D.E. p f r (0 7l?) a0 ( °) () A similar equation applies for the calming section i f we replace z>0 by z<0 and t by t . In the radial direction the equations are subject to the boundary conditions G
c
=
k
+
+
k
z>
]
c
f
= ^ = 0
/
at r=0
-k
/
(2)
3t
/ -K-ww <ν*ο>· ' Boundary conditions in the axial direction follow readily for the long calming section and the adjoining plane (z=0): h
t - t„ ·,
ζ» -
t -t,
%
c
c
r = R
z < 0
(3)
= ||
=0
;
(4,
Z
The boundary condition at the bed exit (z=L) is much less certain. If the bed were long we might use the condition t-t ;
z + +~
w
(IBC)
(5)
as was done by Gunn and Khalid (7). However, in many of our experiments the beds were necessarily quite short ( L « 5 0 dp), otherwise i t would have been impossible to observe significant radial temperature gradients. In these cases, an alternative condition would be §~ = 0
z=L
5
(FBC)
(6)
which assumes plug flow in the space above the packing. We have analyzed our data using both boundary conditions. For the i n f i n i t e bed boundary condition (IBC) the equations can be integrated to give for the test section (7) Vt
-
(__
) = Σ
\
0
n
2
0
where A
Bi(UA ) J ( ) 2
V
n=l A ( B i + a J . n
η
= (1+16
a
l
/ 6 Pe^ P e J r a 2
π
-Pe (A exp { — ι J (a ) °p a
n
1)2
}
ά
J
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
(7)
CHEMICAL REACTION ENGINEERING—HOUSTC
242 Gc dp Gc d Pe , Pe = —rf-— , ι » Ρ a r K κ a
Bi
(axial and radial Peel et numbers)
Γ
= h.R/k (wall Biot number), w r
y = r/R, 3 =
and a are the roots of c* ϋ ( α ) = Β ΐ n
n
For the t -t
Ί
η
η
(FBC), t h e s o l u t i o n becomes - Bi (1+A ) J ( a y )
A-l
-Pe exp i - - { A ρ
-
p e
a(
A
1
n
- )
z
a
Ë
+ η
(Β) The Plug Flow Model
(2L-z)-z}}}
(Pe ==•>)
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
w
r
w
r
w
Re
3
Re
7.3
The Axial Conductivity
(k ) a
The axial Peel et numbers (Pe ) are not well-determined; they f a l l within the range 0.2 + 0.05 to 1.0 + 0.5, in broad agreement a
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
250
CHEMICAL REACTION ENGINEERING—HOUSTON
Figure 7.
Correlation of effective radial conductivity data
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
20.
DIXON
ET
AL.
251
Heat Transfer in Packed Beds
rok
ο
ife
5*δ
3o75
N
Re
400
500
•
Figure 8. Correlation of wall biot number data
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
252
CHEMICAL REACTION ENGINEERING—HOUSTON
with the results of Votruba et al ( 1 4 ) , amongst others. There is no clear dependence on either particle diameter or material, but there does appear to be a tendency for k to increase with N R . More reliable estimates could be obtained only by devising a satisfactory method of taking measurements at the plane z = 0 . G
a
Summary An experimental evaluation of homogeneous continum models of steady state heat transfer in packed beds of low tube/particle diameter ratio has been carried out. It was found that both axial and radial conduction effects were important in such beds for N R £ 5 0 0 , which covers the flow range in many industrial reactors. Heat transfer resistance at the wall was significant, but of secondary importance. A model containing no adjustable parameters was developed for a priori prediction of the effective radial conductivity in terms of Reynolds number, particle size and conductivity. This model gave reliable prediction of the effects of these variables over a wide range. Measured radial temperature profiles contained significant, apparently random, angular variations and indicated the existence of a "hump", roughly 0 . 5 dp from the wall. Neither of these observations are predictable using existing heat transfer models. Nomenclature: (Symbols not defined in text) Cp G J J] k^j 0
specific heat kj/kg °C superficial mass flow velocity kg/m^ hr. zero-th order Bessel function, f i r s t kind. f i r s t order Bessel function, f i r s t kind. turbulent conductivity (based on unit solids area) w/m
Greek Symbols:
ε μ
bed voidage f l u i d viscosity
Dimensionless Groups:
Np Re Pe r
N
kg/m.hr.
= (yc /k ) = (GdpAi) = p
°C
m
Prandtl number Reynolds number Peel et number for radial dispersion of mass.
Literature Cited: 1. 2.
Coberly, C.A., Marshall, W.R., Chem. Eng.Prog. (1951),47, 141. Calderbank, P.H., Pogorsky, L.A., Trans. Inst. Chem. Eng.,
3. 4.
Yagi, S., Yagi, S.,
(1957) 35,
195.
Wakao, Ν., A.I.Ch.E.J. Kunii, D., A.I.Ch.E.J.
(1959), (1960),
5, 6,
79. 71
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
253
20.
DIXON ET AL.
5.
Agnew, J.B. Potter, O.E., Trans. Inst. Chem. Eng., (1970), 48, T15. DeWasch, A.P., Froment, G.F., Chem.Eng.Sci., (1972), 27, 567. Gunn, D.J., Dhalid, Μ., Chem.Eng.Sci., (1975), 30, 261. Paterson, W.R., Ph.D. Thesis, University of Edinburgh (1975). Argo, W.G., Smith, J . M . , Chem.Eng.Prog. (1953), 49, 443. Bernard, R.A., Wilhelm, R.H., Chem.Eng.Prog. (1950), 46, 233. Sehr, R.A., Chem.Eng.Sci. (1958) 9, 145. Kunii, D., Smith, J . M . , Α.I.Ch.E.J. (1960), 6, 71. DeAcetis, J., Thodos, G., Ind.Eng.Chem. (1960), 52, 1003. Votruba, J., Hlavacek, V . , Marek, M. Chem.Eng.Sci. (1972) 27 1845.
6. 7. 8. 9. 10. 11. 12. 13. 14.
Heat Transfer in Packed Beds
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
21 Catalyst Deactivation through Pore Mouth Plugging during Residue Desulfurization F . M . D A U T Z E N B E R G , J. VAN K L I N K E N , K . M. A . P R O N K , S. T . SIE, and J - B . W I J F F E L S * Koninklijke/Shell-Laboratorium, Shell Research B.V., Badhuisweg 3, Amsterdam, The Netherlands
I . Introduction Hydrodesulfurizatio hig metals content i s a commercial proposition today (1,2). Based on previous work of many investigators (e.g. ref. 3 through 9) Shell's major efforts were focussed on the development of a suitable cata l y s t , for which a better understanding of the ageing phenomena oc curring i n the catalyst p a r t i c l e was needed. The present paper deals with the development of a simple two -parameter model describing the deactivation behaviour of residue desulfurization catalysts. The validity of the model i s being checked against the results of a large number of experiments with a variety of catalysts, two feedstocks and under different opera ting conditions. II. Experimental A. Equipment and Test Conditions Most experiments were performed at a fixed standard temperature and pressure i n bench-scale equip ment (about 100 ml catalyst volume) provided with facilities for recycle of H S-free liquid product (recycle r a t i o : 10 volumes of l i q u i d product per volume of fresh feed). This mode of operation was adopted to ensure good catalyst wetting i n small-scale r e actors. It has been established that i n this way reproducible and meaningful results can be obtained. At the high recycle ratios applied, the kinetics of the system approach that of a continuous stirred-tank system. An essential feature of this system i s that the catalyst deactivates uniformly, i.e., catalyst properties are constant throughout the bed at any time during a run. This i s in contrast with the non-uniform deactivation occurring i n a plug flow reactor (fixed bed without recycle). In the l a t t e r system, a deactivation front gradually proceeds through the catalyst bed. In most experiments we used a space velocity of *+.35 kg fresh feed per kg catalyst per hour, while an exit gas rate of 250 NI H2 per kg fresh feed was maintained. In a few cases we used different laboratory test conditions. These differences have been indicated in the figures and tables. * Present address: Shell Internationale Petroleum Mij B . V . , The Hague © 0-8412-0401-2/78/47-065-254$05.00/0 2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
21.
DAUTZENBERG
ET AL.
Deactivation through Pore Mouth Plugging
255
Β
· Feedstocks P r o p e r t i e s o f the Caribbean long residue (Feed I ) and the Middle East long residue (Feed I I ) used as feed stocks i n these s t u d i e s are l i s t e d ir) Table I . C a t a l y s t s Commercial as w e l l as experimental c a t a l y s t s were t e s t e d . I n Table I I we have l i s t e d the compositions o f t h e various c a t a l y s t s . D e t a i l s on shaping and p r e p a r a t i o n a r e a l s o i n cluded i n t h i s t a b l e . C a t a l y s t A has been t e s t e d as 1.5-mm e x t r u dates, but a l s o as 0 . 5 - and 0.8-mm broken p a r t i c l e s . S i m i l a r l y , C a t a l y s t J was t e s t e d as 1.5-mm extrudates and as 0.8-mm p a r t i c l e s . Before t e s t i n g , a l l the c a t a l y s t s were p r e s u l f i d e d i n s i t u . I). C a t a l y s t A c t i v i t y I t has been found t h a t h y d r o d e s u l f u r i z a t i o n o f heavy g a s - o i l f r a c t i o n s i n fixed-bed o p e r a t i o n w i t h a l a r g e product r e c y c l e (simulate described as pseudo one-and-a-hal whereas vanadium removal can be described as pseudo f i r s t order i n vanadium c o n c e n t r a t i o n . We t h e r e f o r e used the f o l l o w i n g formula t o c a l c u l a t e c a t a l y s t a c t i v i t y f o r d e s u l f u r i z a t i o n and metal removal: --X—E.SV
k s III.
s
1.5
Ρ The Mechanism o f C a t a l y s t
Deactivation
A major problem i n t h e c a t a l y t i c h y d r o d e s u l f u r i z a t i o n of r e s i dual o i l s i s the d e a c t i v a t i o n o f the c a t a l y s t by m e t a l - c o n t a i n i n g a s p h a l t e n i c species i n the feed. As can be seen from the r e s u l t s of a t y p i c a l d e s u l f u r i z a t i o n experiment presented i n F i g . 1, t h e c a t a l y s t shows a r a p i d i n i t i a l d e c l i n e which i s attended w i t h a f a s t b u i l d - u p o f coke on the c a t a l y s t . A t a r e l a t i v e l y low c a t a l y s t age Θ, as d e f i n e d i n S e c t i o n IV, a s t a t i o n a r y coke l e v e l i s reached. In c o n t r a s t , t h e d e p o s i t i o n o f the i n o r g a n i c remnants o f the hydrocracked asphaltenes (mainly vanadium and n i c k e l s u l f i d e s ) continues and g r a d u a l l y clogs t h e pores i n t h e outer zone o f the c a t a l y s t p a r t i c l e s , as confirmed by e l e c t r o n microprobe analyses o f spent c a t a l y s t samples (see F i g . 2 ) . This causes a slow f u r t h e r l o s s i n d e s u l f u r i z a t i o n a c t i v i t y over a longer p e r i o d o f time. U l t i m a t e l y , the c a t a l y s t becomes t o t a l l y i n a c t i v e f o r d e s u l f u r i z a t i o n because the - s t i l l a c t i v e - inner core has become completely i n a c c e s s i b l e t o t h e s u l f u r - b e a r i n g molecules. IV. D e a c t i v a t i o n o f a S i n g l e C a t a l y s t P a r t i c l e Since t h e d e p o s i t i o n o f metal compounds determines c a t a l y s t l i f e we developed a model i n which we used the d e p o s i t i o n of metals as t h e p r i n c i p a l parameter t o d e s c r i b e t h e d e a c t i v a t i o n phenomena for equilibrium-coked c a t a l y s t . When coke d e p o s i t i o n becomes over-
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
256
PROPERTIES OF FEEDSTOCKS
UOP
Feed
I
II
Origin
Caribbean
M i d d l e East
distillation
%v a t %v a t
5 10 20 30 ho
2v a t
$v a t at %v a t
50 Density, Mol.
°C °C °C °C °C °C
315 337
Î423
372 koQ
**51 1*87
hh3 k&3
0.918i4
d 70A, g / m l
weight
Chemical
352 372 398
527
0.9183 1*88
analysis,
r
85. 88 1 158
%w o n f e e d #
V,
ppm w o n f e e d
Na, ppm w o n f e e d
208 7
81*.25 11.32
1*8 3
TABLE I I CATALYST PROPERTIES Catalyst r e f . no.
Composition
A Β
Support
Metal load %v on support
Particle size/shape
Bulk density
Co/Mo
1* 3/10.9
A1 0
il
0 78 g/ml
AI2O3
-
C
Ni/Mo
1+ 3/10.9
0 58 g/ml
D
Ni/Mo
k
Ε
Ni/Mo
k 3/10.9
0 65 g/ml
Sol-gel A1 0 Sol-gel A1 0 A1 0
F
Co/Mo
k 3/10.9
0 66 g/ml
A1 0
3
G
Co/Mo
U 3/10.9
0 72 g/ml
A1 0
3
H
Ni/Mo
k 3/10.9
0 58 g/ml
A1 0
3
I
Ni/Mo
k 3/10.9
0 58 g/ml
A1 0
3
J
Ni/Mo
2/16
0 58 g/ml
Si0 .Al 0
3
Κ
Ni/Mo
1/8
0 1*1 g/ml
Si0 .Al 0
3
L
Ni/Mo
2/16
0 hi o/ml
Si0 .Al 0
3
1.5 mm beads 1 .5 mm beads 1.5 mm extrudates 1 .5 mm extrudates 1.6 mm extrudates 1 .7 mm beads 1.7 mm beads 1.5 mm extrudates 1.5 mm extrudates 1 .5 mm extrudates
M
Ni/Mo
2/16
0 1*8 g/ml
Si0 .Al 0
3
Ν
Ni/Mo
2/16
0 U9 g/ml
Si0 .Al 0
3
0
Ni/Mo
2/16
0 U8 g/ml
Si0 .Al 0
3
Ρ
Ni/Mo
1/8
0 U8 g/ml
Si0 .Al 0
3
Q
Ni/Mo
1/8
0 kk g/ml
Si0 .AI2O3
R
Co/Mo
U.3/10.9
0 61 g/ml
A1
S
Co/Mo
3/10.9
1.5 mm extradâtes 0.8 mn extrudates 0.8 mm crushed beads 1.5 mm beads 1.5 mm extrudates 1.5 mm extrudates 1 .6 mm extrudates 1.7 mm beads 1.7 mm beads 1.5 mm extrudates 0.8 mm crushed extrudates 0.8 mm crushed extrudates 0.9 mm extrudates 1.2 mm extrudates 1.2 mm extrudates 1.2 mm extrudates 1.5 mm extrudates 1 .5 mm extrudates 1.5 mm extrudates
0 77 g/ml
Co/Mo
0 58 g/ml
A1 0
3/10.9
3/10.9
2
2
0 62 g/ml
Particle size/shape
Type
-
3
3
2
3
2
3
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2°3 2
3
partly dried gel partlydried gel partly dried g e l partly dried g e l 1 . 5 mm extrudates 1 . 5 mm extrudates
C a t a l y s t s A, B, and S have been commercially prepared. C a t a l y s t s C through I p l u s c a t a l y s t R have been prepared i n t h e l a b o r a t o r y on commercial supports.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
Deactivation through Pore Mouth Plugging
DAUTZENBERG E T A L .
DESULFURIZATION RATE CONSTANT, (ARBITRARY UNITS ) 100|-
2^
I
1
1
Ο
0.1
0.2
0.3
0.4
0.5
0.6
1
0.7
Figure 1. Hydrodesulfurization of a Caribbean long residue (feed I)
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
258
r u l i n g , the model cannot be used. This s i t u a t i o n may a r i s e w i t h a c a t a l y s t operating a t t o o low hydrogen p a r t i a l pressures. For sim p l i c i t y we t h e r e f o r e assume t h a t i n r e s i d u e h y d r o d e s u l f u r i z a t i o n (the i n i t i a l b u i l d - u p o f coke w i l l not be taken i n t o account) only two r e a c t i o n s take p l a c e i n p a r a l l e l : metal removal and hydrode s u l f u r i z a t i o n . S u l f u r i s removed as HgS and ends up i n the gas stream; the product o f the metal-removal r e a c t i o n i s a metal s u l f i d e t h a t i s deposited on the w a l l o f the c a t a l y s t pores. These metal s u l f i d e s reduce the o r i g i n a l d e s u l f u r i z a t i o n a c t i v i t y , but leave the metal-removal a c t i v i t y u n a f f e c t e d ; hence, new d e p o s i t s are formed on top o f o l d l a y e r s . As i n most r e s i d u a l feedstocks vanadium predominates over other metals, i t i s considered t o r e present t o t a l metals. Furthermore, both the d e s u l f u r i z a t i o n and the devanadization r e a c t i o diffusionall insid catalyst particle. According t o t h i s l i n e o f thought, the concentrations o f t h e metal-bearing compounds decrease towards t h e i n s i d e o f the c a t a l y s t p a r t i c l e , and thus t h e r a t e o f deposit formation i s highest p r e c i s e l y at the pore entrance. As time proceeds, new d e p o s i t s a r e formed on top o f o l d l a y e r s , i n c r e a s i n g t h e i r t h i c k n e s s . Thus, t h e pore r a d i u s i n the periphery o f the c a t a l y s t p a r t i c l e i s reduced. As the pore r a d i u s decreases (which means t h a t t h e surface area per u n i t pore volume i s e n l a r g e d ) , the metal-removal r e a c t i o n zone f u r t h e r recedes t o the outer surface r e g i o n o f the c a t a l y s t p a r t i c l e and a "diaphragm" o f metal s u l f i d e s i s constructed i n t h e mouths o f the pores. We w i l l now d e s c r i b e these e f f e c t s i n q u a n t i t a t i v e terms. At any p o i n t i n a pore*, t h e r a t e a t which the t h i c k n e s s o f the depos i t l a y e r increases (or the r a t e a t which the pore r a d i u s i s reduced) i s p r o p o r t i o n a l t o the volume deposited per u n i t surface area per u n i t time:
Since the vanadium c o n c e n t r a t i o n i s highest at t h e o u t s i d e o f the c a t a l y s t p a r t i c l e ( C ) , the pore r a d i u s a t t h e entrance r i s reduced f a s t e s t and, a f t e r i n t e g r a t i o n o f the above equation, i s given by: Q
r
=r.(l -Θ), ο
Q
(2)
ι
i n which r-[ denotes the pore r a d i u s o f the f r e s h c a t a l y s t . The " r e l a t i v e c a t a l y s t age" Θ, which c h a r a c t e r i z e s t h e degree o f d e a c t i v a t i o n o f the c a t a l y s t , i s then d e f i n e d by: (3) and i s n u m e r i c a l l y equal t o the f r a c t i o n o f the pore mouth r a d i u s blocked by m e t a l - s u l f i d e d e p o s i t s . * For reasons o f s i m p l i c i t y the pores a r e considered t o be c y l i n ders o f equal s i z e and c i r c u l a r cross s e c t i o n . In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
21.
DAUTZENBERG ET AL.
Deactivation through Pore Mouth Plugging
259
One has t o look the c a t a l y s t i n t o i t s pore mouth i n order t o t e l l i t s age. With a f r e s h c a t a l y s t * t h e pore mouth i s f u l l y open and 0 = 0 . As soon as 0 = 1, t h e c a t a l y s t has o b v i o u s l y d i e d through complete c l o s u r e o f the "diaphragm" o f metal d e p o s i t s . A c a t a l y s t t h a t i s exposed t o t h e f u l l metal c o n c e n t r a t i o n o f the feed (Cp) w i l l have a l i f e which we w i l l d e f i n e as t h e " m i n i mum l i f e " . The minimum l i f e t ime Tjflin i s found from eq. (3): r. rp
mm
-
f
1
k.C^.V^ F dep A c a t a l y s t t h a t i s i n contact w i t h a l i q u i d o f lower metal c o n c e n t r a t i o n s w i l l remain a c t i v e f o r a longer p e r i o d . Since the d e a c t i v a t i o nadium mole balance f o
^{Aff^rkC,
1. Ν
(5)
where 1 denotes the l e n g t h o f t h e pore measured from the outer surface o f t h e p a r t i c l e , l = x y , where y i s the s u p e r f i c i a l l e n g t h of the pore and τ the t o r t u o s i t y . D denotes the d i f f u s i o n c o e f f i c i e n t o f the vanadium-bearing molecules i n t h e pore. The curvature of the s h e l l i n which the metal removal takes p l a c e has been neglected f o r s i m p l i c i t y . For a f r e s h c a t a l y s t r = r £ and eq. (5) may be solved d i r e c t l y to y i e l d :
C =Cq
e
,
H
(6)
where φ i s the T h i e l e modulus d e f i n e d by: = TR
^
and R i s the c h a r a c t e r i s t i c p a r t i c l e r a d i u s . I f , now, expression (6) i s introduced i n t o eq. (1) we f i n d as a f i r s t approximation for the pore r a d i u s o f an aged c a t a l y s t : r=r.(l-0e
K
(7)
) ,
and i f i n t u r n t h i s expression i s introduced i n t o the vanadium balance ( 5 ) , the vanadium c o n c e n t r a t i o n i n s i d e the pores of an aged c a t a l y s t i s found a f t e r i n t e g r a t i o n as: ί
C=C je o
-φ£ R
+9(e
-2φ^ R
-e
-φ£ R
)
)j.
(8)
* Since we neglected the i n i t i a l "build-up o f coke t h i s r e f e r s t o a f i c t i t i o u s s t a t e o f t h e c a t a l y s t where coke has reached i t s steadys t a t e l e v e l , but where no s i g n i f i c a n t metals have been deposited yet, so t h a t the pores are considered t o be s t i l l f u l l y open, 0 = 0 . In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
260
By t h i s method o f p e r t u r b a t i o n u s i n g t h e r e l a t i v e c a t a l y s t age Θ as t h e p e r t u r b a t i o n parameter the equation f o r the r a t e o f change of the pore r a d i u s can be solved t o any d e s i r e d degree o f accuracy, together w i t h t h e mole balance o f t h e vanadium-bearing molecules over the pore. E x p r e s s i o n (8) i s an approximation f o r the exact pro f i l e n e g l e c t i n g terms o f order 0 and h i g h e r . The c o n c e n t r a t i o n on the o u t s i d e o f the c a t a l y s t p a r t i c l e C serves as a l i n k between the " i n s i d e " and the "outside happening". The e f f e c t i v e n e s s f o r metal removal o f the c a t a l y s t decreases w i t h i n c r e a s i n g age owing t o the p l u g g i n g o f the pore mouths. The e f f e c t i v e n e s s f a c t o r i s d e f i n e d as the r a t i o o f the r a t e o f metal removal f o r the aged c a t a l y s t t o t h a t f o r f r e s h c a t a l y s t : 2
Q
π Γ
ί
D
(
3 Î
)
1
= 0,
0=0
and can be c a l c u l a t e d d i r e c t l y from t h e s o l u t i o n (expressions (7) and (8)) t o give : η = m
1 -0
(10)
i f terms o f order 0^ and higher are neglected . V. Metal Removal and C a t a l y s t L i f e i n a (Simulated) Stirred-Tank Reactor The d e c l i n e i n metal-removal a c t i v i t y o f c a t a l y s t used i n s i mulated s t i r r e d - t a n k r e a c t o r experiments may now be evaluated u s i n g the vanadium weight balance: SV.(V
-V ) =η .k °.V (11 ) f Ρ m ν ρ I f the e f f e c t i v e n e s s f a c t o r i s approximated by n =1 - 0, expression (11) can be i n t e g r a t e d w i t h respect t o time u s i n g r e l a t i o n s (3) and (U) t o y i e l d : k k m
- i - = d τ . mm
+
_X-) e_i._X_.e sv sv
2
#
( 1 2
)
By means o f expressions (10), (11) and (12) i t can be d e r i v e d that the metal content o f t h e product ( f o r i n s t a n c e , Vp) as a f u n c t i o n o f the a c t u a l on-stream time t ( i n hours) i s given by: V
V ° .13)
V Ρ
mm
According t o eq. ( 1 3 ) , a p l o t o f (V^/Vp)^ against run time should be l i n e a r , which indeed proved t o be t r u e f o r a l l our experimental data obtained so f a r . F i g u r e 3 shows a few t y p i c a l examples. * From a more e l a b o r a t e s o l u t i o n we found n = 1 - 0 + -^0 up t o order 0 . As 0 values o f p r a c t i c a l i n t e r e s t are smaller than 0.5 (see s e c t i o n V ) , t h e simple s o l u t i o n represents an e x c e l l e n t ap proximation . 2
m
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
21.
DAUTZENBERG E T
AL.
Deactivation through Pore Mouth Plugging
ι [i
DIAMETRICAL LINE SCAN
0
200
400
600
800
1000
Figure 2. Electron-probe microanalyses of a deac tivated catalyst; semiquantitative vanadium and sul fur concentration profiles
OPEN SYMBOLS: CARIBBEAN LONG RESIDUE (FEED I ) CLOSED SYMBOLS: MIDDLE EAST LONG RESIDUE ( FEED H )
Δ Ne H
200
400
NL/Mo/AL 0 2
3
Ο Ν» Ν
NL/Mo/Si02-Al 0
•
Co/Mo/AL 0
Νβ Β
600
2
2
3
3
800 1000 RUN HOURS
Figure 3. Vanadium removal during hydrodesulfurization of Caribbean and Middle East long residues
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
261
262
CHEMICAL REACTION ENGINEERING—HOUSTON
From the i n t e r c e p t o f the p l o t w i t h the ordinate k ° can be c a l c u l a t e d , u s i n g the vanadium balance (eq. 11) at time zero: v
V o
£ _ sv 1»0 c v.-ν P Furthermore T £ 5 "the minimum l i f e t i m e , can now be c a l c u l a t e d from the slope of the l i n e a r p l o t . I t w i l l be c l e a r t h a t t h e r e l a t i v e c a t a l y s t age 9 can now be determined u s i n g expression ( 1 2 ) , i n t r o d u c i n g T i and k ° , two parameters which have been measured e x p e r i m e n t a l l y by f o l l o w i n g the vanadium content o f t h e l i q u i d product. Long before the c a t a l y s t has l i v e d through i t s a c t i v e p e r i o d the d e s u l f u r i z a t i o n a c t i v i t a p o i n t where f i n a l l y th y p r a p i d l y t o a very low l e v e l (point Β i n F i g . 2 ) . At t h i s p o i n t the c a t a l y s t has reached an age ( T g ^ T j ) which w i l l be r e f e r r e d t o as the s t a r t o f a c c e l e r a t e d d e c l i n e . As i l l u s t r a t e d i n F i g . U, a c a t a l y s t w i l l reach Tg^jj when the e f f e c t i v e n e s s f o r metal removal n has dropped t o 0 . 5 · I n F i g . h we have p l o t t e d the values o f n at T g ^ p f o r v a r i o u s c a t a l y s t s and t e s t s c o n d i t i o n s as a f u n c t i o n o f e x p e r i m e n t a l l y estimated T g ^ p from the d e s u l f u r i z a t i o n performance. On the b a s i s o f these obser v a t i o n s we used n 0 5 as a new d e f i n i t i o n of T g ^ j ) . For simulated s t i r r e d - t a n k experiments the f o l l o w i n g expression can then be d e r i v e d , which allows us t o c a l c u l a t e Tg^-p f o r d e s u l f u r i z a t i o n , u s i n g experimental metal-removal data: k
=
ν
f
m
n
m
n
v
m
m
m
SAD
mm
=
#
f
0.53
ii. • ^ 0.1U
V
f
Ρ
,15)
sv
V
The v a l i d i t y o f expression ( 1 5 ) , based on the c a t a l y s t poremouth plugging model, has been demonstrated i n many experiments performed w i t h Caribbean as w e l l as Middle-East long residues as feeds, i r r e s p e c t i v e o f the c o n d i t i o n s used. VI. E f f e c t o f M e t a l D e p o s i t i o n on the D e s u l f u r i z a t i o n A c t i v i t y According t o t h e proposed model the d e c l i n e o f the d e s u l f u r i z a t i o n a c t i v i t y o f a c a t a l y s t i s governed by t h e d e p o s i t i o n o f metals present i n the feed. Therefore i t i s expected t h a t c a t a l y s t d e s u l f u r i z a t i o n a c t i v i t y i s a f u n c t i o n o f the r e l a t i v e c a t a l y s t age Θ. This t h e s i s was t e s t e d f o r a set of experiments i n which the Caribbean long r e s i d u e (feed I) was processed over 1 .5-mm Co/Mo/ ΑΙρΟβ extrudates ( c a t a l y s t no. R) at v a r i o u s space v e l o c i t i e s , v i z . -lèïl 2 . 0 and 1.0 k g . k g - . h ~ . * In t h i s expression the more elaborate expression f o r n has been used. 1
1
m
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
21.
DAUTZENBERG
Deactivation through Pore Mouth Plugging
ET AL.
263
CARIBBEAN LONG RESIDUE ( FEED I )
Ο
MIDDLE EAST LONG RESIDUE (FEED H )
EXPERIMENTAL η
η
AT POINT Β
0.81-
®
SEE
FIG. 1
1.5
2.0 T
Exp.
Catalyst
Particle
SAO *
R
C
L
A
T
,
V
E
SCALE
Remarks
Ref.
Composition
diam., mm
1 2 3
A A A
C0/M0/AI2O3
0.5 0.8 1.5
granules granules Extr.
k 5
Β Β
C0/M0/AI2O3
0.8 0.8
Extr. Extr.
low-pressure experiment high-pressure experiment
6 7
C D
N1/M0/AI2O3 N1/M0/AI2O3
0.8
granules Beads
8 9
Ε F
N1/M0/AI2O3 C0/M0/AI2O3
1.5 1.5
Extr. Extr.
-
10
G
C0/M0/AI2O3
1.6
Extr.
11 12
H I
NÎ/M0/AI2O3 Ni/Mo/Al 0
1.7
Beads Beads
13
J J J J
Ni/Mo/Si02.Al203
K L M Ν 0 Ρ Q
Ni/Mo/Si0 .Al203 Ni/Mo/Si0 .Al 03 Ni/Mo/Si0 .Al 03 Ni/Mo/Si02.Al 03 Ni/Mo/Si02.Al203 Ni/Mo/Si02.Al203 Ni/Mo/Si02.Al 0
1U 15
16 17 18 19
20 21 22 23
Figure 4.
2
1.5
1.7
3
0.8
2
2
2
2
2
2
2
3
shape
-
-
SV =U.O kg.kg-1 .h-1 SV = h.O kg.kg-1.h-1
1.5 1.5
granules Extr. Extr. Extr.
0.8 0.8 0.9 1 .2 "1.2 1.3 1.6
granules granules Extr. Extr. Extr. Extr. Extr.
SV =U.O kg.kg-1.h-1 SV = U . 0 kg.kg-1. -1
1.5
h
Effectivity of vanadium removal at point B* for various catalysts and test conditions
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
264
For a l l three space v e l o c i t i e s we p l o t t e d (Vf/Vp)^ versus t and found s t r a i g h t l i n e s i n agreement w i t h eq. ( 1 3 ) from which we subsequently c a l c u l a t e d the i n i t i a l vanadium content, Vp° "the o v e r a l l f i r s t - o r d e r r a t e constant, k ° , and the minimum l i f e t i m e of c a t a l y s t s , T i . These were found t o be constant w i t h i n about 10 % which i s about the experimental u n c e r t a i n t y . We t h e r e f o r e conclude t h a t the pore-mouth plugging model i s u s e f u l as a t o o l t o p r e d i c t f o r i n s t a n c e TSAD at low space v e l o c i t i e s from experiments at r a t h e r h i g h space v e l o c i t y . Since we know the i n i t i a l vanadium i n product, Vp°, f o r each space v e l o c i t y and T j _ , we can c a l c u l a t e the r e l a t i v e c a t a l y s t age, Θ, as a f u n c t i o n of run time t u s i n g eq. ( 1 2 ) . In order t o compare the d e s u l f u r i z a t i o n a c t i v i t i e s on a common s c a l e , we w i l l define a r e l a t i v e catalys 5
v
m
n
9
m
1
s
k (0 S
n
(16)
=0.25)'
Since the i n i t i a l d e s u l f u r i z a t i o n r a t e constant i s r a t h e r d i f f i c u l t t o determine a c c u r a t e l y the d e s u l f u r i z a t i o n a c t i v i t y at 0 = 0 . 2 5 has been chosen as reference a c t i v i t y . For a l l t h r e e space v e l o c i t i e s we subsequently p l o t t e d the r e l a t i v e c a t a l y s t a c t i v i t y for d e s u l f u r i z a t i o n as a f u n c t i o n o f 0 (see F i g . 5 A ) . The f i g u r e shows t h a t i r r e s p e c t i v e of the space v e l o c i t y a p p l i e d the same p l o t i s obtained. Encouraged by these r e s u l t s , we analysed i n the same way runs performed at d i f f e r e n t pressures and temperatures. We a l s o compared d i f f e r e n t feedstocks. The r e s u l t s have been p l o t t e d i n F i g . 5 B through 5D. F i g u r e 5 c l e a r l y shows t h a t , although the pore-mouth plugging model does not provide a t h e o r e t i c a l expression f o r the dépendance of n on 0, i t i s p o s s i b l e t o d e r i v e a unique r e l a t i o n between η and 0, which appears t o be independent of space v e l o c i t y , p r e s s u r e , temperature and pressure. This not only confirms our t h e s i s , but i t a l s o demonstrates t h a t 0 i s the c o r r e c t l i f e parameter t o d e s c r i b e c a t a l y s t ageing behaviour. s
s
L i s t o f Symbols r = a c t u a l pore r a d i u s r = pore mouth r a d i u s r£ = pore r a d i u s i n f r e s h c a t a l y s t C = molar vanadium c o n c e n t r a t i o n , i n s i d e the pore C = i b i d , o u t s i d e the c a t a l y s t p a r t i c l e Cf = i b i d , i n the feed ^dep d e p o s i t i o n volume per mole vanadium k = f i r s t - o r d e r s u r f a c e r e a c t i o n r a t e constant f o r vanadium removal k = pseudo f i r s t - o r d e r r e a c t i o n r a t e constant f o r vanadium removal at r e l a t i v e c a t a l y s t age 0
m m m kmol.m-3 kmol.m-3 kmol.m-3 m^.kmol
Q
0
=
5-1
v
kg.kg"
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
DAUTZENBERG E T A L .
Deactivation through Pore Mouth Plugging
CATALYST: C o / M o / A l 0 2
CATALYST. Co/Mo/Al20 (NeB) FEED: MI DOLE EAST LONG RESIDUE ( FEED S ) 3
3
(Νδ R) FEED : CARIBBEAN LONG RESIDUE (FEED I) SYMBOL
WHSV, kq. kg. h"
Ο • Δ
1
EACH DIFFERENT SYMBOL REFERS TO A DIFFERENT PRESSURE
4.35 2.0 1.
0.0 0.2 0.4 0.6 0.8 1.0
0.0 0 2 0.4 0.6 OM 1X> θ
θ
Q Figure 5a. Relationship between relative catalyst activity for desulfurization and relative catalyst age. Runs at various space velocities.
b Figure 5b. Relationship between relative catalyst activity for desulfurization and relative catalyst age. Runs at different pres sures.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
266
CATALYST: Co/Mo/A 1^3 (N« S) FEED: CARIBBEAN LONG RESIDUE (FEED I) • STANDARD TEMPERATURE Δ ST. - 2 5 ° C Ο ST. - 4 5 ° C
Figure 5c. Relationship between rehtive catalyst activity for desulfurization and relative catalyst age. Runs at various tempera tures.
CATALYST: C o / M e / A ^ O g (Ne R) FEED: Ο CARIBBEAN L0M6 RESIDUE ( FEEO I ) Δ MIDOLE EAST LONG RESIDUE ( FEED S )
Figure 5d. Relationship between rehtive catalyst activity for desulfurization and relative catalyst age. Runs with different feed stocks.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
21.
DAUTZENBERG E T A L .
Deactivation through Pore Mouth Plugging
267
= pseudo 1 . 5 t h - o r d e r r e a c t i o n r a t e constant f o r s u l f u r removal at r e l a t i v e c a t a l y s t age Θ kg.kg- .h-1(?wS)-§ t = run time h Θ = r e l a t i v e c a t a l y s t age Tmin minimum l i f e t i m e o f c a t a l y s t h SAD c a t a l y s t age at the s t a r t o f a c c e l e r a t e d d e c l i n e h SV = space v e l o c i t y kg.kg" .h-1 Vf = vanadium content o f t h e feed ppm(w) Vp = vanadium content of t h e product at c a t a l y s t age Θ ppm(w) Sf = s u l f u r content o f the feed %w Sp = s u l f u r content o f t h e product a t c a t a l y s t age Θ %w n = c a t a l y s t e f f e c t i v i t y f o r metal removal n = relative catalys
k
s
1
=
T
=
1
m
f
s
Literature Cited (1) Van Ginneken, A.J.J., van Kessel, M.M., Pronk, K.M.A., and Renstrom, G . , O i l and Gas Journal, A p r i l 28, 1975, p. 59-63. (2) Yamamoto, M.D., Oil and Gas Journal, May 16, 1977 p. 146-165. (3) Hoog, H., K l i n k e r t , H . G . , and Schaafsma, Α., P e t r o l . R e f i n . , (1953) 32 (No. 5), 137. (4) Le Nobel, J.W., and Choufoer, J.H., 1st World Petroleum Congress (1959), Section III, p. 233 paper 18. (5) Van Zoonen, D . , and Douwes, C.Th., J. Inst. of P e t r . , (1963) 49 383. (6) Van Deemter, J.J., Proc. 3rd Eur. Synro. Chem. Reaction Eng., (1964) 215. (7) Larson, O.A., and Beuther, Η., Div. Petr. Chem. ACS Preprints, Pittsburg, (1966) B-95. (8) Newson, E. J., Div. Petr. Chem. ACS Preprints, Chicago, (1970) A141. (9) Moritz, K.H. et. al., Japan Petr. Inst. Fuel Oil Desulfurization Symposium Tokyo, Japan, March (1970).
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
22 Simulation of Thermal Cracking Furnaces H. A .
J.
VERCAMMEN
and
G.
F.
FROMENT
L a b o r a t o r i u m voor Petroehemische T e c h n i e k Rijksuniversiteit, K r i j g s l a a n 271, G e n t , B e l g i u m
Until now the simulation of a thermal cracking coil has g e n e r a l l y bee box by i m p o s i n g either a tube w a l l temperature profile or a heat f l u x profile. I t i s then checked a p o s t e riori whether or not the fire box p e r m i t s such p r o files to be attained. The fire box calculations gene rally proceed a l o n g the Lobo & Evans approach ( 1 ) , a l t h o u g h more recently zone methods have been applied, thus p e r m i t t i n g a temperature distribution in the fire box to be calculated ( 2 , 3, 4, 5 ) . In the work r e p o r t e d here the coil and the fire box were s i m u l a t e d s i m u l t a n e o u s l y by means of an o p t i m i z e d computer package in which the d e s i g n of the r a d i a n t s e c t i o n of the furnace i s an e x t e n s i o n and r e f i n e m e n t of Hottel's zone method ( 3 ) . In this paper the approach i s a p p l i e d to the s i m u l a t i o n of an i n d u s trial ethane c r a c k i n g f u r n a c e . The o n l y a d a p t a b l e parameter left i n the s i m u l a t i o n model is a burner d e s i g n factor, namely the fraction of the heat gene r a t e d i n the burner t h a t i s t r a n s f e r r e d to the burner cup. The parameter i s determined by matching the e x i t conversion. 1. C r a c k i n g c o i l d e s i g n
equations
The c o n t i n u i t y - , e n e r g y - and p r e s s u r e drop equa t i o n s f o r the t u b u l a r c r a c k i n g r e a c t o r are w e l l known : L dz
(1.1) 1=1
© 0-8412-0401-2/78/47-065-271$05.00/0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL
272
1 IF. c
dt dz
k
dp
P
t
k
]_ dv_ V dz 1
t
dz
P
with
ïïd Q(z)-
inlet
at
z=o
In
(1.1)
+
i
k
l
A
H
(1.2)
l
+
t "
=
r
ENGINEERING—HOUSTOÎ
J_ d t ζ t dz Ω β GA
i
(1.3)
F.=(F,) k k o
conditions
r
L Ω Σ 1=1
REACTION
T=T
o
and P = ( P ) t
parameters
A s e t o f r e a c t i o n s h a s t o be c o n s i d e r e d d i c t t h e p r o d u c t d i s t r i b u t i o n . The f o l l o w i n g m o l e c u l a r r e a c t i o n s was a d o p t e d : Order
C
2 6^ 2 4
H
C
H
6 ^ Î
H
C
2
C
H
2
+
H
4
+
4
•C H H 2 4" C H + 2 H , 0 >2C0+3H 2 ( H 0)
C
2
H
2
o
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H
H
2
H
+ H
' 3 6 2 •C H CH
3 8 2C H ^C 2 C
2
2
SV C
2 +
2
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2
4 +
Frequency Factor
4
4
(Kcal/Kmol).10 82
8. i o
1 2
67
7 .i o
1 3
76
1 .i o
1 3
104.6
5 .i o
1 3
1
-3
63 .3
3. 2 . 1 0
1 3
63
3 .2 . 1 0
1 1
45
4. i o
4
to pre s e t of
6
8 .i o
2 C H
0
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Table I r e a c t i o n scheme a n d k i n e t i c
Molecular
t
60
1 3
S i n c e t h e f e e d c o n t a i n e d some p r o p a n e t h e a b o v e scheme a l s o c o n t a i n s d e c o m p o s i t i o n r e a c t i o n s f o r t h i s com ponent . In (1.3) t h e symbol ζ stands f o r 0.0227R, +0.0847d . (1.4) 0.092 _R -0.2 + . D t t
A
e
R;
In (1.4) t h e a d d i t i o n a l bends of t h e h o r i z o n t a l ed f o r .
p r e s s u r e drop i n t h e r e t u r n c r a c k i n g c o i l a r e a l s o account
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
22. 2.
V E R C A M M E N AND
Fire
Thermal Cracking Furnace Simuhtion
FROMENT
box heat
273
transfer
2.1 Non r a d i a t i v e h e a t f l u x e s . The f u r n a c e c o n s i d e r e d i n t h i s work, s c h e m a t i c a l l y r e p r e s e n t e d i n F i g . 1, i s f i r e d by 60 r a d i a n t b u r n e r s , p l a c e d i n t h e s i d e w a l l s . A s m a l l f r a c t i o n only of t h e heat o f combustion i s t r a n s f e r r e d t o t h e r a d i a n t b u r n e r c u p i t s e l f . The major f r a c t i o n of t h e r e l e a s e d heat e n t e r s t h e f i r e box w i t h t h e c o m b u s t i o n gases t h r o u g h r a d i a t i o n and c o n v e c t i o n . The e x a c t v a l u e o f t h i s s p l i t , r e p r e s e n t e d by y , i s n o t g i v e n i n t h e t e c h n i c a l l i t e r a t u r e , however. I t w i l l , t h e r e f o r e , be t h e o n l y a d a p t a b l e p a r a m e t e r l e f t i n t h e d e s i g n model o u t l i n e d here. The s i m u l a t i o s e c t i o n . The c o n v e c t i v to t h e r e f r a c t o r y w a l l s i n t h a t s e c t i o n was c a l c u l a t e d by means o f t h e u s u a l c o r r e l a t i o n s ( 6 , 7, 8 ) . H e a t l o s s by c o n d u c t i o n t h r o u g h t h e r e f r a c t o r y w a l l s a n d b y n a t u r a l convection a t the outside of the furnace w a l l s was a l s o a c c o u n t e d f o r . 2.2 R a d i a t i v e h e a t t r a n s f e r . To o b t a i n a r e p r e s e n t a t i v e temperature d i s t r i b u t i o n i n the r a d i a n t sec t i o n o f t h e f u r n a c e t h e f i r e box and t h e o u t s i d e w a l l o f t h e c o i l w e r e d i v i d e d i n t o a number o f i s o t h e r m a l z o n e s a s shown i n F i g . 2. The s e t o f h e a t b a l a n c e s o n t h e z o n e s c a n be w r i t t e n c o n c i s e l y i n m a t r i x n o t a t i o n a s shown i n ( 2 . 1 ) . I n e a c h z o n e Z. ( v o l u m e o r s u r f a c e ) t h e n e t r a d i a t i o n captured i s equated to the n e t n o n - r a d i a t i v e f l u x l e a v i n g t h e z o n e Q!. The r a d i a t i v e f l u x f r o m Z. t o Z. i s g i v e n by. Ζ. Ζ . Ε . I w h e r e E.= 0 T . a n d w h e r e Z.i. i s t h e t o t a l excàaneâ a r e a b e t w e e n i . a n d Ζ., i n er . i ι . w o r d s t h e f r a c t i o n o f t h e h e a t r a d i a t i o n e m i t t e d b y Z. t h a t i s a b s o r b e d by Ζ. : ^ 1 .Ζ,Ζ z,z . . i -Σ z . z , 1 1 η 1 z z - Σ τ 7 .Ζ Ζη 2 1 ι 2' (2.1) z
z
2
¥. V l
2
Z
Ε
2
Z
n 2
2
Ζ Ζ -Σ η η i
Ζ .Ζ ι η
Ε
Ε η
The s o l u t i o n o f t h i s s e t o f e q u a t i o n s y i e l d s t h e t e m p e r a t u r e s i n t h e volume and s u r f a c e z o n e s . S i n c e t h e s e t i s n o n l i n e a r i t h a s t o be s o l v e d by i t e r a t i o n . A N e w t o n - R a p h s o n p r o c e d u r e was f o u n d t o be v e r y e f f i c i e n t for this. The t o t a l e x c h a n g e a r e a s a r e o b t a i n e d i n s e v e r a l
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
274
CHEMICAL
REACTION
ENGINEERING—HOUST(
Figure 1. Representation of thermal cracking furnace
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
22.
V E R C A M M E N AND
Thermal Cracking Furnace Simulation
FROMENT
275
s t e p s . The f i r s t s t e p i s t h e c a l c u l a t i o n o f t h e v i e w f a c t o r s i . e . t h e f r a c t i o n o f t h e r a d i a t i o n l e a v i n g an e m i t t o r t h a t i s e m i t t e d i n the d i r e c t i o n of a r e c e p t o r The m u l t i p l e i n t e g r a l s i n v o l v e d i n t h i s w e r e o b t a i n e d by M o n t e - C a r l o s i m u l a t i o n , b a s e d u p o n a s a m p l e o f 2 0 0 0 0 e m i t t e d beams. To p e r m i t t h e c a l c u l a t i o n o f v i e v f a c t o r s using other viewfactors obtained i n d i f f e r e n t M o n t e C a r l o i n t e g r a t i o n s and s t i l l a s c e r t a i n t h a t t h e sum o f t h e v i e w f a c t o r s f o r e a c h e m i t t o r e q u a l s o n e , Vercammen & F r o m e n t (9^) d e v e l o p e d a r e g r e s s i o n t e c h n i q u e e l i m i n a t i n g the i n h e r e n t s t a t i s tical errors. The v i e w f a c t o r s f ^ o b t a i n e d i n t h i s way are v a l i d f o r a d i a t h e r m i c medium o n l y The v i e w f a c t o r f between s u r f a c e zone f o l l o w s from : f = f X (2.2) J
* where by :
χ
.
d
.
.
i s t h e mean t r a n s m i s s i o n
.
.
coefficient,
given
S Γ
X
= j
max (2.3) X(S)
DDF(y)
dS
I n (2.3) τ(S) mm i s t h e t r a n s m i s s i o n f o r a beam h a v i n g a l e n g h t S and D D F ( y ) i s t h e d i m e n s i o n l e s s beam l e n g h t d i s t r i b u t i o n f u n c t i o n , w i t h y =(S-S . ) (S -S . )· mm max mm Vercammen and F r o m e n t (SO p r o p o s e d t h e f o l l o w i n g f o r m f o r DDF(y) : DDF (y ) = V y ( l - \ / y ) ( - l n y ) (a+by + c y + . . . )/n ! ( 2 . 4 ) T h i s f o r m has b e e n f o u n d t o be q u i t e c o n v e n i e n t f o r w i d e l y v a r y i n g c o n f i g u r a t i o n s of the s u r f a c e z o n e s . The t e m p e r a t u r e d e p e n d e n t t r a n s m i s s i o n c o e f f i c i e n t X (S) i s r e l a t e d t o t h e a b s o r p t i o n f a c t o r k* by : 9
n
z
(
-kS
2
·
5
)
R b
X(S) = e A c c o r d i n g t o E c h i g o e . a . (J_0) t h e mean a b s o r p t i o n t o r k* i s c a l c u l a t e d f r o m : -kS C_Au)(l-e
) =
r /
fac
- k ( ω )S (1-e
)d(0
(2.6)
When t h e v i e w f a c t o r i s m u l t i p l i e d by t h e s u r f a c e of the e m i t t o r the s o - c a l l e d d i r e c t exchange a r e a i s o b t a i n e d . The d i r e c t e x c h a n g e a r e a s b e t w e e n s u r f a c e z o n e s and v o l u m e z o n e s a r e c a l c u l a t e d f r o m t h o s e r e l a ted to a l l the s u r f a c e zones b o u d i n g the volume z o n e s , f i c t i t i o u s zones i n c l u d e d .
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL
276
REACTION
ENGINEERING—HOUSTON
The t o t a l e x c h a n g e a r e a t a k e s i n t o a c c o u n t t h e d i r e c t r a d i a t i o n , t h e a b s o r b e d r a d i a t i o n and i n a d d i t i o n m u l t i p l e r e f l e c t i o n on t h e s u r f a c e z o n e s ; M a t r i c e s o f t o t a l e x c h a n g e a r e a s w e r e s e t up f o r CO^ and H«0 a b s o r p t i o n b a n d s and a n o t h e r one f o r t h e d o m a i n i n t h e a b s o r p t i o n s p e c t r u m i n w h i c h no r a d i a t i o n was a b s o r b e d . The m a t r i c e s w e r e w e i g h t e d w i t h r e s p e c t t o the e m i t t e d energy a s s o c i a t e d w i t h the domain of the f r e q u e n c y s p e c t r u m b e i n g c o n s i d e r e d and summed up, y i e l d i n g t h e t o t a l e x c h a n g e a r e a m a t r i x shown i n ( 2 . 1 ) . 3.
Simulation
procedure
The s i m u l a t i o d i s c u s s e d h e r i limited th r a d i a n t s e c t i o n of th t a k i n g p l a c e . The s i m u l a t i o the f u r n a c e i s s t r a i g h t f o r w a r d . The s u b d i v i s i o n shown i n F i g . 2 y i e l d e d 110 i n d e p e n d e n t non z e r o v i e w f a c t o r s . F i f t y f o u r r e a l s u r f a c e zones were c o n s i d e r e d , t o g e t h e r w i t h 3 f i c t i t i o u s , h o r i z o n t a l s u r f a c e z o n e s and 4 v o l u m e z o n e s . O p p o s i t e p a r t s o f t h e s i d e w a l l s ( e . g . A. and C j ) a r e considérée t o be one z o n e o n l y . S e c t i o n s o r t h e two p a r a l l e l c o i l s l o c a t e d a t an e q u a l d i s t a n c e o f t h e i n l e t ( R j e.g.) are a l s o l u m p e d i n t o one z o n e . F i n a l l y , a 5 8 x 5 8 m a t r i x f o r t h e c a l c u l a t i o n o f t h e t o t a l e x c h a n g e a r e a s was ob tained . I t s h o u l d be a d d e d t h a t f o r t h e h e a t t r a n s f e r a s p e c t s t h e c o i l s w e r e s t r a i g h t e n e d t o i n c l u d e on e a c h s i d e h a l f o f t h e b e n d . The f u r n a c e l e n g h t was c o r r e s pondingly adapted. To i l l u s t r a t e t h e c a l c u l a t i o n p r o c e d u r e t h e com p l e t e m a t h e m a t i c a l m o d e l i s s u m m a r i z e d as f o l l o w s : φ
(
η *>
- Q =
φ γ
η
ν
(T
(3-D
n
Q
m ,h*,t±) = Q η' η' η ^n dF
ip(t,F,Q)
= If
( 3
2 )
' (3.3)
(3.5) (3.6)
= t* (3.7) η φ(h) = h* (3.8) η The f i r s t two e q u a t i o n s s y m b o l i z e h e a t b a l a n c e s f o r th< z o n e s a t t h e f l u e gas s i d e . The b a l a n c e s f o r t h e c o i l
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
22.
VERCAMMEN AND FROMENT
Thermal Cracking Furnace Simulation
s u r f a c e (3.1) c o n t a i n t h e heat f l u x e s to the r e a c t o r , r e p r e s e n t e d h e r e by Q t o d i s t i n g u i s h them f r o m t h e o t h e r f l u x e s , Q . The b a l a n c e s f o r t h e o t h e r s u r f a c e s and f o r t h e v o l u m e s ( 3 . 2 ) c o n t a i n t h e n o n r a d i a n t f l u x e s Q which a r e l i n e a r f u n c t i o n s of the temperature v e c t o r Τ a t t h e f l_ue g a s s i d e , so t h a t ( 3 . 2 ) c o u l d a l s o be w r i t t e n a s f ( T ) = 0. I n ( 3 . 3 ) t h o s e f l u x e s a r e r e l a t e d t o t h e f l u e g a s t e m p e r a t u r e s Τ , t o t h e mean tem p e r a t u r e s i n t h e c o i l s e c t i o n s , t± a n d t o t h e h e a t t r a n s f e r c o e f f i c i e n t s f o r t h e r e a c t o r w a l l s , h±. Equa tions (3.4)-(3.6) are the conservation equationsf o r the r e a c t i n g m i x t u r e i n s i d e t h e c o i l , a l r e a d y d e t a i l e d as ( 3 . 1 ) - ( 1 . 3 ) . E q u a t i o n s ( 3 . 7 ) a n d ( 3 . 8 ) a l o o w t * a n d h * t o be c a l c u l a t e d calculations i s give The s i m u l a t i o n p r o g r a m c o m p r i s e s a number o f m o d u l e s , g r o u p e d i n o v e r l a y p h a s e s . To s a v e c o m p u t a t i o n time t h e c a l c u l a t i o n o f t h e m a t r i x o f t o t a l exchange a r e a s was k e p t o u t o f t h e i n n e r i t e r a t i o n l o o p . T h i s d i d n o t s i g n i f i c a n t l y a f f e c t t h e speed o f c o n v e r g e n c e of t h e o u t e r i t e r a t i o n c y c l e . W i t h r e a l i s t i c starting e s t i m a t e s f o r Q. a n d Τ o n l y 5 t o 10 i t e r a t i o n s w e r e r e q u i r e d . The C.P.U. t i m e p e r i t e r a t i o n a m o u n t e d t o 50 s e c o n a S i e m e n s 4 0 0 4 - 1 5 0 , a m a c h i n e w h i c h i s 14 t i m e s f a s t e r t h a n t h e IBM 3 6 0 - 3 0 e . g . f
f
4. R e s u l t s The r e s u l t s o f t h e s i m u l a t i o n a r e g i v e n i n T a b l e I I a n d F i g . 4. As m e n t i o n e d a l r e a d y t h e o n l y a d a p t a b l e parameter i n t h e model i s t h e s p l i t f a c t o r y . T h i s f a c t o r was v a r i e d u n t i l l t h e s i m u l a t e d e x i t c o n v e r s i o n m a t c h e d t h e e x p e r i m e n t a l . The a g r e e m e n t o f t h e c a l c u l a ted p r o d u c t d i s t r i b u t i o n w i t h t h e i n d u s t r i a l r e s u l t s s i m p l y r e f l e c t s t h e r e l i a b i l i t y o f t i e k i n e t i c scheme of T a b l e I . T h e v a l u e , o f 0.076 f o r y i s c o n s i d e r e d t o be r e a l i s t i c . From t h i s v a l u e a b u r n e r cup t e m p e r a t u r e o f 1230°C was c a l c u l a t e d i n a g r e e m e n t w i t h i n d u s t r i a l v a l u e s . I n f u r t h e r s u p p o r t o f t h i s γ-value t h e e f f l u e n t gas t e m p e r a t u r e was f o u n d t o be 820°C, a s c o m p a r e d w i t h 830°C f o r t h e p l a n t . A l s o , t h e f l u e g a s t e m p e r a t u r e s are c l o s e t o t h o s e o b s e r v e d i n such a f u r n a c e . N o t i c e t h a t t h e f l u e gas t e m p e r a t u r e s a r e n o t t o o d i f f e r e n t b e t w e e n t h e f o u r h o r i z o n t a l v o l u m e z o n e s . The h e a t f l u x i s s e e n t o t e n d r a b i d l y f r o m £3Kcal/m sec to a con s t a n t v a l u e o f about 14Kcal/m s e c , a g a i n a p l a u s i b l e value. To c o n c l u d e a f l e x i b l e a n d r e l i a b l e m o d u l a r com puter package, i n c o r p o r a t i n g r e c e n t progress i n r a d i a n t h e a t t r a n s f e r t h e o r y , has been d e v e l o p e d and t e s t e d
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
278
CHEMICAL
REACTION
ENGINEERING—HOUSTON
Initialization of Q and Τ
Ξ
Total e x c h a n g e area matrix
Computation
Better
(T)
of Q
estimation
for Q
_*es_
Figure 3.
(atm
Flow diagram of the calculations
S T O P
abs)|
40
Figure 4.
tube section, nr
Results of simulation
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
Ζ
VERCAMMEN ANDFROMENT
22.
Thermal
Cracking
Furnace
Simulation
a g a i n s t i n d u s t r i a l d a t a . F u r t h e r t e s t s on f u r n a c e s w i t h d i f f e r e n t c o n f i g u r a t i o n s and d i f f e r e n t c r a c k i n g r e a c t i o n s a r e u n d e r w a y . They w i l l p r o v i d e a c h e c k f o r the a d a p t a b l e parameter o f t h e model.
Configuration, simulation
Table I I conditions
operating
and r e s u l t s o f
Reactor feed : F e e d f l o w r a t e : 45 Τ H C / d a y / c o i l D i l u t i o n : 0.40 k g s t e a m / k g HC C o m p o s i t i o n (wt%) : C H,:94.3; C H.:3.2; C„H :2.4; 0
Inlet
temperature
0
i
Reactor c o i l : E x t e r n a l d i a m e t e r : 0.126 m I n t e r n a l d i a m e t e r : 0.106 m P i t c h : 0.252 m D i s t a n c e between tube p l a n e s T o t a l l e n g t h : 92.5 m F u e l gas : Composition
Q
: 0.180 m
: CH :95%; H :5% 4
2
F e e d r a t e : 1.5.10^ K c a l / h r / b u r n e r A i r e x c e s s : 15% Number o f b u r n e r s : 60 E m i s s i v i t i e s of : W a l l s : 0.60 Coil : 0.96 Furnace Length Width Height
dimensions : : 8.40 m : 1.63m : 3.02 m
Results : Y i e l d s (wt%) câ eft C
H
2 4 S 6 H
3
c câ+co. Outlet
Indus t r i a l 2.9 5 ,5 . 0.. 2 45,,4 42.,4 1 ,3 , 1 .9 , 0.25
t e m p e r a t u r e (°C)
830
Simula ted 2.9 5 .7 0., 2 45,,4 42,,4 1 .3 1 ,9 . 0.14 820
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
279
CHEMICAL
280
REACTION
ENGINEERING—HOUSTON
Nomenclature a
lk 0^
stoechiometric c o e f f i c i e n t s p e c i f i c h e a t ( K c a l / K m o l °C)
C
c o r r e c t i o n f a c t o r f o r t h e shape of t h e band profile internal coil diameter^(m) e m i s s i v e power ( K c a l / m s ) m o l a r f l o w r a t e (Kmo^/s) mass f l o w r a t e (kg/m s) 2 g l o b a l h e a t t r a n s f e r c o e f f i c i e n t ( K c a l / m s°C) heat of r e a c t i o n ( K c a l / K m o l ) a b s o r p t i o n f a c t o r (I/m) ^ rate c o e f f i c i e n total pressur . 2 non r a d i a n t h e a t f l u x ( K c a l / m h r ) h e a t f l u x t o r e a c t o r ^ K c a l / m s) r e a c t i o n r a t e (Kmol/m s ) r a d i u s o f r e t u r n b e n d (m)
F
d^ E. Fj^ G h -ΔΗ^ k k^ ρ Q r^ n
Re S t Τ ζ Ζ . Z^Z. J
Greek β ζ Λ V X ψ ω -1 Δω Δω
ο
R e y n o l d s number beam l e n g h t t e m p e r a t u r e o f r e a c t i o n m i x t u r e (°K o r °C) temperature vector, furnace side a x i a l reactor coordinate (m) zone i t o t a l exchange) a r e a f o r r a d i a t i o n f r o m z o n e t o zone Ζ. (m ) Letters 2. c o n v e r s i o n f a c t o r ( 9 . 8 6 E - 6 atm m s /kg) f r i c t i o n f a c t o r (1/m) ^ v o l u m e t r i c f l o w r a t e (m / s ) molar f l o w r a t e (Kmol/s) transmission c o e f f i c i e n t function wave number (1/m) b a n d w i d t h o f ω a t gas t e m p e r a t u r e Τ and p a t h lengbh S b a n d w i d t h o f ω a t gas t e m p e r a t u r e Τ and p a t h lengfcfe S = 0 r e a c t o r c r o s s s e c t i o n (m ) 2
Ω
Sub s c r i p t s k 1 η
: r e a c t i n g component : r e a c t i o n index : r e l a t i v e to r e a c t o r
k = 1,...,K 1 = 1,. * ., L outer surface
zone
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
Z.
22.
m i,j
VERCAMMEN AND FROMENT
Thermal Cracking Furnace Simulation
: r e l a t i v e t o zones o t h e r than r e a c t o r o u t e r f a c e zones : g e n e r a l i n d e x e s r e l a t i v e t o z o n e Z., r e s p . Ζ . J
281
sur zone
1
Superscr ipt *
: mean v a l u e
Literature
Cited
1. L o b o , W . E . , E v a n s , J.E., T r a n s . A.I.Ch.E., (1939) 35, 743. 2. Hottel, H.C., R a d i a n McAdams, W.H. (ed) Chap McGraw Hill, New Y o r k , 1954. 3. Hottel, H.C., Cohen, E.S., A.I.Ch.E.J., (1958)4, 3. 4. Hottel, H.C., S a r o f i m , A.F., "Radiative Heat T r a n s f e r " McGraw Hill, New Y o r k , 1967. 5. P e t r y s c h u k , W . F . , J o h n s o n , A.I., C a n . J . C h e m . E n g n g . , (1968) 46, 172. 6. Knudsen, J.G., K a t z , D.L., "Fluid Dynamics and Heat T r a n s f e r " McGraw Hill, New Y o r k , 1958. 7. McAdams, W . H . , "Heat T r a n s m i s s i o n " McGraw Hill, New Y o r k , 1954. 8. H o l l a n d , F.A.,et al., "Heat T r a n s f e r " Heineman Educ. B o o k s , London, 1970. 9. Vercammen, H.A.J., Froment, G.F., to be p u b l i s h e d . 10. E c h i g o , R . , et al., J.S.M.E., (1967) 46, 172.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
23 Determining the Realtime Activity Parameters of a Pseudomonomolecular Kinetic Reforming Model K E N N E T H R. G R A Z I A N I and M I C H A E L P. R A M A G E Mobil Research and Development Corporation, Research Department, Paulsboro, NJ 08066
The s t a r t - o f - c y c l monomolecular reformin steps (1): (1) the determination o f the selectivity kinetic r a t e c o n s t a n t s , f o l l o w e d by (2) the determination o f the activity kinetics. The selectivity kinetics d e s c r i b e the r a t e s o f p r o d u c t i o n o f the chemical species relative t o the r a t e o f p r o d u c t i o n o f a r e f e r ence compound. The activity kinetics modify the selectivity kinetics t o d e s c r i b e the absolute r a t e o f p r o d u c t i o n o f each chemical species on a " r e a l t i m e " o r a c t u a l c a t a l y s t contact time basis. P r e d i c t i o n s o f reforming c a t a l y s t activity, such as the reac t o r inlet temperature (RIT) r e q u i r e d t o make a specific octane, are determined by the activity kinetics. I n the monitoring o f Mobil's commercial reformers, inlet temperatures are c o n t i n u a l l y compared t o model p r e d i c t e d start-of-cycle (SOC) RIT's t o assess commercial c a t a l y s t SOC activity and catalyst activity l o s s over a reformer c y c l e . Accurate p r e d i c t i o n s o f activity are t h e r e f o r e essential. In this paper, a simple mathematical procedure r e q u i r i n g the i n t e g r a t i o n o f the selectivity t r a n s f o r m a t i o n is developed t o determine reforming activity kinetics and a d s o r p t i o n equilibria coefficients. The method is similar t o t h a t reported earlier (2) but i s more r i g o r o u s l y a p p l i e d t o the reforming system. Only experimental C5 (methane t o pentane, i n c l u s i v e ) vs. residence time data and a priori knowledge o f the reforming selectivity kinetics are r e q u i r e d f o r the procedure. -
Theory The reforming r e a c t i o n system may be d e s c r i b e d by the pseudo monomolecular (1_) k i n e t i c i n t e r a c t i o n s o f an a p p r o p r i a t e l y defined s e t o f hydrocarbon component lumps. That i s , the r a t e s o f change of the v a r i o u s species are given by f i r s t - o r d e r mass a c t i o n ©
0-8412-0401-2/78/47-065-282$05.00/0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
23. GRAziANi
AND
Realtime Activity Parameters
RAMAGE
283
k i n e t i c s w i t h the same adsorption isotherm being a p p l i c a b l e t o each r e a c t i o n s t e p . For the purpose o f t h i s paper, the reforming system w i l l be d i s c u s s e d i n terms o f Ν a r b i t r a r i l y d e f i n e d compo nent lumps o b t a i n e d from the C i t o C12 hydrocarbon species i n the g a s o l i n e b o i l i n g range. In m a t r i x n o t a t i o n , the steady s t a t e d i f f e r e n t i a l m a t e r i a l balance over the d i f f e r e n t i a l c a t a l y s t volume dv i s ||=φϋ
( 1 )
( T c\. V
P
I F R T
.
where φ =
^ 1 + K
?
H 2
Ρ
H
+ 2
Φ
—P F "Τ
S
( 2 )
=
Τ' V Τ F F
Κ^2'
P
;
K
c
c
t o t a l and hydrogen pressures = t o t a l c a t a l y s t volume = temperature = t o t a l molar flow = mass flow r a t e hydrocarbon charge = adsorption e q u i l i b r i a c o e f f i c i e n t s
Equation 1 i s d e r i v e d f o r a f i x e d bed c a t a l y t i c reformer assuming p l u g flow and constant c a t a l y s t bed v o i d f r a c t i o n . A nondissocia t i v e Langmuir-Hinschelwood a d s o r p t i o n mechanism i s employed w i t h the hydrocarbon p a r t i a l pressures r e d e f i n e d as
*i
=
PmP-d-Hjai F Mi
( 3 )
i s the molecular weight o f component i . The hydrocarbon weight f r a c t i o n s a^ are d e f i n e d on a H 2 ~ f r e e b a s i s , i . e . , Ν Σ a^ = 1 , where H 2 i s not i n c l u d e d i n the summation. I n i=l a d d i t i o n , s i n c e the hydrogen weight y i e l d based on reformer charge, Η, i s t y p i c a l l y . 0 1 t o . 0 2 , 1-H % 1 may be assumed i n these d e r i v a t i o n s . φ i s the c a t a l y s t a c t i v i t y f u n c t i o n i n c o r p o r a t i n g the a d s o r p t i o n e q u i l i b r i a e f f e c t s . Κ i s the pseudomonomolecular s e l e c t i v i t y r a t e constant m a t r i x whose elements are ^ ι Α φ · k(|) i s d e f i n e d as the r e a l t i m e a c t i v i t y r a t e constant t o which a l l r a t e constants i n Κ are made r e l a t i v e . Thus, one r a t e constant i n Κ i s equal t o 1 . 0 and i t may be chosen a r b i t r a r i l y . k<j) w i l l t h e r e f o r e be the r a t e constant f o r t h i s chosen r e a c t i o n . Determining the reforming k i n e t i c s may then be separated i n t o a s e l e c t i v i t y problem (determine K) and an a c t i v i t y problem (determine φ). This i s accomplished by d e f i n i n g the s e l e c t i v i t y
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
284
CHEMICAL
REACTION
ENGINEERING—HOUSTON
time, τ , by the f o l l o w i n g t r a n s f o r m a t i o n άτ = φάν
(4)
S u b s t i t u t i n g equation 4 i n t o 1, we o b t a i n
§ -
11
whose s o l u t i o n upon i n t e g r a t i o n i s a(T)
= χ
(Άτ) χ " a
EXP
1
(o)
(6)
χ and A a r e the eigenvector m a t r i x K. Since one o 1.0, we do not need t o know τ i n order t o determine Κ. Κ can be determined from composition data alone without regard t o _ r e a c t i o n time (.1) . For t h i s r e p o r t , the s e l e c t i v i t y m a t r i x Κ has been p r e v i o u s l y determined but w i l l be l e f t u n s p e c i f i e d f o r p r o p r i e t a r y reasons a t t h i s time. With Κ known, o n l y the a c t i v i t y f u n c t i o n φ c o n t a i n i n g the r e a l t i m e r a t e constant (k^) and the a d s o r p t i o n e q u i l i b r i u m constants remains t o be determined. These may be found employing a method t h a t r e q u i r e s the i n t e g r a t i o n of the s e l e c t i v i t y time t r a n s f o r m a t i o n equation 4. =
(7)
/ χ dT = / dV 0 Φ
The i n t e g r a t i o n i s taken over the t o t a l c a t a l y s t bed. With equation 2, the i n t e g r a t i o n i m p l i e d i n equation 7 may be more s p e c i f i c a l l y represented as
Κ
Φ
0
F
V
T c
φ s
ο a n d
*T
t h e
Note t h a t F / V " v P c represented e q u i v a l e n t l y as c
c
V
Φ
C
t o t a l
ο
v
c
hydrogen molar flow may
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
be
23.
GRAziANi
where:
Realtime Activity Parameters
AND RAMAGE
285
p = hydrocarbon charge d e n s i t y S = l i q u i d h o u r l y space v e l o c i t y (volume hydrocarbon charge/volume c a t a l y s t - t i m e ) Ύ# = molar hydrogen-to-hydrocarbon feed r a t i o M = molecular weight hydrocarbon charge c
v
c
Equation 8 can then be rearranged t o be l i n e a r i n the r e a l t i m e parameters : Κ
where :
+ I
l !
2
K H
+
I
2
3
(9)
*<(>
Ï-L = S p RT / a άτ v
S Io
RT
v P c
=
(10a)
c
P
0
T
FPt: 13 = S p R T v
c
/
F cPiT
άτ
r
0
S P RT V
C
/
H
Y R
2
M
Ο
(10c)
dT
N
The l e f t - h a n d s i d e i n t e g r a t i o n l i m i t , T f i n equation 7, i s the s e l e c t i v i t y time a t the end o f the c a t a l y s t bed, ν = 1. Since the s e l e c t i v i t y time i s the r e s u l t o f the independent v a r i able t r a n s f o r m a t i o n represented by equation 4, i t does not have p h y s i c a l meaning i n the sense o f c a t a l y s t c o n t a c t time. The s e l e c t i v i t y time can only be found by employing the predetermined s e l e c t i v i t y k i n e t i c s . T f i s determined by a t r i a l and e r r o r matching o f the s e l e c t i v i t y s o l u t i o n from equation 6 t o e x p e r i mental y i e l d s a t the o u t l e t o f the c a t a l y s t bed. That i s , a value o f T f i s converged on when the C$~ y i e l d (methane t o pentane, i n c l u s i v e ) as p r e d i c t e d by equation 6 agrees w i t h the experimental C 5 - y i e l d . The value o f T f so determined r e l a t e s the known s e l e c t i v i t y k i n e t i c s t o the r e a c t o r r e a l t i m e behavior. Ιχ i s determined u s i n g the s e l e c t i v i t y k i n e t i c s . S u b s t i t u t i n g the s e l e c t i v i t y s o l u t i o n (equation 6) f o r a i n t o equation 10a, we o b t a i n - f
ïl = ( S P V
R T C
T
-
f
) X< f
11
EXP(JlT)dT>x" a
o
(11)
As a r e s u l t o f i r r e v e r s i b l e reforming c r a c k i n g r e a c t i o n s , the s e l e c t i v i t y r a t e constant m a t r i x , ÎC, contains one column o f zeros K , t h e r e f o r e , w i l l always y i e l d one zero eigenvalue. L e t — 0, a r b i t r a r i l y . R e a l i z i n g t h a t λ = 0 , the i n t e g r a t i o n o f the expo n e n t i a l diagonal m a t r i x o f equation 11 i s done term-by-term. Expressing the r e s u l t s i n m a t r i x n o t a t i o n , the i n t e g r a t i o n y i e l d s Ν
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL
286
REACTION
i l = (s p RT) χ A* ( I * - EXP [Â T ]j χ " v
f
c
1
ENGINEERING—HOUSTON
â
(12)
0
Λ* i s a diagonal m a t r i x whose elements are .1/λ _χ, Tf. I * i s a diagonal m a t r i x whose elements are 1, 1, ..., 2. The a n a l y t i c a l i n t e g r a t i o n s f o r I2 and I 3 , equations 10b and 10c, are complicated by the dependence o f F and H on τ through the dependence o f the composition on τ. For a s i n g l e - p a s s hydrogen reformer c o n f i g u r a t i o n , i . e . , 100% H2 introduced w i t h naphtha feec i n s t e a d o f r e c y c l e gas, the t o t a l molar flow i s given by Ν
F =P ( ΐ ^ Η ^ ^ + Ρ ^ Ι ^ )
(13)
+
C
A hydrogen balance over the r e a c t o r gives the hydrogen weight y i e l d as Σ
n
a
a
i< io" i>
Η = —
(14) Ν 1 - Σ η.a. i=i 1
1
The n^'s represent the weight f r a c t i o n o f combined hydrogen f o r the i t h k i n e t i c lump. a ^ represents feed composition. I t i s necessary t o determine I2 and I 3 n u m e r i c a l l y . A f i v e p o i n t Simpson's i n t e g r a t i o n r u l e (_3) has been used w i t h the f o l lowing d e f i n i t i o n Q
| l 9 y (o) + 75 y (.2 T ) + 50 y (.4 τ )
/ ydT = — ο»
f
£
+ 50 y (.6 T ) + 75 y (.8 T ) + 19 y ( T ) | S p RTF(τ) v c Γ + ΊΑ y = and f o r I , y = S p RT L T c c f
f
(15)
f
K
Η ( τ )
For
I2/
P
F
3
v
c
2
M
In e v a l u a t i n g the numerical approximation t o I 2 and I 3 , the s e l e c t i v i t y s o l u t i o n , a(τ) from equation 6 must be determined a t each incremental value o f τ. Using equation 13 and 14, F, Η, and subsequently y, may be c a l c u l a t e d a t each increment o f τ. I n t e g r a l s I and I 3 are then determined by the appropriate form of equation 15. The i n t e g r a l s Ιχ, I 2 , and I 3 i n equation 9 can be determined f o r any i s o t h e r m a l reforming experiment from the experimental r e s u l t s and predetermined s e l e c t i v i t y m a t r i x (K) without knowledge of the a c t i v i t y parameters. The s e l e c t i v i t y time, T f , can a l s o be obtained w i t h the same i n f o r m a t i o n . Thus, i f we develop a s e t o f reforming data which covers a wide range o f charge stocks and process c o n d i t i o n s , the i n t e g r a l s can be c a l c u l a t e d e x p l i c i t l y 2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
23.
GRAZIANI A N D R A M A G E
Realtime Activity Parameters
287
f o r each data p o i n t . The a c t i v i t y parameters k±, K ^ d Κ can then be obtained from equation 9 u s i n g parameter e s t i m a t i o n t e c h niques. Note t h a t what we have done i s t o convert one h i g h l y n o n - l i n e a r problem (equation 1) i n t o two l i n e a r problems (equa t i o n s 6 and 9 ) . Not only are the l i n e a r problems e a s i e r t o s o l v e , the r e s u l t s are more accurate due t o decreased confounding between the k i n e t i c parameters. a n
Ho
Experimental Data Data used i n t h i s study were obtained on an i s o t h e r m a l f i x e d bed reforming p i l o t p l a n t . The r e a c t o r s e c t i o n was equipped w i t h f i v e sampling taps spaced along the l e n g t h o f the r e a c t o r . On l i n e gas chromatograph analyse provide composition p r o f i l e i n c r e a s i n g residence time through the c a t a l y s t bed. A l l the data were taken on f r e s h reforming c a t a l y s t . C^" 360°F N i g e r i a n naphtha (naphthenic s t o c k ) , C -360°F Arab l i g h t naphtha ( p a r a f f i n i e stock) and C6~360°F and C -290°F Mid-Continent naphtha (intermediate stock) were employed. Reactor pressures o f 400 p s i a and 197 p s i a and i s o t h e r m a l temperatures ranging from 850°F t o 970°F were s t u d i e d . Hydrocarbon p a r t i a l pressure was 20 p s i a . I n each case, 100% hydrogen was i n t r o d u c e d as r e c y c l e (single-pass hydrogen). The experimental c o n d i t i o n s were chosen t o span the wide v a r i a t i o n i n charge stocks and process c o n d i t i o n s found i n commercial reforming. I n a l l , 75 data s e t s were used. 6
6
Determination o f the Realtime A c t i v i t y K i n e t i c s The s e t o f i n t e g r a t e d d a t a , î^, I and I 3 were determined f o r each o f the 75 data s e t s . The a c t i v i t y parameters and t h e i r temperature and pressure dependencies were found u s i n g Rosenbrock's parameter search technique (4) which minimized the sums o f squares d e v i a t i o n as c a l c u l a t e d from equation 9. The temperature and pressure dependence o f the a c t i v i t y parameters were determined r e l a t i v e t o base c o n d i t i o n s o f 900°F (756°K) and 177 p s i a H . The parameters are expressed i n terms o f process c o n d i t i o n s as 2
2
(16a) (16b) (16c) where H
H
adsi' H k<£ ,KiO,KH 0
0
2
a c t i v a t i o n energy (cal/mole) - heat o f a d s o r p t i o n (cal/mole) = p r e - e x p o n e n t i a l r e a l t i m e and a d s o r p t i o n constants. (Parameters a t base c o n d i t i o n s . ) hydrogen p a r t i a l pressure exponent η 2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
288
CHEMICAL
REACTION
ENGINEERING—HOUSTON
The a c t i v i t y constants so determined are presented i n Table I . The a d s o r p t i o n of hexanes, heptanes and CQ* aromatics are seen t o have the dominant e f f e c t on c a t a l y s t a c t i v i t y . The ad s o r p t i o n of benzene, toluene and hydrogen occur t o a l e s s e r e x t e n t . These a d s o r p t i o n e f f e c t s may be e x p l a i n e d by the dual f u n c t i o n a l nature of reforming c a t a l y s t s . I t has been shown (_5) t h a t species t h a t r e a d i l y undergo hydrogenolysis (hexanes and heptanes) are s t r o n g l y chemisorbed on the metal s i t e s w h i l e experience w i t h z e o l i t e c r a c k i n g c a t a l y s t s (6) i n d i c a t e s a s t r o n g a d s o r p t i o n of h e a v i e r aromatics on a c i d i c s i t e s . Table I Realtim
κψ K A8+ K K Kp Kp H 2
K
A ?
A
?
6
Activit
Parameter
Pre-exponential Term (Ko)
Energy Heat of Adsorption (cal/mole)
0.258 3.2 χ 10~ 0.0456 2.2 χ 10-5 4.9 χ I O " 0.0125 0.05
24,380 -43,726 -39,713 -39,610 -14,743 -25,000 -25,000
5
6
2
Exponent (n) -0.2
Realtime A c t i v i t y P r e d i c t i o n s With the a c t i v i t y parameters given i n Table I , i s o t h e r m a l reformer r e a l t i m e behavior may be s i m u l a t e d u s i n g the d i f f e r e n t i a l m a t e r i a l balance o f equation 1. F i g u r e s 1 and 2 show p r e d i c t e d vs. a c t u a l composition p r o f i l e s f o r two o f the data s e t s used i n the f i t t i n g . F i g u r e 1 presents C7 p a r a f f i n and toluene compositions vs. c a t a l y s t contact time f o r reforming a 120-380°F Arab L i g h t naphtha. F i g u r e 2 s i m i l a r l y presents p a r a f f i n and benzene composition p r o f i l e s f o r reforming a 120-370°F MidContinent naphtha. Very good agreement between the simulated and experimental r e a c t i o n p r o f i l e s i s observed over the wide range of c o n d i t i o n s represented by both examples. In a d i a b a t i c reformer s i m u l a t i o n s , the a c t i v i t y parameters determine the r e a c t o r i n l e t temperature (RIT), r e q u i r e d t o make a s p e c i f i e d reformate octane. With the a c t i v i t y parameters i n corporated i n t o Mobil's k i n e t i c reforming model, i n l e t tempera t u r e p r e d i c t i o n s were compared to numerous a d i a b a t i c reforming p i l o t p l a n t s t u d i e s (Figure 3 ) . The data used i n these com p a r i s o n s covered a wide range of charge stock types and process c o n d i t i o n s commonly encountered i n commercial reforming. The p r e d i c t e d R I T s are i n good agreement w i t h the r e p o r t e d e x p e r i mental RIT's. An average d e v i a t i o n of ± 6.8°F i s observed. 1
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
GRAziANi A N D R A M A G E
Realtime
Activity
Parameters
EXPERIMENTAL DATA Ρ - C PARAFFINS A " TOLUENE 7
0.5
1.0 1.5 2.0 2.5 CATALYST CONTACT TIME, SEC
3.0
3.5
Figure 1. Isothermal reforming reactor profiles for a C -370°F Arab light naphtha. Reformer conditions: 949 °F, 380 psia H , 20 psia hydrocarbon. 6
2
12.5 a*
0
2.5
5 7.5 10 12.5 CATALYST CONTACT TIME, SEC
15
17.5
Figure 2. Isothermal reforming reactor profiles for a C -370°F Mid-Continent naphtha. Reformer conditions: 898 °F, 177 psia H , 20 psia hydrocarbon. 6
2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL
Figure 3.
REACTION
ENGINEERING—HOUSTON
Comparison of activity kinetics predictions to adiabatic pilot plant data
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
23. GRAziANi
AND RAMAGE
Realtime Activity Parameters
291
A l s o , a l i n e a r l e a s t squares f i t through the comparisons shows no b i a s t o the p r e d i c t i o n s . T h i s degree o f accuracy i s very reason able c o n s i d e r i n g the s e n s i t i v i t y o f c a t a l y s t a c t i v i t y t o s t a r t - u p c o n d i t i o n s , environmental c o n t r o l , and the d i f f i c u l t y i n d e f i n i n g a p r e c i s e s t a r t - o f - c y c l e RIT due t o i n i t i a l temperature t r a n s ients . Thus, the a c t i v i t y k i n e t i c s found u s i n g the method o f i n t e g r a t i o n o f the s e l e c t i v i t y t r a n s f o r m a t i o n are seen t o a c c u r a t e l y model reformer c a t a l y s t a c t i v i t y . Literature Cited (1) Wei, J., and C. D. P r a t e r , Advances in C a t a l y s i s (1962), 13 203. (2) Kugelman, Α. Μ., an 10-21. (3) Lapidus, L., "Digital Computation f o r Chemical Engineers", McGraw-Hill, New York (1962). (4) Rosenbrock, H. H., Comp. J. (October, 1960), 3 (3), 175-184. (5) Sarkany, Α., L. Guczi and P. T e t e n y i , J. o f Cat. (1975), 39, 181-189. (6) Jacob, S. Μ., B. Gross, S. Ε . V o l t z , and V. W. Weekman, AIChE J. (July, 1976), 22 (4), 701-713.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
24 Heuristic Approach to Complex Kinetics J. B. CROPLEY Research and Development Department, Union Carbide Corporation, Chemicals and Plastics Division, P.O. Box 8361, South Charleston, WV 25303
Non-linear reactio quate f o r r e a c t o r d e s i g known parameters than can be e v a l u a t e d by e i t h e r classical kinetics or n o n - l i n e a r statistical methods. Sucl e x p r e s s i o n s are e n c o u n t e r e d i n both heterogeneous and homogeneous catalysis, and i n b i o c h e m i s t r y . F i f t e e n or more n o n - l i n e a r parameters are not uncommon i n r a t e models f o r complex industrial reactions. The heuristic approach d e s c r i b e d i n this paper utilizes linear statistical methods t o f o r m u l a t e the b a s i c h y p e r b o l i c n o n - l i n e a r model i n a particularly u s e f u l d i m e n s i o n l e s s form. E s s e n t i a l terms are identified and o t h e r s r e j e c t e d at t h i s s t a g e . Reaction stoic h i o m e t r y is combined w i t h the i n h e r e n t m a t h e m a t i c a l characteristics of the d i m e n s i o n l e s s r a t e e x p r e s s i o n to reduce the number o f unknown parameters t o the critical few t h a t must be e v a l u a t e d by n o n - l i n e a r e s t i m a t i o n . Typically, o n l y f o u r o r f i v e parameters remain at t h i s p o i n t , and initial e s t i m a t e s are a v a i l a b l e f o r t h e s e . The approach is e q u a l l y a p p l i c a b l e t o c a s e s where the rate-limiting mechanism is known and where it is not. The heuristic approach is illustrated by an example t h a t utilizes the fictitious but realistic catalytic vapor-phase o x i d a t i o n o f dammitol t o v a l u a l d e hyde and water. Some carbon d i o x i d e i s a l s o produced. I t w i l l be assumed t h a t water i s known t o have no e f f e c t on the r e a c t i o n , but the e f f e c t s of the o t h e r components and temperature are unknown. No knowledge o f the r a t e - l i m i t i n g s t e p i s a v a i l a b l e . The f i r s t s t e p i n the development of the model i s to o b t a i n a s e t of s u i t a b l e e x p e r i m e n t a l d a t a . In t h i ; case s u i t a b l e means t h a t the n e c e s s a r y i n f o r m a t i o n i s a c t u a l l y l a t e n t i n the d a t a , t h a t the ranges of the v a r i a b l e s are r e a l i s t i c , and so on. The experimental reactor s h o u l d be s p e c i f i c a l l y d e s i g n e d t o o b t a i n dat; ©
0-8412-0401-2/78/47-065-292$05.00/0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
24.
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f o r t h e k i n d o f r e a c t i o n k i n e t i c s one i s working w i t h . The e x p e r i m e n t a l p l a n s h o u l d be c a r e f u l l y drawn so t h a t the p r i m a r y , i n t e r a c t i v e , and c u r v i l i n e a r e f f e c t s o f the v a r i a b l e s can be o b s e r v e d . U s u a l l y t h i s w i l l mean some s o r t o f s t a t i s t i c a l l y - d e s i g n e d e x p e r i m e n t a l a r r a y . For most vapor-phase c a t a l y t i c r e a c t i o n s , use a g r a d i e n t l e s s r e a c t o r l i k e the back-mixed c a t a l y s t a u t o c l a v e d e v e l o p e d by J . M. B e r t y ( 1 ) . T h i s r e a c t o r p e r m i t s t h e independent v a r i a t i o n o f mass- and s p a c e - v e l o c i t i e s and the d i r e c t o b s e r v a t i o n o f r e a c t i o n r a t e s . F o r t h e experiment a r r a y , I p r e f e r an o r t h o g o n a l central-composite d e s i g n ( 2 ) , (3), which c o n s i s t s o f t h r e e main p a r t s , as shown i n T a b l e I . The f i r s t i s a c o n v e n t i o n a l 16-experiment f r a c t i o n a l f a c t o r i a l de sign for f i v e variable p r i s e s three i d e n t i c a c e n t e r - p o i n t , c o n d i t i o n s f o r t h e f i r s t 16 e x p e r i m e n t s . The f i n a l p a r t comprises two o u t - l i e r e x p e r i m e n t s f o r each v a r i a b l e . These augment the b a s i c two l e v e l de s i g n t o p r o v i d e an e s t i m a t e o f c u r v a t u r e f o r t h e r e sponse t o each v a r i a b l e . The o v e r a l l e f f e c t o f t h e d e s i g n i s t o s a t u r a t e e f f e c t i v e l y the multi-dimensional v a r i a b l e space. I t i s more e f f e c t i v e than t h e conven t i o n a l one-variable-at-a-time" approach. F o r purposes o f i l l u s t r a t i o n , t h e " o b s e r v e d " r a t e s i n T a b l e I were d e v e l o p e d from an assumed " t r u e " r a t e e x p r e s s i o n by a p p l y i n g random e r r o r as f o l l o w s ; f!
(Rate) , = (Rate)^ 'observed true x
u
v
χ INL R
7
where N i s a random normal number from a s e t w i t h a mean o f 1.0 and a s t a n d a r d d e v i a t i o n o f 0.20. Thus, the " o b s e r v e d " d a t a c o n t a i n 20 p e r c e n t random e r r o r . T h i s e r r o r l e v e l i s n o t i n o r d i n a t e l y h i g h f o r complex s i t u a t i o n s t h a t may i n v o l v e d i f f i c u l t a n a l y t i c a l methods and m u l t i p l e p r o d u c t s . The " t r u e " r a t e e x p r e s s i o n used i n t h i s example i s r
-20000 4.67(10 )e 5ÏÏ0ÏÏ U
r
l+5.52(10" )e 4
R
T
R
T
(P
0
2
)' (P ) '° 5
1
D
5ÏÏUÏÏ
(P )· +7.64(10' )e 5
Q 2
4
R
T
(Ρ )
2
γ
where r i s r e a c t i o n r a t e , g m o l s / v a l u a l d e h y d e / k g c a t a l y s t /hr; Τ i s temperature, °K; R i s t h e gas c o n s t a n t ; Ρ i s p a r t i a l p r e s s u r e , p s i a ; and s u b s c r i p t s 02, D, and ν r e f e r t o oxygen, dammitol, and v a l u a l d e h y d e , r e s p e c t ively. This rate expression implies that the r a t e -
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL
294
REACTION
ENGINEERING—HOUSTON
TABLE I A SUMMARY OF SYNTHETIC DATA THE OXIDATION OF DAMMITQL TO VALUALDEHYDE #
OBSERVED RATE GMOL/KG/HR
TEMPERATURE, °C
PARTIAL PRESSURES, PSIA OXYGEN DAMMI- VALUALC02 TOL DEHYDE
THE BASIC FRACTIONAL FACTORIAL SET 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
4. 07 8. 70 2. 29 5. 69 1. 58 10. 58 1.40 4. 63 1. 25 4. 34 0. 62 1.65 1. 15 3. 66 0. 63 1.44
7 7
10 10
3 1
3 1
3 3 3 3 7 7 7 7 3 3 2 3
10 10 4 4 10 10 4 4 10 10 4 4
3 1 3 1 3 1 3 1 3 1 3 1
1 3 3 1 1 3 3 1 3 1 1 3
100 100 100
5 5 5
7 7 7
2 2 2
2 2 2
91.,7 108. 3 100. 100. 100. 100. 100. 100. 100. 100.
5 5 1,.67 8,.33 5 5 5 5 5 5
2 2 2 2 2 2 0..34 3.,66 2 2
2 2 2 2 2 2 2 2 0.,34 3.,66
105 105 105 105 105 105 105 105 95 95 95 95 95 95 95 95
THE CENTER-POINTS 17 18 19 THE 20 21 22 23 24 25 26 27 28 29
2. 92 3. 16 2. 72 H
OUT-LIERS 1,,66 3.,57 1.,96 4.,11 1.,15 4.,70 4.,12 0..91 2.,95 3..16
!f
7 7 7 7 2 12 7 7 7 7
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
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295
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l i m i t i n g s t e p i s the s u r f a c e r e a c t i o n between chemisorbed oxygen and unadsorbed dammitol. Two molecules o f v a l u a l d e h y d e chemisorb (perhaps as a dimer) on a s i n g l e c a t a l y s t s i t e , and carbon d i o x i d e does not i n f l u e n c e the r e a c t i o n . H y p e r b o l i c e q u a t i o n s l i k e the above are t y p i c a l l y used t o d e s c r i b e r a t e phenomena i n b o t h heterogeneous and homogeneous c a t a l y s i s , b i o c h e m i s t r y , and i n many homogeneous r e a c t i o n s i n which c h e m i c a l e q u i l i b r i a a r e important. They are more d e s c r i p t i v e o f the r e a c t i o n ' c h e m i s t r y than i s the u s u a l e x p o n e n t i a l r a t e e x p r e s s i o n , and they a v o i d the problems e n c o u n t e r e d i n the e x p o n e n t i a l models i f one of the components i s absent. In t h i s paper we w i l l use t h e e x p o n e n t i a l e x p r e s s i o n as a s t e p p i n g - s t o n and u s e f u l h y p e r b o l i g p r i s e the h e u r i s t i c approach: Rule
1:
Develop a m o d i f i e d e x p o n e n t i a l r a t e model of f o l l o w i n g t y p e , u s i n g l i n e a r r e g r e s s i o n methods: l n ( r ) = f [In X., where the Χ . are p r o c e s s Ί
2
(In X . ) ,
X.)]
( I n Χ.)(1η
v a r i a b l e s o f the
the
form:
The s u b s c r i p t cp r e f e r s t o the c e n t e r - p o i n t c o n d i t i o n s of T a b l e I and Ε i s the apparent a c t i v a t i o n energy i n cal/gmol. The e x p o n e n t i a l form of the model d e v e l o p e d from the d a t a i n T a b l e I i s :
r
=
2
.
7
7
e " ^ ^ )
3
2
( ^ )
7
3
( ! v )
(
- -
5
9
L
^
-
l
-
M
)
The " t r u e " and " o b s e r v e d " r a t e s are compared w i t h the r a t e s p r e d i c t e d by t h i s model i n T a b l e I I . The s t a n d a r d d e v i a t i o n of the e r r o r w i t h r e s p e c t t o the "ob s e r v e d " d a t a i s 22 p e r c e n t , o r v e r y l i t t l e more than the random e r r o r i n the d a t a . The model a l s o a c t s as a f i l t e r f o r the random e r r o r , i n the sense t h a t the s t a n d a r d d e v i a t i o n w i t h r e s p e c t t o the " t r u e " v a l u e s i s o n l y 14 p e r c e n t . A l l i n a l l , i t i s not a bad model, but we can do b e t t e r , p a r t i c u l a r l y f o r d e s i g n p u r p o s e s where the c o n c e n t r a t i o n o f v a l u a l d e h y d e at the e n t r a n c e
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
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296
TABLE I I A COMPARISON OF RESULTS
"TRUE" RATES 4. 50 12. 34 1. 80 4. 94 3. 11 9. 43 1. 24 3. 77 1. 86 5. 32 0. 75 2. 13 1. 29 4. 11 0. 52 1. 64 3. 00 3. 00 3. 00 1. 44 6. 05 1. 92 3.63 0. 86 5. 14 6. 56 1. 30 3. 00 3. 00
#
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
MEAN MEAN ERROR(a) obs ( > true ( ) s
s
NOTES:
3.47
DATA "OBSERVED" RATES ( c ) 4. 07 8. 70 2. 29 5. 69 1. 58 10. 58 1 40
4. 34 0. 62 1. 65 1. 15 3. 66 0. 63 1. 44 2. 92 3. 16 2. 72 1. 66 3. 57 1. 96 4. 11 1. 15 4. 70 4. 12 0. 91 2. 95 3. 16
4. 60 0. 74 2. 36 1. 10 3. 50 0. 56 1. 80 2. 77 2. 77 2. 77 1. 35 5. 49 1. 95 3. 26 1. 11 4. 10 3. 79 1. 06 2. 77 2. 77
4. 43 0. 88 2. 35 1. 19 3. 26 0. 59 1. 77 2. 93 2. 93 2. 93 1. 43 5. 81 1. 80 3. 62 1. 13 4. 29 5. 89 1. 32 2. 93 2. 93
4.54 0.80 2.29 1.25 3.34 0.55 1.74 2.93 2.93 2.93 1.43 5.81 1.85 3.58 0.95 4.48 6.03 1.31 2.93 2.93
3.13
3.08 0.07 °· ° ·
3.24 0.01 °·
3.25 0.02 °°'
b
2 2
b
(a) (b)
(c)
MODEL PREDICTIONS EXPOHEURISTIC NENTIAL #1 #2 4.24 4. 13 3. 34 10. 28 10.54 10. 68 2. 05 1.85 1. 71 5.31 5. 45 5. 48 2. 76 2. 54 2.91 7. 58 8. 14 7.76 1 37 1.27 1 31
1
2 6
4
0
Λ
2
2 7
0 8
E r r o r i s d e f i n e d as ( D a t a - P r e d . ) / D a t a . S k and S ^ are standard deviations of the e r r o r as d e f i n e d above, based on t h e " o b s e r v e d " and " t r u e " d a t a , r e s p e c t i v e l y . "Observed" r a t e s were d e r i v e d from " t r u e " r a t e s by imposing a 20 p e r c e n t random normal e r r o r . Models a r e based on "Observed" R a t e s . Q
s
r u e
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
24.
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297
t o t h e c a t a l y s t bed may be z e r o . We w i l l use some o f the i n f o r m a t i o n i n t h i s model i n t h e development o f t h e h y p e r b o l i c model. I f temperature and t h e c o n c e n t r a t i o n s o f a l l t h e c h e m i c a l s p e c i e s i n t h e study were important i n both the numerator and denominator o f t h e h y p e r b o l i c model, t h e r e would be, f o r η s p e c i e s , ( 4 n + 2 ) unknown p a r a meters i n t h e model. In t h e example study, t h e r e would be 18 parameters. In t h e " t r u e " expression, t h e r e are 10 parameters, because not a l l s p e c i e s a r e impor t a n t i n both numerator and denominator. Even i f t h e " t r u e " mechanism were known, t h e r e would be t o o many parameters t o e s t i m a t e s i m p l y by t o s s i n g t h e d a t a i n t o a n o n - l i n e a r e s t i m a t i o n program The heuristi lem down t o a s i z e t h a the form o f t h e e q u a t i o n a b i t t o permit good v a l u e s of t h e parameters t o be c a l c u l a t e d . The problem o f f i n d i n g i n i t i a l estimates i s completely e l i m i n a t e d . Rule 2: E l i m i n a t e from c o n s i d e r a t i o n any v a r i a b l e t h a t was not s i g n i f i c a n t i n t h e e x p o n e n t i a l model. In t h e example, t h e p a r t i a l p r e s s u r e o f carbon d i o x i d e i s thus e l i m i n a t e d . Rule 3: E l i m i n a t e t h e temperature terms i n t h e denomina tor. I f they a r e i n d e e d n e c e s s a r y , they can be added later. U s u a l l y a change o f t h r e e o r f o u r k i l o c a l o r i e s i n t h e apparent a c t i v a t i o n energy compensates ade q u a t e l y f o r t h e i r absence. Rule 4: Develop t h e h y p e r b o l i c e q u a t i o n i n terms o f t h e d i m e n s i o n l e s s v a r i a b l e s o f Rule 1. By d o i n g so one b r e a k s t h e i n t e r d e p e n d e n c e o f e x p o n e n t i a l and p r e e x p o n e n t i a l terms, and one o f t h e b i g problems o f non l i n e a r estimation i s minimized. (See Rule 7.) Rule 5: A r b i t r a r i l y a s s i g n exponents t o t h e terms i n t h e denominator. Here one u t i l i z e s h i s knowledge o f t h e c h e m i s t r y and t h e s t o i c h i o m e t r y o f t h e assumed ad sorption e q u i l i b r i a . These may be changed l a t e r , but f o r now use v a l u e s o f 1/2, 1.0, o r 2.0. (The 1/2 i s
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
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c h a r a c t e r i s t i c f o r c h e m i s o r p t i o n o f d i a t o m i c gases l i k e oxygen, the 2.0 f o r m o l e c u l e s t h a t adsorb as d i m e r s . ) Rule
was
6: Use the v a l u e f o r E, the a c t i v a t i o n energy, t h a t o b t a i n e d i n the e x p o n e n t i a l model.
Rule
7:
Determine the p r e - e x p o n e n t i a l term i n the numer a t o r by o b s e r v i n g t h a t the c o n c e n t r a t i o n and tempera t u r e terms are a l l u n i t y at the c e n t e r - p o i n t l e v e l s . Hence, the h y p e r b o l i age r a t e at the c e n t e r?
A
=
C P
1
+ΣΚ.
or, A
=
r
c
p
(l
+EK ) 1
where A i s the p r e - e x p o n e n t i a l f a c t o r and the are the adsorption e q u i l i b r i u m constants. At t h i s p o i n t , the h y p e r b o l i c model i s ready f o r n o n - l i n e a r e s t i m a t i o n and l o o k s l i k e t h i s f o r our example :
-23295/1
V r
i + K
o2 vy +
e
R
1\
a
b
^ ^(!og) (V) 37
-
T h e r e are f i v e parameters t o e s t i m a t e : a, b, K Q 2 , K ^ , and K . V a l u a l d e h y d e was e l i m i n a t e d from the numerator because i t s exponent i n the e x p o n e n t i a l e q u a t i o n was s t r o n g l y n e g a t i v e , which a l s o suggested the denominator exponent of 2.0. y
Rule
8:
Set the n o n - l i n e a r s e a r c h ranges f o r the numerator exponents between 0 and 2.0. They w i l l seldom be found o u t s i d e t h a t range. Set the s e a r c h ranges f o r the denominator
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
K's
24.
CROPLEY
Heuristic Approach to Complex Kinetics
299
between 0 and 5. The l o g i c f o r t h i s r u l e i s q u i t e s i m p l e . At t h e c e n t e r - p o i n t c o n d i t i o n s , t h e v a l u e s f o r a l l t h e d i m e n s i o n l e s s v a r i a b l e terms w i l l be u n i t y , and the denominator w i l l be, as noted b e f o r e i n Rule 7: 1
+ΣΚ
£
f
In o r d e r t o have i n f l u e n c e on t h e r a t e , each o f t h e K s must be s i g n i f i c a n t w i t h r e s p e c t t o t h e 1.0, and, a t the same time, not overwhelm i t . Most K s w i l l be found i n t h e 1.0 t o 3.0 range. f
Rule 9: U t i l i z e computerize numerator exponents and t h e denominato f i n a l r e s u l t i n o u r example i s : •23295/1
1 \
s
s
K-values.
e
ftl
20.18e r =
The p r e d i c t e d v a l u e s u s i n g t h i s model a r e shown i n T a b l e I I under H e u r i s t i c Model #1. The s t a n d a r d d e v i a t i o n s o f t h e e r r o r f o r t h e " o b s e r v e d " and " t r u e " d a t a a r e about 26 and 12 p e r c e n t , r e s p e c t i v e l y . Thus the h e u r i s t i c model p r e d i c t s t h e " t r u e " d a t a s l i g h t l y b e t t e r than t h e e x p o n e n t i a l model does, but doesn't f i t t h e "observed" d a t a as w e l l . I t i sactually the b e t t e r model, a l t h o u g h t h e comparison seems t o pose a paradox. A c t u a l l y , t h e h e u r i s t i c model i s t h e more c o n s t r a i n e d o f t h e two, because i t has been s t r u c t u r e d to r e f l e c t a p a r t i c u l a r chemistry. It i sless likely t o be i n f l u e n c e d by t h e e r r o r s t r u c t u r e o f t h e d a t a than i s t h e e x p o n e n t i a l model, which i s more g e n e r a l . Rule 10: Examine t h e h e u r i s t i c model f o r any c l u e s o r s u g g e s t i o n s t h a t may improve t h e form o f t h e model. Two p o s s i b i l i t i e s a r e immediately apparent. The numer a t o r exponent f o r t h e oxygen i s v e r y c l o s e t o 0.5, and i t i s t h e r e f o r e a good i d e a t o s i m p l y s e t i t t o 0.5 t o agree w i t h t h e exponent i n t h e denominator. Likewise, the exponent f o r dammitol i n t h e numerator i s n o t f a r removed from 1.0 ( i t s exponent i n t h e denominator) and so we w i l l s e t i t t o 1.0. The s e a r c h v a r i a b l e s have
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
300
CHEMICAL
REACTION
ENGINEERING—HOUSTON
been narrowed t o t h r e e : the e q u i l i b r i u m constants i n the denominator. A f t e r r e - f i t t i n g , the r e s u l t i s
21.lie r
2.0
1+1.83 The r e s u l t s o f t h e p r e d i c t i o n s o f t h i s model a r e shown i n T a b l e I I as H e u r i s t i c Model #2. The s t a n d a r d d e v i a t i o n o f t h e e r r o r w i t h r e s p e c t t o t h e "observed" d a t a i s not q u i t e a d eithe f th othe models, but i t p r e d i c t ter — the standard o n l y about 8 p e r c e n t . Once a g a i n we see t h e paradox. The b e s t model o f t h e t h r e e f o r p r e d i c t i o n and d e s i g n purposes a c t u a l l y f i t s t h e d a t a from which i t was developed t h e p o o r e s t . I t i s , t h e r e f o r e , the l e a s t l i k e l y t o be used i n p r a c t i c e . T h i s happens q u i t e f r e q u e n t l y w i t h e r r o r - c o n t a i n i n g d a t a , and i s , i n t h e a u t h o r ' s judgment, a f r e q u e n t cause f o r t h e f a i l u r e o f models t o p r e d i c t d e s i g n e d performance a d e q u a t e l y . The o b v i o u s q u e s t i o n i s how t o t e l l when a model i s adequate f o r d e s i g n and when i t i s not — o r which i s t h e b e s t o f s e v e r a l . One o b v i o u s l y cannot use a model merely because i t conforms t o a mechanism o f some s o r t and doesn't f i t t h e d a t a v e r y w e l l . But j u s t f i t t i n g t h e d a t a w e l l i s o b v i o u s l y not enough. There a r e t h r e e answers t o t h e above q u e s t i o n . The f i r s t i s t o improve t h e a c c u r a c y o f t h e d a t a t o the extent p r a c t i c a b l e . Ten p e r c e n t d a t a i s d i f f i c u l t t o produce, but t h e problems c i t e d here a r e u s u a l l y not s e r i o u s with data of that q u a l i t y . The second answer i s t o t e s t t h e model e x t e n s i v e l y a g a i n s t d a t a t h a t were not used i n i t s development, and p r e f e r a b l y i n a r e a c t o r o f d i f f e r e n t geometry. If a f i x e d - b e d c a t a l y t i c r e a c t o r i s t o be used, then t h e model s h o u l d be t e s t e d i n a t e s t r e a c t o r o f s i m i l a r d e s i g n — a s i n g l e p l a n t - s c a l e tube makes an e x c e l l e n t test reactor. The t h i r d answer i s t o u t i l i z e n o n - k i n e t i c means to d i s c e r n t h e t r u e mechanism o f the r e a c t i o n . I t i s p o s s i b l e t o determine, f o r example, whether a s p e c i e s l i k e dammitol chemisorbs t o an a p p r e c i a b l e e x t e n t on a catalyst. Had such i n f o r m a t i o n been a v a i l a b l e i n the study o f t h e example, dammitol would have been e l i m i n a t e d from t h e denominator and t h e s t a n d a r d d e v i a t i o n o f t h e e r r o r f o r t h e " t r u e " d a t a would have been
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
24.
CROPLEY
Heuristic Approach to Complex Kinetics
301
o n l y about two p e r c e n t . But the paradox would s t i l l remain — the s t a n d a r d d e v i a t i o n f o r the " o b s e r v e d " d a t a would have been about the same as f o r the o t h e r h e u r i s t i c models, and not as good as t h a t f o r the e x p o n e n t i a l model. But the a b i l i t y o f the h e u r i s t i c models t o p r e d i c t " t r u e " v a l u e s i s t y p i c a l l y b e t t e r than t h a t of the more f l e x i b l e p o w e r - s e r i e s model f o r complex r e a c t i o n s . A Comparison With Modern S t a t i s t i c a l
Methods
There has been s u b s t a n t i a l p r o g r e s s o v e r the past twenty y e a r s i n the use o f modern s t a t i s t i c a l methods to develop non-linea t h e s e approaches emphasiz t o narrow the c o n f i d e n c e i n t e r v a l s of the e s t i m a t e d parameters and t e c h n i q u e s t o d i s c r i m i n a t e between r i v a l mechanisms. There i s an e x t e n s i v e l i t e r a t u r e on the s u b j e c t , and the r e a d e r i s r e f e r r e d t o one or two e x c e l l e n t r e v i e w a r t i c l e s as s t a r t i n g p o i n t s ( 4 ) , ( 5 ) . In g e n e r a l , t h e s e approaches have not met w i t h w i d e - s p r e a d s u c c e s s i n i n d u s t r y because they are v i r t u a l l y l i m i t e d t o n o n - l i n e a r models o f fewer than f o u r o r f i v e unknown p a r a m e t e r s . As the number o f p a r a meters i s i n c r e a s e d t o d e s c r i b e complex c h e m i s t r y more a d e q u a t e l y , the ranges of the r e a c t i o n c o n d i t i o n s r e q u i r e d f o r the e s t i m a t i o n of unique parameter v a l u e s c o r r e s p o n d i n g l y widen. I t o f t e n happens t h a t the r e q u i r e d ranges are u n r e a l i s t i c because the r a t e l i m i t i n g mechanisms change b e f o r e such ranges can be reached. The h e u r i s t i c approach was d e v e l o p e d t o b l e n d mathematics w i t h a knowledge o f c h e m i s t r y t o accomp l i s h f o r complex systems what n e i t h e r i s a b l e t o alone. Conclusions In t h i s paper I have attempted t o demonstrate a method f o r the development of h y p e r b o l i c r a t e models t h a t are adequate f o r the d e s i g n o f c h e m i c a l r e a c t o r s . The method i s r a p i d and overcomes most of the problems t h a t h i s t o r i c a l l y have hampered the development o f such models f o r complex r e a c t i o n s . I have shown t h a t the q u a l i t y o f f i t o f a model t o e r r o r - c o n t a i n i n g d a t a i s a poor c r i t e r i o n f o r model d i s c r i m i n a t i o n , and t h a t s e v e r a l models may p r e d i c t almost e q u a l l y w e l l . This, of c o u r s e , has been known f o r a l o n g time, but i t has not been w i d e l y r e c o g n i z e d t h a t the model t h a t f i t s the d a t a l e a s t w e l l may be the b e s t model, and t h a t the c o n v e r s e a l s o may be t r u e . In the f i n a l a n a l y s i s
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION
302
ENGINEERING—HOUSTON
a model must be t e s t e d t h o r o u g h l y b e f o r e r e a c t o r design i s f i x e d . Because o f i t s r a p i d i t y and s i m p l i c i t y , t h e h e u r i s t i c approach p e r m i t s t h e i n v e s t i g a t o r more time f o r c r i t i c a l t e s t i n g and m o d i f i c a t i o n . Literature (1) (2) (3)
(4) (5)
Cited
B e r t y , J., Chem. Eng. P r o g . , (1974), 7 0 ( 5 ) . Box, G.E.P., B i o m e t r i c s , (1954), 10, 16-60. D a v i e s , O.L., "Design and A n a l y s i s o f I n d u s t r i a l Experiments", 534-5, Hafner P u b l i s h i n g Company, New York, 1960. Reilly, P.M., and B l a u , G.E., Can. J . Chem. Eng., (1974) 52, 289-299 Kittrell, J.R., and Chemical R e a c t i o E n g i n e e r i n g " , 119-32, American C h e m i c a l S o c i e t y P u b l i c a t i o n s , Washington, D.C., 1967.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
25 Kinetics of Catalytic Liquefaction of Big Horn Coal Y. T. S H A H , D . C. C R O N A U E R , H . G . M c I L V R I E D , and Gulf Research and
Development Co.,
J. A.
PARASK0S
Pittsburgh, PA 15230
A number o f coal l i q u e f a c t i o n processes, i n c l u d i n g Gulf CCL, are being developed to help counter the coming l i q u i d f u e l shortages. In most coal l i q u e f a c t i o n processes, coal i s l i q u e f i e d i n the presence o f a solvent. In a d d i t i o n , the c o a l - o i l s l u r r y may be contacted by a hydrogen-rich gas, and a c a t a l y s t may also be present. The process of l i q u e f a c t i o n produces a wide b o i l i n g range l i q u i d , as well as l i g h t gases (C -C ) and by-products, such as water, ammonia, hydrogen s u l f i d e , e t c . Data f o r the k i n e t i c s of coal l i q u e f a c t i o n have been p u b l i s h ed i n the l i t e r a t u r e (1-11). A review o f the reported studies has r e c e n t l y been given by Oblad (12). The reported data were mostly obtained i n bench-scale r e a c t o r s . Guin et al. (7) studied the mechanism of coal p a r t i c l e d i s s o l u t i o n , whereas Neavel (7), Kang et al. (8), and Gleim (10) examined the r o l e of solvent on coal l i q u e f a c t i o n . T a r r e r et al. (9) examined the e f f e c t s of coal minerals on r e a c t i o n rates during coal l i q u e f a c t i o n , whereas Whitehurst and M i t c h e l l (11) studied the short contact time coal l i q u e f a c t i o n process. It i s b e l i e v e d that hydrogen donor solvent plays an important r o l e i n the coal l i q u e f a c t i o n process. The r e a c t i o n paths i n a donor solvent coal l i q u e f a c t i o n process have been reviewed by Squires (6). The reported studies examined both thermal and c a t a l y t i c l i q u e f a c t i o n processes. So f a r , however, very little e f f o r t has been made to present a d e t a i l e d k i n e t i c model f o r the intrinsic k i n e t i c s of coal l i q u e f a c t i o n . The primary purpose of t h i s paper i s to describe the k i n e t i c s of c o a l l i q u e f a c t i o n derived from a p i l o t - s c a l e u n i t . The s p e c i f i c coal studied was Big Horn subbituminous c o a l . The experimental data were obtained i n a p i l o t - s c a l e Gulf patented (13) r e a c t o r . The data i l l u s t r a t e the e f f e c t s of r e a c t o r space time and temperature on the product d i s t r i b u t i o n . Since the r e a c t o r behaves as a bubble column, the i n t r i n s i c k i n e t i c s of the l i q u e f a c t i o n process can be extracted by means of a kinematic model o f the r e a c t o r . The experimental data were found to be 1
©
4
0-8412-0401-2/78/47-065-303$05.00/0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
304
CHEMICAL
REACTION
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adequately c o r r e l a t e d by a simple r e a c t i o n mechanism. Experimental A schematic o f the experimental u n i t i s shown i n Figure 1. This u n i t p r i m a r i l y c o n s i s t e d o f a feed tank, charge pump, p r e heater, r e a c t o r and product r e c e i v e r s . A separate hydroclone u n i t was used t o prepare r e c y c l e s o l v e n t . The r e a c t o r was 6 cm I.D. by 122 cm long. The u n i t was operated w i t h a cocurrent upflow c o a l s l u r r y r a t e o f 1.8 kg/hr, the feed s l u r r y c o n s i s t e d of mixture o f 40% c o a l and 60% hydroclone overflow. Big Horn (WY) subbituminous c o a l was used f o r t h e experiments. I t was p u l v e r i z e d and screened t o minus 20 mesh, but was not p r e d r i e d ; t h e r e f o r e , t h e moisture l e v e l o f t h e feed c o a l was t y p i c a l l y 22 wt%. The ash conten carbon, hydrogen and oxyge and 19.9 wt%, r e s p e c t i v e l y . A l l runs were made a t 24.1 MPa pressure and a gas r a t e o f 2575 dm /hr. A G u l f developed c a t a l y s t was used. S u f f i c i e n t analyses were made t o o b t a i n d e t a i l e d m a t e r i a l balances over the l i q u e f a c t i o n r e a c t o r . S o l v a t i o n o f the c o a l organic matter on a moisture and ash-free (maf) b a s i s was c a l c u l a t e d u s i n g t h e f o l l o w i n g equation: 3
ο ο , ^. maf c o a l feed - maf u n d i s s o l v e d c o a l % Solvation = τ—ζ—ι x 100 maf c o a l feed Ί Λ η
Έ
Reactor. The r e a c t o r used i n t h i s study was a p i l o t p l a n t v e r s i o n o f the G u l f patented (13) segmented bed r e a c t o r . The c a t a l y s t was h e l d i n tubes o f 17 mm I.D. by 114 cm length con s t r u c t e d o f 10-mesh (U.S.) s t a i n l e s s s t e e l screen. In many o f the runs, the c a t a l y s t charge was placed i n f o u r o f the above tubes which t y p i c a l l y h e l d 750 g o f the c a t a l y s t . Some runs were made u s i n g only one o r two c a t a l y s t tubes by b l o c k i n g o f f a p o r t i o n o f the r e a c t o r cross s e c t i o n . Glass model s t u d i e s (14) w i t h an upflow a i r - w a t e r system have shown t h a t gas flow p l a y s a s i g n i f i c a n t r o l e i n a c h i e v i n g a x i a l mixing i n t h e open spaces between the c a t a l y s t tubes and r a d i a l mixing w i t h i n t h e c a t a l y s t tubes; both a x i a l and r a d i a l mixing i n c r e a s e d w i t h an i n c r e a s e i n the hydrogen flow r a t e . I t i s b e l i e v e d t h a t the r e a c t i o n process i n v o l v e s depolymeri z a t i o n and s o l v a t i o n o f t h e c o a l , w i t h these r e a c t i o n s o c c u r r i n g p r i m a r i l y i n t h e open spaces between the c a t a l y s t tubes. Once the c o a l fragments a r e l i b e r a t e d , they a r e e i t h e r s t a b i l i z e d by hydrogen o r repolymerized. Thus, the molecular weight o f the l i q u e f a c t i o n products i s determined by a combination o f c o a l p r o p e r t i e s and hydrogénation a c t i v i t y w i t h i n the r e a c t o r . The process o f s o l v a t i o n i s improved as t h e hydrogen donor c a p a c i t y of the l i q u i d phase i s increased. I n order t o improve the a v a i l a b i l i t y o f the c a t a l y s t surface t o the r e a c t a n t s , entrapment
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
SHAH
ET AL.
Catalytic Liquefaction of Coal
Simplified Flow Unit Bench Scale Liquefaction Unit SOLVENT HYDROGEN COAL
VENT
GAS METER COLD SEPARATOR
LIGHT E N D S RECEIVER
CATALYST TUBES.114cm
LONG
SLURRY RECEIVER
Hvdrocyclone Unit (Batch Operation) NITROGEN
VENT
Figure I.
Experimental set-up
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL
306
REACTION
ENGINEERING—HOUSTON
of c o a l p a r t i c l e s w i t h i n the c a t a l y s t tube must be minimized, and a high degree o f r a d i a l mixing w i t h i n the c a t a l y s t tubes must be achieved. Both o f these can be improved by increased hydrogen and o i l flow r a t e s . Upgrading o f the product o i l occurs p r i m a r i l y w i t h i n the c a t a l y s t tubes. The d i s s o l v e d hydrogen r e q u i r e d f o r both s o l v a t i o n and upgrading i s continuously s u p p l i e d from the gas phase. Both the l i t e r a t u r e and a v a i l a b l e experimental data on hydrogen s o l u b i l i t y i n c o a l l i q u i d s at r e a c t i o n temperature and pressure i n d i c a t e that mass t r a n s f e r of hydrogen from the gas i n t o the l i q u i d phase i s not a l i m i t i n g f a c t o r i n the r e a c t i o n process. Reactor Model. The i n t r i n s i c k i n e t i c i n f o r m a t i o n f o r the l i q u e f a c t i o n process can be evaluated from the data by accounting f o r mass t r a n s f e r e f f e c t s system was modeled by makin and l i q u i d flow as a uniform s l u r r y w i t h i n the r e a c t o r . Based on the study o f Kato et al», (15) i t i s reasonable to assume that the backmixing c h a r a c t e r i s t i c s of c o a l and o i l are about the same. (2) There are no r a d i a l c o n c e n t r a t i o n or temperature gradients w i t h i n the r e a c t o r . (3) The c o n c e n t r a t i o n of hydrogen i n the s l u r r y i s always i n excess o f that r e q u i r e d f o r r e a c t i o n , and (4) The a x i a l d i s p e r s i o n e f f e c t w i t h i n the r e a c t o r i s s i g n i f i c a n t . In the present study, we have assumed a simple r e a c t i o n mechanism f o r c o a l s o l v a t i o n i l l u s t r a t e d by Equation (1). Gaseous Products (H 0, 9
k Coal
1->
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
<
Δ,Ο.Ο
Experimental
Α,φ,φ
M o d e l P r e d i c t e d Data
0.6
Data
Oils
0.4 Gases
ο CO i_
Ο)
0.2
Ο J J n c o n v e r t e d Coal • —-=^~-
ο
Ο
C o a l S l u r r y R e a c t o r S p a c e T i m e , hr. Figure 2.
Experimental and model predicted data for reactor space time effect on coal solvation and productions of oils and gases
30.0 20.0 Coal — O i l
2 10.0 c ο
Ε = 4 5 , 9 0 0 c a l / g m mole
(Λ C
ω
ε
5.0
ο C o a l — + gases
c
E= 6 4 , 0 0 0 c a l / g m m o l e
CO (Λ C
ο ο
ω c
1.0
Γ = 0.75 ( g . s l u r r y / g . cat./nr.)
0.3 139
14.5
14.0
Inverse A b s o l u t e T e m p e r a t u r e , 1 χ 1 0 ( Κ ) 4
Figure S.
β
}
Arrhenius plots for reaction rate constants
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
25.
SHAH ET
AL.
Catalytic Liquefaction of Coal
311
as w e l l as s i g n i f i c a n t evaporation o f the l i q u i d products, both of which would give a poorer product d i s t r i b u t i o n . In the present study, the g a s - l i q u i d mass t r a n s f e r c o e f f i c i e n t s under the p r e v a i l i n g experimental c o n d i t i o n s were e s t i mated using the c o r r e l a t i o n s o f A k i t a and Yoshida (17). The r a d i a l d i s p e r s i o n c o e f f i c i e n t s w i t h i n the c a t a l y s t tubes were measured as a f u n c t i o n o f gas flow r a t e i n a glass model of the r e a c t o r . The d e t a i l s o f these measurements w i l l be r e l e a s e d i n a subsequent p u b l i c a t i o n . Based on t h i s knowledge and an estimated value o f the c a t a l y t i c k i n e t i c constant f o r solvent hydrogénation at the highest temperature and pressure c o n d i t i o n s examined i n t h i s study, the minimum gas flow r a t e r e q u i r e d to permit n e g l e c t i n g mass t r a n s f e r r e s i s t a n c e s was obtained. This value o f the gas flow r a t d i a l l experiments Conclusions As a r e s u l t o f the present study, the f o l l o w i n g conclusions are drawn. 1. The simple k i n e t i c model f o r c o a l l i q u e f a c t i o n presented here appears to c o r r e l a t e well the experimentally observed e f f e c t s o f space time and temperature on coal s o l v a t i o n and the production o f o i l s . The model must be r e f i n e d f u r t h e r to account f o r hydrogen donor and hydrocracking r e a c t i o n s and to p r o p e r l y e x p l a i n the e f f e c t o f pressure on the l i q u e f a c t i o n process. 2. It appears that a f t e r a r e l a t i v e l y short space time, the product d i s t r i b u t i o n during a c a t a l y t i c coal l i q u e f a c t i o n process run remains e s s e n t i a l l y unchanged. 3. The conversion of c o a l i n t o gases and o i l s appears to be a very temperature-sensitive r e a c t i o n . 4. Since the l i q u e f a c t i o n of c o a l i n a r e g u l a r packed bed c a t a l y t i c r e a c t o r would cause plugging problems, the data i l l u s t r a t e the f e a s i b i l i t y o f using a novel type of r e a c t o r to continuously operate a three-phase g a s - l i q u i d - s o l i d (reactant) r e a c t i o n i n the presence of a c a t a l y s t . Literature Cited 1. Neavel, R. C., Fuel (1976), 55, 237. 2. P l e t t , E. G., A l k i d a s , A. C., Roger, F. E., Mackiewicz, A. Z., and Summerfield, M., a paper presented at University-ERDA Contractors Conference, (October 22-23, 1975), S a l t Lake C i t y , UT. 3. Curran, G. P., Struck, R. T., and Gorin, E., Proceedings, Symposium on P y r o l y s i s Reactions o f F o s s i l F u e l s , " Div. Petroleum Chem., ACS (March 23-26, 1966), P i t t s b u r g h , PA, C-130. 4. Guin, J . Α., T a r r e r , A. R., P i t t s , W. S., and Prather, J . W., Proceedings f o r "Symposium on Coal L i q u e f a c t i o n , " Div. Petro leum Chem., ACS (August 1976), San F r a n c i s c o , CA, 170.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
312
CHEMICAL
REACTION
ENGINEERING—HOUSTON
5. Fu, Y. C. and Batchelder, R. F., Proceedings o f Div. Fuel Chemistry, ACS (August 29-September 3, 1976), 21 (5), 78. 6. Squires, A. M., "Reactor Paths i n Donor Solvent Coal Liquefac t i o n , " a paper presented at conference on coal g a s i f i c a t i o n / l i q u e f a c t i o n , Moscow, U.S.S.R. (October 1976), sponsored by U.S.-U.S.S.R. Trade and Economic C o u n c i l , Inc. 7. Guin, J . , T a r r e r , Α., T a y l o r , L., Jr., Prather, J . , and Green, S., Jr., I&EC Process Design and Dev. (1976) 15 (4), 490. 8. Kang, C. C., Nongbri, G., and Stewart, Ν., Proceedings o f Div. Fuel Chemistry, ACS (August 29-September 3, 1976), San F r a n c i s c o , CA, 21 (5), 19. 9. T a r r e r , A. R., Guin, J. Α., Pitts, W. S., Henley, J . P., Prather, J . W., an Chemistry, ACS (Augus CA, 21 (5), 59. 10. Gleim, W. K. T., Proceedings o f Div. Fuel Chemistry, ACS (August 29-September 3, 1976), San Francisco, CA, 21 (5), 91. 11. Whitehurst, D. D. and M i t c h e l l , T. O., Proceedings o f Div. o f Fuel Chemistry, ACS (August 29-September 3, 1976), San F r a n c i s c o , CA, 21 (5), 127. 12. Oblad, A. G., C a t a l y s i s Reviews, Science and Engineering (1976), 14 (1), 83. 13. Chun, S. W., Cronauer, D. C., and L e s l i e , T. W., U.S. Patent No. 3,957,619 (1976). 14. Shah, Y. T., Ratway, C. Α., and M c I l v r i e d , H. G., B r i t i s h Trans. Inst. o f Chem. Engrs. ( i n p r e s s ) . 15. Kato, Y., Nishiwaki, Α., Fukuda, T., and Tanaka, S., J. o f Chem. Engineer, o f Japan (1972), 5 (2), 112. 16. Paraskos, J . Α., Shah, Y. T., McKinney, J., and Carr, N. L., I&EC Process Design and Dev., (1976), 15, 165. 17. A k i t a , K. and Yoshida, F., Ind. Eng. Chem. (1974), 13 84.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
26 Development of Reaction Models for Complex Gas Phase Reactions K. H . E B E R T ,
H . J. E D E R E R ,
and P. S. S C H M I D T
Institut für Angewandte Physikalische Chemie der Universität, Im Neuenheimer Feld 253, D-6900 Heidelberg, West Germany
Gas phase r e a c t i o n ting up a r e a c t i o n mechanis kinetic scheme does n o t seem v e r y p r o m i s i n g . I n particular, t h i s concerns thermal decomposition r e a c t i o n s o f h y d r o c a r b o n s , in which t h e number o f reactive and s t a b l e s p e c i e s is l a r g e . The effort t o a c c o m p l i s h 'master s e t ' kinetics is huge and u s u a l l y does n o t justify the results o b t a i n a b l e . We have tried t o d e v e l o p a g e n e r a l l y a p p l i c a b l e method t o find o u t t h e ' r e l e v a n t ' elementary r e a c t i o n s , which m a i n l y c o n t r i b u t e t o t h e overall r e a c t i o n s and put them t o g e t h e r t o a c o n s i s t e n t r e a c t i o n mechanism. In a s e m i - q u a n t i t a t i v e a n a l y s i s we have tried t o det e r m i n e t h e different s p e c i e s and their relative abundance a t low p r e s s u r e in a certain temperature range. S t a r t i n g a t low temperatures a t which t h e numb e r o f s p e c i e s is s m a l l a r e a c t i o n mechanism c o n s i s t i n g o f elementary r e a c t i o n s is set up, and calculat i o n s based on this mechanism s h o u l d be verified by comparison w i t h experiments a t normal p r e s s u r e . I n d e v e l o p i n g t h e mechanism t o h i g h e r temperatures and c o n v e r s i o n s one e x p e c t s t h a t more elementary s t e p s have t o be added t o t h e mechanism, b u t t h e number s h o u l d be k e p t t o a minimum. In t h e p r e s e n t paper we have t r i e d t o d e s c r i b e o u r development o f a r e a c t i o n scheme f o r t h e p y r o l y s i s o f e t h y l b e n z e n e . I t seemed t o us t h a t t h i s r e a c t i o n was c b m p l i c a t e d enough t o g e t s u f f i c i e n t d e t a i l s and some o f them w i t h more g e n e r a l s i g n i f i c a n c e . On t h e o t h e r hand, we hoped t h a t , due t o a s i n g l e i n i t i a t i o n r e a c t i o n w i t h i n a f a i r l y wide temperature range, t h e r e a c t i o n would be r e l a t i v e l y e a s i l y c o v e r e d by t h e methods applied.
©
0-8412-0401-2/78/47-065-313$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
314 Experimental
Methods
Low P r e s s u r e Apparatus (LPA). The low p r e s s u r e experiments have been c a r r i e d o u t i n a f l o w a p p a r a t u s made o f q u a r t z and d e p i c t e d i n F i g u r e 1 . The r e a c t i o n took p l a c e i n a r e a c t i o n zone, which had a l e n g t h o f approx. 1 0 c m , t h e r e a c t i o n zone b e i n g heated w i t h a t a n t a l u m w i r e . The a p p a r a t u s was s u i t a b l e f o r tempera t u r e s up t o 1 0 0 0 ° C , t h e l i m i t i n g f a c t o r b e i n g t h e heating of the i o n i s a t i o n source. A t t h e end o f t h e r e a c t i o n zone a sample f l o w o f t h e r e a c t i o n p r o d u c t s was l e d t h r o u g h a n o z z l e d i r e c t l y i n t o t h e e l e c t r o n impact i o n i s a t i o n chamber o f a time o f f l i g h t (TOF) mass s p e c t r o m e t e r The main f l o w of t h e p r o d u c t s wa The p r e s s u r e i 1 0 x 1 0 " " mm. We a d j u s t e d t h e p r e s s u r e i n t h e r e a c t o r t o such a l e v e l t h a t t h e p r e s s u r e i n t h e i o n i s a t i o n s o u r c e o f t h e TOF was l e s s then 10"**mm. V a r i a t i o n o f t h e pumping speed a l l o w e d t o choose r e a c t i o n t i m e s between 0 . 0 0 1 and 1 s e c . To keep fragmentation i n the i o n chamber low we used an e l e c t r o n energy o f 1 2 e V i n most e x p e r i m e n t s . As a r e s u l t a s u r v e y p a t t e r n was o b t a i n e d on a l l species contained i n the r e a c t i o n , i n c l u d i n g free radi c a l s . By changing t h e temperature o f t h e r e a c t i o n zone we o b t a i n e d i n f o r m a t i o n on t h e temperature dependence o f t h e abundances o f t h e r e a c t i o n p r o d u c t s and r a d i c a l s . The r e s u l t s a r e o f a s e m i - q u a n t i t a t i v e c h a r a c t e r because t h e i o n i s a t i o n p r o b a b i l i t i e s o f t h e spec i e s and t h e i r mass d i s c r i m i n a t i o n i n t h e f l o w system a r e n o t known. 2
Normal P r e s s u r e Apparatus (NPA). To v e r i f y o u r c a l c u l a t i o n s based on t h e r e a c t i o n scheme from t h e LPA experiments we s e t up a r e a c t o r which a l l o w e d us t o c a r r y o u t a c c u r a t e q u a n t i t a t i v e measurements on t h e p y r o l y s i s o f e t h y l b e n z e n e . T h i s a p p a r a t u s was made o f q u a r t z and i s d e p i c t e d i n d e t a i l i n F i g u r e 2 . The r e a c t i o n i n t h i s f l o w r e a c t o r s t a r t s i n t h e m i x i n g chamber i n which o v e r h e a t e d argon j o i n s t h e e t h y l b e n z e n e f l o w . The temperature o f t h e argon f l o w was kept a t a s p e c i f i c v a l u e i n o r d e r t h a t t h e r e a c t i o n temperature was o b t a i n e d s i m p l y by t h e m i x i n g o f t h e two streams. The r e a c t i o n zone o f 1 0 c m l e n g t h was k e p t a t a c o n s t a n t temperature by independent c o n t r o l o f s e v e r a l c o i l s . The r e a c t i o n gas was quenched w i t h c o l d argon a t t h e end o f t h e r e a c t i o n zone. The temperature i n t h e r e a c t o r was c o n t i n u o u s l y c o n t r o l l e d w i t h a moveable thermocouple a l o n g t h e c e n t e r o f t h e r e a c t o r . The r e -
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
315
a c t i o n time was a d j u s t e d by the r a t e o f the argon f l o w t h r o u g h the r e a c t o r . A sample o f the r e a c t i o n p r o d u c t s was passed t o the i n j e c t i o n l o o p o f a gas chromatograph f o r a n a l y s i s . Argon was used as c a r r i e r gas f o r t h e gas chromatograph. Thus, the c a r r i e r gas i n the r e a c t o r was o f no i n f l u e n c e on the s e p a r a t i o n . We used two s e p a r a t i o n columns i n p a r a l l e l , one f o r t h e gases (112,01111,02116, C2Uk) i the o t h e r f o r t h e l i q u i d s (ethylbenzene, s t y r e n e , t o l u e n e , b e n z e n e ) . Flame i o n i s a t i o n and t h e r mal c o n d u c t i v i t y were used as d e t e c t o r s . G r e a t c a r e was t a k e n t o ensure h i g h s e n s i t i v i t y and r e p r o d u c i b i l i t y o f the a n a l y t i c a l method. a
n
(
Mathematical
Method
The d i f f e r e n t i a l e q u a t i o n s which a r i s e i n almost a l l c h e m i c a l k i n e t i c s t u d i e s o f complex r e a c t i o n schemes a r e " s t i f f d i f f e r e n t i a l e q u a t i o n s " . In c h e m i c a l k i n e t i c s t h e s t i f f n e s s i s caused by t h e huge d i f f e r ences i n the r e a c t i o n r a t e constants of the v a r i o u s elementary r e a c t i o n s . I t i s i m p o s s i b l e t o s o l v e such a system o f d i f f e r e n t i a l e q u a t i o n s by the u s u a l RungK u t t a methods. T h e r e f o r e we used a program, d e s c r i b e d by Gear (JT_) as a s p e c i a l m u l t i s t e p p r e d i c t o r - c o r r e c t o r method w i t h s e l f a d j u s t i n g optimum s t e p s i z e control. The program needs not o n l y the s u b r o u t i n e f o r t h e d e r i v a t i v e s o f the dependent v a r i a b l e s , i . e . concent r a t i o n s o f t h e c h e m i c a l s p e c i e s i n v o l v e d o v e r time, which c o n s t i t u t e s a system o f m s t i f f d i f f e r e n t i a l e q u a t i o n s , b u t a l s o a s u b r o u t i n e which e v a l u a t e s the p a r t i a l d e r i v a t i v e s of the d i f f e r e n t i a l e q u a t i o n s w i t h r e s p e c t t o the c o n c e n t r a t i o n s o f the d i f f e r e n t species, resulting i n m equations. Because i t i s v e r y cumbersome t o s e t up the m d i f f e r e n t i a l e q u a t i o n s and the m e q u a t i o n s f o r the partial d e r i v a t i v e s , we have d e v e l o p e d a program which d i r e c t l y g e n e r a t e s t h e two s u b r o u t i n e s from t h e c h e m i c a l r e a c t i o n scheme and the a s s i g n e d k i n e t i c p a r a m e t e r s . The o u t p u t o f the program g i v e s t h e conc e n t r a t i o n o f each c h e m i c a l s p e c i e s i n dependence on t i m e . We a l s o o b t a i n e d i n f o r m a t i o n on t h e c o n t r i b u t i o n of each elementary r e a c t i o n on t h e o v e r a l l r e a c t i o n . These c a l c u l a t i o n s must be r e p e a t e d f o r d i f f e r e n t p r e s e l e c t e d r e a c t i o n t e m p e r a t u r e s . The e f f o r t r e q u i r e d f o r the c o m p u t a t i o n o f the r e a c t i o n k i n e t i c s a t a p a r t i c u l a r temperature was approx.10 sec of CPU time on an IBM 370. 2
2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
316 R e s u l t s and D i s c u s s i o n
E x p e r i m e n t a l r e s u l t s on t h e p y r o l y s i s o f e t h y l benzene o b t a i n e d i n t h e low p r e s s u r e a p p a r a t u s (LPA) a r e shown i n F i g u r e 3, i n which t h e d i s t r i b u t i o n o f t h e v a r i o u s s p e c i e s i s shown i n dependence on t h e r e a c t i o n temperatures as an a n a l o g p l o t t i n g . 72 d i f f e r e n t s p e c i e s were d e t e c t e d . Those w i t h an abun dance s m a l l e r than 2% a r e s u p p r e s s e d i n F i g u r e 3. Up t o t e m p e r a t u r e s o f 750°C t h e f o l l o w i n g 9 s p e c i e s a r e o b t a i n e d : methane, e t h y l e n e , t o l u e n e , s t y r e n e , e t h y l b e n z e n e , d i b e n z y l , m e t h y l , b e n z y l and e t h y l b e n z y l . The most s i m p l e r e a c t i o n scheme i n v o l v i n g t h e s e c o n s i s t s o f seven e l e m e n t a r y r e a c t i o n s : -CH CH
(1) (2)
2
C H
3
+
(3)
Φ-ΟΗ
3
φ—CH —CH 3
->
4>-CH-CH
3
+
CH
4>-CH-CH3
->
4>-CH=CH2
+
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->
-CH-CH3
+
H
->
Φ"ΟΗ
2
(4)
H
+ 4>-CH -CH
(5)
H
+
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+
(6) (7)
CH
2
3
4>-CH2 CH
2φ-ΟΗ
3
->
C
2
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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
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.
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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
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/
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/
! /·/·
!
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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 <
Table III. Scheme of sulfonation experiments in c y c l o n e reactor.
gas load ( U ) . T h e results
L
< 1.8 m/s; 0.04 < f
A
0.08;f < 0.33). T h e Figure
shows that by-product forma tion is much less in these reac tors than in the stirred cell re
actor. However, the difference is less than may be expected from eqn. (14) with k and Figure 3 respectively. Therefore, k
L
L
from Table II
is probably also lowered by interface viscosity effects in
the cyclone and in the tube reactor during sulfonation o f 30 vol. % bezene and of neat benzene, additional arguments support this hypothesis [3]. This does not exclude the possibility that the /alue of the mass transfer coefficient, as measured in the cyclone and in the tube reactor with the (0 -)C0 -aqueous 2
2
N a O H system, remains a relative measure of the actual k
L
in those reactors
during sulfonation, provided that gas and liquid loads are similar in both types of experiment. Figure 7 presents average values of Ί-η' as a function of this liquid-side, mass transfer coefficient in both the cyclone and the tube reactor (from Figure 3, partly by extrapolation). Thus presen ted, the (1-1?' ) values fall o n a single line within the experimental error.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
334
Figure 5. k O as a function of surface temperature from aver aged experimental results. (Φ) 5.3 vol % benzene; (A) 30 vol % benzene; (O) neat benzene. 2
3
1
Χ)/η [·κ-]
U
s
A
[m/s]
Figure 6. By-product formation in sulfonation of benzene (average values). (Φ, j neat benzene at = 20° C in cyclone reactor ( Φ ), tube reactor ( ) and stirred-cell reactor ( «#, ζ 0.05, Τ = 25°C) respectively. (Ο, -Θ-, * θ ) 30 vol % benzene in 1,2-dichloroethane at = 20°C in cyclone reactor (O), tube reactor (-Θ-), and stirred-cell reactor ( «Ο, ζ = 0.1, Τ = 25°C) respec tively. (A) neat benzene at = 40°C in cyclone reactor (ζ = 0.04). (Δ, ^ Δ ) 30 vol % benzene at = 40°C in cyclone reactor (Δ, ζ = 0.1) and stirred-cell reactor ( +Α,ζ^ 0.15, Τ = 45°C). }
Figure 7. By-product formation (1 — η) in sulfonation of 30 vol % ben zene in 1,2-dichloroethane at 20°C, as a function of k as measured with the system 0 -C0 -hydroxide. (O) in cyclone reactor, (A) in tube re actor. L
2
100
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
BEENACKERS
335
S u l f o n a t i o n of 10 vol.% benzene results in 100 % selectivity in a cyclone reactor (see Table IV). C o m p a r e d to 30 v o l . % benzene sulfonation, the term Ό
1
Έ
ΒΒ
+ Z
D
A
M
A G
C
decreases f r o m ν.
f
X
Τ
ζ
A
[m/s]
[m/s]
2.4
to
1.4
(Table
I).
A p p a r e n t l y this is sufficient to produce
[°c]
a
substantially higher k
(by
L
lowering
of C j . ) and thus for a far better selectivi 0.025
6.80
0.105
0.259
1.00
23.0
t y . C o m p a r i s o n of the 10 v o l . % bezene
0.030
3.46
0. 107
0. 327
1.00
20.0
cyclone experiments
0.042
5.89
0.088
0.459
0.995
20.6
%
benzene
cell
reactor
product Table IV.
with the 5.3
sulfonation
in
shows that
formatio
i
the
vol.
stirred
minimum found
by
i
th
S u l f o n a t i o n o f 10 v o l . %
dichloroethane in a c y c l o n e reactor a f o r m a t i o n . A t these low c"
values the difference in η possibly follows f r o m e q n . (14)
B
with
k
L
f r o m Table II and Figure 3 respectively.
Nomenclature A
sulfur trioxide
Β
benzene
Τ
temperature, ° K , ° C superficial liquid v e l o c i t y , m / s
c
concentration, k m o l / m
d
diameter, m
U
3
s
superficial
gas v e l o c i t y ;
in c y c l o n e
reactor
related t o porous wall area; in tube reactor as usual, m / s
2
D
d i f f u s i o n coefficient, m / s
Ε
enhancement factor, i.e., factor by w h i c h rate
ν
liquid v e l o c i t y , m / s
of absorption is increased by reaction (2)
χ
m o l f r a c t i o n in liquid d i p h e n y l sulfone
enhancement factor w h e n reaction (2) is in
X
stantaneous
z
stoichiometric coefficient f r o m equation (2)
ΔΕ
activation energy, J / k m o l
ζ
conversion of benzene
77
selectivity, fraction of converted benzene that
17'
differential selectivity ("p^B)
heat of a b s o r p t i o n , J / k m o l
λ
thermal c o n d u c t i v i t y , W / m ° C
heat o f reaction, J / k m o l
μ
viscosity, s Pa
p y r o s u l f o n i c acid (benzenesulfonic acid, m o -
β
liquid density, k g / m
f
m o l fraction in gas feed
G
gas phase
Ha
Hatta n u m b e r
ΔΗ ΔΗ
9
Γ
I
is converted t o benzenesulfonic acid
_ (V k, D
A
Cg/k
)
L
r
r
3
n o a n h y d r i d e with sulfonic acid) Γ
C H S 09H 6
5
3
(benzenesulfonic
acid,
mono-
a n h y d r i d e with disulfuric acid) k, , k
absorption rate per u n i t area, k m o l / m s
Subscripts
reaction
A
2
J 2
rate constants, defined in eqns. (2)
sulfur trioxide
3
and (3), m / k m o l s k.Q
gas phase
mass
transfer
Β
benzene
m/s
G
gas phase
coefficient, m / s
i
at interface; in inlet
I
p y r o s u l f o n i c acid
coefficient,
k^
liquid
oo
pre-exponential factor in e q n . (17)
k
phase mass transfer
L
liquid phase
m
solubility
Ν
speed of revolution o f impeller, rev/s
Ρ
benzene sulfonic acid
(C^^L^CA'^G
rate o f f o r m a t i o n , k m o l / m s
R
gas constant, J / k m o l Κ
liquid phase benzenesulfonic acid
S
solvent
Superscript
3
r
L Ρ
0
Re
Reynolds
number;
in stirred
Sc
Schmidt number ( μ / p D )
Sh
S h e r w o o d number (k, d / D )
— cell:
in bulk o f liquid
pNd Ιμ 2
with d = diameter o f stirrer
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
336
CHEMICAL REACTION ENGINEERING—HOUSTON
Literature Cited
[1] Van de Vusse, J.G., Chem. Eng. Sci., (1966),[11] 21,631 [2] Beenackers, A.A.C.M., and van Swaaij, W.P.M. "Chem.React. Eng., Proc. Eur., 6th, Int., [12] 4th, Symp.", p.VI 260, Dechema, Frankfurt [13] (M), 1976 [3] Beenackers, A.A.C.M., "Ph. D.Thesis", Twente University of Technology, Enschede, 1977 [14] [4] Danckwerts, P.V., "Gas-Liquid Reactions", [15] McGraw Hill, London, 1970 [5] Harriott, P., Can. J. Chem. Eng., (1970), 48, [l6] 109 [6] Teramoto, M., Nagayasu, T. shimoto, K. and Nagata, S., Eng Jpn., (1969), 2, 186 [7] Inoue, H. and Kobayashi, T., "Chem. React. [l8] Eng., Proc. Eur. Symp., 4th", 147, Pergamon, Oxford, 1968 (pub. 1971) [8] Pangarkar, V.G. and Sharma, M.M., Chem. [19] Eng. Sci., (1974), 29, 561 [9] Nakao, K., Hashimoto, K. and Otake, T., J. Chem. Eng. Jpn., (1972), 5, 264 [10] Teramoto, M., Hashimoto, K. and Nagata, S.,[20] J. Chem. Eng. Jpn., (1973),6,522
Hikita, H., Ishikawa, H. and Murakami, Y., Bull. Univ. Osaka Prefect., Ser. Α., (1970), 19, 34 Jhaveri, A.S. and Sharma, M.M., Chem. Eng. Sci., (1967), 22, 1 Koetsier, W.T., "Ph. D. Thesis", Twente Uni versity of Technology, Enschede, 1973 Calderbank, P.H. and Moo-Young, M.B., Chem. Eng. Sci., (1961), 16, 39 Porter, K.E., King, M.B. and Varshney, K.C., Trans. Inst. Chem. Eng., (1966), 44, T274 Danckwerts P.V d Sharma M.M. Chem AlChE J., (1973), 19, 916 Govier, G.W., and Aziz, K., "The flow of complex mixtures in pipes", van Nostrand Reinhold Comp., New York, 1972 Gregory, G.A., and Scott, D.S. in: "Co-cur rent Gas-Liquid Flow", (Edited by E.Rhodes and D.S. Scott), Plenum Press, New York, 1969 Bosscher, J.K., "Ph. D. Thesis", Gemeentelijke Universiteit, Amsterdam, 1967
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
28 Axial Mixing of Liquid in Packed Bubble Columns and Perforated Plate Columns of Large Diameter P E T E R M A G N U S S E N and V O L K E R
SCHUMACHER
B A S F Aktiengesellschaft, Amoniaklaboratrium, 6700 Ludwigahafen, West Germany
In many cases bubbl -reactions. Their construction is very simple, is difficult to precalculate their optimal design. The simplist form of a bubble column is a verti cal tube in which a gas distributor i s placed at the b o t t o m ; packed or plate bubble columns are also u s e d . The gas bubbles rise t h r o u g h the liquid phase, w h i c h may f l o w through the column either cocurrent or countercurrent to the g a s . As a result of the short residence time of the gas bubbles in the liquid phase, bubble column reactors are preferred for reactions which require a short gas and a long liquid reaction time. Therefore the residence time distribution of the liquid phase is a characteristic factor for the design of the reactor. The dependence of the residence time distribution upon the column d i a m e t e r has to be known for any scale-up of bubble columns. The residence time distribution of a reactor i s a function of the axial mixing within the reactor. The extreme cases a r e : 1) the i d e a l c o n t i n u o u s s t i r r e d tank r e a c t o r (CSTR) w i t h complete m i x i n g and, 2) the i d e a l p l u g f l o w r e a c t o r (PFR) w i t h o u t any b a c k m i x i n g of the l i q u i d d u r i n g i t s f l o w t h r o u g h the r e a c t o r . The b e h a v i o r of r e a l r e a c t o r s l i e s between t h e s e e x t r e m e s . I t may be d e s c r i b e d by c o m p a r i s o n to a s t i r r e d tank cascade of as many tanks as n e c e s s a r y to o b t a i n the b e h a v i o r of the r e a l r e a c t o r ; the r e s u l t of t h i s comparison i s c a l l e d "number of e q u i v a l e n t t a n k s " . I n t h i s model the CSTR e q u a l s 1 i d e a l tank and the PFR i s e q u i v a l e n t to a cascade w i t h an i n f i n i t e number of t a n k s . T h i s d e s c r i p t i o n c o r r e s p o n d s to the mathe m a t i c a l c e l l model. The d i s p e r s i o n m o d e l i s a n o t h e r way o f c h a r a c t e r i z i n g the r e s i d e n c e time d i s t r i b u t i o n of a r e a l r e a c t o r . In t h i s model i t i s assumed t h a t a x i a l m i x i n g i s s u p e r ©
0-8412-0401-2/78/47-065-337$05.00/0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
338
CHEMICAL
REACTION
ENGINEERING—HOUSTON
imposed upon p l u g f l o w t h r o u g h t h e r e a c t o r . T h i s a x i a l m i x i n g w i d e n s t h e r e s i d e n c e t i m e c u r v e and i s c h a r a c t e r i z e d by t h e P e c l e t - n u m b e r Pe ( i n German t h i s i s u s u a l l y c a l l e d Bodenstein-number Bo) w h i c h i s d e f i n e d by e q u a t i o n ( 1 ) : Ve-2-JL±
(,)
D ax = superficial liquid velocity = l e n g t h of the r e a c t o r ( h e i g h t of column) 0^ = mixing coefficient
u L
the
bubble
χ
In t h i s e q u a t i o n D i c i e n t and i s i n d e p e n d e n t o the g mechanis ( i . e . m o l e c u l a r d i f f u s i o n , b a c k m i x i n g e t c . ) . The m i x i n g c o efficient D = 0 i n an i d e a l PFR y i e l d s Pe = oo . The b o u n d a r y vaîue f o r t h e i d e a l CSTR w i t h i n f i n i t e m i x i n g a p p r o x i m a t e s Pe = 0. S e v e r a l e q u a t i o n s a r e used to compare b o t h m o d e l s . A s i m p l e a p p r o x i m a t i o n i s g i v e n by e q u a t i o n ( 2 ) : ^
number o f e q u i v a l e n t t a n k s η =
ι
2
( )
+ ι
2 A t s m a l l P e - n u m b e r s a d d i t i o n a l c o r r e c t i o n t e r m s may be used . B o t h m o d e l s may be u s e d t o d e s c r i b e t h e r e s i d e n c e t i m e d i s t r i b u t i o n i n b u b b l e c o l u m n s . The r e s i d e n c e t i m e b e h a v i o r d e p e n d s u p o n t h e c o l u m n L/D r a t i o . B u b b l e c o l u m n s o f l a r g e L/D r a t i o s may be c o m p a r e d w i t h P F R s ; b u b b l e c o l u m n s o f s m a l l L/D ratios a r e s i m i l a r t o CSTRs. The o b j e c t i v e o f o u r w o r k was t o d e t e r m i n e t h e r e l a t i o n s h i p b e t w e e n a x i a l m i x i n g and c o l u m n d i a m e t e r w i t h an end o f f i n d i n g a way t o r e d u c e a x i a l mixing i n l a r g e diameter bubble columns. L i t e r a t u r e about a x i a l m i x i n g i n bubble columns is quite extensive, i . e . (1), (2), (3). Unfortunately most of t h e p u b l i c a t i o n s r e f e r t o column d i a m e t e r s of l e s s t h a n 200 mm. O n l y a f e w s t u d i e s h a v e b e e n done on b u b b l e c o l u m n s o f l a r g e d i a m e t e r . A r g o and C o v a ( 4 ) as w e l l as T o w e l l and A c k e r m a n n ( 5 ) h a v e s t u d i e d empty b u b b l e c o l u m n s up t o a d i a m e t e r o f 1 m. No l i t e r a t u r e i s known a b o u t p a c k e d c o l u m n s o f t h i s s i z e . The l a r g e s t d i a m e t e r p a c k e d c o l u m n s s t u d i e d by C a r l e t o n e t a l . ( 6 ) and by H o o g e n d o o r n e t a l . ( 7 ) had a d i a m e t e r o f l e s s t h a n 0.5 m. I n o u r s t u d i e s we h a v e i n v e s t i g a t e d t h e r e s i d e n c e t i m e b e h a v i o r i n l a r g e d i a m e t e r b u b b l e c o l u m n s w i t h and w i t h o u t p a c k i n g s ( f i g . l ) . We h a v e u s e d s e v e r a l c o l u m n s
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
28.
MAGNUSSEN
AND SCHUMACHER
Axial Mixing in Bubble and Plate
339
w i t h h e i g h t s f r o m 1 t o 4 m a n d d i a m e t e r s f r o m 40 mm t o 1000 mm. D i f f e r e n t p a c k i n g s o f R a s c h i g - r i n g s a n d P a l l r i n g s v a r y i n g i n s i z e f r o m 10 t o 50 mm w e r e u s e d a s w e l l as p e r f o r a t e d p l a t e s w h i c h a r e d e s c r i b e d l a t e r . A l l m e a s u r e m e n t s h a v e b e e n made w i t h a i r a n d t a p - w a t e r i n c o u n t e r c u r r e n t f l o w a t a m b i e n t t e m p e r a t u r e . The w a t e r f l o w r a t e was m a i n t a i n e d a t 40 m^/m^.h.The super f i c i a l a i r v e l o c i t y was v a r i e d f r o m 0.01 t o 0.1 m/s. S e v e r a l t e s t i n g m e t h o d s a r e known f o r m e a s u r i n g r e s i d e n c e t i m e d i s t r i b u t i o n s i n a r e a c t o r . I t was n e c e s s a r y t o s e l e c t a m e t h o d w h i c h was s u i t a b l e f o r a l l columns s t u d i e d i n t h i s work. Steady s t a t e methods used f o r m e a s u r i n g a x i a l mixing consist of i n j e c t i n trace i th middl f the s t u d i e d i n t e r v a c e n t r a t i o n . There a r problem larg packe as i t i s v e r y d i f f i c u l t t o g e t a h o m o g e n e o u s d i s p e r s i o n o f t h e t r a c e r and t o o b t a i n an average sample p r o f i l e without d i s t u r b i n g the l i q u i d flow i n the column. Unsteady s t a t e methods f o r m e a s u r i n g a x i a l mixing c o n s i s t of i n j e c t i n g a t r a c e r a t the r e a c t o r i n l e t and m e a s u r i n g t h e r e s p o n s e f u n c t i o n a t t h e o u t l e t . I n t h i s i n v e s t i g a t i o n t h e p u l s e m e t h o d was u s e d . T h i s m e t h o d was s e l e c t e d b e c a u s e o n l y s m a l l a m o u n t s o f t r a c e r s u b s t a n c e h a d t o be p r e p a r e d . I m p o s i n g a s t e p c o n c e n t r a t i o n c h a n g e w o u l d h a v e r e q u i r e d much g r e a t e r amounts o f t r a c e r l i q u i d ; f o r example i n a c o l u m n o f 1 m d i a m e t e r 36 m^/h w o u l d be r e q u i r e d . The m e a s u r e m e n t s w e r e d o n e b y a d d i n g a s u d d e n p u l s e o f c o n c e n t r a t e d sodium h y d r o x i d e s o l u t i o n t o t h e water i n l e t . T h e c o n c e n t r a t i o n of t h e sodium h y d r o x i d e a t t h e c o l u m n o u t l e t was m e a s u r e d b y a p H - m e t e r . pH measurement i s h i g h l y a c c u r a t e a t s m a l l c o n c e n t r a t i o n s because of the l o g a r i t h m i c c o n c e n t r a t i o n f u n c t i o n . D a i l y t e s t s w e r e d o n e t o c o m p e n s a t e f o r c h a n g e s i n pH i n d i c a t i o n c a u s e d by c h a n g i n g w a t e r c o m p o s i t i o n . In order to i n t e r p r e t t h e experimental residence t i m e c u r v e s , c o m p a r i s o n may be made w i t h a n i d e a l s t i r r e d t a n k c a s c a d e . I n t e r p o l a t i o n m e t h o d s a r e known t o g e t t h e number o f e q u i v a l e n t t a n k s f r o m t h e n o r m a l i z e d r e s i d e n c e time curves ( 8 ) . T h i s i s o n l y pos s i b l e i f t h e e x p e r i m e n t a l r e s i d e n c e time d i s t r i b u t i o n i s a n i d e a l o n e . I n many c a s e s t h i s i s n o t t r u e . F u r t h e r m o r e t h e r e s i d e n c e t i m e c u r v e s we g e t f r o m o u r experimental arrangement comprise not only the r e s i dence time b e h a v i o r o f t h e b u b b l e column i t s e l f b u t a l s o t h e b e h a v i o r o f t h e l i q u i d and gas d i s t r i b u t o r s . T h e s e a d d i t i o n a l e f f e c t s m u s t n o t be n e g l e c t e d . In order to determine the e f f e c t s of the d i s t r i b u t o r s
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
340
as w e l l a s t h e a p p r o a c h e f f e c t s i n t h e b u b b l e p h a s e , e v e r y t e s t was r u n i n two c o l u m n s o f d i f f e r i n g l e n g t h s ( L j and L ) u s i n g i d e n t i c a l l i q u i d and gas d i s t r i b u t o r s ( f i g . 2 ) . The d i f f e r e n c e i n t h e c u r v e s o b t a i n e d f r o m t h e columns w i t h h e i g h t s L and L a l l o w s one t o c a l c u l a t e t h e r e s i d e n c e time b e h a v i o r of a column w i t h h e i g h t L = L j - L . The a n a l y s i s was d o n e by t h e mo m e n t s m e t h o d o f L e v e n s p i e l a n d S m i t h ( 9 ) . The f i r s t moment ^ i s the center of the curve corresponding to t h e mean r e s i d e n c e t i m e . The s e c o n d moment s^ i s r e l a t e d t o t h e d i s p e r s i o n o f t h e r e s i d e n c e t i m e c u r v e by a x i a l m i x i n g . The p a r t i a l d i f f e r e n t i a l e q u a t i o n s may be c o n v e r t e d by L a P l a c e - t r a n s f o r m a t i o n i n t o l i n e a r e q u a t i o n s f r o m w h i c h t h Pe-numbe b calculated without retransformation I t s h o u l d be n o t e d t h a t t h e c h o i c e o f t h e b o u n dary c o n d i t i o n s f o r the c a l c u l a t i o n of the response f u n c t i o n i s v e r y i m p o r t a n t . Most p u b l i s h e d p r o p o s a l s f o r b o u n d a r y c o n d i t i o n s d e r i v e f r o m two r e s i d e n c e t i m e d i s t r i b u t i o n curves recorded simultaneously upstream and d o w n s t r e a m o f t h e s t u d i e d i n t e r v a l . S t a r t i n g f r o m t h e b o u n d a r y c o n d i t i o n s s u g g e s t e d by v a n d e r L a a n ( 1 0 ) we h a v e d e v e l o p e d new b o u n d a r y c o n d i t i o n s a p p l i c a b l e t o t h e r e s i d e n c e t i m e c u r v e s o f two c o l u m n s w i t h d i f f e r e n t h e i g h t s . The r e s u l t i n g e q u a t i o n f o r c a l c u l a t i n g t h e P e - n u m b e r i s shown i n f i g u r e 3. T h i s e q u a t i o n i s t r u e when t h e t r a c e r i s a d d e d and t h e r e s p o n s e f u n c t i o n i s measured o u t s i d e of t h e t e s t i n t e r v a l . I t i s a s s u m e d t h a t m i x i n g a b o v e t h e l i q u i d l e v e l and b e y o n d the gas s p a r g e r i s n e g l i g i b l e compared t o t h e m i x i n g w i t h i n t h e bubble column i t s e l f . The i n f l u e n c e o f t h e b o u n d a r y c o n d i t i o n s a t h i g h Pe-numbers i s s m a l l . A t s m a l l Pe-numbers, as o b t a i n e d i n C S T R s , t h e e f f e c t may be o f c o n s i d e r a b l e m a g n i t u d e . T h i s m u s t be t a k e n i n t o a c c o u n t when c o m p a r i n g s m a l l Pe-numbers c a l c u l a t e d from d i f f e r e n t w o r k s . q
The r e s u l t s o f o u r s t u d i e s show a r a p i d i n c r e a s e of a x i a l m i x i n g c o r r e s p o n d i n g t o a r a p i d d e c r e a s e o f Pe-number w i t h i n c r e a s i n g c o l u m n d i a m e t e r ( f i g . 4 ) . F o r e x a m p l e , a n empty b u b b l e c o l u m n o f a h e i g h t o f 4 m a n d a d i a m e t e r o f 40 mm y i e l d s a P e - n u m b e r o f 16 w h i c h corresponds t o a 9 stage tank cascade. A bubble column o f t h e same h e i g h t w i t h a n i n c r e a s e d d i a m e t e r o f 1 m y i e l d s Pe = 0.6 w h i c h i s c o m p a r a b l e t o a CSTR: The t o t a l l i q u i d h o l d u p o f 3 m^, w h i c h h a d a mean r e s i d e n c e t i m e o f 6 m i n u t e s , was h o m o g e n e o u s l y c o l o r e d 20 s e c o n d s a f t e r a d d i n g a dye t o t h e w a t e r i n p u t . Compared t o t h e i n f l u e n c e o f column d i a m e t e r t h e e f f e c t o f g a s v e l o c i t y i s f a i r l y s m a l l ( f i g . 5 ) . An i n -
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
MAGNUSSEN
Axial Mixing in Bubble and Phte
AND SCHUMACHER
water column
2
40m3/m -fT
height:
diameter :
L= 1m
AO m m
2"
k"
80
'*
PR 10 "
225
"
PR 15 "
450
"
PR 25
1000
"
PR 50 "
"
perforated plates ( 2 0 7 . free a r e a ) plate distance : 2 m 1m
air 40-400m3/rr>2.h
Figure 1.
NaOH
packings RR 10mm
Survey of tested bubble columns
X
1 L
1 =
1.3m 2.3m
J
4.3m water - · * -
-t
pHmeter
0
:03m
PHmetcr
Figure 2. Experimental arrangement for the measurement of residence time distribution
K e
Figure 3.
-
D
Calculation of Pe number
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
342
CHEMICAL
Ο φ
REACTION
ENGINEERING—HOUSTON
empty bubble column packed bubble column (Pall-rings 15mm)
1
P e / L (m" ]
column diameter Imml
Figure 4. Axial mixing in bubble columns—effect of diameter
-O
t m
P * y bubble column
- φ packed bubble column 1
Cm" ! Pe/L
(Pall-rings 15 mm)
gas flow raff
Figure 5.
400 Cm3fon?-M
Axial mixing in bubble columns —effect of gas flow rate
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
28.
MAGNUSSEN
AND SCHUMACHER
Axial Mixing in Bubble and Plate
343
c r e a s e o f t h e g a s f l o w r a t e i n empty b u b b l e c o l u m n s b y a f a c t o r 10 ( f r o m 40 t o 4 0 0 m^/m^.h) d e c r e a s e s t h e P e number b y o n l y 40 %. I n p a c k e d b u b b l e c o l u m n s t h e e f f e c t i s even s m a l l e r . T h e r e f o r e a l l data g i v e n i n t h i s w o r k a r e mean v a l u e s a v e r a g e d o v e r a l l g a s f l o w rates. The l o g a r i t h m i c s c a l e d i a g r a m ( f i g . 6 ) shows t h e l i n e a r r e l a t i o n o f Pe-number t o t h e c o l u m n d i a m e t e r . The s l o p e o f -1 a g r e e s w e l l w i t h t h e p u b l i s h e d v a l u e s f r o m o t h e r w o r k s w h i c h v a r y f r o m -1 t o - 1 . 5 . P a c k e d b u b b l e c o l u m n s show a r e d u c t i o n o f a x i a l mixing which increases with decreasing s i z e of packing. In packed bubble columns t h e r e l a t i o n s h i p between Penumber a n d c o l u m n d i a m e t e i th i bubble columns.The a x i a n a l t o t h e column d i a m e t e r . e opposite effect s ob s e r v e d w i t h n a r r o w columns where t h e p a c k i n g s i z e i s l a r g e compared w i t h t h e column d i a m e t e r . I n t h i s case w a l l e f f e c t s o c c u r . Some l i q u i d s t r e a m s r u n t h r o u g h t h e c o l u m n much f a s t e r t h a n o t h e r s r e s u l t i n g i n a w i d e n i n g of t h e r e s i d e n c e time c u r v e d e c r e a s i n g t h e Pe-number. By i n s e r t i n g 50 mm p a c k i n g s i n a 1 m d i a m e t e r c o lumn t h e P e - n u m b e r i s d e c r e a s e d . T h i s may be c a u s e d b y s t a t i s t i c a l n o n u n i f o r m i t i e s o f t h e p a c k i n g . Dye a d d e d t o t h e w a t e r i n p u t shows t h e f o r m a t i o n o f c h a n n e l s ; o t h e r p a r t s o f t h e l i q u i d r e m a i n much l o n g e r i n d e a d w a t e r r e g i o n s . The r e s u l t i n g e x t e n s i o n o f t h e r e s i dence time c u r v e y i e l d s t h e e x t r e m e l y l o w Pe-number. T h i s e x a m p l e shows t h a t p a c k i n g s o f u s u a l t e c h n i c a l s i z e do n o t d i m i n i s h a x i a l m i x i n g i n l a r g e b u b b l e c o l u m n s b u t may h a v e t h e o p p o s i t e e f f e c t . An i n h i b i t i o n o f a x i a l m i x i n g i s p o s s i b l e o n l y by u s i n g u n u s u a l l y s m a l l p a c k i n g . I n some c a s e s t h e c o s t o f t h i s p a c k i n g may be p r o h i b i t i v e e s p e c i a l l y when e x p e n s i v e c o n s t r u c t i o n m a t e r i a l s h a v e t o be u s e d . We h a v e t r i e d t o f i n d a l e s s e x p e n s i v e way o f r e d u c i n g a x i a l m i x i n g by t h e u s e o f p e r f o r a t e d p l a t e s . Perforated plates that f i t i n t o bubble columns l i k e s i e v e t r a y s a r e s t i l l used i n c o c u r r e n t bubble columns (11). U s u a l l y t h e r e s u l t a n t f r e e area o f the openings i s v e r y s m a l l , i . e . 1 - 5 % of t h e t o t a l p l a t e a r e a . T h e s e p l a t e s may t o t a l y s u p p r e s s backmixing by f o r m i n g a g a s b u f f e r b e y o n d e a c h p l a t e w h i c h p r e v e n t s l i q u i d b a c k f l o w . S u c h p l a t e s c a n n o t be u s e d i n c o u n t e r c u r r e n t f l o w i n a s much a s t h e r e q u i r e d p r e s s u r e drop through t h e h o l e s prevents t h e l i q u i d downflow. S e v e r a l p o s s i b i l i t i e s have been suggested f o r t h e u t i l i z a t i o n of p e r f o r a t e d p l a t e s i n countercurrent bubble c o l u m n s , i . e . s p e c i a l k i n d s o f downcomers w i t h o r without c o n t r o l v a l v e s (12) (13) or a d d i t i o n a l p u l s i n g
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
344
CHEMICAL REACTION ENGINEERING—HOUSTON
of
the l i q u i d holdup (14). I n s t e a d o f t h e s e more c o m p l i c a t e d a p p a r a t u s we have used s i m p l e p e r f o r a t e d p l a t e s of g r e a t e r f r e e a r e a . H o l e s o f 10 mm d i a m e t e r w i t h a r e s u l t i n g f r e e a r e a o f 20% o f t h e t o t a l p l a t e a r e a a l l o w an u n d i s t u r bed c o u n t e r c u r r e n t f l o w a t t h e f l o w r a t e s m e n t i o n e d a b o v e . We u s e d 1,3,7 o r 15 p l a t e s a t a c o l u m n h e i g h t o f 4 m f o r m i n g 2,4,8 o r 16 c o m p a r t m e n t s w i t h a h e i g h t o f 2, 1, 0.5 o r 0.25 m e a c h . D e s p i t e t h e l a r g e f r e e a r e a o f t h e p l a t e s we ob tained a remarkable reduction i n a x i a l mixing (fig.7). F o r e x a m p l e , 7 p l a t e s f i t t e d i n t o a 450 mm d i a m e t e r c o l u m n d e c r e a s e m i x i n g ( a n d i n c r e a s e t h e P e - n u m b e r ) by a f a c t o r 6. T h i s i greate e f f e c t tha could b ob t a i n e d by u s i n g 15 m are necessary i n a 1 giv d e c r e a s e i n a x i a l m i x i n g . On t h e o t h e r h a n d t h e e f f i c i e n c y of the p l a t e s i n r e d u c i n g a x i a l m i x i n g de c r e a s e s w i t h s m a l l e r column d i a m e t e r s . In c o n t r a s t to packed bubble columns, the d e c r e a se o f P e - n u m b e r w i t h i n c r e a s i n g c o l u m n d i a m e t e r i s much l e s s i n p e r f o r a t e d p l a t e b u b b l e c o l u m n s t h a n i n empty o n e s . T h i s i s t r u e i f t h e p l a t e d i s t a n c e H i s c o n s t a n t v a r y i n g o n l y t h e c o l u m n d i a m e t e r D. A t c o n s t a n t v a l u e s o f H/D as shown by t h e d o t t e d l i n e s i n f i g u r e 7 t h e same s l o p e i s f o u n d as f o r empty b u b b l e columns. The p a c k i n g and p l a t e e f f i c i e n c y i s c o m p a r e d i n f i g u r e 8, w h e r e t h e i n c r e a s e o f P e - n u m b e r i s p l o t t e d v e r s u s the column d i a m e t e r . I t i s seen t h a t the p l a t e e f f i c i e n c y i n c r e a s e s r a p i d l y w h i l e the p a c k i n g effi c i e n c y i s independent of the column diameter. Summary R e s i d e n c e t i m e d i s t r i b u t i o n s h a v e b e e n m e a s u r e d i n emp t y , p a c k e d and p e r f o r a t e d p l a t e b u b b l e c o l u m n s w i t h d i a m e t e r s f r o m 40 mm t o 1 m. I n empty b u b b l e c o l u m n s t h e a x i a l m i x i n g as e x p r e s s e d by t h e P e - n u m b e r i s n e a r l y i n d e p e n d e n t o f t h e gas f l o w r a t e . M i x i n g i n c r e a s e s r a p i d l y w i t h i n c r e a s i n g column d i a m e t e r , t h e Pe-number i s i n v e r s e l y p r o p o r t i o n a l to the column d i a m e t e r . The r e d u c t i o n o f a x i a l m i x i n g by u s e o f p a c k i n g s d e p e n d s on t h e s i z e o f t h e p a c k i n g . F o r g o o d e f f i c i e n c y s m a l l p a c k i n g s h a v e t o be u s e d . The d e p e n d e n c e o f a x i a l m i x i n g on t h e c o l u m n d i a m e t e r i s t h e same as i n empty b u b b l e c o l u m n s . The u s e o f p e r f o r a t e d p l a t e s i n l a r g e b u b b l e c o l u m n s r e d u c e s a x i a l m i x i n g . The p l a t e e f f i c i e n c y i n c r e a s e s w i t h i n c r e a s i n g column d i a m e t e r .
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
28.
Axial Mixing in Bubble and Plate
MAGNUSSEN AND SCHUMACHER
345
©empty bubble column • 10mmRaschig-rings
1
Pe/L (m"]
-|—θ 10 mm Pall-rings Φ 15 mm
40| 30 20
10
7
-ii-
β 25 mm -M-
Pe/L r
-H-
® 50mm
Or
1
Im" ] 1
-
010 007-
-
r
1
«
«
·
40
80
225
450
005L
1
1000 (mm) column diameter
Ο Φ Φ
d) ®
empty bubble column 1 3 7 15
perforated perforated perforated perforated
plate. H=2.00m plates. H=1.00m p l a t e s , Η = 0.50 m p l a t e s . H =0.25 m
Figure 7. Axial mixing in bubble columns—effect of plates
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—
Ρβ/Ρβempty column
column diameter €) φ
packed column. R i l l - r i n g s 15 mm 1 p e r f o r a t e d plate,
H=2.00m
Φ
3 perforated plates,
H=1.00m
©
7 perforated plates,
Η = 0.50 m
®
15 p e r f o r a t e d p l a t e s ,
H =0.25 m
Figure 8. Comparison of plate efficiency and packing efficiency at varying diame ter
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
28.
MAGNUSSEN AND SCHUMACHER
Axial Mixing in Bubble and Plate
347
Literature cited:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)
Kölbel H . , Dechema Monographie (1972) 68, 35-73 Mashelkar R . A . , British Chemical Engineering (1970) 15 (10), 1297 - 1301 Tadaki T., Maeda, S., Kagaku Kogaku (1964) 2, 195-198 Argo W.B., Cova D.R., I & EC Process Design and Development (1965) 4 (4), 352-359 Towell G.D., Ackerman G.H., 2nd Internat Symp. Chem. React. Engng., Amsterdam (1972) Carleton A.I., Flain R . I . , Rennie I., Valentin F.H.H., Chemical Engineering Science (1967) 22, 1839-1849 Hoogendoorn C.I., Chemical Engineering Pippel W., Chemische Technik (1965) 17, 729-738 Levenspiel O., Smith W.H., Chemical Engineering Science (1957) 6, 227-233 van der Laan E.Th., Chemical Engineering Science (1958) 7, 187-191 Blass E . , Koch K . H . , Chemie Ingenieur Technik (1972) 44, 913-921 Kastanek F . , Zahradnik J., Coll. Czech. Chem. Communications (1973) 38, 3725-3741 Judat Α., Judat H . , (Bayer AG) West German OLS 2331 195 (1975) Hackl Α., Dechema Monographie (1974) 73 (1410 1431), 37-49
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
29 Computer-Aided Development of the Cyclohexane Oxidation Process J. A . DE LEEUW D E N B O U T E R , L. L. VAN D I E R E N D O N C K , and W . O . B R Y A N C R O / D S M , P.O. Box 18, Geleen, The Netherlands
1. INTRODUCTION Within the scope of its program aimed at process improvements, the Corporate Department for Research and Patents of DSM is now seeking ways of optimizing the cyclohexane oxidation route towards cyclohexanone (anone) and cyclohexanol (anol). These products are intermediates in the preparation of caprolactam. Caprolactam is polymerised to nylon-6. As DSM has a great interest in the world production of caprolactam, much effort is put into research and optimization of the various process steps. In the oxidation of cyclohexane, the efficiency is relatively low, which is the reason why research into and optimization of this process step was taken in hand. The flowsheet of the oxidation section is shown in fig. 1. Fresh cyclohexane is mixed with the recycled cyclohexane from the top of the cyclohexane distillation column. The mixture is fed to the condensation section to exchange heat with the vapour stream from the reactors. Next, the cyclohexane is oxidized with air in a cascade of stirred reactors. The oxidate leaving the reactors undergoes an after-treatment in a decomposition reactor, while the acids formed as byproduct in the oxidation section are neutralized in a mixer-settler unit. In the cyclohexane distilation section non-converted cyclohexane is separated from cyclohexanol, cyclohexanone and byproducts. DSM studied the catalysed process in the years before 1960. Steeman et a l . (1) on the basis of experimental work, calculated the optimum degree of cyclohexane conversion to be 7-8 % at an efficiency of 75 %. Alagy e t a l . ( 2 ) , i n t r o d u c i n g b o r i c a c i d (metaborate) i n t o the o x i d a t i o n s e c t i o n , achieved e f f i c i e n c y f i g u r e s i n the range 85-90 %. The metaborate used by these authors r e a c t s w i t h cyclohexanol (anol) t o form an e s t e r , thereby p r e v e n t i n g o x i d a t i o n o f anol to anone, and, as a consequence, suppressing the anone c o n c e n t r a t i o n . Since the bulk of the byproducts i s formed v i a anone, the use o f b o r i c a c i d t h e r e f o r e brings i n t h i s © 0-8412-0401-2/78/47-065-348$05.00/0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
29.
DE L E E U W
ETAL.
Cyclohexane Oxidation Process
349
case an improvement i n e f f i c i e n c y . The new process v a r i a n t i n v e s t i g a t e d a t DSM i s a l s o based on suppression o f the anol and anone concentrations, which i s achieved by l e a v i n g out the c a t a l y s t . A p p l i c a t i o n o f appropriately chosen c o n d i t i o n s counteracts decomposition o f the c y c l o h e x y l hydroperoxide intermediate (PER), thus lowering the anol and anone concentrations and as a consequence improving the e f f i c i e n c y . Depending on the degree o f cyclohexane conversion, e f f i c i e n c i e s of 85-95 % can now be obtained. Of course, the degree to which the o v e r a l l e f f i c i e n c y i s increased a f t e r the decomposition o f the peroxide depends on the s e l e c t i v i t y o f the peroxide conversion step, but t h i s w i l l not be considered here. The process improvement has been thoroughly evaluated i n bench-scale experiment d afterward bee t r i e d ti commercial p l a n t process i n gear with computer mode l a b o r a t o r y experiments a k i n e t i c model was developed on an analog computer. Next, a r e a c t o r model based on the k i n e t i c model was worked out on a d i g i t a l computer. In the f o l l o w i n g step, a model o f the new process v a r i a n t was set up by means o f the DSM flowsheet s i m u l a t i o n system TISFLO. F i n a l l y , the process model was used f o r o p t i m i z i n g the process. The various stages o f the i n v e s t i g a t i o n s and the supporting a c t i v i t i e s are s c h e m a t i c a l l y shown i n Table I. Table I. Survey o f the work done on improvement o f the CHo x i d a t i o n process Experimental
Model c a l c u l a t i o n s
Bench s c a l e experiments
Analog s i m u l a t i o n o f the reaction kinetics. D i g i t a l s i m u l a t i o n of a g a s - l i q u i d r e a c t o r . Simulation o f an actual plant for test-run planning
Test runs i n an e x i s t i n g p l a n t
Correction of several q u a n t i t i e s i n the model a f t e r the t e s t runs. Optimization of the design.
The present paper b r i e f l y o u t l i n e s the development of the computer models and some o f the r e s u l t s achieved with these. 2. KINETIC MODEL In bench-scale batch experiments, cyclohexane was o x i d i z e d with a i r i n a s t i r r e d autoclave. To d e s c r i b e the change i n the concentrations o f the p r i n c i p a l o x i d a t i o n products, we p o s t u l a t e d the f o l l o w i n g r e a c t i o n scheme:
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL
350 k
i
k
2
R + 0
REACTION
ENGINEERING—HOUSTON
— PER
(2.1)
ANOL + J 0
PER k
(2.2)
2
3
PER
ANONE +
(2.3)
k 2 - * ANOL + ANONE + H O + J Ο
2 PER ANOL + J 0
(2.4)
—ANONE + H O
2
(2.5)
ANONE + 3/2 0 1—"acids This scheme i s p r a c t i c a l l y analogous to those put forward by Steeman e t a l . (JL), Alagy e t a l . (2) and Vasey e t a l . ( 3 ) . The d i v e r s i t y o f byproducts, such as a c i d s , e s t e r s , heavies, l i g h t s , CO, C 0 and alkanes, a r e included under " a c i d s " . Reaction (2.1) i s regarded as the sum o f two r a d i c a l r e a c t i o n s : 2
2
R* + Ο
— ROO* k — » PER + R*
2
ROO' + R
(2.7) (2.8)
The c y c l o h e x y l r a d i c a l s a r e generated during the breakdown o f the PER according t o the r e a c t i o n s (2.2), (2.3) and (2.4). Along the same l i n e s as followed by Emanuel ( 4 ) , i t can be d e r i v e d that the r a t e o f t h i s a u t o - o x i d a t i o n system i s p r o p o r t i o n a l t o the square root o f the r a d i c a l - g e n e r a t i n g components. S i m p l i f i c a t i o n o f the r a d i c a l r e a c t i o n equations y i e l d s the f o l l o w i n g expression f o r the formation r a t e s o f the various components : (
) =
" 4 t ^
k
l*[°2]- f 1 [ (
PER
+
P E R
1
· [ANON])^
On the b a s i s of the above reasoning, equations can be s e t up: ^dt^
=
k
x
. [ 0 ] . ([PER]
^jjf^ = k
2
d[ANONE] ^
4
the f o l l o w i n g d i f f e r e n t i a l
+ [PER] . [ANONE])^ - ( k + kg) .
2
. [PER] - k
(2.9)
£
. [ P E R ] . [ ANONE]
(2.10)
. [ P E R ] + k . [ P E R ] .[ANONE] - k ^ A N O L ] . [θ ] (2.11) 4
fc ] ER
+
K
4
2
. [
P
E
R
] . [ A N O N E ]
+ k .[ANOL].[0 ] 6
2
- k .[AN0NE].[0 ] ?
2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
(2.12)
29.
d C
DELEEUW
";;
l d 8
"
]
Cyclohexane Oxidation Process
ET AL.
= k .[ANONE]{0 ] 7
(2.13)
2
d[0 ]
~~dtT
ι
" l ' [°2] f
=
k
i . k
351
,(
PER
3
+
C
PER
]
· C ANONE]) 5
. [ANOL].[0 ] - l j . k .[ANONE].[0 ] + J.k. [PER]
5
2
g
+
2
+ J.k .[PER] . [ANONE]
(2.14) s
t t e c
For the 0 -consuming r e a c t i o n s the product o f k -[Og] * f i *. Equation (2.14) allowed us to c a l c u l a t e the s t o i c h i o m e t r i c oxygen need o f the r e a c t i o n s . Thi d b related t independent supply o f a i r to the r e a c t o r s The f a c t o r F i s define 2
Q
2
F
0
supply
Z
0
2
0
2
consumed i n the s t o i c h i o m e t r i c
conversion
The k-values were f i t t e d f o r those experiments i n which F^ > 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
where K. i s a f u n c t i o n of the temperature, pressure and composilion o f the l i q u i d ( x . ) . The dependence o f Κ on tfte l i q u i d concentrations was brought i n t o account i n that the a c t i v i t y c o e f f i c i e n t s were c a l c u l a t e d w i t h the a i d of Wilson's equation. The Wilson constants f o r s e v e r a l binary systems were derived from experimental f i g u r e s by means o f non-linear r e g r e s s i o n .
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL
352
REACTION
ENGINEERING—HOUSTON
The component balance f o r each i n d i v i d u a l component can be w r i t t e n as : (F
. y
Q
p
+ F
L
. x
p
= L . χ + G . y - V. r ) .
(3.2)
The enthalpy balance of the r e a c t o r reads: F
u
.
ϋ
+ F
L
. Hf = L . H L
L
+ G. H
u
- Q
(3.3)
r
S o l u t i o n of the s e t of equations (3.1), (3.2) and (3.3) y i e l d s the model of the g a s - l i q u i d r e a c t o r . Except f o r the terms (V. r ) . and Q , the above s e t of equations i s equal to that defining
an a S i a b a t i c
f l a s h e r . Supplementation of an
adiabatic
f l a s h standard c a l c u l a t i o n r o u t i n e w i t h these terms provided a program f o r the g a s - l i q u i compositions and f l o w r a t e streams have been c a l c u l a t e d , the e f f e c t i v e r e a c t o r volume can be determined. 4. SIMULATION OF A PLANT OXIDATION SECTION BY MEANS OF TISFLO For f u r t h e r e v a l u a t i o n of the process, the r e a c t o r model was i n c o r p o r a t e d i n a flowsheet c a l c u l a t i o n r o u t i n e executed w i t h the standard flowsheet s i m u l a t i o n program TISFLO. TISFLO i s a component of TIS ( T e c h n o l o g i c a l Information System), a system developed by DSM (5,6) f o r e x e c u t i n g chemical process c a l c u l a t i o n s . The flowsheet model on which the c a l c u l a t i o n s were c a r r i e d out i s i l l u s t r a t e d i n f i g . 1. The flowsheet may comprise e i t h e r one r e a c t o r or s e v e r a l r e a c t o r s connected i n series. The independent v a r i a b l e s i n the s i m u l a t i o n s were so chosen as to correspond w i t h the c o n t r o l v a r i a b l e s i n the p l a n t . These independent v a r i a b l e s were: - the pressure, - the f l o w r a t e of the feed stream to the f i r s t r e a c t o r , - the temperature of the f i r s t r e a c t o r , - the a i r feed to each r e a c t o r . We can now c a l c u l a t e the f o l l o w i n g c h a r a c t e r i s t i c data: degree of cyclohexane c o n v e r s i o n , o x i d a t i o n e f f i c i e n c y and p r o d u c t i o n l e v e l . With the a i d of the flowsheet s i m u l a t i o n program the mass and heat balances can be determined and a s c e n a r i o i s prepared f o r undertaking experiments i n an e x i s t i n g p l a n t equipped w i t h two s e r i e s - c o n n e c t e d r e a c t o r s . The program comprised s i x experiments, w i t h a planned maximum d u r a t i o n of 24 h each. The pressure d u r i n g the experiments was kept constant. The p l a n t was run at two feed flow r a t e s w i t h simultaneous v a r i a t i o n of a i r supply and temperature. Checking the model was done w i t h r e f e r e n c e to the temperatures measured i n the r e a c t o r s and to the analyses of samples taken of the l i q u i d and vapour streams from the r e a c t o r s . The
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
29.
DELEEUW
ET AL.
Cyclohexane Oxidation Process
353
c a l c u l a t e d r e a c t o r temperatures according to the model were found to deviate by a few degrees from those recorded i n the p l a n t , but a f t e r i n t r o d u c t i o n o f the heat o f r e a c t i o n of each p a r t r e a c t i o n proper agreement was obtained. An important f i n d i n g made during the c a l c u l a t i o n was that s e t p o i n t changes give r i s e t o i n s t a b l e s i t u a t i o n s . In f i g . 3 we have p l o t t e d the r e a c t o r temperature versus the a i r flow r a t e for two temperatures o f the f i r s t r e a c t o r . A change over from s i t u a t i o n A t o s i t u a t i o n D should be conducted along the path ABCD, i . e . by f i r s t reducing the a i r feed and then lowering the temperature of the f i r s t r e a c t o r , and not the other way about, because t h i s would give r i s e t o an i n s t a b l e s i t u a t i o n l e a d i n g to a blow out o f the r e a c t i o n . This i n s t a b i l i t y was demonstrated i n the p l a n t . 5. OPTIMIZATION The o p t i m i z i n g c a l c u l a t i o n s were c a r r i e d out on the s i m p l i f i e d flowsheet model i l l u s t r a t e d i n f i g . 4, where RE represents a s e r i e s o f g a s - l i q u i d r e a c t o r s , and WW denotes tRe heat exchanger. The equipment f o l l o w i n g the r e a c t o r s i s i n d i c a t e d by one block, OPW. Stream 5 i s the offgas from the r e a c t o r and stream 7 the product from the top o f the cyclohexane d i s t i l l a t i o n column. Because of the complexity o f the process and the great many v a r i a b l e s i n v o l v e d , the o p t i m i z a t i o n was c a r r i e d out by means of a s e n s i t i v i t y a n a l y s i s . The cost f u n c t i o n i s composed o f the following factors: (a) raw m a t e r i a l s consumption (cyclohexane and c a u s t i c ) , (b) condensation of r e a c t o r offgas ( c o s t s c a l c u l a t e d from energy consumption and investments), (c) d i s t i l l a t i o n o f the cyclohexane r e c y c l e stream ( d i t t o ) , (d) investment i n r e a c t o r s ( c o s t per cu.m. o f r e a c t o r volume).
The v a r i a b l e s that p l a y an important r o l e i n the r e a c t o r section are: (1) f r e s h cyclohexane feed, (2) a i r flow r a t e to each r e a c t o r , (3) p r o d u c t i o n l e v e l , (4) degree of cyclohexane conversion, (5) o x i d a t i o n e f f i c i e n c y , (6) temperature o f f i r s t r e a c t o r , (7) f l o w r a t e o f cyclohexane r e c y c l e stream, (8) f l o w r a t e of r e a c t o r feed stream, (9) pressure, (10) number of r e a c t o r s , (11) s p l i t o f a l l components over s e c t i o n OPW (see f i g . 4 ) , (12) s p l i t o f a l l components over the heat exchanger (WW/offgas), (13) r e a c t o r volume.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL
REACTION
ENGINEERING—HOUSTON
off gas cyclohexane recycle
caustic
rilkfU J I
feed
W
salt solution
f
—
anol anone mixture circulation vessel
decomposition
CH-distillation
heat exchange
Figure 1.
Flowsheet for the cyclohexane oxidation section
cone, m o l /Kg
Figure 2. Comparison of a hatch experiment with the model on the analog computer
reactor
temperature
C
Figure 3. Reactor-temperature as a function of the air flowrate at two reactor feed temperatures
D"
-air flow rate
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
29.
DELEEUW
ET AL.
Cyclohexane Oxidation Process
355
Before s t a r t i n g on the o p t i m i z a t i o n , we determined the number o f degrees o f freedom by a n a l y z i n g the i n t e r r e l a t i o n s between the v a r i a b l e s . S p e c i f y i n g f i x e d values f o r : - the s p l i t o f the components over s e c t i o n OPW, - the s p l i t o f the components over s e c t i o n WW. We found that there a r e s i x more degrees o f freedom to be s e l e c t e d from the above l i s t . The o p t i m i z a t i o n i s c a r r i e d out i n two steps. In our f i r s t o p t i m i z i n g e f f o r t , we s e l e c t e d as v a r i a b l e f a c t o r s those that had an unambiguous e f f e c t on the cost f u n c t i o n : the number o f r e a c t o r s and the a i r feed to each reactor. This o p t i m i z a t i o n was c a r r i e d out by using f i x e d values f o r the r e a c t o r volume, the pressure, the degree of conversion, and the production. The i n f l u e n c e o f the way i n which the a i r i s d i s t r i b u t e d over the r e a c t o r be seen here a d i s t r i b u t i o be p r e f e r r e d to the s i t u a t i o n where the a i r feed r a t e s to a l l r e a c t o r s a r e equal. I t i s a l s o seen that the cost f u n c t i o n decreases w i t h an increase i n the number o f r e a c t o r s . For p r a c t i c a l reasons the number o f r e a c t o r s was i n a l l cases taken equal to s i x . In the second o p t i m i z i n g step, we f i x e d the number o f r e a c t o r s , the volume o f each r e a c t o r , the a i r feed t o the r e a c t o r s ( i n compliance w i t h the requirement F^ = 1 f o r each r e a c t o r ) . As the remaining three degrees o f 2 freedom we chose: the pressure, the temperature o f the f i r s t r e a c t o r and the f l o w r a t e o f the cyclohexane r e c y c l e . To determine the optimum working p o i n t o f a given r e a c t o r c o n f i g u r a t i o n , we c a l c u l a t e d the cost f u n c t i o n a t two temperature l e v e l s o f the f i r s t r e a c t o r (T^ < Τ^) and three pressure l e v e l s (P^ < P^ < P^) as a f u n c t i o n of the cyclohexane r e c y c l e f l o w r a t e (see f i g . 6 ) . The two p r i n c i p a l f a c t o r s opposing each other are: the use o f more raw m a t e r i a l s when the r e c y c l e r a t e i s low (as a r e s u l t of low s e l e c t i v i t y ) , and the high cost o f d i s t i l l a t i o n when the r e c y c l e r a t e i s high. I t appeared that f o r each of the s i x combinations o f Ρ and Τ there e x i s t s an optimum production c a p a c i t y and a l s o that the production increases w i t h the f l o w r a t e o f the cyclohexane r e c y c l e stream. 6. FINAL REMARKS The o p t i m i z i n g c a l c u l a t i o n s a r e based on the k i n e t i c model and the r e a c t o r model o u t l i n e d i n paragraphs 2 and 3. Notwithstanding that the research work had progressed so f a r as t o enable the p l a n t r e a c t o r performance t o be f a i r l y a c c u r a t e l y p r e d i c t e d from the r e s u l t s o f batch experiments we considered i t d e s i r a b l e to b u i l d a complete p i l o t i n s t a l l a t i o n comprising r e c i r c u l a t i o n , n e u t r a l i z a t i o n and s a p o n i f i c a t i o n u n i t s . The
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL
356
REACTION
ENGINEERING—HOUSTON
8 5
•RV
9
WW
2
RE
4
6
OPW
N
3
Figure 4.
Flowsheet representation of the cyclo hexane oxidation section
Figure 5. Results of the first optimization 1
2
3
4
5
6
7
cost function ι in f l / t o n
Figure 6.
Results of the second optimization
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
29.
DE LEEUW
ET AL.
Cyclohexane Oxidation Process
357
p r i n c i p a l o b j e c t i v e s u n d e r l y i n g t h i s d e c i s i o n were: a) checking the r e s u l t s o f o p t i m i z i n g c a l c u l a t i o n s by downscaling from p l a n t to s e m i - t e c h n i c a l s c a l e , b) examining i f the r e c y c l e streams have an e f f e c t on the efficiency, c) production o f o x i d a t i o n l i q u i d f o r f u r t h e r research o f the decomposition step and the n e u t r a l i z a t i o n o f a c i d s , d) t e s t i n g the q u a l i t y o f caprolactam prepared from anone made i n the p i l o t p l a n t , e) a v a i l a b i l i t y o f an i n s t a l l a t i o n f o r c a r r y i n g out research on behalf o f p l a n t s a l l over the world under c o n d i t i o n s o b t a i n i n g there, f) o f f e r i n g the p o s s i b i l i t y o f t r a i n i n g operating s t a f f . The r e s u l t s o f the o p t i m i z i n g c a l c u l a t i o n s have a l s o been used f o r determining wha The new procedure has and e x i s t i n g i n s t a l l a t i o n s . The cost o f r e b u i l d i n g and the l o s s of production during r e b u i l d i n g w i l l normally be more than o f f s e t by the g a i n i n p r o f i t and e f f i c i e n c y . We have shown how the development o f processes i n the chemical i n d u s t r y i s supported by means o f mathematical models. Recognizing that the b a s i c k i n e t i c model s t i l l has s e v e r a l weak p o i n t s , we a r e convinced that these have h a r d l y any e f f e c t on the trends d i s c l o s e d by the o p t i m i z a t i o n , and a l s o that the r e s u l t s o f our study w i l l c o n t r i b u t e towards improved operation of the r e a c t o r s e c t i o n i n e x i s t i n g p l a n t s as w e l l as towards more exact design o f new i n s t a l l a t i o n s . LIST OF SYMBOLS dimension R PER ANONE ANOL R* R00*
cyclohexane c y c l o h e x y l hydroperoxide c yc1ohexanone cyclohexanol cyclohexyl r a d i c a l c y c l o h e x y l hydroperoxide r a d i c a l oxygen f a c t o r (see eq. 2.14)
Κ
gas l i q u i d e q u i l i b r i u m constant (eq. 3.1) mole f r a c t i o n i n the l i q u i d mole f r a c t i o n i n vapour temperature pressure feed r a t e l i q u i d f l o w r a t e from r e a c t o r gas f l o w r a t e from r e a c t o r l i q u i d volume i n r e a c t o r
χ y τ
ρ F L G V r
C kPa kmoles/hr kmoles/hr kmoles/hr
r e a c t i o n r a t e (—) dt
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
358
H Q r
enthalpy heat o f r e a c t i o n
kJ/kmoles kJ/kmoles
INDICES F G L
feed gas phase l i q u i d phase
7. LITERATURE CITED 1. Steeman J.W.M. et al. Chem. Eng. Sci (1960) 14 39. 2. Alagy J . et al. Ind. Eng. Chem. Proc. Des. Developm. (1974) 13 317. 3. Vasey C.H. et al. Symp april 1975. 4. Emanual' N.M. et al. 'The Oxidation of cyclohexane', Pergamon Press, Oxford (1966). 5. de Leeuw den Bouter J.Α., Swenker A.G. Symp. 'Computer application in process development' 2-3/4 '74 Erlangen. 6. de Leeuw den Bouter J.Α., Swenker A.G. Symp. 'Computers in the design and erection of chemical plants' 1-4 sept. 1975 Karlsbad.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
30 Detailed Analysis of CO -Interphase Mass Transfer in a 2
Bubble Column to Prove the Validity of a Design Model W.-D.
D E C K W E R and I. A D L E R
Institut für Technische Chemie, TU Hannover, Callinstr. 3, 3000 Hannover 1, West Germany A. Z A I D I Institut für Technische Chemie, TU Berlin, Strasse des 17, Juni 135, 1000 Berlin 12, West Germany
The common treatment b a s e d o n the axial sion models were first d e v e l o p e d for several k i n d s of extraction e q u i p m e n t , a n d these m o d e l s w e r e also over -taken t o describe t h e behaviour o f gas-liquid contac tors like b u b b l e c o l u m n s (1-3). T h e favorable applica tion o f bubble c o l u m n s presents t h e performance o f gas -liquid reactions w h i c h t a k e place in the s l o w reaction r e g i m e of mass transfer theory. In this absorption re gime b u b b l e c o l u m n s provide for sufficient interfacial a r e a s for mass transfer a n d at the same t i m e t h e liquid v o l u m e n e e d e d for the reaction is large e n o u g h . I n in dustry high conversions a r e desired. Thus t h e m o l a r g a s flow rate may vary considerably a l o n g t h e column since the reaction products is usually non-volatile a n d the mass capacity o f the g a s p h a s e is small c o m p a r e d to that o f the liquid p h a s e . F o r that r e a s o n design m o d e l s proposed for extractors a r e not a realistic description o f b u b b l e c o l u m n s . Recently a theoretical m o d e l for bubble columns of industrial size was proposed w h i c h accounts for variations of g a s flow rate a n d pressure (4). T h e r e it was demonstrated by numerical simulations that even a t isobaric conditions t h e g a s flow rate h a s to be considered as variable since gas volume d e c r e a s e by absorption l e a d s to increased g a s residence t i m e which i n t u r n improves t h e c o n v e r s i o n . S i m p l e r models l i k e t h o s e f o r e x t r a c t o r s c a n be a p p l i e d o n l y i f t h e column o p e r a t e s a t e l e v a t e d p r e s s u r e s and i f , i n a d d i t i o n , t h e gas s h r i n k a g e due t o a b s o r p t i o n i s s m a l l . When t h e a b s o r p t i o n a n d r e a c t i o n o f i s o b u t e n e i n s u l f u r i c a c i d was s t u d i e d i n a t a l l b u b b l e c o l u m n i t was f o u n d t h a t t h e c o n v e r s i o n s m e a s u r e d a t t h e c o l u m n e x i t c o u l d be e x p l a i n e d r e a s o n a b l y o n l y o n t h e b a s e o f t h i s i m p r o v e d m o d e l (5_) . H o w e v e r , t h e c o m p a r i s o n o f e x p e r i m e n t a l and p r e d i c t e d c o n c e n t r a t i o n p r o f i l e s w o u l d p r e s e n t a b e t t e r mean t o p r o v e t h e v a l i d i t y o f a p a r t i ©
0-8412-0401-2/78/47-065-359$05.00/0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL
360
REACTION
ENGINEERING—HOUSTON
c u l a r m o d e l and t o d i s c r i m i n a t e among r i v a l m o d e l s . Ob v i o u s e x p e r i m e n t a l d i f f i c u l t i e s d i d n o t a l l o w t h e de t e r m i n a t i o n of c o n c e n t r a t i o n p r o f i l e s f o r the absorp t i o n and r e a c t i o n o f i s o b u t e n e . T h e r e f o r e t h e a b s o r p t i o n and d e s o r p t i o n o f CO2 i n w a t e r was s t u d i e d . Owing t o t h e l a r g e i n t e r p h a s e mass t r a n s f e r due t o t h e h i g h CO^ s o l u b i l i t y t h e C O ^ - w a t e r s y s t e m i s v e r y a p p r o p r i a t e to s i m u l a t e c o n d i t i o n s which are encountered i n i n d u s t r i a l a p p l i c a t i o n s o f b u b b l e c o l u m n s as r e a c t o r s . Experimental The i n v e s t i g a t i o n s w e r e c a r r i e d o u t i n a b u b b l e c o lumn ( B C D o f 20 cm I.D d height f 723 Th e x p e r i m e n t a l s e t up was made f r o m g l a s s operate and c o u n t e r c u r r e n t f l o w . The g a s was s p a r g e d by 56 n o z z l e s o f 1 mm I.D. Tap w a t e r was u s e d as l i q u i d p h a s e and i t s t e m p e r a t u r e was m a i n t a i n e d a t 16 C. The l i q u i d f l o w r a t e was 3 m^/h f o r a l l runs r e p o r t e d here. A n o t h e r b u b b l e c o l u m n ( B C I I ) o f s m a l l e r s i z e was u s e d t o r e g e n e r a t e t h e l i q u i d p h a s e w h i c h was r e c y c l e d . Gas samples were w i t h d r a w n from s e v e r a l a x i a l p o s i t i o n s by means o f a s p e c i a l d e v i c e . The s a m p l e s w e r e a n a l y z e d on t h e i r C O 2 " - c o n t e n t . F o r some m e a s u r e m e n t s liquid p h a s e c o n c e n t r a t i o n p r o f i l e s w e r e d e t e r m i n e d t o o . The m a n o m e t r i c m e t h o d was u s e d t o m e a s u r e l o c a l v a l u e s o f t h e g a s h o l d up a l o n g t h e c o l u m n . The i n t e r f a c i a l a r e a was o b t a i n e d f r o m p h o t o g r a p h i c p i c t u r e s w h i c h w e r e t a k e n f r o m t h e g a s - l i q u i d d i s p e r s i o n a t 350 and 610 cm above the s p a r g e r . A d e t a i l e d d e s c r i p t i o n of the e x p e r i m e n t a l arrange' ment and t h e a p p l i e d a n a l y t i c a l t e c h n i q u e s i s given elsewhere (7_) . T y p i c a l e x p e r i m e n t a l c o n d i t i o n s f o r ab s o r p t i o n and d e s o r p t i o n m e a s u r e m e n t s a r e p r e s e n t e d i n t a b l e 1. The o v e r a l l C O ^ b a l a n c e was f u l f i l l e d w i t h i n 3 per cent f o r a l l runs. Gas
Hold
up
and
Interfacial
Area
The m a j o r i t y o f e x p e r i m e n t a l r e s u l t s on b u b b l e c o l u m n s was o b t a i n e d f r o m c o n d i t i o n s a t w h i c h t h e a p p l i e d c o n c e n t r a t i o n s o f the t r a n s f e r components are kept low. Hence t h e m o l a r g a s f l o w r a t e c a n be a s s u m e d as s u f f i c i e n t l y c o n s t a n t . From t a b l e 1 i t c a n be d i s c e r n e d t h a t i n t h i s s t u d y t h e m o l e f l o w r a t e o f t h e gas p h a s e varies considerably. Therefore a l l fluiddynamic proper t i e s r e v e a l marked l o c a l d e p e n d e n c i e s . F r o m t h e mea s u r e d l o c a l gas h o l d up t h e c o n c e n t r a t i o n p r o f i l e s and the bubble s i z e d i s t r i b u t i o n s a x i a l p r o f i l e s of the i n -
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
DECKWER
ET
CO^-Interphase Mass Transfer
AL.
vent gas
vent
Figure 1.
gas
Experimental set-up
Table 1 : Operational conditions of t y p i c a l experimental runs No. flow W 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
X
u
X
ο
1
Go cm/s
u , Ρ . Gl Li cm/s Torr
_
2
10 k
d G
s mm
f
R
Β cm/s
II
0. 0. 0. 0. 0.
0.59 0.48 1.68 691 0.45 1.00 2.94 601 0.36 1.55 3.75 559 0.33 1.90 4.50 514 0.17 4.26 7.65 501
0.038 0.070 0.073 0.130 0.150
3.08 2.94 2.56 2.79 2.50
3 3 2 2 2
0.61 0.57 0.50 0.53 0.47
11
0. 0. 0. 0. 0.
0.51 0.50 0.39 1 .CO 0.33 1.53 0.24 2.51 0.17 4.00
733 670 662 612 581
0.032 0.060 0.089 0.091 0.155
3.15 3.10 2.79 2.90 2.56
0.91 0.73 0.71 0.69 0.75
fl ΙΦ
0.76 0.65 0.75 0.69 0.56 0.42
0.12 0.71 0.30 0.14 1.05 0.65 0.20 1.44 0.78 0.23 1.77 1.13 0.21 1.96 1.72 0.20 2.58 3.06
102 118 119 103 111 94
0.013 4.50 0.025 3.76 0.032 3.65 0.049 3.10 0.076 2.83 0.120 2.68
3 4 3 4 4 2 2 2 3 3 2
4i
1.60 2.63 3.55 4.95 7.20
T
L
2.09 1.80 1.14 0.82 0.92 0.96
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
362
CHEMICAL
REACTION
ENGINEERING—HOUSTON
t e r f a c i a l a r e a , t h e l i n e a r g a s v e l o c i t y , t h e mean b u b b l e r i s e v e l o c i t y and f r e q u e n c y f a c t o r s f o r c o a l e s c e n c e a n d b r e a k up o f b u b b l e s c o u l d be o b t a i n e d . T h e s e d a t a o f f e r a s o p h i s t i c a t e d i n s i g h t on t h e b e h a v i o u r o f g a s - l i q u i d d i s p e r s i o n a t h i g h i n t e r p h a s e mass t r a n s f e r r a t e s , a n d t h e y a r e d i s c u s s e d i n d e t a i l i n r e f s . (7_, 8^) . For the purpose of t h i s paper i t w i l l s u f f i c e t o p o i n t o u t t h a t t h e m e a s u r e d l o c a l v a l u e s o f t h e g a s h o l d up £ç a r e d e s c r i b e d b y a r e g r e s s i o n f u n c t i o n o f t h e d i m e n s i o n l e s s a x i a l c o o r d i n a t e z:
£ (z) with
€GY(z)
=
G
(l) 2
*f (z
£ p r e s e n t s t h e i n t e g r a l v a l u e ( s e e t a b l e 1) w h i c h i s o b t a i n e d from t h e l o c a l v a l u e s by:
i S i n c e t h e mean S a u t e r d i a m e t e r d was f o u n d t o be a p p r o x i m a t e l y i n d e p e n d e n t on ζ t i i e i n t e r f a c i a l a r e a a i s c a l c u l a t e d f r o m t h e s m o o t h e d h o l d up d a t a b y : a(z)
Model
6 fe Φ ( z ) / d . \j s
=
(4)
Assumptions
The m e a s u r e d f l u i d d y n a m i c p r o p e r t i e s a n d t h e r e a s o n s o u t l i n e d i n {4) recommend t h e 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 a l c o n c e n t r a t i o n p r o f i l e s on t h e b a s e o f t h e following assumptions: (1) H e n r y ' s l a w i s v a l i d : Px
=
He. L
=
ρ
(5)
(P = t o t a l p r e s s u r e , χ = m o l e f r a c t i o n , Η = H e n r y ' s c o n s t a n t , c = l i q u i d phase c o n c e n t r a t i o n , ρ = par t i a l pressure) L
(2) (3) (4) (5) (6)
oxygen and n i t r o g e n a r e i n e r t s a x i a l d i s p e r s i o n i n l i q u i d phase p l u g f l o w i n gas phase neglect of radial dispersion p r e s s u r e d e p e n d s l i n e a r on z :
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
Ρ where P (7) (8) (9) (10)
T
363
B
=
P
T
£ l + <*(l-z)]
i s the pressure
a t column
(6) top
g a s h o l d up a n d i n t e r f a c i a l a r e a v a r y w i t h ζ gas v e l o c i t y u i s v a r i a b l e n e g l e c t o f r e a c t i o n o f CC^ w i t h w a t e r g a s p h a s e r e s i s t a n c e t o mass t r a n s f e r c a n b e neglected. G
Owing t o t h e i r l o w s o l u b i l i t y t h e amounts o f O 2 a n d N 2 t r a n s f e r e d from one phase t o t h e o t h e r i s always l e s s t h a n 2 % o f t h e e x c h a n g e d C O 2 . Thus a s s u m p t i o n ( 2 ) is j u s t i f i e d with sufficien Th d i s p e r s i o c o e f f i c i e n t s o f the f r o m (60 : D (d
=
column
T
=
2.7 d
1
4
' a
0
'
3
(7)
diameter).
Eqn (7) was e s t a b l i s h e d f r o m m e a s u r e d d a t a i n t h e u s e d c o l u m n s a n d i t s s i g n i f i c a n c e was c o n f i r m e d b y o t h e r i n v e s t i g a t o r s (j),JU)) . T h e a v a i l a b l e i n f o r m a t i o n o n g a s phase d i s p e r s i o n c o e f f i c i e n t s (jj^) j u s t i f i e s assumption (4). I f merely l i n e a r processes occur r a d i a l d i s p e r s i o n e f f e c t s n e e d n o t b e a c c o u n t e d f o r (J_2_) · S i n c e t h e m o d e l eqns a p p l i e d i nt h i s study are n o n - l i n e a r and f u r t h e r more m e a s u r e d t r a c e r d i s t r i b u t i o n s i n t h e l i q u i d p h a s e show m a r k e d r a d i a l p r o f i l e s p a r t i c u l a r l y a t c o u n t e r c u r r e n t f l o w (_1_3_) a t w o - d i m e n s i o n a l d e s c r i p t i o n may be more p e r t i n e n t . C O 2 c o n c e n t r a t i o n m e a s u r e m e n t s a t d i f f e rent r a d i a l p o s i t i o n s did,however,not y i e l d any s i g n i f i c a n t d i f f e r e n c e s . T h e r e f o r e the o n e - d i m e n s i o n a l model i s t h o u g h t t o be a s u f f i c i e n t a p p r o x i m a t i o n . A l t h o u g h gas h o l d up may v a r y c o n s i d e r a b l y a l o n g t h e c o l u m n t h e v a l u e o f ©c i n eqn (6) c a n be t a k e n a s a p p r o x i m a t e l y c o n s t a n t , o c r e p r e s e n t s t h e r a t i o o f t h e maximum h y d r o s t a t i c head t o the p r e s s u r e a t the t o p o f the bubble column: *C=
g—S—
(
8
,
Τ
The v a r i a t i o n o f t h e g a s h o l d up a n d t h e i n t e r f a c i a l a r e a a r e t a k e n i n t o a c c o u n t by eqns (1) a n d ( 4 ) , r e s p e c t i v e l y . A s s u m p t i o n (8) a c c o u n t s f o r a v a r i a b l e g a s v e l o c i t y . T h e r e f o r e an a d d i t i o n a l r e l a t i o n i s r e q u i r e d . T h i s i s o b t a i n e d from a b a l a n c e on the i n e r t s w h i c h yields :
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL
364
u
P(l-x)
Q
=
REACTION
ENGINEERING—HOUSTON
u P (l+OC) ( l - x ) G o
T
(9)
Q
The i n d e x ο r e f e r s t o c o n d i t i o n s a t c o l u m n i n l e t . A s s u m p t i o n (10) m u s t n o t be f u l f i l l e d a c t u a l l y as 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 c a n be s u b s t i t u t e d by t h e o v e r a l l t r a n s f e r c o e f f i c i e n t . Model
Equations
The g o v e r n i n g d i f f e r e n t i a l b a l a n c e e q u a t i o n s a r e n o t d e r i v e d h e r e as t h i s i s o u t l i n e d f o r s i m i l a r p r o b l e m s i n d e t a i l i n r e f . (4_) . C o n s i d e r a t i o n o f eqn (9) l e a d s t o eqn (10) f o r t h e C 0 - b a l a n c e o f t h e gas p h a s e :
Jf
=
(ζ ( 1 - χ ) ( β ( ζ ) χ
-S
Τ For one
the p a r t i a l p r e s s u r e of C0 i n the l i q u i d phase o b t a i n s on t h e b a s e o f t h e made a s s u m p t i o n s :
2
d p
p^
2
Pe
T
1
+
dp
T
-±
_
a
Pe
T
St
T
L
=
4> (z) (P_Ô(z)x-p ).
L
,
T
(11) I n e q n s (10) t i t i e s were o b t
and (11) t h e introduced: Y
t
K
G
P>(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
1-B
n
P (0)
Ρ Li
P
L
d
and
*>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
Literature Cited (1)
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.
(1976) 31 225
Sci.
(7) (8)
(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.,
Can.J.Chem.Engng.
(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 <
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
378
CHEMICAL
REACTION
1
Ref Réf. Hf) *» 15 ο 160 3000 24 T 406 2600 19 α 150 1200 21 V 610 JUUU 19 m 300 1200 25 fi 457 3000 22 152 4000 26 Φ 1066 3000 23 • 290 3800 26 240 2500 I ! 20 * 200 7230 ι !
«
1
m„
—-, π
ί
o -
ENGINEERING—HOUSTON
ε
*i
o.?
-
system air/water
0,02
ι , ,
0.
Figure 3. Dependency of gas holdup on column di mensions for the system air/water
Δ xylol, dL =0.5mm A
xylol, d|_ = 1.0 mm
ο propanoic =0.5mm • 2
4
6
propanol,d(_ = 1.0 mm
8
gas phase linear velocity u [cm/s] • D
Figure 4. Sauter mean bubble diameter as a function of gas linear velocity for the aeration of xylene and propanol
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
31.
PiLHOFER E T A L .
Parameters in Bubble Column Design
379
d i s p e r s i o n c o e f f i c i e n t o f t h e l i q u i d phase h a s been measured f r e q u e n t l y , b u t m o s t l y i n a i r / w a t e r systems. F o r t h i s , c o r r o b a t e d e q u a t i o n s h a v e b e e n p r e s e n t e d (15) (l6). T h e r e f o r e , o u r i n v e s t i g a t i o n s were f o c u s s e d on the i n f l u e n c e o f l i q u i d phase p r o p e r t i e s . P r e l i m i n a r y t e s t s showed, t h a t t h e d i s p e r s i o n c o e f f i c i e n t depends i n t h e same way o n t h e g a s t h r o u g h p u t a s t h e g a s h o l d up. T h e r e f o r e , m a i n l y t h e i n f l u e n c e o f t h e l i q u i d v i s c o s i t y w a s s t u d i e d . R e f e r r i n g t o f i g u r e 6, t h e r e i s a c l e a r dependency o f t h e l i q u i d phase d i s p e r s i o n c o e f f i cient on thel i q u i d v i s c o s i t y . A d d i t i o n a l l y , f i g u r e 6 shows l i n e s f o r t h e r e l a t i o n b e t w e e n d i s p e r s i o n c o e f f i c i e n t and gas throughput according t o H i k i t a and Kikukawa (_17 ). T h i s e q u a t i o n a g r e e s with our experimental d a t a a n d c a n b e recommende D
c
= ( 0,15 + 0,69·ιι °' )· d g ' 0
- (10 /η )
(13)
_ 3
ε
Up t o now, t h e r e a r e o n l y f e w m e a s u r e m e n t s o f t h e gas phase d i s p e r s i o n c o e f f i c i e n t ; i . e . s e e t h e p a p e r o f T o w e l l / A c k e r m a n n (JL§.) · * e x p e r i m e n t s we a p p l i ed a new m e t h o d b a s e d o n f r e q u e n c y a n a l y s i s f o r t h e measurement o f g a s phase d i s p e r s i o n . There i s a n i n s o l u b l e g a s t r a c e r , v a r y i n g i n t i m e i n a s i n o u s mode so t h a t t h e d e s c r i b i n g e q u a t i o n s ( l ) a n d (2) a r e d e c o u p l e d b e c a u s e o f t h e a b s e n c e o f mass t r a n s f e r . The shortened equation ( l ) can be solved t h e o r e t i c a l l y , a l l o w i n g t h e d e t e r m i n a t i o n o f t h e gas phase d i s p e r s i o n c o e f f i c i e n t asa function o f theamplitude r a t i o o f the t r a c e r c o n c e n t r a t i o n s between two m e a s u r i n g p o i n t s . Three l i q u i d s were u s e d i n t h e e x p e r i m e n t s . A s a r e s u l t , f i g u r e 7 shows t h e g a s p h a s e d i s p e r s i o n c o e f f i c i e n t a s a f u n c t i o n o f t h e r e l a t i v e v e l o c i t y w^. T h e m e a s u r e d p o i n t s can be d e s c r i b e d b y t h e f o l l o w i n g equation: no
D
=
D
u
0,002-w ' 3
r
56
R
(14)
T h i s e q u a t i o n c a n b e recommended f o r d e s i g n p u r p o s e s . The r e l a t i v e v e l o c i t y c a n b e d e t e r m i n e d b y a p p l y i n g e q u a t i o n (10) a n d (7) f o r t h e c h u r n t u r b u l e n t r e g i m e , neglecting thel i q u i d velocity. Additionally, i t i s t o c o n s i d e r , t h a t e q u a t i o n (l4) i s v a l i d o n l y f o r a c o l u m n d i a m e t e r o f 100 mm. H o w e v e r , t h e r e i s a s t r o n g d e p e n dency o f t h e gas phase d i s p e r s i o n c o e f f i c i e n t on t h e column d i a m e t e r . I n comparing o u r r e s u l t s w i t h l i t e r a t u r e d a t a , we g o t t h e f o l l o w i n g d e p e n d e n c y : D
D
„
d g
1
^
(
1 5
)
This f a c t i st o be taken i n t o account i n determining gas phase d i s p e r s i o n c o e f f i c i e n t s f o r column d i a m e t e r s o t h e r t h a n 100 mm.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
380
CHEMICAL
2
4
6
REACTION
8
linear gas velocity
10
ENGINEERING—HOUSTON
cm/s
12
u0
Figure 5. Central values and standard deviations for the ap proximation of bubble size distributions by log normal distri butions
ι
ι
1
1
1 1
1
1
A propanol • glycol
'
=.
- v ^ •
-
equation (13) 1
3
1
1
1
1
1 1
10
cm/s
20
linear gas velocity u
D
Figure 6. Liquid phase dispersion coefficient as a function of linear gas velocity
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
piLHOFER E T A L .
Parameters in Bubble Column Design
104
ψ
cm2/s
OD 0t>
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
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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
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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
2
V i
(9c)
Ch
and c a t a l y s t u t i l i z a t i o n i s d i r e c t l y p r o p o r t i o n a l t o f r a c t i o n of i n t e r n a l pore f i l l up. This shows t h a t f o r l a r g e m o d u l i i n^g i s the dominant v a r i a b l e , f o r small modulii becomes the important parameter. One of the questions t o be answered i s how w e l l expression (8) f o r the e f f e c t i v e n e s s f a c t o r compares t o the r e s u l t s computed on the b a s i s of a more r i g o r o u s model f o r a p a r t i a l l y wetted p e l l e t .
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
MILLS
391
Mathematical Model For Reaction I n P a r t l y Wetted C a t a l y s t P e l l e t s I t i s i n s t r u c t i v e t o consider f i r s t a simpler problem, name l y that o f a r e a c t i o n on a p a r t l y e x t e r n a l l y but completely i n t e r n a l l y wetted c a t a l y s t p e l l e t . This case i s of i n t e r e s t i n p a r t i c u l a r f o r hydrocarbon feeds which presumably r e a d i l y wet the i n t e r n a l pore s t r u c t u r e . C l e a r l y i f the k i n e t i c r a t e i s very slow the r e d u c t i o n i n the "supply a r e a " i . e . e x t e r n a l area wetted through which r e a c t a n t s a r r i v e t o the p e l l e t w i l l h a r d l y a f f e c t p e l l e t u t i l i z a t i o n but f o r h i g h e r k i n e t i c r a t e s a r e d u c t i o n i n u t i l i z a t i o n due t o incomplete e x t e r n a l w e t t i n g should become apparent. The s o l u t i o n f o r the problem i n c a r t e s s i a n coordinates f o r slab geometry i s presented here Th governin equation 2
8 u 9x
a£u
2
8y
au
u =
(10)
l
2
0 at χ = 0 for y
9 x
+
" B r ë
U
=
l
a
t
x
=
0
f
Q
o
r
° -
y
-
(11)
y
o
( 1 2 )
m ~
= 0 a t y = 0 and y = 1
(13)
where u i s the dimensionless r e a c t a n t c o n c e n t r a t i o n . C l e a r l y , n u m e r i c a l l y yQ - n^g. One method of s o l u t i o n may be o u t l i n e d as f o l l o w s . D i v i d e the r e g i o n of i n t e r e s t i n t o two subregions by l i n e p a r a l l e l t o χ a x i s a t y = yg. L e t u = u i and u = U2 i n r e g i o n 1 and 2, respec t i v e l y , and s o l v e by s e p a r a t i o n of v a r i a b l e s the corresponding d i f f e r e n t i a l equations and boundary c o n d i t i o n s . This r e s u l t s i n an i n f i n i t e s e r i e s o f c o s ( X ( l - x ) ) f o r u^ and a s e r i e s of cos(nirx) for U2- The eigenvalues λ a r e the r o o t s of the t r a n s c e n d e n t a l equation X t a n X = B l ^ , the s i x f i r s t values are t a b u l a t e d (23) the others can r e a d i l y be obtained. The e x p r e s s i o n f o r the e f f e c t i v e n e s s f a c t o r takes the f o l l o w i n g form: n
η
n
n
tanh(
tanh φ_ ι
Σ n=l
a s ixni i
Bi λ Α
n
a
η
λη
0
m
Γ tanh (p νy ) Γtanh(ρ n Λ
L
ο
(l-y )) tt aa nn hh ^^ (1-y 1 2 n
+
.
Φ Ρ τ
η
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
(14)
CHEMICAL REACTION
392
ENGINEERING—HOUSTON
The c o e f f i c i e n t s a are found by the s o l u t i o n of an i n f i n i t e s e t of l i n e a r a l g e b r a i c equations ( i n f i n i t e m a t r i x ) which r e s u l t s 3u^ 3 u n
2
when one r e q u i r e s u^ = U£ and
a t the a r t i f i c i a l boundary
y = Υ0·
Σ
a
a
i j j
= b
5
i
i
=
1
(15)
2
> "
j=l where: sin λ Γ φ α.. « — — + U λ I Pj 1
"1
tanh(q y ) ΓΤ-^ΎΤ û tanh( n
(16a)
f o r j = 1,2,3...c
2λ. s i n λ. r . X J
2
2
2
X -(i-l) ir
tanh p.y~
[Pj
1
q^^anh q _ (l-y ) ±
1
( )
J
f o r i = 2,3,4. ..<° , j = 1,2...~ 2 b
= - γ sin Φ
P j
= >/φ
±
2 τ
; b
Τ
+ Xj
2
i
ΥΦ
Τ
=
s i n h φ ; i = 1,2,3.. .°° (16c) χ
2
;
2
q. = \ / φ + i *
2
(16d)
Bi m Bi
m
C O s h
Φ
Τ
+
Φ
(16e) Τ
S i n h
Φ
Τ
The i n f i n i t e s e t of equations (15) has unique s o l u t i o n s s i n c e 00
Σ
00
Σ
ι
00
ι
i j
c o n v e r
S
e s
anc
* 2
ι
ι
|bjM converges
(24,25).
The s o l u -
i-1 j - 1 i-1 t i o n s f o r a of i n c r e a s i n g accuracy are obtained by t r u n c a t i n g the i n f i n i t e m a t r i x a f t e r v a r i o u s , i n c r e a s i n g number of terms which i s a method o f t e n employed i n s o l u t i o n of mixed boundary v a l u e prob lems (26,27). When JQ = T\Q% = 1.0 a l l a = 0 and the value f o r the e f f e c t i v e n e s s f a c t o r reduces p r o p e r l y t o the e x p r e s s i o n f o r a t o t a l l y wetted s l a b . For yo ζ 0 a l s o = 0 as expected. S o l u t i o n s f o r e f f e c t i v e ness f a c t o r s i n other geometries of i n t e r e s t such as p a r t i a l l y e x t e r n a l l y wetted sphere or c y l i n d e r of f i n i t e l e n g t h can a l s o be developed but a r e omitted here f o r b r e v i t y and w i l l be presented elsewhere. n
n
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
32. DUDUKOvic A N D
MILLS
Catalyst Effectiveness in Trickle-Bed Reactors 393
In the l i m i t o f no e x t e r n a l mass t r a n s f e r r e s i s t a n c e ( B i ^ °°) the Robin type boundary c o n d i t i o n (12) becomes a simpler D i r i c h l e t c o n d i t i o n o f u = 1. This problem was solved a l s o . Discussion A study was performed t o a s c e r t a i n the e f f e c t of m a t r i x t r u n c a t i o n on c a l c u l a t e d values of the c a t a l y s t e f f e c t i v e n e s s f o r both the D i r i c h l e t and Robin c o n d i t i o n s . The r e s u l t s are summarized i n Table I I f o r a T h i e l e modulus of 1.0, an e x t e r n a l c o n t a c t i n g e f f i ciency of 0.5 and f o r matrices of s i z e Ν χ Ν. The answers seem t o be accurate on the f i r s t two decimal places and the r e s u l t s f o r B i = 10^ and B i = computed from two d i f f e r e n t expressions agree w e l l . 00
m
m
E f f e c t of M a t r i x Truncation on C a l c u l a t e d E f f e c t i v e n e s s Factors Catalyst Effectiveness Ν = 50 B i o t Number Ν = 30 Ν = 40 =7" 0.49610 χ 10" 10 0.49610 χ 10" 0.49610 χ 10' 0.46356 χ 10-1 0.46356 χ 10' ίο 0.46356 χ 10" 2
-1
1.0 ΙΟ ΙΟ ΙΟ
10 00
1 2
3
1
0.28018 0.57047 0.64285 0.65199 0.65292 0.65302
0.28019 0.57051 0.64312 0.65251 0.65347 0.65358
0.28019 0.57053 0.64326 0.65282 0.65380 0.65391
I t i s a l s o of i n t e r e s t t o compare the above derived s o l u t i o n f o r the e f f e c t i v e n e s s f a c t o r t o the approximate form of A r i s (15) and Mears (4·). For an i n f i n i t e B i o t number f o r l i q u i d - s o l i d t r a n s port t h i s comparison i s presented i n F i g u r e 1. Mears approxima t i o n d e v i a t e s d r a s t i c a l l y from the true values a t low and i n t e r mediate m o d u l i i and becomes a good approximation only i n the r e g i o n of strong i n t e r n a l d i f f u s i o n a l l i m i t a t i o n s i . e . h i g h m o d u l i i . As expected the a c t u a l e f f e c t i v e n e s s f a c t o r i n k i n e t i c a l l y c o n t r o l l e d regime ( s m a l l m o d u l i i ) i s much greater than pre d i c t e d by the product o f the e f f e c t i v e n e s s f a c t o r f o r t o t a l l y wetted p e l l e t and f r a c t i o n of e x t e r n a l area wetted as suggested by Mears (4). A r i s formula (15) a l s o d e v i a t e s s u b s t a n t i a l l y from the computed values e s p e c i a l l y a t intermediate m o d u l i i . However, t h i s expression represents a u s e f u l lower bound on the e f f e c t i v e ness f a c t o r and i s expected to be i n c l o s e r agreement w i t h com puted r e s u l t s f o r other geometries. In Figure 2 a comparison of the e f f e c t of the l i q u i d - s o l i d B i o t number and incomplete c o n t a c t i n g on e f f e c t i v e n e s s f a c t o r i s presented. 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 are more pronounced even a t r e l a t i v e l y high degree of e x t e r n a l w e t t i n g (nç^ 0.5) f o r higher m o d u l i i which i s t o be expected s i n c e by reducing the area f o r supply o f r e a c t a n t s the r e a c t a n t f l u x cannot keep up w i t h f
1
>
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION
394
a)
NUMERICAL
b)
APPROXIMATION
BY ARIS
- — —-c)
APPROXIMATION
BY MEARS
··»
Ο
0.2 CONTACTING
Figure 1.
0.4
ENGINEERING—HOUSTON
SOLUTION OF THE MODEL
0.6
EFFICENCY ,
0.8
1.0
Q E C
Catalyst effectiveness in partly externally wetted slab
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
32. DUDUKovic
AND MILLS
Catalyst Effectiveness in Trickle-Bed Reactors 395
Figure 2. Contacting efficiency and effectiveness factor
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION
396
ENGINEERING—HOUSTON
r e a c t i o n demands a t higher k i n e t i c r a t e s . F i g u r e 3 represents the e f f e c t of incomplete e x t e r n a l c o n t a c t i n g and B i o t number on e f f e c t i v e n e s s f a c t o r i n a d i f f e r e n t form. The models f o r c a t a l y s t e f f e c t i v e n e s s i n t r i c k l e bed r e a c t o r s developed i n t h i s paper r e q u i r e e x p l i c i t measurements or p r e d i c t i o n s of e x t e r n a l c o n t a c t i n g , ης , and pore f i l l - u p , η^. I n l a b o r a t o r y c o n d i t i o n s t h i s can be accomplished by t r a c e r techniques (22,28). F r a c t i o n a l pore f i l l up may be determined by the d i f f e r ence i n f i r s t moments of the impulse response t r a c e r t e s t s p e r formed on two beds of same p a r t i c l e s i z e and shape when one bed c o n s i s t s of porous the other of nonporous p a r t i c l e s . F r a c t i o n a l pore f i l l - u p can a l s o be assessed from the measured v o l u m e t r i c a l l y s t a t i c holdup. E x t e r n a l c o n t a c t i n g i s measured by adsorbable t r a c e r t e s t s on beds of nonporous p a r t i c l e s (28) In i n d u s t r i a l c o n d i t i o n s n ^ g and rij woul U n f o r t u n a t e l y a t presen u n s a t i s f a c t o r y s i n c e they were developed f o r f i x e d bed adsorbers w i t h l a r g e r packing and c o r r e l a t i o n s f o r ηχ a r e nonexistent but may be developed i n the f u t u r e . Ε
Conclusions Catalyst effectiveness factor i n t r i c k l e - b e d reactors i s a f u n c t i o n of the T h i e l e modulus, φχ, incomplete e x t e r n a l w e t t i n g , T i C g , and f r a c t i o n a l pore f i l l - u p , η^. Exact formulas f o r r e p r e s e n t a t i o n of the e f f e c t i v e n e s s f a c t o r i n p a r t i a l l y i n t e r n a l l y and e x t e r n a l l y wetted p e l l e t s can be d e r i v e d only i f the geometry of the wetted r e g i o n and i t s boundary i s known. I n t h i s paper a s o l u t i o n i s d e r i v e d f o r the case of t o t a l i n t e r n a l and p a r t i a l e x t e r n a l w e t t i n g . This seems t o be the case i n a number of t r i c k l e bed r e a c t o r s . A lower bound f o r the general case i s a l s o presented. Acknowledgemen t The authors a r e g r a t e f u l t o the N a t i o n a l Science Foundation f o r p a r t i a l f i n a n c i a l support of t h i s work (Grant No. ENG 57406A). Nomenclature k L f
B i o t number f o r l i q u i d - s o l i d mass t r a n s f e r , dimensionless e f f e c t i v e d i f f u s i v i t y of the l i q u i d r e a c t a n t i n c a t a l y s t p a r t i c l e , cm^s" diameter of c a t a l y s t p e l l e t , cm 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 , cm s""*
D ff e
1
2
U d T
2D ff(l-e)
parameter i n equation
(5c),
dimensionless
e
H
TL
t o t a l l i q u i d holdup, cm dimensionless
3
liquid/cm
3
reactor,
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
DUDUKovic
AND MILLS
Figure 3.
Catalyst Effectiveness in Trickle-Bed Reactors
Contacting efficiency and effectiveness factor
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL
398
REACTION
ENGINEERING—HOUSTON
1
- e x t e r n a l mass t r a n s f e r c o e f f i c i e n t , cm s " - r e a c t i o n r a t e constant, cm l i q u i d / c m c a t a l y s t and second, s"" " true r e a c t i o n r a t e constant, cm l i q u i d / c m catalyst s" - l i q u i d s u p e r f i c i a l mass v e l o c i t y , g cm~ s"" - l i q u i d h o u r l y space v e l o c i t y , hr*" 3
ky.
3
1
3
ktc
3
1
2
Lm LHSV
^^ 2
%o
E
~ Bodenstein number f o r a x i a l d i s p e r s i o n i n
Z
3(l-e)k N
g t
=
1
1
question (5a), dimensionless
~ Li
Stanton number i n equation (5b), dimensionless
Greek L e t t e r s 3
ε
3
- bed p o r o s i t y , cm voidage/cm r e a c t o r , dimensionless ~ 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 , dimensionless - f r a c t i o n a l pore f i l l - u p , dimensionless - 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 , dimensionless "~ 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 n t r i c k l e - b e d r e a c t o r s , dimensionless - k i n e t i c v i s c o s i t y , crn^s" - s u r f a c e t e n s i o n of l i q u i d , dyne cm" - c r i t i c a l s u r f a c e t e n s i o n of the s o l i d , dyne cm"" - a c t u a l space time r e q u i r e d to reach f i f t y percent c o n v e r s i o n , s - space time a t complete w e t t i n g r e q u i r e d f o r f i f t y percent c o n v e r s i o n , s - T h i e l e modulus, dimensionless - m o d i f i e d modulus i n t r i c k l e - b e d s , dimensionless
HCE i Πχ τίΤΒ n
1
ν σ σ τ^-
1
1
0
ΐιβ' Φχ ΦχΒ 2z ω = -τP
-
a x i a l c o o r d i n a t e , dimensionless
d
Literature Cited 1. 2. 3. 4. 5. 6.
Le Nobel, J . W., Choufoer, J . Η., "Fifth World Petr. Cong. Proc. Sect III," Paper 18, Fifth World Petr. Cong., Inc., New York, 1959. Van Deemter, J . J., "Proc. Third Eur. Symp. Chem. Reaction Eng.," p. 215, Pergamon Press, 1964. Adlington, D., Thompson, Ε . , "Proc. Third Eur. Symp. Chem. Reaction Engr.," p. 203, Pergamon Press, 1964. Mears, D. E . , 3rd Int. Symp. Chem. React. Eng., Adv. Chem. Ser., (1974) 133, 218. Satterfield, C. Ν., AIChE J., (1975) 21(2). Van Zoonen, D., Douwes, C. Th., J . Inst. Petroleum, (1963), 49, 383.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
32. DUDUKOvic A N D M I L L S
Catalyst Effectiveness in Trickle-Bed Reactors
7.
399
Satterfield, C. Ν., Mah, Υ. Η., Sherwood, Τ. Κ., Inst. Chem. Eng. Symp. Ser., (1968) 28, 22. 8. Germain, A. H . , Lefebure, A. G., L'Homme, G. Α., 3rd Int. Symp. Chem. React. Eng., Adv. Chem. Ser., (1974)133, 164. 9. Cecil, R. R., Mayer, F. X . , Cart, Ε. Ν., Jr., "Fuel Oil Hydrodesulfurization Studies in Pilot Plant Reactors," paper presented at the 68th AIChE Annual Meeting, Los Angeles, Calif., Dec. 1-5, 1968. 10. Murphree, Ε. V . , Voorhies, Α., Jr., Mayer, F. X . , Ind. Eng. Chem. Process Des. Develop., (1964) 3(4), 381. 11. Henry, H. C . , Gilbert, J . Β . , Ind. Eng. Chem. Process Des. Develop., (1973) 12(3), 328. 12. Ross, L. D., Chem. Eng. Progr., (1965) 61(10), 77. 13. Schwartz, J . G., Roberts G W. Ind Eng Chem Process Design Develop., (1973 14. Mears, D. Ε . , Chem Eng 15. Aris, R., Chem. Eng. Sci., (1957) 6, 262. 16. Koros, R. Μ., "Fourth Int. Chem. React. Symp. Proceedings," Vol. 1, p. IX 372, Dechema, Frankfurt, 1976. 17. Bondi, Α., Chem. Tech., (1971) 1, 185. 18. Puranik, S. S., Vogelphhl, Α., Chem. Eng. Sci. (1974) 29,501. 19. Sylvester, N. D., Pitayagulsarn, P., Can. J. Chem. Eng., (1974) 52, 539, 20. Suzuki, Μ., Smith, Η. Μ., (1970) AIChE J., 16(5), 882. 21. Duduković, M. P., AIChE J., 1977 (in press). 22. Colombo, A. J., Baldi, G . , Sicardi, S., Chem. Eng. Sci., (1976) 31, 1101. 23. Carslaw, H. S., Jaeger, J. C. "Conduction of Heat in Solids" Oxford University Press, Oxford (1959). 24. Reisz, F . , "Les Systemes d'equations lineaires a une infinite d'inconnues," Gauther-Villars, Paris, 1913. 25. Whittaker, E. T . , Watson, G. Ν., A Course of Modern Analysis, Cambridge University Press, Cambridge, 1935. 26. Sell, M. G., Jr., Hudson, J. C . , Int. J. Heat Mass Transfer (1966) 9, 11. 27. Snedonn, I. Ν., "Mixed Boundary Value Problems in Potential Theory," Wiley, New York, 1966. 28. Schwartz, J. G . , Weger, Ε . , Duduković, M. P., AIChE Jr., (1976) 22(5).
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
33 Modeling the Slugging Fluidized Bed Reactor J. R A G H U R A M A N
and Ο. E . P O T T E R
Department of Chemical Engineering, Monash University, Clayton 3168, Victoria, Australia
In some industrial, and nearly all pilot-plant, fluidized bed reactors the aspect ratio is such that slugging behaviour can be expected, as Davidson and his co-workers have suggested. Scale-up therefore frequently involves a jump from slugging-bed behaviour to freely bubbling bed behaviour. Slugging behaviour occurs when the bubbles present in the bed have diameters approaching that of the vessel. By 'freely bubbling' is meant that there are many bubbles present, each bubble being of a diameter much less than that of the vessel. Fryer and Potter (1,2,3) have compared the counter-current backmixing model with experimental results and the predictions of other models and have demonstrated that the countercurrent back mixing model is appropriate to the freely bubbling bed and has advantages over other models which have been proposed. Raghuraman and Potter (4) have extended the concepts of the countercurrent backmixing model to the slugging fluidized bed, basing the analysis on the solids m i x i n g model o f Thiel a n d Potter (5,6). C o m p a r i s o n o f the predictions o f the new model w i t h t h e experi m e n t a l d a t a o f Hovmand and D a v i d s o n ( 7 , 8 ) and Hovmand, Freedman and D a v i d s o n ( 9 ) shows better a g r e e m e n t w i t h e x p e r i m e n t t h a n i s exhibited by the t w o - p h a s e model o f Hovmand and D a v i d s o n . In t h i s p a p e r an e x t e n s i o n o f t h e new model i s d e s c r i b e d . T h i s e x t e n s i o n o f t h e model h a s t h e a i m o f f a c i l i t a t i n g a d e t a i l e d d y n a m i c i n v e s t i g a t i o n o f t h e s l u g g i n g f l u i d i z e d bed r e a c t o r whether o f t h e c a t a l y t i c t y p e o r o f t h e t y p e e x h i b i t i n g r e a c t i o n between g a s and s o l i d a s i n m i n e r a l r o a s t i n g and f l u i d i z e d bed combustion. The e x t e n d e d model r e p o r t e d h e r e s e e k s t o d e s c r i b e t h e c y c l i c v a r i a t i o n s w h i c h o c c u r due t o s l u g g i n g i n a s t e a d y s t a t e c a t a l y t i c system. A l t h o u g h t h e s t u d i e s c o m p l e t e d and p r o p o s e d have d i r e c t a p p l i c a t i o n o n l y t o s l u g g i n g f l u i d i z e d bed r e a c t o r s t h e r e w i l l be i n s i g h t s g i v e n i n t o t h e b e h a v i o u r o f f r e e l y b u b b l i n g beds. P o t t e r (10) h a s r e c e n t l y r e v i e w e d t h e m o d e l l i n g o f f l u i d i z e d bed reactors. © 0-8412-0401-2/78/47-065-400$05.00/0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
33.
RAGHURAMAN
Slugging Fluidized Bed Reactor
AND POTTER
401
Model o f D a v i d s o n and C o - w o r k e r s Hovmand and D a v i d s o n (8_) p r o p o s e d a t w o - p h a s e model a n d compared t h e p r e d i c t i o n s o f t h a t model w i t h t h e e x p e r i m e n t a l d a t a o f Hovmand a n d D a v i d s o n (7_) a n d Hovmand, Freedman and D a v i d s o n (9). The model assumes c o - c u r r e n t p i s t o n - f low o f b u b b l e g a s (U-U ^) a n d d e n s e - p h a s e g a s ( U ^ ) , w i t h t o t a l m i x i n g o c c u r r i n g when s l u g s c o a l e s c e . This latter a s s u m p t i o n has n o t been j u s t i f i e d a s y e t . The new model r e t a i n s t h e a c c o u n t o f g a s - e x c h a n g e g i v e n by Hovmand a n d D a v i d s o n ( 8 ) . Gas e x c h a n g e due t o d i f f u s i o n and b u l k - f l o w a r e a d d i t i v e .
2_ = ±
^mf U
Dm
In e q u a t i o n
1/2
1
+
mf
1
+
£
Λ ]
Γ
(1)
π
mf
I J
(1) m 4V
J
D
is slug-length.
1/9
L S
S
495
-
°·
I i s surface
,..(2)
+ 0.061
D
integral
tabulated
in Table I .
Table I Value of Surface Integral I L /D s
I
0.3
0.5
1.0
2.0
3.0
4.0
5.0
0.13
0.21
0.39
0.71
0.98
1.24
1.48
The a u t h o r s a l s o g i v e a n e x p r e s s i o n f o r g a s - e x c h a n g e w h i c h t a k e s i n t o a c c o u n t i n t e r a c t i o n between d i f f u s i o n and b u l k - f l o w b u t recommend f o r use t h e g a s - e x c h a n g e r a t e c a l c u l a t e d by e q u a t i o n ( 1 ) . The s l u g - r i s e v e l o c i t y , w i t h r e s p e c t t o s t a t i o n a r y s o l i d s a h e a d , i s g i v e n by Kehoe a n d D a v i d s o n ( 1 1 ) U
=
s
and t h e r i s e v e l o c i t y o f c o n t i n u o u s l y g e n e r a t e d s l u g s U
SA
U-U
f
,.(3)
0.35 ( g D ) '
+ 0.35 ( g D )
i s g i v e n by:
:
(4)
The e x c h a n g e c o e f f i c i e n t , Q/V , i s used by D a v i d s o n a n d c o - w o r k e r s f o r g a s e x c h a n g e between t h e s l u g and t h e r e s t o f t h e b e d , o r dense p h a s e . The New M o d e l , T i m e - A v e r a g e d T h i e l and P o t t e r ( 4 , 6 ) have shown t h a t m i x i n g o f s o l i d s i n r o u n d - n o s e d s l u g g i n g beds c a n be a c c o u n t e d f o r by a s s u m i n g t h a t t h e s l u g i s f o l l o w e d by a wake o f w e l l - m i x e d s o l i d s w h i c h t a k e s up a b o u t t w o - t h i r d s o f t h e i n t e r s l u g m a t e r i a l . The r e m a i n d e r o f t h e i n t e r - s l u g m a t e r i a l i s i n piston-flow. Thus t h e model a d o p t s t h e g a s - e x c h a n g e r a t e a s g i v e n i n e q u a t i o n ( 1 ) b u t c o n s i d e r s i t a p p l i c a b l e t o gas e x c h a n g e between
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
402
wake and s l u g , Q/V~ being r e l a b e l l e d K^. So f a r as gas-exchange between wake and tne p i s t o n - f l o w region i s concerned, t h i s i s considered t o be determined by the s o l i d s movement, allowance being made f o r gas flow U ^ , with respect t o s t a t i o n a r y s o l i d s . The s o l i d s phase flows i n and out of the wake, which i s of vo I urne f V at a volumetric r a t e , U This exchange can be expressed i n terms of an exchange c: o e f f i c i e n t , namely the volume of s o l i d s phase exchanged with the wake per u n i t s l u g volume per u n i t time, (IL πΟ /4)/V^. If there were no flow of gas through the s o l i d s phase, then the gas-exchange r a t e would be (ε U π ϋ / 4 ) / ν . Following Stewart and Davidson (12) the flow out of the s l u g nose and i n a t the base of t h e s l u g w i l l be U ^ -nD /4. So, the net volume of gas exchanged between the p a r t i c u l a t e p i s t o n - f l o w region and the wake pe ç
r
2
$
f
z
(U
S
mf 4 V
U )πϋ mf
ζ
χ
,(5)
r
If the f r a c t i o n of the bed-volume occupied by slugs i s ε^, then
...(6) B
V
2
+ TD(wD /4)
s
where Τ i s the r a t i o of mean i n t e r - s l u g spacing t o column diameter. Therefore, equation (5) may be a l t e r n a t i v e l y presented : (1-ε > Β
Κ
CP
TD ε
,(7)
υε ,- U S mf mf ο
Β
#
Figure 1 i l l u s t r a t e s the gas-exchange process. For f i r s t - o r d e r s t e a d y - s t a t e chemical r e a c t i o n , the m a t e r i a l balances on reactant gas, on a time-averaged b a s i s , a r e as f o l lows : dO,
Slug
Β U GB dz
Wa ke
U G
K
BC
K
CP
(C
,(8)
)ε
C " °Β Β
dCç c
dz
( C
C
P
) £
C B
+
K
k
Pi ston-flow reg ion
5
U GP dz
K
( C
C
CP C " P
) e
B "
k
( C
C
BC B " C
f
ε
) £
B ,(9)
C
w Β C 1
ε
- Β
Π +
ν ...(10)
Here the wake f r a c t i o n i s given by : f
2
w
= wUD /4)TD/V S c
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
...(11)
33. w
RAGHURAMAN
is the
and
of
the
estimated
conditions
U
GB
=
U
GP
=
Ζ
=
material
and Potter
which
to
by Raghuraman
403
i s we I I - m i x e d
be 0 . 7
*
0.2.
and Potter
(4_).
The
...(12)
=
U
U
and
At
inter-slug
by T h i e l
are given
average,
where
Slugging Fluidized Bed Reactor
POTTER
proportion
has been
boundary
On
AND
+
GB
U
-
U
U
, mf
U
U
m f -
o,
ε
c
+
GC
U
U
GC =
Vmf GB
,f,,(U-U
mf w = c
B
GP
...(13)
,)
mf
...(14)
0
...(15)
and U
-
The
exit
The
New M o d e l ,
at
initial
The
reacting
cycle
slug
flow
time
C
at
Figure
of
that
piston-flow
when
2
shows
distributor moment on.
of
Since of
top
the bed a t
from
= 0
it
from
0
i n t e r s lug
one-third.
risen
by o n e - t h i r d
reached
the top of
In
At t of
we
7
)
from t h e bed from
non-reacting
time.
here
1
follow
region
the top of
with
(
Only
for
the
comparison
model
of
Hovmand a n d
to
rise
a
t h e bed and s l u g s
above
are
cycle
it
above
bursting
is
seen
also
a
1
Figure
at
being
2 this
τ / 3 , slug
0
the
i n t e r s lug
spacing
t h e bed and b u r s t s ,
is
as
necessarily
t
= 0
from
the
an
is
α
a new
to
forming,
α
at
the
2 and s o
integral remains
detaching
fraction
=
section
renumbered
amount
t h e new s l u g
piston is
produce
renumbered
in general,
fractional
when
that
is
It
calculation.
itself
has detached, 1;
to
are not
in the
the bed
and
the top.
in the top
detach
in
conditions
a s t h e wake
and a t
i s no s l u g
to
situations
Special
t h e flow
2,
the
cycle
account
of
through each
1,
not contain,
the time
the distributor.
mately
of
slug
to
regions,
form
is approached
zero
the top.
into
Figure
t h e bed does
number of
t
at
the f i r s t
+
and a t
this
bed t o
progressive
to
is just about
detachment
In
fluidized
and slug
taken to
Form
f o r the slug
there
is
0
- - ·
the two-phase
bursts
formation
again
C
At the beginning
behind
since
:
data.
the
during
New s l u g
numbered
C
and the p i s t o n - f l o w
t h e bottom
slug
C
mf
admitted
TD/U^.
and t h i s
Referring
C
are presented
and r i s e
a
U
Cyclic
version,
in
slug,
G C
by
the bed i s
mixing. phase
U
the steady-state
gas is
a r e formed
becomes
=
0
the fluidized
Thus
at
t h e bottom
assumed
C
+
GB B
i s the time
a r e formed
regimes
)
the slug,
i.e.
is admitted
slugs
obtain
U
=
solutions
length
renumbered. as
G B
and the experimental
inter-slug new
of
the time-averaged
Davidson
U
is given
in which
steady-state
with
H
bursts.
state
and then
final
C
t h e bottom
the slug
-
Mechanistic
t h e wake
formation
gas
U
gas concentration
slug,
where
(
=
U
each
+
P
Ζ
At
an
C
GP
is all
a n d s Iug 5
illustrated,
at
the
itself
approxi slugs has a
later.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
have just
moment
CHEMICAL REACTION ENGINEERING—]
4*i
Β
f
**0
I
i=^-wJTD
Figure 1. Slugging fluidized bed. (A) well-mixed wake region; (B) piston-flow region.
β β β β aβ β a β ft
ft
ft
ft
β β β β β β β β β β β β f.Wr
Figure 2. The mechanistic model portrayed over one time cycle
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
33.
RAGHURAMAN
405
Slugging Fluidized Bed Reactor
AND POTTER
The l e n g t h o f t h e w e l l - m i x e d r e g i o n b e h i n d a s l u g i s wTD. T h e r e f o r e a t t i m e W T , f r a c t i o n w o f a new s l u g 0 h a s f o r m e d a n d t h e l e n g t h o f t h e i n t e r - s l u g m a t e r i a l b e h i n d s l u g 1 i s wTD. As the r e s t o f t h e i n t e r - s l u g m a t e r i a l , behind s l u g 1, f a l l s into p l a c e , a p i s t o n - f l o w r e g i o n i s commenced u n t i l a t t = τ the s i t u a t i o n has r e t u r n e d t o t h a t d e p i c t e d f o r t = 0~. +
Due t o t h e f r a c t i o n o f TD r e m a i n i n g a t t h e t o p o f t h e b e d , t h e t o p s e c t i o n i s o u t o f p h a s e w i t h t h e f o r m a t i o n o f new s l u g s at t h e bottom of the bed. Thus, r e f e r r i n g t o Figure 2, a t time t = τ/3 the top-most slug bursts, l e a v i n g a l e n g t h TD o f p a r t i c u l a t e phase o r i n t e r - s l u g m a t e r i a l , l y i n g above s l u g 4 w h i c h h a s now b e c o m e t h e t o p - m o s t s l u g . As t i m e i n c r e a s e s t o WT, t h e l e n g t h o f t h i s i n t e r - s l u g ( o r s h o u l d we now s a y "above-slug") material decreases. A t WT t h e new w a k e r e g i o n b e h i n d s l u g 1 i s complete. At τ the piston-flo complete and the s l u g detaches length o f i n t e r - s l u g m a t e r i a l w i l l have f a l l e n t o o n e - t h i r d o f TD. T h e b e h a v i o u r now r e p e a t s i t s e l f a n d i s t h u s c y c l i c a l . T h e m o d e l b r i e f l y d e s c r i b e d a b o v e i s now c o n s i d e r e d f r o m a chemical reaction point of view. Fresh r e a c t a n t gas i s s u p p l i e d at a steady flow U and of t h i s flows c o n t i n u a l l y through the b e d w h i l e d J - U ^ ^ a c t s g r a d u a l l y t o r a i s e t h e b e d a b o v e t h e new s l u g a n d , i n a s e n s e , o n l y e n t e r s t h e b e d , a s r e a c t a n t i n t h e new s l u g a t t h e moment o f i t s d e t a c h m e n t . The s t e a d y - s t a t e results p r e s e n t e d here have been a p p r o a c h e d from an i n i t i a l s t a t e i n which t h e bed i s c y c l i n g a s above w i t h no r e a c t a n t gas p r e s e n t , t h e p r o c e s s s t a r t i n g when t h e e n t e r i n g g a s i n s t a n t a n e o u s l y h a s i t s reactant concentration adjusted to C . are and
C o n s i d e r a g e n e r a l c e l l , j . C e l ? s , as d e p i c t e d i n F i g u r e 1, counted from t h e bottom upwards, so t h a t (j+1) i s above c e l l ( j - 1 ) below i t . Material
Balances
on general
j
cell
SI ug 0
^
=
Wake
^BcS-Vj dC
m f
+
M f
p
1
•••
(18)
.
•••
^ B C ^ C - V j
V ^ J - ^ e . j + l *
+ k f
(19)
w C C
P i s t o n - F l o w Region o f P a r t i c u l a t e Phase Since piston-flow o b t a i n s , a c c u m u l a t i o n terms c a n , i n t h i s c a s e , be i g n o r e d a l t h o u g h q u a l i f i c a t i o n s w o u l d b e made t o t h i s s t a t e m e n t i f space permitted. However t h e r e remains a d i s t a n c e - v e l o c i t y l a g w h i c h needs t o be t a k e n i n t o a c c o u n t . If ζ i s t h e length dimension and ζ = 0 a t t h e bottom o f the w e l l - m i x e d wake,
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL
406
jnf
REACTION ENGINEERING—HOUSTON
dC, P
'J'
...(20)
+ kC . =0 P,j,z
Z
n
dz
and -kz
exp
,(21) "mf
Note t h a t C earlÎ e r .
.
p
i s r e l a t e d t o C , j , 0 a t time
z
[z/(U -U /ε^)]
p
s
mf
M a t e r i a l Balances on Ce I I 1 The slug-balance i s the same as equation (18). The wake and p i s t o n - f l o w regions are no longer of constant dimensions but of dimensions which vary with time. The wake begins t o form immediately and when i t has grown t o f u l l s i z e , the p i s t o n - f l o w region commences t o form. Wake
ε ,f 0 = - E U xw
. f 4r ( t c . j + K ( C _ - C _ ) C " C 1 "ΒΓ W T dt ΧΓ
W
B pV
D
k f U X + (υ ε mf o S mf ο
U JC mf Ρ
w tc
D
e,2
xw
p 1
(22)
CI
P i s t o n - f l o w Region This region commences t o form a t time wx and the region extends from ζ = 0 t o ζ = [(t/x)-w]TD. Equation (21) a p p l i e s with t h i s p r o v i s o . M a t e r i a l Balances on Top-most Region When a slug reaches t h e top of the bed and b u r s t s , i t leaves behind a well-mixed wake region and p i s t o n - f l o w region and i t i s assumed t h a t flow i s p i s t o n - f l o w t h e r e a f t e r . This material f a l l s around the r i s i n g top-most slug and of course disappears e n t i r e l y a t the moment of slug b u r s t i n g , only t o be replaced by the i n t e r - s l u g m a t e r i a l b,elow t h e b u r s t i n g s l u g . Equation (21) a p p l i e s . When 0 < t £ ατ, the top-most region decreases in length from ζ = aTD t o ζ = 0; when ατ 4 t <τ, the new top-most region decreases in length from ζ = TD t o ζ = aTD. Results and Discussions The above equations were solved with the boundary c o n d i t i o n t h a t C . . = C . and the i n i t i a l c o n d i t i o n t h a t a t t = 0, C = E ' ; C = C and a l l other concentrations are zero. The e x i t concentration i s given by : p
p
J
D 1
J
01
n
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
33.
RAGHURAMAN
U
= (U-U J C
nu
CH
mf
Slugging Fluidized Bed Reactor
AND POTTER
B,N DK 1
(+=ατ)+ U ,
mf
0
f
C
P,N 1,i +
d
+
+
C P,N,i C
407
d t
,.(23)
The e n t i r e c a l c u l a t i o n s were repeated u n t i l steady s t a t e was achieved. Figures 3 and 4 show the experimental data on decomposition of ozone given by Hovmand and Davidson ( 8 ) , the p r e d i c t i o n s o f the Hovmand-Davidson model, the p r e d i c t i o n s of the time-averaged countercurrent backmixing model and o f the mechanistic c e l l model of t h i s paper. The same value o f Τ was used in both the v e r s i o n s of the new model. I t can be seen t h a t the new model in both i t s forms has a s u p e r i o r p r e d i c t i v e c a p a c i t y t o t h a t of the HovmandDavi dson model. A t high values o f k the experimental data show b e t t e r conversion than p r e d i c t e expected as the models d region a t the bottom of the bed before the t r a n s i t i o n t o slugging behaviour occurs. I t w i l l be p o s s i b l e t o a l l o w f o r t h i s by using the countercurrent backmixing model f o r f r e e l y bubbling beds, i n t h i s region. Cone I us ion A model has been formulated which f o l l o w s the c y c l i c a l behaviour of the slugging f l u i d i z e d bed and adequately incorpor ates mixing of the s o l i d s . The r e s u l t s f o r the s t e a d y - s t a t e agree with a p r e v i o u s l y formulated time-averaged model. The new mechanistic model provides a p o i n t of departure f o r s t a b i l i t y s t u d i e s and f o r the a n a l y s i s of f l u i d i z e d bed combustion and r o a s t i n g of ores. NomencIature Co C C C C D B
C
H
P
g H k k K
f
BC
KCP Lc
-3 reactant c o n c e n t r a t i o n a t i n l e t , moles cm -3 reactant c o n c e n t r a t i o n i η s i u g gas, moles -3 cm cloud-wake gas, reactant c o n c e n t r a t i o n i η mol es cm reactant c o n c e n t r a t i o n i η e x i t gas, moles cm •3 reactant c o n c e n t r a t i o n i η p i s t o n - f l o w region moles cm column diameter 2 -1 gas phase reactant d i f f u s i v i t y , cm s r a t i o of wake volume [ s o l i d s plus a s s o c i a t e d gas] t o s l u g vo I ume 2 g r a v i t a t i o n a l a c c e l e r a t i o n , cm s height o f the expanded bed, cm height o f i n c i p i e n t l y f l u i d i z e d bed, cm i n t e g r a l given in Table I f i r s t order r e a c t i o n r a t e constant based on u n i t volume -1 of s o l i d s and a s s o c i a t e d gas a t ε k H /U
mf
mf
volumetric r a t e o f gas exchange between s l u g and cloudwake per u n i t s l u g volume, s~' between cloud-wake and volumetric rate of gas exchange p i s t o n - f l o w region per u n i t s l u g volume, s~1 length of s Iug, cm
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
408
Figure 3. Comparison of the mechanistic model with experimental data, the model of Hovmand and Davidson, and the time-averaged model. (- · -) ( ) ( ) (-··-) U
w /
Mechanistic model Hovmand and Davidson Time-averaged model CSTR
= 3 cm s' ; H = 255 cm; e = 0.48; D = 46 cm; D = 0.2 cm s' + U = 0.185 m s' ; · U = 0.101 m s" 1
m/
1
mf
G
1
1
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
2
33.
RAGHURAMAN
AND
POTTER
Slugging Fluidized Bed Reactor
409
Figure 4. Comparison of the mechanistic model with experimental data, the model of Hovmand and Davidson, and the time-averaged model. (- • -) ( ) ( ) (----) \J
mf
=
J
cm s' ; 1
H
M /
=
Mechanistic model Hovmand and Davidson Time-averaged model CSTR 130 cm; e = 0.5; cm s' . mf
2
D =
10 cm; D
G
=
1
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
0.2
CHEMICAL REACTION ENGINEERING—HOUSTON
410
m Q
= =
Τ U UQQ UQP U f
= = = = = =
m
^SA V5 w ζ
=
= = =
Greek ε ef β
m
= =
shape f a c t o r f o r s l u g , e q u a t i o n ( 2 ) v o l u m e t r i c r a t e o f g a s e x c h a n g e between s l u g a n d p a r t i c u l a t e p h a s e , cnP s r a t i o o f i n t e r s lug s p a c i n g t o column d i a m e t e r s u p e r f i c i a l v e l o c i t y o f f l u i d i z i n g g a s cm s"^ s u p e r f i c i a l v e l o c i t y o f c l o u d - w a k e g a s cm s~^ ^ s u p e r f i c i a l v e l o c i t y i n p i s t o n - f l o w r e g i o n , cm s s u p e r f i c i a l g a s v e l o c i t y a t i n c i p i e n t f l u i d i z a t i o n cm s~ r i s e v e l o c i t y o f an i s o l a t e d s l u g , cm s~^ r i s e v e l o c i t y o f continuously generated slugs with r e s p e c t t o v e s s e l , cm s~^ s Iug νοIume, cm^ r a t i o o f wake volume t o volume o f i n t e r s l u g m a t e r i a l h e i g h t above t h Letters f r a c t i o n o f bed volume o c c u p i e d by s l u g s v o i d a g e o f bed a t i n c i p i e n t f l u i d i z a t i o n .
Literature Cited 1.
3. 4.
Fryer, Colin and Potter, O.E., Ind. Eng. Chem. Fund. (1972) 11, 338. Fryer, Colin, and Potter, O.E., "Proc. Internat. Symp. on Fluidization and its Applications", p.440, Soc. Chim. Ind., Toulouse, (1973). Fryer, Colin, and O.E. Potter, A.I.Ch.E. J ., (1976), 22, 38. Raghuraman, J. and Potter, O.E., submitted for publication.
5.
Thiel,
2.
l
W. and Potter, O.E., submitted for publication,
6.
Potter, O.E. and Thiel, W., "Fluidization Technology", ed. D. Keairns, 185, Vol. II, Hemisphere Publ. Corp.,Washington, (1976). 7. Hovmand, S. and Davidson, J . F . , Trans. Inst. Chem. Engrs., (1968), 46, T190. 8. Hovmand, S. and Davidson, J.F.,"Fluidization", ed. J . F . Davidson and D. Harrison, Ch.5, Academic Press, London,(1971). 9. Hovmand, S., Freedman, W. and Davidson, J . F . , Trans. Inst. Chem. Enqrs. (1971), 49, 149. 10. Potter, O.E., to be published in Catalysis Reviews - Science and Engineering. 11. Kehoe, P.W.K. and Davidson, J . F . , 'Chemeca 70', Chem. Eng. Conf. Australia, Butterworth & Co. (Aust.), (1970), Sec. 1, 97. 12. Stewart, P.S.B. and Davidson, J . F . , Powder Technology, (1967), 1, 61.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
34 Modeling of a Trickle-Bed Reactor: The Hydrogenation of 2-Butanone on a Ruthenium Catalyst A. G E R M A I N , M. C R I N E , P. M A R C H O T , and G . A . L ' H O M M E Laboratoire de Chimie Industrielle et de Génie Chimique, Université de Liège, Rue A . Stévart, 2, B-4000 Liège, Belgique
It is generally reactor operating mechanism latility of the processed liquid. When its vapor pres sure is very low, the chemical reaction can only occur on the irrigated catalyst particles and the reactor production increases with the catalyst wetting effici ency i.e. with the liquid flow rate ( L . F . R . ) . In that case the rather empirical models which have been deve lopped (1,2) allow the reactor design estimation or at least the correlation and extrapolation of experimental measurements. Such low volatilities are frequently met in hydrotreating heavy petroleum fractions. But when the processed liquid is volatile, the chemical reaction can occur on the non irrigated particles as on the ir rigated ones. Because of the comparatively weaker transfer resistance in the gaseous phase, the more ef ficient catalyst particles are the non irrigated ones. So it happens that the highest specific reaction rates are observed at the lowest wetting efficiency i.e. at the lowest L . F . R . T h a t paradoxical behaviour appeared during various experimental investigations a b o u t the operation of trickle-bed reactors with test chemical r e a c t i o n s (3_,£, 5_, 6_,7J · these s t u d i e s , the produc t i o n i n c r e a s e a t l o w L.F.R. i s e x p l a i n e d b y t h e a p p e a rance o f d r y c a t a l y s t p a r t i c l e s on which t h e r e a c t i o n r a t e c a n be f a s t e r , f o r t h e d i f f u s i o n i n s i d e t h e i r p o res i s e a s i e r . Y e t , t i l l now, a q u a n t i t a t i v e t r e a t m e n t o f t h e s e phenomena i s l a c k i n g . I n a d d i t i o n , s e v e r a l o b s e r v a t i o n s remain c o m p l e t e l y u n e x p l a i n e d : d r y zones f o r m a t i o n even w i t h p r e w e t t e d beds, s t a t i o n n a r y o p e r a t i o n slow s e t t l i n g , h y s t e r e s i s . . . T h a t i s t h e r e a s o n why we h a v e c h o s e n t o i n v e s t i g a t e t h e hydrogénation o f 2 - b u t a n o n e i n t o 2 - b u t a n o l on a r u t h e n i u m s u p p o r t e d c a t a l y s t . I n deed t h i s c h e m i c a l r e a c t i o n c a n be s t u d i e d o v e r a l a r g e I
©
n
0-8412-0401-2/78/47-065-411$05.00/0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION
412
ENGINEERING—HOUSTON
range o f t e m p e r a t u r e u s i n g a ketone aqueous s o l u t i o n which enables t omodify s t r o n g l y the r e a c t a n t v o l a t i l i ty. Experimental
Set-up
A s i m p l i f i e d diagram o f the experimental apparatus i s g i v e n o n F i g u r e 1. I t c o n s i s t s o f a j a c k e t e d r e a c t o r t h r o u g h which hydrogen and t h e k e t o n e aqueous s o l u t i o n f l o w c o c u r r e n t l y down. The r e a c t o r i s p r o v i d e d w i t h a n a x i a l t h e r m o c o u p l e w e l l and a s l i d i n g t h e r m o c o u p l e , and w i t h s a m p l i n g v a l v e s a l l o w i n g t h e i n l e t and o u t l e t f l o w s a n a l y s i s . A n i n e r t b e d , r e a l i z e d w i t h a l u m i n a pel l e t s s i m i l a r t o the c a t a l y s t p e l l e t s , ensures the pre h e a t i n g and a good d i s t r i b u t i o small 1/16 pipes provid t o p o f t h e c o l u m n . The e s s e n t i a l r e a t o r f e a t u r e s a n d the e x p e r i m e n t a l c o n d i t i o n s v a r i a t i o n range a r e g i v e n i n T a b l e 1. A l l t h e e x p e r i m e n t s w e r e r e a l i z e d o n a com p l e t e l y p r e w e t t e d b e d o b t a i n e d b y f l o o d i n g . So i t i s p o s s i b l e t o r e c o r d w e l l r e p r o d u c i b l e measurements, w i t h o u t any h y s t e r e s i s e f f e c t . An o p e r a t i n g s t a t i o n n a r y s t a t e i s reached d u r i n g t h e hour which f o l l o w s t h e s e t t l i n g o f t h e f l o w r a t e s and o f t h e h e a t i n g f l u i d t e m p e r a t u r e . F u r t h e r d e t a i l s a r e g i v e n by Germain ( 8 J . M
Table I. EXPERIMENTAL
VARIABLES
a. BED PARAMETERS DIAMETER, m
0.040
HEIGHT OF LOWER ALUMINA LAYER, m
0.114
HEIGHT OF UPPER ALUMINA LAYER, m
0.086
HEIGHT OF CATALYST LAYER, m
0.250
WEIGHT OF CATALYST LAYER, kg
0.280
b
*
CATALYST
(0,5% Ru on γ - Α Ι ^ ) COATED CYLINDER
BULK FORM BULK DIMENSIONS, HEIGHT, mm DIAMETER, mm PELLET APPARENT DENSITY, kg.m"*3 PELLET POROSITY, % c.
3.2 3.2 1470 54
RANGE OF VARIABLES
TOTAL PRESSURE TEMPERATURE, Κ LIQUID SUPERFICIAL MASS FLOW RATE, k g . m " 2 . s _ 1 (L.F.R.) GAS SUPERFICIAL MASS FLOW RATE, k g . m " " 2 . s _ 1 2-BUTAN0NE CONCENTRATION, mol.ra" 3
atmospheric 269
- 326
0.135 - 1 . 1 3 2.5 10~* - 7.7 10 0.245 - 0.893
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
GERMAIN ET AL.
Figure 1.
2-Butanone Hydrogénation
on Ruthenium Catalyst
Butanone hydrogénation in trickle-bed reactor
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION
414
Experimental
ENGINEERING—HOUSTON
Result
We h a v e d e t e r m i n e d t h e i n t r i n s i c r e a c t i o n r a t e e q u a t i o n f o r t h e hydrogénation o f t h e 2 - b u t a n o n e i n t o the 2 - b u t a n o l on R U - A I 2 O 3 i n a p r e l i m i n a r y k i n e t i c i n v e s t i g a t i o n using a p e r f e c t l y agitated s l u r r y reactor. A f t e r some c o r r e c t i o n s due t o a p a r t i a l d i f f u s i o n a l r e sistance a t the l i q u i d - s o l i d i n t e r f a c e , this equation takes t h e form : r
5
= 3.27 1 0 ~ e x p [ 5 3 6 7 . 9 ( 1 / 3 1 3 - 1 / T ) ] . C . p ° ' R
5
[ l ]
H
C o n t r a r y t o w h a t we o b s e r v e d f o r t h e hydrogénation of α - m e t h y l s t y r e n e on Pd-Al203 i n a c o u n t e r c u r r e n t tri c k l e - b e d r e a c t o r (_4 very easy i n t h e p r e s e n and t h e g a s a r e p r e h e a t e d , t h e j a c k e t h e a t t r a n s f e r i s s u f f i c i e n t t o ensure the i s o t h e r m i c i t y of the c a t a l y t i c bed. Hot s p o t s o r d r y c a t a l y s t p a r t i c l e s a r e n o t o b s e r ved, c o r r o b o r a t i n g t h e assumption t h a t t h e h o t spot for m a t i o n i s r e l a t e d t o t h e d r y i n g o f some c a t a l y s t p a r t i cles. As shown on F i g u r e s 2 a n d 3, t h e L.F.R. a p p e a r s t o be a v e r y i m p o r t a n t p a r a m e t e r i n t h e o p e r a t i o n o f t h i s t r i c k l e - b e d r e a c t o r ; however i t s i n f l u e n c e on t h e r e a c t o r p r o d u c t i o n depends on t h e c a t a l y t i c bed t e m p e r a t u r e . A t l o w t e m p e r a t u r e (T<297 Κ ) , t h e s p e c i f i c r e a c t i o n r a t e i n c r e a s e s w i t h t h e L.F.R., w h i l e a t h i g h t e m p e r a t u r e t h e o p p o s i t e e f f e c t i s o b s e r v e d . A t 326 Κ f o r i n s t a n c e , the s p e c i f i c r e a c t i o n r a t e i s i n c r e a s e d by a f a c t o r 3 when t h e L.F.R. i s l o w e r e d f r o m 1.2 t o 0.2 k g . m " s ~ l . There i s a t e m p e r a t u r e where t h e r e a c t o r p r o d u c t i o n i s n e a r l y i n d e p e n d e n t o f t h e L.F.R. e v e n i f t h e l a t t e r i s v a r i e d over a r a t h e r wide range. C l e a r l y t h e apparent a c t i v a t i o n e n e r g y o f t h e r e a c t i o n r a t e i s a L.F.R. f u n c t i o n . A t t h e l o w e s t L.F.R. i n v e s t i g a t e d i t a m o u n t s a b o u t 12 k c a l . m o l - 1 ; a t t h e h i g h e s t i t i s much s m a l l e r , a b o u t 6.5 k c a l . m o l " ! s h o w i n g t h a t d i f f e r e n t phenomena p l a y t h e p r o m i n e n t p a r t a t h i g h o r l o w L.F.R. A t l o w L.F.R., i t i s p r o b a b l e t h a t t h e r e a c t i o n i m p l i e s a d i f f u s i o n n a l step i n t h e gaseous phase; t h i s i s a h i g h l y a c t i v a t e d p r o c e s s due t o t h e h i g h l a t e n t h e a t o f v a p o r i zation of the ketone. At t h e o p p o s i t e o f t h e usual o b s e r v a t i o n s the gas f l o w r a t e i n f l u e n c e , m e a s u r e d a t 315 K, i s n o t n e g l i g i b l e . The s p e c i f i c r e a c t i o n r a t e i s a p p r o x i m a t i v e l y pro p o r t i o n n a i t o t h e 0.4 p o w e r o f t h e g a s f l o w r a t e , i m p l y i n g , a t l e a s t , a d i f f u s i o n n a l step i n the gaseous phase (Figure 3 ) . I t h a s b e e n p r o p o s e d (_3f£j_5) t o e x p l a i n s u c h k i n d 2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
2-Butanone Hydrogénation
GERMAIN ET AL.
r
s p
( φ ο ί m"
3
1
s )
T(K) o
on Ruthenium Catalyst
C
K
(mol
3
m~ )
2.5
410
284
G (kg m"
• 7
2
10~
326
410 proposed model
L(kg m" 0
0,1
0.2
Figure 2.
0.3
0.4
0.5
0.6
0.7
4
)Q'
0.8
0.9
1
1.1
2
1
s" )! 1.2
Superficial liquid velocity dependence of reaction rates
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
415
CHEMICAL REACTION ENGINEERING—HOUSTON
416
o f r e s u l t s by assuming i n c o m p l e t e w e t t i n g o f t h e c a t a l y s t p a r t i c l e s a t l o w L.F.R. a n d c o n s i d e r i n g t h a t t h e d r y c a t a l y s t i s more a c t i v e t h a n t h e w e t t e d o n e a t h i g h t e m p e r a t u r e , b u t l e s s a c t i v e a t l o w t e m p e r a t u r e due t o ketone t r a n s f e r l i m i t a t i o n i n t h e gaseous phase. I n t a b l e I I , we c o m p a r e o u r e x p e r i m e n t a l r e s u l t s with t h ee f f e c t i v e r e a c t i o n rates Γ ^ and r g . These are c a l c u l a t e d using the i n t r i n s i c rate equation [ l ] and a s s u m i n g d i f f u s i o n l i m i t a t i o n s r e s p e c t i v e l y i n t h e l i q u i d and gas f i l l e d pores o f t h e c a t a l y s t , b u t e x c l u ding e x t e r n a l c o n c e n t r a t i o n g r a d i e n t s (the t o r t u o s i t y f a c t o r i s s e t e q u a l t o 4) . We s e e t h a t r j ^ e always smaller than T Q b u t always l a r g e r than the experimen t a l r a t e s measured i n o t u s e f u l t o assum t i c l e s , w h i c h i n f a c t have n e v e r been o b s e r v e d i n t h i s s t u d y . B u t t o e x p l a i n t h e L.F.R. dependence o f t h e r e a c t i o n r a t e we m u s t a s s u m e t h e e x i s t e n c e i n t h e c o m p l e t e l y w e t t e d b e d o f d i f f e r e n t types of areas the a c t i v i t y o f w h i c h i s d e t e r m i n e d b y d i f f e r e n t mass t r a n s f e r p r o c e s s e s . T h a t i s why we h a v e t o l o o k f o r a more s o p h i s t i c a t e d t o p o logical description of thel i q u i d d i s t r i b u t i o n i n the c a t a l y t i c bed. /
Θ
(
i
e
s
F e
3
Table
I I . EXPERIMENTAL
T(K)
AND
G,e
CALCULATED
l
SPECIFIC
L,e
59.8
5.54 14.5
11.2
326
609
28
26
r
r
-1
.gr.Ru
-1
L
0.809
=
2.8
2
243
i n mol.s
«
0.269
308.5
r
RATES
exp -
284
REACTION
i n kg.m
-2
3.2
9.1
6.9
17.5
8.9
-1
*
calculated effective w i t h o u t any e x t e r n a l
*
c a l c u l a t e d e f f e c t i v e r e a c t i o n r a t e on t h e w e t t e d catal y s t w i t h o u t a n y 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
g
experimental
reaction
reaction rate mass t r a n s f e r
1.078
rate
on t h e d r y c a t a l y s t , limitation
i n the t r i c k l e - b e d
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
reactor
34.
GERMAIN E T AL.
2-Butanone Hydrogénation on Ruthenium Catalyst 417
T o p o l o g i c a l Model o f t h e L i q u i d D i s t r i b u t i o n i n a Trickle-Bed A c l o s e v i s u a l i n s p e c t i o n o f an o p e r a t i n g t r i c k l e bed r e a c t o r a l l o w s t o d e f i n e t h r e e t y p e s o f z o n e s c h a r a c t e r i z e d by d i f f e r e n t l o c a l v a l u e s o f t h e i r i n t e r f a c i a l s p e c i f i c areas. We d i s t i n g u i s h ( F i g u r e 4) : ( i ) t h e c a t a l y s t p a r t i c l e s c o v e r e d by a t r i c k l i n g f i l m ( F z o n e s ) ; (ii) the c a t a l y s t p a r t i c l e s p a r t i a l l y o r t o t a l l y c o v e r e d by t h e s t a g n a n t o r n e a r l y stagnant l i q u i d forming the menisci l o c a l i z e d a t the c o n t a c t p o i n t s b e t w e e n t h e p a r t i c l e s (S z o n e s ) ; ( i i i ) the c a t a l y s t p a r t i c l e s s o a k e d up b y t h l i q u i d b e c a u s f capillarit (C z o n e s ) . (x) The l i q u i d r e p a r t i t i o n b e t w e e n F a n d C z o n e s i s f i x e d o n one h a n d by t h e l i q u i d k i n e t i c e n e r g y a n d o n t h e o t h e r hand by t h e e n e r g y u s e d t o overcome t h e l o c a l dew e t t i n g f o r c e s . We c o n s i d e r t h e c a t a l y t i c b e d a s a s e t o f t r a n s p o r t c e l l s , e a c h f o r m e d b y one S z o n e a n d i t s own c o l l e c t i o n o f a d j a c e n t F a n d C z o n e s . A f o r c e b a l a n ce e s t a b l i s h e d on a c e l l l e a d s t o a s t a b i l i t y c r i t e r i o n for the F zones. At t h i s s c a l e the a c t i n g f o r c e s are ( F i g u r e 5 ) : Λρ, t h e s t a g n a t i o n f o r c e r e s u l t i n g f r o m t h e conversion of the l i q u i d k i n e t i c energy i n t o s t a t i c p r e s s u r e ; As, r e s u l t i n g from t h e d i f f e r e n c e o f the g a s s o l i d and l i q u i d - s o l i d s u r f a c e t e n s i o n ; A f , r e s u l t i n g from g a s - l i q u i d s u r f a c e t e n s i o n h e t e r o g e n e i t i e s on t h e film (9). For a l a m i n a r f i l m f l o w and n e g l e c t i n g t h e c u r v a t u re e f f e c t s o f t h e i n t e r f a c e s and t h e p r e s s u r e drop o f t h e g a s f l o w , we o b t a i n : ρ = 0. 5 9 2 . Φ . p . s i n ~ a . a ~ . ( - 2 - ) L py 2
1
1
/
5
Τ
•
( a
LG
+
D
S
0
.
" LG
C
O
S
θ )
"
3 / 5
M
g i v i n g the e x i s t e n c e p r o b a b i l i t y of F zones. Peculiar catalyst d i s p o s i t i o n s d r i v e the l i q u i d ( F zones) along p r e f e r e n t i a l d i r e c t i o n s stable i n time; t h i s k i n d o f a n i s o t r o p i c t r a n s p o r t i s a p e r c o l a t i o n p r o c e s s . The S z o n e s l i q u i d r e n e w a l i s d e t e r m i n e d by t h e v a l u e s o f t h e k i n e t i c a n d p o t e n t i a l e n e r g y o f ( x ) R e s i d e n c e t i m e d i s t r i b u t i o n measurements by t h e t r a c e r m e t h o d r e a l i z e d o n t h e o p e r a t i n g r e a c t o r h a v e shown that the t o t a l l i q u i d hold-up i s not compatible with t h e e x i s t e n c e o f d r y z o n e s . T h a t i s t h e r e a s o n why t h e se a r e n o t t a k e n i n t o a c c o u n t i n t h e p r e c e e d i n g classi fication .
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
418
CHEMICAL REACTION ENGINEERING—HOUSTON
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
2-Butanone Hydrogénation
GERMAIN ET AL.
Figure 4.
on Ruthenium Catalyst
Representation of reactants mass transfers
Figure 5.
Force balance on transport cell
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
420
the l i q u i d i t s e l f ; t h i s k i n d of i s o t r o p i c t r a n s p o r t i s a d i f f u s i o n n a l p r o c e s s , (x) The p e r c o l a t i o n t h e o r y ( 10.rU_#i^rU.) a l l o w s t o e s t a b l i s h a n a l y t i c a l c o r r e l a t i o n s ( o b t a i n e d by M o n t e C a r l o s i m u l a t i o n s ) g i v i n g t h e F and S zones s p a t i a l d i s t r i b u t i o n s , r e g a r d i n g t o t h e i r m a g n i t u d e s and a s s u m i n g t h e l i q u i d f l o w c o n t i n u i t y between them. M o d e l l i n g t h e S zones as l i q u i d b r i d g e s between two s p h e r e s o f t h e same c h a r a c t e r i s t i c d i m e n s i o n (14) g i v e s t h e i r i n t e r f a c i a l s p e c i f i c a r e a s . The d y n a m i c hold u p s a r e c o m p u t e d a s s u m i n g a v i s c o u s d i s s i p a t i o n on t h e F z o n e s and a n e a r l y c o m p l e t e d i s s i p a t i o n o f t h e l i q u i d k i n e t i c e n e r g y i n t h e S z o n e s (1_5) · T h a t p r o v i d e s a q u a n t i t a t i v e d e s c r i p t i o n of the r e a c t o r w e t t i n g e f f i ciency (J^6) . M a t h e m a t i c a l Model o Reactor The t r i c k l e - b e d r e a c t o r p e r f o r m a n c e s c a n be e x p r e s s e d i n t e r m s o f mass t r a n s f e r s b e t w e e n F, C a n d S z o n e s , i n t h e g a s e o u s and l i q u i d p h a s e s , a s shown on F i g u r e 4. I n t h e l i q u i d p h a s e t h e mass t r a n s f e r * l i m i t a t i o n s a r i s e f r o m t h e h y d r o g e n a b s o r p t i o n i n t o F and S z o n e s (ΦΗ) ^ f r o m i t s t r a n s p o r t b e t w e e n t h e s e z o n e s ($ι,) · 9 ~ seous phase the t r a n s f e r l i m i t a t i o n s a r i s e from the ke t o n e v a p o r i z a t i o n on t h e F a n d S z o n e s (Φκ)' f r o m i t s transport (Φβ) and i t s c o n d e n s a t i o n o n t o t h e C z o n e s <*K> · T h e s e t r a n s f e r p h e n o m e n a a r e d e s c r i b e d by t h e f o l l o w i n g e q u a t i o n s (x x) . (Ac ) . k . a . h = . A C [3 J ( m a t e r i a l b a l a n c e f o r t h e k e t o n e v a p o r i z a t i o n and c o n densation) ANC
I n
K
l
n
G
G
t
0
K
. k . a . h = ΦΤ,.ΔΟΗ H l n ( m a t e r i a l balance f o r the hydrogen zones)
Uc )
e
a
K
r . h = Φ . AC ( m a t e r i a l b a l a n c e f o r t h e k e t o n e c o n s u m p t i o n on zones) c
n
L S
absorption
on
[4] the C
[5] the S
(x) I n a d i f f u s i o n n a l p r o c e s s t h e s t o c h a s t i c s c a t t e r i n g o f one p a r t i c l e i s a p r o p e r t y o f t h e p a r t i c l e s t u d i e d w h i l e i n a p e r c o l a t i o n p r o c e s s the s t o c h a s t i c s c a t t e r i n g o f a p a r t i c l e i s a p r o p e r t y o f t h e s c a t t e r i n g medium. (xx) S z o n e s a r e c o n s i d e r e d as i n a c t i v e b e c a u s e strong e x t e r n a l hydrogen t r a n s f e r l i m i t a t i o n s .
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
of
34.
GERMAIN E T A L .
r
.
F
h
=
(material F zones)
k
L F
.
2-Butanone Hydrogénation a.
h
balance
.(ACH)
F
+
«&L
·
Ac
on Ruthenium Catalyst 421 [6]
H
f o r t h e hydrogen c o n s u m p t i o n on t h e
where h i s t h e l e n g t h o f a t r a n s f e r z o n e , s u p p o s e d t o be e q u a l t o dp,- k t h e mass t r a n s f e r c o e f f i c i e n t i n v a p o r p h a s e a t l o w g a s f l o w r a t e (V7_) ; k t h e mass t r a n s fer c o e f f i c i e n t a t low l i q u i d flow rate (18); k the mass t r a n s f e r c o e f f i c i e n t i n a t h i n s t a g n a n t liquid film. The v a p o r - l i q u i d i n t e r f a c e d a t a m u s t be e s t i m a t e d u n d e r t r a n s f e r c o n d i t i o n s . The k e t o n e b e h a v e s l i k e a n h y d r o p h o b i c m a t e r i a l a n d t e n d s t o be r e j e c t e d f r o m t h e w a t e r phase by p r e f e r e n t i a l l y c o n c e n t r a t i n g on t h e s u r f a c e . I n s u c h a cas f e r e n t from t h e s u r f a c t i v i t y c o e f f i c i e n t s (1_9) . I t i s r e a s o n a b l e t o s u p p o s e t h a t i n vapor pressure r e l a t i o n s f o r m i x t u r e s , surface c o m p o s i t i o n s p l a y a more i m p o r t a n t r o l e t h a n b u l k com p o s i t i o n s . T h a t i s why we h a v e c o r r e l a t e d t h e v a p o r phase c o m p o s i t i o n s t o t h e s u r f a c e c o n c e n t r a t i o n s by mean o f t h e UNIFAC m e t h o d o f a c t i v i t y c o e f f i c i e n t s d e t e r m i n a t i o n (20) a n d b y t h e r e l a t i o n o f Tamura e t a l (21) g i v i n g t h e s u r f a c e t e n s i o n f o r a q u e o u s m i x t u r e s . So we c o m p u t e maximum c o r r e c t i o n v a l u e s f o r s u r f a c e t e n s i o n (DS) a n d k e t o n e v a p o r p r e s s u r e (PVAP) c o r r e s p o n d i n g t o a non e q u i l i b r i u m s t a t e where b u l k a n d s u r f a c e c o m p o s i t i o n a r e e q u a l . The a d j u s t e d c o r r e c t i o n s ( T a b l e I I I ) a m o u n t t o a b o u t 15% o f t h e i r maximum v a l u e s . G
L S
L F
Table
III.
ADJUSTED CORRECTIONS FOR SURFACE TENSION KETONE VAPOR PRESSURE (DVAP) IN TRANSFER
T(K)
DS(N.nT )
(DS) AND CONDITIONS
DVPA
269
5.38
10~
5
0.046
284
5.47
10"
5
0.062
308.5
5.62
10~
5
0.142
315
5.66
10"
5
0. 152
326
5.72
10"
5
0.233
Assuming t h e e x i s t e n c e o f a s t a t i o n n a r y s t a t e r e l a t e d t o t h e i n i t i a l c o n d i t i o n s , we c o m p u t e t h e r e a c t a n t c o n c e n t r a t i o n a t t h e c a t a l y s t e x t e r n a l s u r f a c e i n F and C zones and, c o n s e q u e n t l y , t h e i r s p e c i f i c production.The s p e c i f i c r e a c t i o n r a t e s c a l c u l a t e d u s i n g t h i s model a r e
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
422
shown b y t h e c o n t i n u o u s l i n e s o n F i g u r e s 2 a n d 3. I t c a n be s e e n t h a t t h e a g r e e m e n t w i t h t h e e x p e r i m e n t s i s f a i r even a t t h e h i g h e s t t e m p e r a t u r e . Conelusion The p r e d i c t i o n o f t h e p e r f o r m a n c e t o f a t r i c k l e - b e d r e a c t o r i s p o s s i b l e knowing o n l y the i n t r i n s i c r a t e e q u a t i o n , i f a good d e s c r i p t i o n o f t h e t o p o l o g i c a l l i q u i d d i s t r i b u t i o n i s a v a i l a b l e . T h i s o n e c a n be o b t a i ned u s i n g t h e p e r c o l a t i o n t h e o r y a n d r e s o l v i n g t h e l o c a l f o r c e s b a l a n c e s a t t h e g a s - l i q u i d and l i q u i d - s o l i d i n t e r f a c e s . F o r t h e hydrogénation o f 2 - b u t a n o n e , we could obtain calculated values of the conversion i n s a t i s f a c t o r y agreement w i t h t h e e x p e r i m e n t s , p r o v i d e t h a t we t a k e i n t o a c c o u n t a l l t h e p o s s i b l e mass t r a n s f e r p r o c e s s e s between a l l for the f i r s t time th bution i n a trickle-bed c a t a l y t i c reactor i s sufficient ly d e t a i l e d to allow the q u a n t i t a t i v e p r e d i c t i o n of the performances o f such a r e a c t o r u s i n g a v o l a t i l e l i q u i d reac t a n t . List a C^ dp DS g h k
o f symbols g e o m e t r i c s p e c i f i c s u r f a c e a r e a (m ) ketone concentration ( m o l m~3) e q u i v a l e n t p a r t i c u l e d i a m e t e r (m) _^ g a s - l i q u i d s u r f a c e t e n s i o n c o r r e c t i o n (Nm ) g r a v i t y a c c e l e r a t i o n (m s~2) l e n g t h o f a t r a n s f e r z o n e (m) k e t o n e mass t r a n s f e r c o e f f i c i e n t i n v a p o r p h a s e (m s " ) ^LS h y d r o g e n mass t r a n s f e r t c o e f f i c i e n t i n l i q u i d p h a s e (m s * ) k-LF h y d r o g e n mass t r a n s f e r t c o e f f i c i e n t i n a t h i n s t a g n a n t l i q u i d f i l m (m s~*) ρ e x i s t e n c e p r o b a b i l i t y o f F zones (adim.) PH h y d r o g e n p r e s s u r e (atm) PVAP k e t o n e v a p o r p r e s s u r e c o r r e c t i o n f a c t o r (adim.) r i n t r i n s i c r e a c t i o n rate (mol(gr Ru)~l) TQ a p p a r e n t s p e c i f i c r e a c t i o n r a t e on C z o n e s (mol m ~ 3 s l ) F a p p a r e n t s p e c i f i c r e a c t i o n r a t e on F z o n e s (mol m-3 s ~ l ) r experimental s p e c i f i c reaction rate i n the t r i c k l e - b e d (mol m ~ 3 - l ) Τ t e m p e r a t u r e (K) α mean o r i e n t a t i o n a n g l e o f l i q u i d - s o l i d i n t e r f a c e ACH d i f f e r e n c e between i n l e t and o u t l e t h y d r o g e n l i q u i d concentration o n a t r a n s f e r z o n e ( m o l m~ ) ( A C H ) F hydrogen concentration difference across the l i q u i d f i l m ( m o l m~3) G
1
1
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In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
34.
GERMAIN E TA L .
Δθκ (AC^)in (AC )^ H
<EG $L θ y °"LG
n
2-Butanone Hydrogénation
on Ruthenium Catalyst 423
d i f f e r e n c e between i n l e t and o u t l e t ketone v a p o r c o n c e n t r a t i o n o n a t r a n s f e r z o n e ( m o l m~3) l o g a r i t h m i c mean d r i v i n g c o n c e n t r a t i o n diffe r e n c e f o r k e t o n e t r a n s f e r ( m o l m~3) l o g a r i t h m i c mean d r i v i n g c o n c e n t r a t i o n diffe r e n c e f o r h y d r o g e n t r a n s f e r ( m o l m~3) g a s s u p e r f i c i a l v e l o c i t y (m s ~ M 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 (m s~* ) apparent contact angle l i q u i d v i s c o s i t y ( k g m"* s~*) l i q u i d d e n s i t y ( k g m~3) g a s - l i q u i d s u r f a c e t e n s i o n ( Ν m~ * )
Literature cited (1) HENRY, H.C. and cess Design Devel., (1973) 12, 328. (2) MEARS, D.E.,"Chem. Reaction Eng. II",Adv. in Chem. Ser., (1974) 133, 218. (3) WARE, C . H . , Ph. D. Thesis, Univ. of Pennsylvania, (1959). (4) SEDRICKS, W. and KENNEY,C.Ν., Chem. Eng. Sci.,(1973) 28, 559. (5) GERMAIN, A . H . , LEFEBVRE, A . G . and L'HOMME, G.A.;Che mical Reaction Engineering II; Adv. in Chem. Series, (1974) 133, 164. (6) HANIΚΑ, J., SPORKA, K . , ULBRICHOVA, Z., NOVAK, J., and RUZICKA, V . , Coll. Zech. Chem. Commun., (1974) 9, 210. (7) SATTERFIELD, C . N . , PELOSSOF, A . A . and SHERWOOD,Τ.Κ., Α . I . C h . Ε . J. , (1969) 15, 226. (8) GERMAIN Α . , Collection des Publications de la Facul t é des Sciences a p p l i q u é e s , U n i v e r s i t é de L i è g e (1977) 65, 1. (9) ZUBER, Ν . , STAUBE, F . W . , Int. J. Heat Mass Transfer, (1966) 9, 897. (10) BROADBENT, S.R. and HAMMERSLEY, J.M., Proc. Camb. phil. Soc., (1957) 53, 629. (11) HAMMERSLEY, J.M., Proc. Camb. phil. S o c . , (1957) 53, 642. (12) SHANTE, V . K . S . and KIRKPATRICK, S . , A d ν . P h y s . , (1971) 20, 325. (13) KIRKPATRICK, S . , Rev. Mod. Phys., (1973) 45, 574. (14) BUCHANAN, J.E., Ind. Eng. Chem. Fund., (1967) 6 ,400. (15) HUTTON, B.E.T. and LEUNG, L.S., Chem.Eng. Sci.; (1974) 29, 1681. (16) CRINE, M . , MARCHOT, P. and L'HOMME,G.,tο be publis hed. (17) PETROVIC, L.J. and THODOS, G . , Ind. Eng. Chem. Fund., (1968) 7, 274.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
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(18) GOTO,S. and SMITH, J.M., A . I . C h . E . J. , (1975) 21, 706. (19) REID, R . C . , PRAUSNITZ, J . M . and SHERWOOD, T . K . , "The Properties of Gases and Liquids", 612, Mc Graw Hill, New York (1977). (20) Op. cit., 347. (21) TAMURA, M . , KURATA, M. and ODANI, H . , Bull. Chem. Soc. Japan, (1955) 28, 83.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
35 Determination of the Extent of Catalyst Utilization in a Trickle Flow Reactor B. BAKER, III Shell Development Company, Westhollow Research Center, P. O . Box 1380, Houston, TX 77001
This study concern heavy oil. In these reactors and certain compounds in the o i l are saturated with hydrogen. Vapor (mostly H ) and liquid (oil) are passed cocurrently downward over a fixed bed of small catalyst particles. The liquid flows over the particles in films and rivulets; the vapor flows through the remaining voids. As discussed below, these hydrodynamical conditions may lead to incomplete catalyst wetting, axial disper sion, and restricted interphase mass transfer and may therefore result in incomplete catalyst u t i l i z a t i o n . Since the catalyst is f a i r l y expensive and the conditions of temperature and pressure require expensive reactor vessels, there is considerable incentive to ensure that maximum u t i l i z a t i o n of the catalyst is obtained. It appears that these effects may be more serious in the process development scale units (PDU), due to their low velocities and short lengths, than in the commercial units they simulate. Hence conversions i n these u n i t s may not be s u i t a b l e t a r g e t s f o r commercial performance. The assessment o f t h i s l a t t e r p o s s i b i l i t y i s the o b j e c t i v e o f t h i s study. In t h i s study a t r i c k l e flow r e a c t o r i s considered to be o b t a i n i n g maximum c a t a l y s t u t i l i z a t i o n i f i t i s o p e r a t i n g i n plug flow w i t h the c a t a l y s t f u l l y contacted and there are no i n t e r phase mass t r a n s f e r l i m i t a t i o n s e x t e r n a l to the c a t a l y s t p a r t i cles. An i l l u s t r a t i v e conversion ( d e s u l f u r i z a t i o n ) f o r a f u l l y contacted plug flow r e a c t o r w i t h no mass t r a n s f e r l i m i t a t i o n s i s p l o t t e d as a f u n c t i o n of LHSV i n Figure 1.** _ Improving c a t a l y s t u t i l i z a t i o n by decreasing the s i z e o f the c a t a l y s t p a r t i c l e s o r changing p a r t i c l e p o r o s i t y , i . e . , improving i n t r a p a r t i c l e mass t r a n s f e r , i s not considered. ** In Figure 1, o v e r a l l conversion i s assumed to be represented by a second-order equation; t h i s does approximately f i t experimental d e s u l f u r i z a t i o n data. Therefore, the lowest l i n e i s simply the second order p l u g flow r e a c t o r equation. 2
©
0-8412-0401-2/78/47-065-425$05.00/0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
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In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
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Incomplete C a t a l y s t Wetting. I t has been w i d e l y reported i n the l i t e r a t u r e that l i q u i d c o n t a c t i n g i s not complete i n t r i c k l e flow r e a c t o r s (1,J2,_3,_4,5) . A l l o f the c a t a l y s t p a r t i c l e s may not be wetted on an i n d i v i d u a l b a s i s because o f the tendency of the l i q u i d flow t o occur i n r i v u l e t s . Data (1) on non-porous p a r t i c l e s i n d i c a t e that w e t t i n g i s a t a maximum a t a p a r t i c l e s i z e of around 4 mm and decreases as the p a r t i c l e s i z e increases o r de creases from t h i s v a l u e . An improvement as the l i q u i d v e l o c i t y i s increased i s a l s o i n d i c a t e d . The data would suggest that i n a commercial heavy o i l u n i t c o n t a i n i n g 1.5 mm extrudate c a t a l y s t , n e a r l y a l l the p a r t i c l e s may be wetted but that i n a PDU* s i m u l a t i n g the commercial u n i t having only a 30 cm/hr 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 , l i q u i d c o n t a c t i n g may be only 80% o r l e s s . The e f f e c t o f not c o n t a c t i n F i g u r e 1,** i s t o i n c r e a s l e s s conversion i s obtained compared t o the f u l l y contacted case. Other s t u d i e s (2) i n d i c a t e that i n some cases 66% o f the c a t a l y s t i s not contacted. Thus, there i s c o n s i d e r a b l e i n t e r e s t t o estab l i s h o r not t h i s i s r e a l l y the case i n PDU c o n t a i n i n g porous c a t a l y s t p a r t i c l e s d i l u t e d w i t h s m a l l e r diameter, non-porous i n e r t particles. A x i a l D i s p e r s i o n . I t has a l s o been reported that a x i a l d i s p e r s i o n (backmixing) i s much more pronounced i n two-phase flow i n packed beds than i n single-phase flow (6) and that t h i s may e f f e c t conversion i n t r i c k l e flow r e a c t o r s ( 7 ) . I n p a r t i c u l a r , the short PDU a r e more l i k e l y to be a f f e c t e d than the longer com m e r c i a l u n i t s s i n c e the a x i a l c o n c e n t r a t i o n gradient caused by the r e a c t i o n i s much steeper. The conclusions i n (6) i n d i c a t e that 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 decreases as the p a r t i c l e s i z e i s decreased so that the adverse l e n g t h e f f e c t i n a PDU can be p a r t i a l l y o f f s e t by d i l u t i n g the c a t a l y s t bed w i t h s m a l l i n e r t p a r t i c l e s . D i l u t i o n a l s o serves t o lengthen the bed, which reduces the a x i a l c o n c e n t r a t i o n g r a d i e n t . A very rough estimate of the e f f e c t o f a x i a l d i s p e r s i o n from the above s t u d i e s i n d i c a t e s that f o r the commercial u n i t above, there would be no a x i a l d i s p e r s i o n e f f e c t but that there might be an a x i a l d i s p e r s i o n e f f e c t i n the above PDU w i t h a l i q u i d a x i a l P e c l e t number o f about 10. The e f f e c t o f a x i a l d i s p e r s i o n o f t h i s magnitude on conversion i s
In the PDU, the 1.5 mm extrudate c a t a l y s t p a r t i c l e s , which are c y l i n d e r s 1.5 mm i n diameter and 4.5 mm i n l e n g t h , are d i l u t e d w i t h an equal volume o f approximately s p h e r i c a l , nonporous i n e r t p a r t i c l e s , 1.0 mm i n diameter. The e f f e c t i v e LHSV i s the apparent LHSV d i v i d e d by 0.8; o t h e r wise the i d e n t i c a l second order plug flow r e a c t o r equation i s p l o t t e d f o r t h i s case.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
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a l s o i l l u s t r a t e d i n Figure 1,* Again i t i s of i n t e r e s t to examine i f a x i a l d i s p e r s i o n i s i n f l u e n c i n g PDU r e s u l t s . Interphase Mass T r a n s f e r . There are a number of interphase mass t r a n s f e r steps that must occur i n a t r i c k l e flow r e a c t o r . The mass t r a n s f e r r e s i s t a n c e s can be considered as o c c u r r i n g a t the more o r l e s s stagnant f l u i d l a y e r i n t e r f a c e s , i . e . , on the gas and/or the l i q u i d s i d e o f the g a s / l i q u i d i n t e r f a c e and on the l i q u i d s i d e of the l i q u i d / s o l i d i n t e r f a c e . The mass t r a n s f e r c o r r e l a t i o n s ( 8 ) i n d i c a t e that the g a s / l i q u i d i n t e r f a c e and the l i q u i d / s o l i d i n t e r f a c e mass t r a n s f e r r e s i s t a n c e s decrease w i t h higher l i q u i d v e l o c i t y and smaller p a r t i c l e s i z e . Thus, i n the PDU, the use o f s m a l l i n e r t p a r t i c l e s p a r t i a l l y o f f s e t s the adverse e f f e c t of low v e l o c i t y These c o r r e l a t i o n s i n d i c a t e that f o r t h i s system, e x t e r n a l mass t r a n s f e i n the PDU than i n the l i q u i d v e l o c i t y , but that probably there i s no l i m i t a t i o n i n e i t h e r . I f a mass t r a n s f e r l i m i t a t i o n were present, i t would l i m i t conversion i n a way s i m i l a r to that shown f o r a x i a l d i s p e r s i o n and incomplete c a t a l y s t w e t t i n g i l l u s t r a t e d i n Figure 1. Due to the u n c e r t a i n t y i n the c o r r e l a t i o n s and i n the p h y s i c a l p r o p e r t i e s of these systems, p a r t i c u l a r l y the molecular d i f f u s i v i t i e s , i t i s of i n t e r e s t to examine i f e x t e r n a l mass t r a n s f e r i s i n f l u e n c i n g the PDU r e s u l t s . S e l e c t i o n o f a System to Determine Maximum C a t a l y s t U t i l i z a t i o n In order to determine maximum c a t a l y s t u t i l i z a t i o n , a s m a l l s c a l e system that e l i m i n a t e d w e t t i n g problems, a x i a l d i s p e r s i o n , and mass t r a n s f e r l i m i t a t i o n s was necessary. I n a d d i t i o n , r e s u l t s d i r e c t l y a p p l i c a b l e to heavy o i l h y d r o t r e a t i n g were d e s i r e d . The l i q u i d f u l l (flooded bed) upflow r e a c t o r w i t h an e x t e r n a l hydrogen e q u i l i b r a t o r shown i n Figure 2 was s e l e c t e d . Only d i s s o l v e d hy drogen passes through the r e a c t o r , e l i m i n a t i n g the gas phase. A high l i q u i d r e c y c l e r a t e and an e f f i c i e n t e q u i l i b r a t o r prevent hydrogen d e p l e t i o n o f the l i q u i d i n the system. The high l i q u i d r e c y c l e r a t e a l s o i n s u r e s adequate e x t e r n a l mass t r a n s f e r . Since the r e a c t o r i s completely w e l l mixed, there can be no a x i a l d i s p e r s i o n e f f e c t . Furthermore, w i t h t h i s arrangement, s w i t c h i n g between t r i c k l e flow and l i q u i d f u l l o p e r a t i o n can be accomplished without d i s t u r b i n g the c a t a l y s t bed. Although the system could have been operated i n a continuous mode, i t was decided t o operate i t i n a batch mode. I n the batch h i g h - r e c y c l e mode the r e a c t o r mass balance i s that f o r a s t i r r e d tank batch r e a c t o r and thus over a p e r i o d o f time i s analogous to the mass balance f o r a plug flow r e a c t o r over a d i s t a n c e along
The c a l c u l a t i o n s f o l l o w (7) f o r a second order r e a c t o r w i t h a x i a l dispersion.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
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H FEED FOR TRICKLE FLOW 2
REACTOR H MAKE - UP -FOR BATCH OPERATION 2
PRE HEATER
LIQUID FEED FOR TRICKLE FLOW
(PACKED WITH INTALOX
PRE HEATER
PHASE SEPARATOR
LIQUID TRICKLE
Figure 2.
LIQUID SEPARATOR
INERT
GAS PRODUCT FROM TRICKLE FLOW "
PRODUCT
FROM
FLOW O P E R A T I O N
SADDLES)
LIQUID PRODUCT
RECYCLE PUMP
FROM
BATCH OPERATION
Experimental system for determining maximum catalyst utilization
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
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the r e a c t o r . In the continuous h i g h - r e c y c l e mode, the mass b a l ance equation f o r a c o n t i n u o u s - s t i r r e d tank r e a c t o r (CSTR) would be o p e r a t i v e . When numerous r e a c t i o n s occur over a spectrum of r e a c t i o n r a t e s , as f o r a heavy o i l feed, i t i s d i f f i c u l t to r e l a t e measurements of o v e r a l l conversion ( d e s u l f u r i z a t i o n , H2 uptake) between a CSTR and a plug flow r e a c t o r . The c o n d i t i o n s f o r i n s u r i n g that the batch r e c y c l e r e a c t o r i s analogous to a once-through r e a c t o r , i n a d d i t i o n to o p e r a t i n g at the same temperature and pressure, are as f o l l o w s : 1.
LHSVL ^ , = LHSVl' t r .i cuk l e 'batch
where
V TITOTT!
LHSVL _ , = — •batch V
batch,
std
,
F LHSV
t r i c k l e , &, s t d V cat V F 9 batch, g, reac _ t r i c k l e , g, reac V " F batch, £, reac t r i c k l e , £, reac The f i r s t c r i t e r i o n i s simply the well-known analog between a plug flow continuous r e a c t o r and a w e l l - s t i r r e d batch r e a c t o r men tioned above. The second c r i t e r i o n i s the analogy between a con tinuous one-stage e q u i l i b r i u m f l a s h and a batch e q u i l i b r i u m f l a s h . Since some of the gas d i s s o l v e s i n the l i q u i d and some of the l i q u i d v a p o r i z e s , t h i s c r i t e r i o n insures that the v a p o r i z a t i o n con d i t i o n s are the same as w e l l as i n s u r i n g that the c o n c e n t r a t i o n of any r e a c t i o n i n h i b i t i n g r e a c t i o n products, namely, H2S are the same Other c o n s i d e r a t i o n s were (1) The e q u i l i b r a t o r was designed to r e p l a c e at l e a s t 99% of the d i s s o l v e d H2 l o s t from the l i q u i d per pass through the r e a c t o r . (2) The amount of d i s s o l v e d H2 was e s t i mated from f l a s h c a l c u l a t i o n s , but there were no data to e s t a b l i s h the H2 uptake at the high r e c y c l e r a t e s being considered. To en sure that the l i q u i d was not e x c e s s i v e l y depleted of H2 before r e e q u i l i b r a t i o n and that the e q u i l i b r a t i o n was adequate, batch exper iments were run at the same LHSV at s e v e r a l r e c y c l e r a t e s to estab l i s h a r e c y c l e r a t e high enough to i n s u r e no s i g n i f i c a n t decrease i n conversion because of H d e p l e t i o n . (3) I t was e s t a b l i s h e d by c a l c u l a t i o n that the time r e q u i r e d to change the c o n c e n t r a t i o n pro f i l e s i n s i d e the c a t a l y s t p a r t i c l e s was extremely small compared to the l e n g t h of the batch experiment so that the p r o f i l e s at a c e r t a i n p o i n t along the once-through t r i c k l e r e a c t o r can be d u p l i c a t e d at a corresponding time i n the batch experiment. (4) By operating the system without c a t a l y s t , i t was e s t a b l i s h e d that homogeneous r e a c t i o n s do not occur over the much longer exposure to r e a c t i o n temperature and pressure i n the batch experiment to any s i g n i f i c a n t extent. trickle
2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
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Catalyst Utilization in Trickle Flow Reactor
431
Apparatus. The system was constructed by modifying an e x i s t ing t r i c k l e - f l o w once through PDU r e a c t o r . A 2.5 cm diameter r e a c t o r was packed w i t h a mixture o f 100 cm of 1/16-inch extrudate c a t a l y s t and 100 cm o f 1.0 mm s i l i c o n carbide non-porous i n e r t s , producing a 60 cm long c a t a l y s t bed. There were 25 cm long s e c t i o n s o f i n e r t s above and below the c a t a l y s t . Isothermal con d i t i o n s were maintained throughout the bed w i t h i n about 5°C. The 8 cm diameter e q u i l i b r a t o r v e s s e l contained a 60 cm long bed o f 1 cm I n t a l o x saddles. 3
3
Procedure. The u n i t was brought up and l i n e d - o u t as a normal t r i c k l e flow r e a c t o r . A f t e r a t h r e e - f o u r day l i n e o u t p e r i o d , the r e a c t o r reached s t e a d y - s t a t e as i n d i c a t e d by constant product quality. At t h i s time l i q u i t o r and the batch s i d e wa was c i r c u l a t e d through the r e c y c l e bypass around the r e a c t o r , and brought t o the d e s i r e d e q u i l i b r a t i o n temperature. The system was then switched t o the batch mode by the f o l l o w i n g procedure. The t r i c k l e f l o w l i q u i d / g a s feed f l o w was switched out o f the r e a c t o r i n t o the t r i c k l e bypass and the batch l i q u i d r e c y c l e flow was switched out o f i t s bypass i n t o the r e a c t o r . Lined-out batch con d i t i o n s were reached i n 2-3 minutes. The l e n g t h of the batch ex periment r e q u i r e d from 8-16 hours, depending on the LHSV d e s i r e d . At the end o f t h i s p e r i o d , the batch l i q u i d r e c y c l e f l o w was switched out o f the r e a c t o r back i n t o i t s r e c y c l e l i n e and the t r i c k l e flow l i q u i d / g a s feed f l o w was switched from the t r i c k l e bypass back i n t o the r e a c t o r . The batch r e c y c l e l i q u i d was then sampled. Meanwhile the t r i c k l e flow run was continued. I t was found that 24-48 hours were r e q u i r e d f o r the t r i c k l e flow run t o again reach s t e a d y - s t a t e . There, were three s e r i e s o f experiments performed. The charac t e r i s t i c s o f the feed used i n a l l o f the experiments are shown i n Table I . The same bed of c a t a l y s t was used i n S e r i e s 1 and 2. I n Table I CHARACTERISTICS OF FEED USED IN THE EXPERIMENTS Specific Gravity Carbon, %w Hydrogen, %w S u l f u r , %w N i t r o g e n , %w MW 50%w D i s t i l l e d , °C
0.8868 85.19 12.04 2.04 0.13 374 450
S e r i e s 3, a more a c t i v e c a t a l y s t was used i n order to study high conversions. The average set o f c o n d i t i o n s f o r each s e r i e s i s
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
432
shown i n Table I I . I n S e r i e s 1, the batch vapor and l i q u i d were e q u i l i b r a t e d a t 230°C and the l i q u i d reheated t o the 365°C Table I I REACTOR CONDITIONS DURING COMPARISONS OF TRICKLE AND BATCH OPERATIONS Series 1 T r i c k l e Batch
Series 2 T r i c k l e Batch
Series 3 T r i c k l e Batch
Reactor Temperature, °C Pressure, kg/cm
365 2
365
365
365
360 350
360 350
230
-
365
-
360 350
48.
Equilibrator Temperature, °C
-
H2/O1I Feed R a t i o , moles H2/mole o i l Inlet 2.84 Outlet
1.85
Start End
-
2.05 1.92
2.84
-
1.85
-
-
2.05 1.92
2.94 2.84 1.85 1.85 -
2.05 1.92
r e a c t i o n temperature a f t e r the r e c y c l e pump, s i n c e i t was f e l t a t the time t h a t the r e c y c l e pump could not t o l e r a t e l i q u i d at 365°C. This i n t u r n r e q u i r e d a compensating change i n pressure and r e s u l t e d i n a somewhat l e s s p r e c i s e comparison. L a t e r i t was found that the modified pump would operate on l i q u i d a t the higher temperature so that i n S e r i e s 2 and 3, the batch vapor and l i q u i d were e q u i l i b r a t e d a t the same temperature as the r e a c t o r . R e s u l t s and D i s c u s s i o n The system described above has considerable v e r s a t i l i t y i n examining questions o f maximum c a t a l y s t u t i l i z a t i o n . However, i t s use i n the present study was l i m i t e d to the question of whether o r not maximum u t i l i z a t i o n was being obtained i n the 60 cm l o n g , 2.5 cm diameter PDU reactors' used to simulate a heavy o i l h y d r o t r e a t e r . These normally operate a t a LHSV around 1.0 hr w i t h a H / o i l feed r a t i o of 1.5-3.0 moles H2/mole o i l . Approxi mate conversions obtained a r e d e s u l f u r i z a t i o n 60-90%, d e n i t r o genation 20-50%, and H2 uptake 0.7-1.0 moles ^ / m o l e o i l . 2
S e r i e s 1. The r e s u l t s from S e r i e s 1 using d i l u t e d c a t a l y s t are shown i n F i g u r e 3 ( t o p ) . For both d e s u l f u r i z a t i o n and H2 uptake, as w e l l as d e n i t r o g e n a t i o n (not shown), there were no d i f f e r e n c e s
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
Catalyst Utilization in Trickle Flow Reactor
BAKER
0.3 SERIES
1
(0.71)
0*ί£·47) (H
2
UPTAKE, MOLES H / 2
^ • ( 0 . 8 1 )
0.2
M O L E OIL)
Ι|Βΐσ83) (0.91)
RECYCLE 10
3
(1.11)
RATE 3
TRICKLE 4
]
Δ •
•
CM /HR
φ
Ο
w
8 f
Δ (0.96) BATCH
12J
I
I
1/LHSV
SERIES
2 AVERAGE
• •
H
AVERAGE H
•
I 0.4
TRICKLE - 0.96
D E S U L F U R I Z A T I O N - 77%
ο
0.2
UPTAKE
2
UPTAKE
2
BATCH
- 0.96
D E S U L F U R I Z A T I O N - 82%
1 0.6
1 1.0
1 0.8
1 1.2
1 1.4
1.6
1/LHSV
0.20 SERIES
3 AVERAGE
H
2
UPTAKE]
φ
B A T C H - 1.04
L
TRICKLE-1.00
J#
•
φ 0.10
— -
^fAVERAGE
_
· 660°F
φ
H
2
UPTAKE
J
BATCH-1.15
I
TRICKLE-1.09
680°F 0.06 0.6
ι
I 0.8
ι
I
ι
1.0
I 1.2
ι
I 1.4
ι 1.6
1/LHSV
Figure 3.
Comparison of trickle flow and batch operation—desulfurization and Η2 uptake
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
434
evident between the t r i c k l e flow and batch r e s u l t s at LHSV=1.3 for recycle rates 8000 cm /hr. The e f f e c t of the batch l i q u i d r e c y c l e r a t e was s t u d i e d by performing runs at r e c y c l e r a t e s of 4000, 8000, and 12,000 cm /hr. Only at the lowest r a t e of 4000 cm /hr was any decrease i n conversion or H2 uptake evident, i n d i c a t i n g t h a t a r e c y c l e r a t e _> 8000 cm /hr was s u f f i c i e n t to prevent excessive H2 d e p l e t i o n i n the r e c y c l e l i q u i d at these r e a c t o r c o n d i t i o n s . The d e s u l f u r i z a t i o n r e s u l t s i n d i c a t e d a sub s t a n t i a l d i f f e r e n c e between the s i n g l e t r i c k l e and batch compari son a t LHSV=0.7. The d e n i t r o g e n a t i o n and H2 uptake r e s u l t s d i d not confirm a d i f f e r e n c e , however. 3
3
3
3
S e r i e s 2. The r e s u l t s from S e r i e s 2 on the same d i l u t e d bed of c a t a l y s t are shown i n Figure 3 (middle). No d i f f e r e n c e s i n d e n i t r o g e n a t i o n (not shown runs at LHSV ^ 1.3 hr d i f f e r e n c e i n d e s u l f u r i z a t i o n , which i s probably not s i g n i f i c a n t c o n s i d e r i n g the experimental s c a t t e r . 1
S e r i e s 3. In order to make f u r t h e r comparisons at higher conver s i o n and lower space v e l o c i t y , a few experiments were run using a d i l u t e d bed of more a c t i v e c a t a l y s t . The r e a c t i o n r a t e s f o r t h i s more a c t i v e c a t a l y s t are equivalent to the f i r s t c a t a l y s t at a 17°C lower temperature. The r e s u l t s shown i n Figure 3 (bottom), i n d i c a t e no s i g n i f i c a n t d i f f e r e n c e s i n d e s u l f u r i z a t i o n , H2 uptake, or d e n i t r o g e n a t i o n (not shown). Conclusions A modified process development u n i t apparatus has been u t i l i z e d i n t h i s study i n which, f o r the same 200 cm packed bed of c a t a l y s t , normal once-through t r i c k l e flow o p e r a t i o n can be com pared to l i q u i d - f u l l batch o p e r a t i o n . In the l a t t e r , the p o s s i b i l i t i e s of incomplete c a t a l y s t w e t t i n g , a x i a l d i s p e r s i o n , and interphase mass t r a n s f e r l i m i t a t i o n s are not present and thus, maximum c a t a l y s t u t i l i z a t i o n i s obtained. Comparison of the r e s u l t s of the two modes of o p e r a t i o n f o r the s p e c i f i c system of i n t e r e s t leads to the f o l l o w i n g c o n c l u s i o n s : 1. D i l u t e d bed* heavy o i l hydrogénation t r i c k l e flow process development u n i t s at l e a s t 60 cm long o b t a i n maximum c a t a l y s t u t i l i z a t i o n a t up to 90 percent d e s u l f u r i z a t i o n at LHSV as low as 0.75 hr . Maximum c a t a l y s t u t i l i z a t i o n f o r d e n i t r o g e n a t i o n and hydrogen uptake a t these c o n d i t i o n s i s a l s o obtained. 2. The conversions measured i n these u n i t s a r e , t h e r e f o r e , s u i t able t a r g e t s f o r commercial u n i t performance. 3
1
D i l u t e d w i t h an equal volume of 1.0 mm diameter s i l i c o n inerts.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
carbide
35.
Catalyst Utilization in Trickle Flow Reactor
BAKER
435
Generalization I t i s known that i n some t r i c k l e flow systems, incomplete c a t a l y s t c o n t a c t i n g , a x i a l d i s p e r s i o n , and 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 do occur. Studies using t h i s same approach could be used t o examine a wider v a r i e t y o f systems, i n c l u d i n g i n p a r t i c u l a r , r e a c t i o n s i n which extremely high conversion, > 99% i s d e s i r e d . This approach may a l s o be u s e f u l i n e s t a b l i s h i n g the c o n d i t i o n s , i f any, under which a r e a c t o r might b e t t e r be designed as a packed bed i n g a s / l i q u i d upflow r a t h e r than i n t r i c k l e flow ( g a s / l i q u i d downflow). Nomenclature Ε L LHSV Pe S tbateh ν V ^batch
a x i a l dispersio reactor length vj^/L, l i q u i d hourly space v e l o c i t y , h r vL/E a x i a l P e c l e t number s u l f u r c o n c e n t r a t i o n , w% time o f batch r e a c t i o n , h r s u p e r f i c i a l v e l o c i t y cm/hr volume, cm volume i n e n t i r e batch system, cm
1
3
3
Subscripts cat F g I Ρ reac std
catalyst feed gas o r vapor liquid product at reactive conditions after f l a s h a t standard c o n d i t i o n s , 1 atm, 15.6°C
Literature Cited 1.
2.
3. 4. 5. 6. 7. 8.
Wiffels, J . Β . , et al., "Chemical Reaction Engineering - II," Adv. i n Chem., Series 133, Hulburt, H. M . , E d . , p. 151, ACS Publishers, Washington, D . C . , 1974. Schwartz, J. G . , et al., "Fourth International Symposium on Chemical Reactor Engineering Preprints," p. 382, DECHEMA Publishers, Frankfurt, FRG, 1976. Hoffman, Η . , Int. Chem. Eng., (1977) 17, 19. Satterfield, C. Ν . , AIChE J., (1975) 21, 209. Montagna, A. and V. T. Shah, Ind. Eng. Process D/D, (1975) 14, 479. Furzer, I. A. and R. W. Michell, AIChE J., (1970) 16, 380. Mears, D. E., CES, (1971) 26, 1361. Goto, S. and J. M. Smith, AIChE J., (1975) 21, 706.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
36 Two-Phase Theory and Fluidized Bed Reactor Models P. N. R O W E Department of Chemical and Biochemical Engineering, University College of London, Torrington Place, London WCIE, 7JE, England
The concept of tw fluid phase i bubblin fluidised bed and its application to Johnstone and colleague y (1,2) Since then numerous and different modifications have been made to the basic model (3) but practically all these variants assume that the interstitial flow (the interstitial or dense phase) is the minimum fluidisation value. Flow in the form of bubbles (the bubble or cloud phase) is the difference between interstitial and total flow. This is simply formulated
A few models concede that interstitial flow may be greater than indicated by Eq. 1 and introduce a multiplier of U that is greater than unity. This formulation of the two-phase theory is over—simplified and in the first part of this paper a more rigorous expression is derived to take account of the reduction in cross sectional area of the interstitial phase as the bed fills with bubbles and also of gas expansion which must occur as pressure falls with bed height. In many cases these corrections can be ignored when the expression reduces to Eq. 1. In addition, especially with finely divided powders, the particles constituting the dense phase can expand, increase the phase voidage and hence its permeability. In these circumstances the local interstitial gas velocity exceeds Umf and more gas passes in this phase than Eq. 1 allows. The consequences of this for overall conversion in a fluidised bed chemical reactor are examined in the second part of the paper by considering the pre dictions of an appropriate model. mf
The Two-Phase Theory Examined Gas in a bubbling fluidised bed can be thought of as divided into three phases; that flowing interstitially (the dense phase), that associated with the bubble wakes and that in the essentially empty space of the bubbles. If f is the fraction of bed volume © 0-8412-0401-2/78/47-065-436$05.00/0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
36. ROWE
Two-Phase Theory and Fluidized Bed Reactor
437
occupied by a given phase and U L i s the absolute gas v e l o c i t y , Q
i
Q
=
U
Gi
^ " V V
A
= U A
B
B
f
£
i
( 2 )
(U)
B
The sum o f these three flows i s equal to the t o t a l flow. Three assumptions are introduced: ( i ) f = f ^ / 3 that i s , the wake a s s o c i a t e d with each bubble i s about 1/3 i t s own volume, ( i i ) ^GW ^ ^ ^- » f a s s o c i a t e d with the wake t r a v e l s at the bubble v e l o c i t y , ( i i i ) = ε^. that i s , the p a r t i c l e voidage i n the wake i s e s s e n t i a l l y the same as i n the dense phase. Neglect i n g any gas expansion, a volumetric flow balance leads to =
i a
s
U
or
Gi
a
s
"[ i O e
Q./A = U -
(3+ε.)/3Α
(6)
P a r t i c l e s move upwards i n the bubble wakes at bubble v e l o c i t y and, assuming t h a t none i s l o s t , there must be an equal volumetric flow r a t e downwards i n the dense phase. That i s -U .
(3-Uf )
= Qg/A
s
(7)
B
The r e l a t i v e v e l o c i t y between gas and p a r t i c l e s i n the dense phase follows from Eqs. 5 and 7 U
G/S
[ -V ] U
=
A
3/e.(3^f ) B
(8)
Now assume t h a t the dense (and wake) phase voidage remains constant at i t s minimum f l u i d i s a t i o n value. I f the voidage does not change then the p e r m e a b i l i t y i s u n l i k e l y t o change and the i n t e r s t i t i a l gas v e l o c i t y must be maintained at i f the bed i s to remain i l u i d i s e d without a net force l i f t i n g p a r t i c l e s out o f the bed. Thus, \J , = U „/ε „ and Eq. 8 becomes b/b rai mi n/c
Q /A = U - U B
mf
(3-Uf )/3 B
(9)
This i s the simplest way i n which the two-phase theory can be ex pressed and d i f f e r s from the usual expression by the m u l t i p l i e r o f U ^ which, i t should be noted, i s l e s s than u n i t y . I t reflects the fact that as the bed f i l l s with bubbles there i s l e s s cross~ s e c t i o n a l area a v a i l a b l e f o r i n t e r s t i t i a l flow. Gas i n the wake phase forms a small p r o p o r t i o n o f the whole and i t makes l i t t l e p r a c t i c a l d i f f e r e n c e whether i t i s i n c l u d e d with the i n t e r s t i t i a l or with the bubble phase. As a consequence o f assumption ( i i ) i t i s i n c l u d e d here with the bubble phase. The term ( 3 - ^ ί β ) / 3 i s o f t e n not very d i f f e r e n t from u n i t y
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
438
CHEMICAL REACTION ENGINEERING—HOUSTON
f o r f g i s r a r e l y as b i g as 0.5The numbers 3 and h i n Eq.9 arise from the assumption that the wake volume i s 1/3 o f the bubble volume and small changes around t h i s make l i t t l e d i f f e r e n c e . The bubble f r a c t i o n , f ^ , i s r e l a t e d t o bubble flow r a t e and average r i s e v e l o c i t y through Eq. k so i t can be e l i m i n a t e d from Eq. 9 with the i n t r o d u c t i o n o f Ug. I f and only i f the dense phase voidage remains constant at ε _ mi B - mf when i t can be measured d i r e c t l y . Because o f pressure drop through the bed there must be gas expansion and i n c r e a s e d volumetric flow with height. Fluidised beds are o f uniform temperature so the expansion must be i s o t h e r mal and = f
=
1
( H
/ H )
( 1 0 )
where the s u f f i x D denotes the d i s t r i b u t o r plane and H, a plane height Η above i t . The increase i s small f o r most l a b o r a t o r y s c a l e equipment with bed heights only a few tens of centimeters but i t i s not n e g l i g i b l e f o r t y p i c a l i n d u s t r i a l dimensions even with l i g h t powders o f bulk d e n s i t y , (ΐ-ε)ρ l e s s than that o f wa t e r as Figure 1 shows. ^ The e f f e c t o f gas expansion on Eq.9 a f f e c t s only the term U so that i t becomes (
V H A )
U
= D
[l+(H(l- )p g)/p ] - U £ i
p
H
m f
(3-Uf )/3 B
(12)
This i s a r e f i n e d v e r s i o n o f the "true volume i d e a l two-phase theory" (k). The amount o f gas that flows i n t e r s t i t i a l l y can d i f f e r from Eq. 12 only i f the dense phase p e r m e a b i l i t y changes which i n prac t i c e means change o f voidage with a given powder. This c e r t a i n l y happens with f i n e powders where the voidage changes with gas v e l o c i t y , U, and u s u a l l y depends on the p a r t i c l e s i z e distribution and i s p a r t i c u l a r l y i n f l u e n c e d by proportions at the smaller end o f the p a r t i c l e s i z e range. This e f f e c t can be i n c o r p o r a t e d i n Eq. 12 by i n t r o d u c i n g a f u r t h e r m u l t i p l i e r o f U ^» a c o e f f i c i e n t , greater than u n i t y , t h a t i s some f u n c t i o n o f gas v e l o c i t y and may a l s o vary with height. The nature o f t h i s c o e f f i c i e n t i s not w e l l understood but i t can be approximated i n some cases by a constant. Experimental work with one p a r t i c u l a r powder (a t y p i c a l i n d u s t r i a l grade of c a t a l y s t ) shows t h a t with f i n e powders (d <60ym) more gas flows i n t e r s t i t i a l l y than Q « and thus i s strongly^depen dent on the f i n e s content (d
F l u i d i s e d Bed Reactor Model Most f l u i d i s e d bed r e a c t o r models incorporate the two-phase
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
ROWE
Two-Phase Theory and Fluidized Bed Reactor
Ο
ΙΟ
2·0 H-m
Figure 1. Increase in volumetric gasflowwith bed height
Volumetric Interstitial Flow, 6 Q//A cm/s
Ο
2
4
6
β
Volumetric Flow into the
ΙΟ
12
Bed, Q / A
14
16
cm/s
Figure 2. How the interstitialflowincreases with gas velocity and "fines" content. At low gas velocities, downward particle movement (balancing upwardflowas wakes) can result in a net downward interstitial gas flow.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
440
CHEMICAL REACTION ENGINEERING—HOUSTON
theory i n the form
Q /A = U - U B
m f
^ (13)
The c o r r e c t i o n o f t h i s t o Eq. 9 i s s l i g h t when U / U ^ i s not very much g r e a t e r than u n i t y f o r then f ^ i s small. I t i s a l s o s l i g h t when U/U £>>l f o r then the p r o p o r t i o n o f gas flowing i n t e r s t i t i a l l y is negligible. The a d d i t i o n a l c o r r e c t i o n f o r gas expansion i m p l i e d by Eq.12 may be more important. The r e s u l t i s a net mass t r a n s f e r from the i n t e r s t i t i a l t o the l e s s e f f i c i e n t bubble phase and hence an over a l l r e d u c t i o n i n the expected performance. Again, i f U^>>U ^ the effect i s negligible. In r e a c t o r modelling t h i s c o r r e c t i o n cannot be s e n s i b l y considered without a d d i t i o n a l l y t a k i n g i n t o account change i n gas volume as a r e s u l t o f chemical r e a c t i o n . In many reactions reduction i n to maleic anhydride, h y d r o f l u o r i n a t i o no change (e.g. c h l o r i n a t i o n o f s a t u r a t e d hydrocarbons, hydrogen r e d u c t i o n o f ores) and i n some there i s volume i n c r e a s e (e.g. ox i d a t i o n o f e t h y l e n e , c a t a l y t i c c r a c k i n g ) . I f t h i s i s t o be taken i n t o account then the extent o f r e a c t i o n must be known which may r e q u i r e an i t e r a t i v e c a l c u l a t i o n t o follow the consequence o f the model. I t i s not p o s s i b l e t o g e n e r a l i s e the treatment t h i s c o r r e c t i o n r e q u i r e s . In many cases the m o d i f i c a t i o n w i l l be n e g l i g i b l e and i t i s easy t o judge from Eq. 11 and the known chemistry whether or not i t i s important. The o n l y consequent c o r r e c t i o n to the r e a c t o r model i s t o replace the bubble phase flow o f Eq.13 by that o f Eq. 12 with a d d i t i o n a l c o r r e c t i o n o f the m u l t i p l i e r o f Up t o account f o r volume change by chemical r e a c t i o n . I n t e r s t i t i a l flow g r e a t e r than as i n d i c a t e d by Figure 2 i s l i k e l y t o be a much more important c o r r e c t i o n than those men t i o n e d above whenever f i n e p a r t i c l e s are i n v o l v e d . Since t h i s i n cludes most gas phase s o l i d s c a t a l y s e d organic r e a c t i o n s , i t i s an important category. With f i n e powders the i n t e r s t i t i a l gas v e l o c i t y i s small compared with bubble v e l o c i t y , clouds form around the bubbles and are l i t t l e b i g g e r than t h e i r parents so that gas/ s o l i d c o n t a c t i n g i n the bubble phase i s very poor. An appropriate model f o r t h i s s i t u a t i o n i s one i n which i n t e r s t i t i a l gas moves in plug flow r e a c t i n g r e a d i l y with the s o l i d s , there i s no r e a c t i o n i n the bubble phase but exchange between the two phases as bubbles r i s e through the bed. This i s s i m i l a r to the model o f Davidson and H a r r i s o n (6) where f i r s t order r e a c t i o n k i n e t i c s i s a d d i t i o n a l l y assumed. C a l c u l a t i o n s have been made using t h i s model assuming a super f i c i a l gas v e l o c i t y , U = 0.5 m/s and n e g l e c t i n g volume change by expansion and by chemical r e a c t i o n (or assuming the two e f f e c t s c a n c e l ) . The r e a c t o r diameter i s assumed l a r g e r than any bubble so that no s l u g g i n g occurs. The powder =.002 m/s and i t s voidage, ε=0.38 which corresponds to a t y p i c a l commercial cataLyst. The mean bubble r i s e v e l o c i t y i s assumed given by m
m
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
36.
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Ttvo-Phase Theory and
441
Fluidized Bed Reactor
3/8
7Γ
(U-U
,)
l A
H
3 / 8
(IU)
mi i i with Κγ = 1.3 (ii.) · The f i r s t o r d e r _ j a t e constant was assumed to be 50 s"*^( f a s t r e a c t i o n ) and 0.5 s (slow r e a c t i o n ) with some intermediate v a l u e s . The i n t e r s t i t i a l gas flow was taken as Q « and 0.3Q with two equal steps between. The only remaining qantity needed i s the main model parameter, the exchange c o e f f i c i e n t be tween the two phases, q^/V . There are means o f e s t i m a t i n g the exchange c o e f f i c i e n t from the known p h y s i c s o f a b u b b l i n g f l u i d i s e d bed and Davidson and H a r r i s o n show one method (6). Various methods o f e s t i m a t i o n i n d i c a t e a t y p i c a l value o f o r d e r 1 s but d i f f e r by a f a c t o r o f two or more. This parameter a l s o conceals some o f the i d e a l i s a t i o n s o f the model suc i n the bubble phase. Consequentl c o e f f i c i e n t i s regarded as an a r b i t r a r y v a r i a b l e changing by an order o f magnitude from 0.2 t o 2.0 s . It i s therefore l i k e l y to span the values experienced i n p r a c t i c e . Figures 3 to 8 show the r e s u l t s o f c a l c u l a t i o n as a p l o t o f c o n c e n t r a t i o n o f a reactant species against bed h e i g h t . Figure 3 shows one extreme, a high chemical r a t e constant (K = 50 s^ ) and a high r a t e o f interphase gas exchange (^.g/Vg = 2.0 s ). The r e a c t o r performance approaches the p l u g flow case (but with r a t e c o n t r o l l e d by the exchange c o e f f i c i e n t , not the chemical k i n e t i c s ) and the p r e d i c t i o n not very s e n s i t i v e to the p r o p o r t i o n o f gas flowing i n t e r s t i t i a l l y . Even so, the bed height needed to achieve a given l e v e l o f conversion i s m a t e r i a l l y reduced as the i n t e r s t i t i a l flow p r o p o r t i o n i n c r e a s e s . _^ Figure k r e f e r s t o a slow chemical r e a c t i o j (K = 0.5 s ) and the same high gas exchange r a t e (ÇL-g/Vg 2.0 s ). Markedly l e s s conversion occurs than would i n a plug flow r e a c t o r with t h i s chemical rate constant so performance i s s t i l l dominated by the rate o f phase exchange. The e f f e c t o f i n t e r s t i t i a l flow proport i o n i s s i m i l a r t o the previous case but r e a c t i o n to near complet i o n would be v i r t u a l l y unobtainable even i f 50% o f the gas flowed i n t e r s t i t i a l l y and continued t o exchange at t h i s very high r a t e . Of course, i f i t a l l flows i n t e r s t i t i a l l y i t i s a p l u g flow r e a c t o r and 99% conversion occurs i n a height o f k^6 m. Figure 5 shows the f a s t r e a c t i o j (K=50 s ) with a low phase exchange c o e f f i c i e n t (q^/V = 0.2 s ). Performance i s now l i m i t e d by the exchange r a t e and the extent o f conversion i s l a r g e l y determined by the p r o p o r t i o n t h a t flows i n t e r s t i t i a l l y . This i s a case where f o r a c a t a l y s t such as r e f e r r e d to i n Figure 2, the conversion achievable would l a r g e l y depend on t h e ^ f i n e s content. Figure 6 r e f e r s t o a slow r e a c t i o n (K=0.5 s ) and a low exchange c o e f f i c i e n t (q^/V^ = 0.2 s ). Comparison with Figure 5 shows t h a t an extreme change i n chemical r a t e produces only a small change i n r e a c t o r performance i f the phase exchange r a t e i s low. The p r o p o r t i o n o f i n t e r s t i t i a l gas flow i s important i n determining the bed height needed f o r a given conversion but shows t h a t i t i s =
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
442
CHEMICAL REACTION ENGINEERING—HOUSTON
H-l
Figure 3. Predicted variation of composition with bed height—fast reaction; fast exchange
Figure 4. Predicted variation of composition with bed height—slow reaction; fast exchange
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
36.
ROWE
Two-Phase Theory and Fluidized Bed Reactor
Figure 6. Predicted variation of composition with bed height —slow reaction; slow exchange
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
powerless to improve the maximum achievable conversion i f the exchange rate i s low ( u n l e s s , o f course, n e a r l y a l l flows i n t e r s t i tially) . Figures 7 and. 8 show some intermediate values which probably correspond t o more r e a l i s t i c values f o r the exchange c o e f f i c i e n t . In these cases the p r o p o r t i o n o f i n t e r s t i t i a l flow i s important i n determining the bed height needed. Conclusions In cases where the dense phase p e r m e a b i l i t y remains constant at i t s minimum f l u i d i s a t i o n value, the amount o f gas flowing i n t h i s phase w i l l i n a l l cases be l e s s than that p r e d i c t e d by the u s u a l l y formulated two-phase theory. This w i l l g e n e r a l l y a f f e c t r e a c t o r performance adversel s m a l l . The reason f o r s e c t i o n a l area a v a i l a b l e f o r i n t e r s t i t i a l flow and gas expansion causes a net t r a n s f e r to the bubble phase. With f i n e powders such as f l u i d i s e d c a t a l y s t s the dense phase p e r m e a b i l i t y does i n f a c t increase with gas v e l o c i t y and the above c o r r e c t i o n s become n e g l i g i b l e i n many cases. In a chemical r e a c t o r the degree o f conversion then becomes importantly dependent on the p r o p o r t i o n of gas that flows i n t e r s t i t i a l l y but i s dominated by the r a t e o f exchange between the two phases. I t i s not p o s s i b l e t o g e n e r a l i s e the consequences because o f complex i n t e r a c t i o n between the three main v a r i a b l e s , r e a c t i o n rate constant, i n t e r s t i t i a l flow p r o p o r t i o n and interphase exchange r a t e . P a r t i c u l a r examples o f model c a l c u l a t i o n s are given i n Figures 3 to 8. I t appears t h a t exchange rate w i l l determine the maximum degree o f conversion that i s a t t a i n a b l e i n p r a c t i c e but, w i t h i n p r a c t i c a l l i m i t s , the depth o f bed needed depends l a r g e l y on the p r o p o r t i o n o f gas flowing i n t e r s t i t i a l l y . L i s t of Symbols 2
A CJJ d f^
cross s e c t i o n a l area o f the f l u i d i s e d bed c o n c e n t r a t i o n o f react ant at height H average p a r t i c l e diameter f r a c t i o n o f t o t a l bed volume occupied by bubbles
m ^ kg/m pm
.D
f^. g H H Ky p^ Q
f r a c t i o n o f t o t a l bed volume occupied by bubble wakes gravitational acceleration bed height above the d i s t r i b u t o r plane bed height at minimum f l u i d i s a t i o n f i r s t order r a t e constant velocity coefficient (Eq. 1*+) gas pressure at height H volumetric gas flow i n t o the bed volumetric gas flow i n the form o f bubbles volumetric gas flow across the d i s t r i b u t o r plane volumetric gas flow across a h o r i z o n t a l plane at height H
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
^ m/s m m s
m
N^m m^/s m^/s m/s ^ 3^ s
36.
ROWE
Two-Phase Theory and Fluidized Bed Reactor
H-m
Figure 7. Predicted variation of composition with bed height—intermediate reaction; intermediate exchange
Figure 8. Predicted variation of composition with bed height—intermediate reaction; fast exchange
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
445
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CHEMICAL REACTION ENGINEERING—HOUSTON
volumetric i n t e r s t i t i a l gas flow v o l u m e t r i c gas flow as p a r t o f bubble wakes q phase exchange r a t e υ s u p e r f i c i a l gas v e l o c i t y i n t o the bed = Q/A tL average bubble r i s e v e l o c i t y s u p e r f i c i a l gas v e l o c i t y across the d i s t r i b u t o r plane = Q /A s u p e r f i c i a l gas v e l o c i t y i n the dense phase ^G/S ^ r e l a t i v e v e l o c i t y between i n t e r s t i t i a l gas and p a r t i c l e s v e l o c i t y o f gas i n the wake phase U ς s u p e r f i c i a l minimum f l u i d i s a t i o n v e l o c i t y average ( v e r t i c a l ) v e l o c i t y o f p a r t i c l e s i n the dense phase V.g average bubble volum ε. voidage o f the dens ε^ voidage o f the wake phase ρ individual p a r t i c l e density n
a v e r a
m
3^ m^/s m/s m/s m/s s
m/s m/s
e
m/s m/s m/s m^s
kg/m"
Literature Cited (1) Toomy, R.D. and Johnstone, H . F . , Chem. Eng. Prog.(1952)48,220. (2) Johnstone, H . F . , Batchelor, J.D. and Shen, C . - Y . , AIChE Jnl, (1955) 1, 318. (3) K u n i i , D. and Levenspiel, O. "Fluidisation Engineering", John Wiley, New York, (1962). (4) Rowe, P.N. and Yacono, C.X.R., Chem. Eng. Sci.(1976) 31, 1179. (5) Rowe, P . N . , Santoro, L . and Yates, J . G . , Chem. Eng. Sci., to be published. (6) Davidson, J . F . and Harrison, D."Fluidised Particles",p.97, Univ. Press, Cambridge, (1963).
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
37 Multiphase Kinetic Studies with a Spinning Basket Reactor E . C . M Y E R S and Κ. K. R O B I N S O N Amoco O i l Company, P . O . Box 400, Naperville, I L 60540
The study of multiphas hydrotreating requires laborator contact between gas, l i q u i d , and solid phases at high temperatures and pressures. Numerous reactors have been developed for process studies and fall mainly into two categories: fixed bed and agitated (gradientless). For multiphase catalytic systems, the experimental studies are normally performed in a trickling fixed bed reactor. This type reactor is subject to problems with catalyst contacting and flow maldistribution unless certain pre cautions are taken. External mass transport limitations are also possible, particularly with the more active catalysts that are currently available. Vigorous gas-liquid-catalyst contacting will often remedy this situation. Weekman (1) concluded that the gradientless reactors are far superior to the fixed bed in terms of sampling ease, temperature maintenance, mass transport, and other operating variables. Although several gradientless reactors are available for studies of gas-phase reactions (2-6), none of them are suitable
for studying multiphase systems, p a r t i c u l a r l y at the high pressure
required i n such petroleum processes as distillate hydrotreating. Russian workers (7) did report a gradientless multiphase reactor but it was only suitable for atmospheric pressure operation. Now we have developed a high-pressure version to study hydrotreating reactions. It comprises a spinning basket held i n a 500 cc s t i r r e d autoclave. Baffles around the basket ensure good mixing and contacting of the l i q u i d and also eliminate vortexing at the gas-liquid interface. The flow pattern of the oil approximates that obtained in a single perfectly mixed reactor because the vaporized hydrocarbons which exit in the off-gas stream are recycled. The spinning basket reactor was used to study the desulfuri z a t i o n kinetics of a model sulfur compound—dibenzothiophene i n white o i l . This study i s confirming data for an e a r l i e r study by Frye and Mosby (8) with a t r i c k l e bed type reactor and actual petroleum fractions. There i s good agreement between the two k i n e t i c studies. This current study has achieved a further © 0-8412-0401-2/78/47-065-447$05.00/0 American Chemical Society Library 1 1 55 16th St., N.W. Weekman, V., et al.; In Chemical Reaction Engineering—Houston; Washington, D.C. 20 036 Washington, DC, 1978. ACS Symposium Series; American Chemical Society:
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refinement i n the k i n e t i c model; c o m p e t i t i v e a d s o r p t i o n e f f e c t s by the r e a c t a n t s u l f u r compound are accounted f o r . Experimental M a t e r i a l s . The feedstock was white o i l s p i k e d w i t h dibenzothiophene. The white o i l was obtained from the W h i t i n g r e f i n e r y o f Amoco O i l Company. The dibenzothiophene (Eastman Chemicals) and the hydrogen ( L i q u i d Carbonic) were used as received. The h y d r o d e s u l f u r i z a t i o n c a t a l y s t s were 1/16" c y l i n d r i c a l extrudates of commercial cobalt-molybdenum on alumina. Spinning Basket Reacto basket of the r e a c t o r i h e l d i n p l a c e by w i r e mesh i n an annular space i n s i d e the basket, where i n t e r n a l b a f f l e s are between the c a t a l y s t space and t h e center support s h a f t . The basket i s a l s o surrounded by a b a f f l e system which d i r e c t s the f l u i d f l o w and prevents l i q u i d v o r t e x i n g . A 500 cc autoclave designed and b u i l t by Autoclave Engineers serves as the b a s i s f o r the r e a c t o r system and i s equipped w i t h a p a c k l e s s magnetic d r i v e t o r o t a t e the basket. Good c o n t a c t i n g i s provided by t h e l i q u i d and e n t r a i n e d gas bubbles f l o w i n g r a p i d l y past the c a t a l y s t . This h i g h l y t u r b u l e n t g a s - l i q u i d mass i s a l i q u i d continuous bubble swarm. Backmixed ( g r a d i e n t l e s s ) o p e r a t i o n i s assured by good mixing i n the r e a c t o r . The f l o w p a t t e r n , shown i n F i g u r e 2, i s as f o l l o w s : (1) F l u i d enters near the center of the basket through the cutouts a t the top and bottom; (2) the f l u i d i n s i d e the basket r o t a t e s a t the same r a t e as the basket and moves by c e n t r i f u g a l f o r c e i n t o the c a t a l y s t ; (3) f l u i d e x i t s the c a t a l y s t and moves up o r down between the basket and autoclave w a l l ; (4) t h e f l u i d moves i n t o the spaces above and below the basket where i t then r e - e n t e r s the basket. Process D e s c r i p t i o n . The o v e r a l l flow scheme i s shown i n Figure 3. Hydrogen i s metered t o the r e a c t o r from the p i l o t p l a n t feed system. L i q u i d feed i s pumped t o the r e a c t o r by a Whitey pump which r e g u l a t e s the f l o w r a t e . Hydrogen, hydrogen s u l f i d e , and v a p o r i z e d o i l are removed from the vapor space above the s p i n n i n g basket. I t i s heated to r e a c t i o n temperature t o prevent condensation and r e f l u x i n g , then cooled t o room temperature i n a condenser where i t enters a s e p a r a t o r . The l i q u i d hydrocarbon i s r e c y c l e d w i t h an a i r d r i v e n Haskel pump t o the r e a c t o r . The uncondensed gas, hydrogen and hydrogen s u l f i d e , passes through the u n i t pressure c o n t r o l v a l v e t o the wet t e s t meter, which measures the gas f l o w r a t e . The l i q u i d e x i t s the r e a c t o r t o a high-pressure separator w i t h an overflow pipe p o s i t i o n e d i n s i d e . L i q u i d l e v e l i n the r e a c t o r i s maintained a t the same l e v e l as the top o f the over-
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
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Figure 1. Annular catalyst basket
Catalyst
Figure 2.
Multiphase spinning basket reactor
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION
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flow p i p e i n the s e p a r a t o r . The l i q u i d overflows from the p i p e i n t o the body o f t h e s e p a r a t o r . The l i q u i d l e v e l i n the body of t h e separator i s maintained below t h e top o f the overflow pipe. R e s u l t s and D i s c u s s i o n The s t u d i e s which we w i l l examine can be s u b d i v i d e d i n t o two areas: (1) Development o f the r e a c t o r system, (2) a k i n e t i c study on the h y d r o d e s u l f u r i z a t i o n of dibenzothiophene. Reactor D e v e l o p m e n t — C a t a l y s t Basket. The r e a c t o r i n t e r n a l s and f l o w scheme were designed a t Amoco O i l Research and Develop ment. Two types o f s p i n n i n basket designed d built the i n i t i a l design used adopted an annular shape improve desig i n a l l t e s t work. The improved design was an annular-shaped basket ( F i g u r e 1 ) , w i t h a basket c a p a c i t y o f 35 cc (^25 gm c a t a l y s t ) . The b a f f l e was designed t o i n c l u d e a l a r g e r i n g above the basket t o prevent v o r t e x i n g and b a f f l e extensions added below the basket t o d e c e l e r a t e the l i q u i d and a l l o w i t t o enter the middle o f the basket. M i x i n g and c o n t a c t i n g performance o f the improved b a s k e t - b a f f l e design was t e s t e d w i t h a i r and water a t ambient pressure and temperature i n a p l e x i g l a s s mockup of the r e a c t o r . The p l e x i g l a s s mockup s t u d i e s showed the f l o w p a t t e r n s s a t i s f i e d the requirements f o r e f f e c t i v e m i x i n g and c o n t a c t i n g i n the s p i n n i n g basket r e a c t o r . A h i g h degree of gas entrainment was observed i n the l i q u i d phase and resembled a bubble swarm. Reactor D e v e l o p m e n t — O v e r a l l System. A second p o r t i o n o f the o v e r a l l development was t h e system design f o r f e e d i n g o i l and hydrogen and removing l i q u i d product and o f f - g a s . F o r a n a l y s i s of the d a t a , the residence time d i s t r i b u t i o n o f the l i q u i d must be c l e a r l y d e f i n e d ; the s p i n n i n g basket r e a c t o r should approximate a s i n g l e backmixed r e a c t o r . H i g h l y v a p o r i z e d feeds work a g a i n s t t h i s o b j e c t i v e , however. To m a i n t a i n the p a r t i a l pressure o f the r e a c t i o n s p e c i e s (e.g. hydrogen s u l f i d e ) a t the d e s i r e d l e v e l , hydrogen i s c o n s t a n t l y fed and withdrawn from the r e a c t o r . As hydrogen i s withdrawn, so i s the v a p o r i z e d l i q u i d . T h i s r e s u l t s i n the residence time of the l i g h t e r components b e i n g l e s s than the r e s t of the r e a c t i o n m i x t u r e . To prevent t h i s , v a p o r i z e d l i q u i d l e a v i n g the r e a c t o r w i t h the gas stream should be condensed and then r e c y c l e d back t o the r e a c t o r . T h i s c o n t r o l s and d e f i n e s the r e s i d e n c e time d i s t r i b u t i o n of t h e l i q u i d i n the r e a c t o r by r e q u i r i n g a l l o f i t which enters t o e x i t the r e a c t o r as l i q u i d assuming h y d r o c r a c k i n g r e a c t i o n s are n e g l i g i b l e . More s p e c i f i c a l l y , the o f f - g a s i s cooled t o ambient temperature t o condense the l i g h t hydrocarbons b e f o r e being vented. Then the l i g h t hydrocarbons a r e returned to t h e r e a c t o r w i t h an a i r - d r i v e n r e c y c l e pump.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
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ROBINSON
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Kinetic
Studies
451
L i q u i d l e v e l i n the r e a c t o r was c o n t r o l l e d w i t h an overflow pipe l o c a t e d i n an e x t e r n a l separator. A l l l i q u i d then e x i t s through the overflow pipe i n t o the separator; the l e v e l i s measured w i t h a d i f f e r e n t i a l pressure t r a n s m i t t e r and maintained s l i g h t l y below the overflow t i p . K i n e t i c Study—Dibenzothiophene D e s u l f u r i z a t i o n . E a r l i e r work a t Amoco by Frye and Mosby (8) s t u d i e d the r a t e o f r e a c t i o n of s i n g l e s u l f u r compounds i n l i g h t c a t a l y t i c c y c l e o i l . Conclusions from that study were (1) the r e a c t i o n k i n e t i c s a r e f i r s t order i n hydrogen and reactant s u l f u r ; (2) hydrogen s u l f i d e i n h i b i t s the r e a c t i o n ; (3) o v e r a l l energy o f a c t i v a t i o n i s around 28-30 k c a l . A r e a c t i o n k i n e t i stud w i t h model s u l f u compound dibenzothiophehe, was A mixture o f dibenzothiophene i n white o i l was h y d r o d e s u l f u r i z e d over a wide range o f r e a c t i o n c o n d i t i o n s , v a r y i n g temperature, pressure, space v e l o c i t y , and hydrogen s u l f i d e l e v e l . The s t o i c h i o m e t r y f o r h y d r o d e s u l f u r i z a t i o n o f d i b e n z o t h i o phene may be w r i t t e n as f o l l o w s :
ODD dibenzothiophene
two
biphenyl
The k i n e t i c study o f dibenzothiophene d e s u l f u r i z a t i o n had objectives: 1. Evaluate r e a c t o r performance t o determine the minimum a g i t a t i o n r a t e which leads t o k i n e t i c a l l y c o n t r o l l e d conditions. 2. Confirm e a r l i e r d e s u l f u r i z a t i o n k i n e t i c s developed by Frye and Mosby on s e l e c t e d s u l f u r compounds using a t r i c k l e bed r e a c t o r ; r e f i n e t h e i r k i n e t i c model i f necessary.
A g i t a t i o n Tests. The observed r e a c t i o n r a t e should represent the c a t a l y t i c k i n e t i c s unclouded by phenomena such as the t r a n s f e r o f hydrogen a t the g a s - l i q u i d i n t e r f a c e o r r e a c t i o n species through the stagnant f i l m surrounding the c a t a l y s t . The minimum s t i r r i n g r a t e i s u s u a l l y e s t a b l i s h e d from a simple d i a g n o s t i c t e s t i n which conversion i s measured f o r v a r i o u s l e v e l s o f a g i t a t i o n . A g i t a t i o n r a t e was v a r i e d between 500 t o 1000 rpm and d e s u l f u r i z a t i o n l e v e l measured. R e s u l t s o f the a g i t a t i o n t e s t s are l i s t e d i n Table I . R a i s i n g a g i t a t i o n .
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
452
r a t e from 500 t o 700 rpm i n c r e a s e s t h e d e s u l f u r i z a t i o n conversion by 2.6%. By r a i s i n g the a g i t a t i o n r a t e f u r t h e r t o 1000 rpm, a s m a l l e r 1.4% i n c r e a s e i n conversion was observed. I t was concluded t h a t 750 rpm should be an adequate a g i t a t i o n r a t e s i n c e h i g h speeds put s t r e s s on the s t i r r e r mechanism and eventually lead to bearing f a i l u r e . TABLE I EFFECT OF AGITATION RATE ON PERFORMANCE
Press., psig
Feedstock Dibenzothiophene i n White O i l .5% S
30 300 300
Agitation WHSV Temp., rpm °F Wo/hr-Wc
540 540
2.06 2.06
750 1000
Desulfurization %
70.6 72.0
K i n e t i c Study. The experimental method c o n s i s t e d o f changing a s i n g l e process v a r i a b l e (such as temperature o r t o t a l pressure) and then o b s e r v i n g the e f f e c t on conversion. G e n e r a l l y , t h e e f f e c t o f each v a r i a b l e was observed by making two excursions from a s e t o f base c o n d i t i o n s . Table I I summarizes the experimental r e s u l t s . TABLE I I DIBENZOTHIOPHENE IN WHITE OIL Pressure, psig 300 (*) * * * * * * 100 500 * * * *
Temperature, °F 540(*) * * * 523 545 566 * * * * 523 566
WHSV Wo/hr-Wc
H 2 Rate ft /hr
2.0(*) 6.25 1.69 .62 *
0.42(*) .87 .37 .23 .37 .46 .36 .46 .40 .10 1.5 .31 .99
* * * * * 1.17 4.4
3
Desulfurization, % 74.6 40.0 76.5 94.5 63.0 76.0 89.0 52.0 82.0 62.5 85.5 80.4 84.5
*Base C o n d i t i o n s K i n e t i c M o d e l l i n g . I f t h e r e a c t i o n were s t r i c t l y f i r s t order i n dibenzothiophene, then a p l o t o f r e a c t i o n r a t e versus
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
37. MYERS AND ROBINSON
453
Multiphase Kinetic Studies
s u l f u r c o n c e n t r a t i o n would y i e l d a s t r a i g h t l i n e . F i g u r e 4 shows t h a t t h i s r e l a t i o n s h i p does not h o l d . Frequently c a t a l y t i c k i n e t i c s can be described u s i n g a Hougan-Watson k i n e t i c model, an e x t e n s i o n o f the e a r l i e r Langmuir-Hinshelwood forms. The general form of the model p a r a l l e l s the e a r l i e r work by Frye and Mosby (8) on s i n g l e s u l f u r compounds i n petroleum f r a c t i o n s . The b a s i c d i f f e r e n c e i s that competitive a d s o r p t i o n of the reactant i s accounted f o r which helps t o d e s c r i b e the n o n - f i r s t order behavior. The k i n e t i c model i s p
r
* DBPH2
=
" DB
(1 + K where
D B
P
n
p
D B
+ %S Hs)
m
- r ^ g = rat k = rat ~P± = p a r t i a l pressure o f species i , atm K± = a d s o r p t i o n constant o f species i , atm ^DB = dibenzothiophene hydrogen HS = hydrogen s u l f i d e n,m = i n t e g e r constants, 1 o r 2 -
=
The two i n t e g e r constants, η and m, f o r hydrogen p a r t i a l pressure and the a d s o r p t i o n term were assigned values o f 1 o r 2. This r e s u l t s i n four p o s s i b l e models t o d e s c r i b e the experimental data. The data were f i t t e d w i t h the f o u r models by n o n - l i n e a r r e g r e s s i o n techniques. The r e s u l t s are summarized i n Table III. TABLE I I I KINETIC MODEL SUMMARY Integer Powers η m
Model A Β C D
l
l 1 2 2
2 2 1
F i t t e d Constants S t d . Dev. o f Rate k χ Ι Ο Κρβ KHS σ χ ΙΟ 6
4.64 2.47 .147 .32
8
607.9 90.0 89.1 671.8
9.5 1.4 2.7 2.2
.64 .81 1.25 1.14
Models A and Β which were f i r s t order i n hydrogen p a r t i a l pressure gave the best f i t . F i g u r e s 5 and 6 show f i t t e d v s . observed r e a c t i o n r a t e s f o r these two models. Furthermore, t h e s t a t i s t i c a l s i g n i f i c a n c e of the three f i t t e d parameters, k, Kj)g, and Kjjg, was c o n s i d e r a b l y b e t t e r f o r models A and B. U n f o r t u n a t e l y the data do not a l l o w d i s c r i m i n a t i o n on the power f o r the adsorption term.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
454
CHEMICAL REACTION ENGINEERING—HOUSTON
Pressure sensor
0~
Pressure regulator Hydrogen I Flow ι control _j valve Pressure drop sensor
1
Pressure control valve
Ί
To
vent n
Wet t e s t meter
Condenser
Feed tank
Liquid level valve
Feed scale Metering pump Figure 3.
Process flow diagram
W t % S in product
Figure 4.
Reaction rate as a function of product sulfur
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
Sample receiver
MYERS AND ROBINSON
Figure 6.
Multiphase Kinetic Studies
Calculated vs. observed rate—dual site model
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION
456
ENGINEERING—HOUSTON
An u n s u c c e s s f u l attempt was made t o f i t the a c t i v a t i o n energies f o r the k i n e t i c and a d s o r p t i o n c o n s t a n t s . The para meters were a l l h i g h l y i n t e r c o r r e l a t e d s i n c e the experiments were not designed t o uncouple the temperature e f f e c t s . As an a l t e r n a t e approach the o v e r a l l temperature response was determined by p l o t t i n g r a t e versus r e c i p r o c a l temperature i n F i g u r e 7 and the s l o p e , -ΔΕ/R, c a l c u l a t e d . F i g u r e 7 shows t h e o v e r a l l temperature response by l e a s t squares f i t t o be 28.0 k c a l . The o v e r a l l energy o f a c t i v a t i o n i n c l u d e s the e f f e c t of temperature on the vapor pressure o f dibenzothiophene. As discussed by Frye and Mosby ( 8 ) , the apparent energy of a c t i v a t i o n f o r a l i q u i d - v a p o r system i s a combination of s e v e r a l f a c t o r s which i n c l u d e the a d s o r p t i o n e n t h a l p i e s o f dibenzo thiophene and hydrogen r e a c t i o n a c t i v a t i o n energy v a p o r i z a t i o n i s 13 kcal/mole, then the a c t i v a t i o n energy i s about 15 k c a l / m o l . This a l s o suggests that f i l m d i f f u s i o n e f f e c t s a r e not c o n t r o l l i n g the observed r e a c t i o n r a t e . With the e x c e p t i o n of the r e a c t i o n order f o r the dibenzothiophene, good q u a l i t a t i v e agreement e x i s t s w i t h the r e s u l t s o f both s t u d i e s . The discrepancy i n the apparent r e a c t i o n order c o u l d be e x p l a i n e d by the d i f f e r e n c e s i n the r e a c t i o n environment. In c o n t r a s t to white o i l , l i g h t c a t a l y t i c c y c l e o i l i s h i g h l y aromatic. These aromatics c o m p e t i t i v e l y adsorb and i n h i b i t the d e s u l f u r i z a t i o n r e a c t i o n . At h i g h aromatics c o n c e n t r a t i o n , the dibenzothiophene a d s o r p t i o n would be masked by aromatic a d s o r p t i o n . Apparent f i r s t order k i n e t i c s w i t h respect t o dibenzothiophene would then be observed. Conclusions The Amoco annular s p i n n i n g basket r e a c t o r system i s a u s e f u l t o o l f o r s t u d y i n g the fundamental k i n e t i c s o f l i q u i d - v a p o r - s o l i d c a t a l y z e d r e a c t i o n systems. We b e l i e v e i t i s g e n e r a l l y s u p e r i o r to t r i c k l e bed systems f o r the study of pure compound k i n e t i c s i n l i q u i d - v a p o r - s o l i d c a t a l y z e d systems. A d e s u l f u r i z a t i o n k i n e t i c study w i t h dibenzothiophene i n white o i l was s u c c e s s f u l l y completed. The r e s u l t s of the study compare f a v o r a b l y w i t h an e a r l i e r study performed i n a t r i c k l e bed r e a c t o r by Frye and Mosby ( 8 ) . Abstract A s p i n n i n g basket r e a c t o r has been developed f o r s t u d y i n g multiphase r e a c t i o n s a t h i g h pressure. Studies have been performed on the h y d r o d e s u l f u r i z a t i o n of v a r i o u s petroleum f r a c t i o n s and a model s u l f u r compound. Hydrogen and l i q u i d feed are c o n t i n u o u s l y f e d t o t h e r e a c t o r and contacted w i t h the c a t a l y s t which i s h e l d i n a r o t a t i n g annular basket. The
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
MYERS AND ROBINSON
Figure 7.
Multiphase Kinetic Studies
Reaction rate vs. reciprocal temperature
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING-HOUSTON
458
residence time d i s t r i b u t i o n of the o i l approximates a s i n g l e backmixed r e a c t o r by r e c y c l i n g the l i g h t hydrocarbons which e x i t i n the o f f - g a s stream. A c a t a l y s t b a s k e t - b a f f l e design was developed which assures good m i x i n g and c o n t a c t i n g and e l i m i n a t e s v o r t e x i n g a t the g a s - l i q u i d i n t e r f a c e . P l e x i g l a s s mock-up s t u d i e s provided guidance i n the design of the r e a c t o r internals. D e s u l f u r i z a t i o n k i n e t i c s were s t u d i e d w i t h a model s u l f u r compound system, a dibenzothiophene i n white o i l . Tests on basket a g i t a t i o n r a t e i n d i c a t e that mass t r a n s f e r and c o n t a c t i n g e f f e c t s are s m a l l above 750 rpm. The r e a c t i o n k i n e t i c s agreed w e l l w i t h e a r l i e r work. The Langmuir-Hinshelwood k i n e t i c model was f u r t h e r r e f i n e d to account f o r competitive a d s o r p t i o n e f f e c t s due to dibenzothiophen well hydroge s u l f i d e Literature Cited 1. 2. 3. 4. 5. 6. 7.
8.
Weekman, V. W., AIChE J., 20, 833 (1974). Carberry, J. J., Ind. Eng. Chem., 56, 39 (1964). Tajbl, D. J.; Simons, J. B.; and Carberry, J. J.; Ind. Eng. Chem. Fundam., 5, 171 (1966). Bennett, C. O.; C u t l i p , M. B.; and Yang, C. C . ; Chem. Eng. Sci., 27, 2255 (1972). Berty, J., Chem. Eng. Prog., 70, V o l . 6, 78 (1974). Mahoney, J. Α., J. of Cat., 32, 247 (1974). Tikhonov, G. F.; Shestov, G. K.; Temkin, O. N.; and Flid, R. M . ; "Gradientless Reactor Suitable for Studying the Kinetics of Liquid Phase Reactions in Gas-Liquid Systems," Kinetika, K a t a l i z , 7, No. 5, 914, Sept-0ct (1966). Frye, C. G . , and Mosby, J. F . , "Kinetics of Hydrodesulfur i z a t i o n , " Chem. Eng. Prog., 63, No. 9, 66 (1967).
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
38 Carbon Monoxide Oxidation in an Integral Reactor: Transient Response to Concentration Pulses in the Regime of Isothermal Multiplicities S E H . OH, KENNETH B A R O N , J A M E S C . C A V E N D I S H , and L . L O U I S
HEGEDUS
General Motors Research Laboratories, Warren, M I 48090
The idea of deliberate unsteady state operation of chemical reactors for performance improvement has received considerable attention in the literature of the past decade. Typically, pe riodic variations of one or more system parameters have been used (e.g., 1, 2, 3, 4). Extensive discussion of this subject is given in the book of Douglas (5) and in a review article by Bailey (6). Most of the earlier theoretical and experimental studies in the area of unsteady state operation have two common features. F i r s t , the parameter variations considered were periodic in na ture ( i . e . , sine wave, square wave, or sawtooth). Secondly, it has been widely assumed, with the exception of recent studies by Sincic and Bailey (7) and Wandrey and Renken (8), that the sys tems under consideration have a unique (and stable) steady state within the range of parameter variation. In this paper we investigate the possibility of enhancing the conversion of an isothermal, integral catalytic reactor in the multiple steady state regime by means of a single inlet concentration perturbation. This study is essentially a follow-up of the earlier work by Hegedus et a l . (9) on CO oxidation over Pt, where wide ranges of stable steady state multiplicities were observed under isothermal conditions. Experimental Part Spherical, alumina-supported Pt catalyst pellets were used in the experiments (see Table I for the catalyst properties). The catalyst was aged for 1000 hours in the exhaust gas of a dynamometer-mounted V-8 automobile engine. The pellets were found to be surrounded by a partially impervious poison layer with a reduced d i f f u s i v i t y ( 1 0 ) . A detailed description of the techniques used to characterize the catalyst can be found elsewhere
©
0-8412-0401-2/78/47-065-461$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
462
For the catalyst used here, both the noble metal impregnation profile and the poison profile were found to be reasonably sharp along the pellet radius, so that the catalyst pellets can be vis ualized as a composite material with four different layers, as shown in Fig. 1 (e.g., 10).Zones 2 through 4 of the pellet were Zone 1 : Unimpregnated Core originally impregnated by Pt, Zones 2, 3. 4: Noble Metal Impregnated Shell zone 1 being l e f t unimpregnated. Zone 3: Poisoned Shell Zone 4: Partially Impervious Deposit Zone 3 represents a poisoned lay er without pore plugging while zone 4 i s partially obstructe (thereby reducing i t s aged catalyst pellet diffusivity) and poisoned. The d i mensions of these zones are also given in Table I. We chose such a complex catalyst in this study because this catalyst was shown to exhibit a wide range of steady state multiplicities (9j. Table I Catalyst
Properties
P t (w%)
0.06 ( e s t . )
Ρ
(g/cm )
3.61
Pt d i s p e r s i o n (%)
40 ( e s t . )
Ρρ (g/cm )
1.16
a
2352 ( e s t . )
R (cm)
0.1766
2
(cm P t / cnr p e l l e t ) 2
3
S
3
Pb (w%)
1.31
r
3
(cm)
0.1759
Ρ (w%)
0.39
r
2
(cm)
0.1753
r
1
(cm)
0.1562
V
macro
(Λ)
0.070
V
micro
(Λ)
0.515
D
13099
D
220
ε
57
£
r
macro
r
micro
s (m /g) 2
^ ο ^
r 2Î 3 (cm / s e c ) * D
4
D
(cm /sec) 2
ρ,Γ ρ,2 ε
P,4
= ε
ρ,3
0.0589 0.00393 0.679 0.045 (est.)
•Computed from the random pore model o f Wakao and Smith [Smith ( 1 1 ) ] , and given here a t 1 atm and 838 K. D v a r i e s w i t h t h e 1.4th power o f T.
The integral reactor used in our experiments has been de scribed previously (9). The reactive section (total volume 10
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
38.
OH ET AL.
CO
Oxidation
in Integral
463
Reactor
cm ), packed with the Pt-alumina catalyst, was sandwiched be tween two catalytically inactive SiC layers which serve as a heat transfer medium and also help to provide a f u l l y developed flow pattern through the reactor section. The stainless steel reactor tube was heated to the desired temperature by an elec t r i c furnace, and both the inlet and outlet temperatures of the reactive section were monitored using thermocouples. Also, electrochemical and infrared analyzers were used to measure i n let and outlet 0 and CO concentrations, respectively. CO concentration pulses were injected to the reactor inlet using four solenoid valves which, when energized, allowed a sec ond (supplemental) CO stream (instead of the main CO stream) to feed the reactor for a predetermined period of time. The pulse amplitudes were varied by adjusting the concentrations in the main and supplemental ing the solenoid operatio negligibly 2
Theoretical Part In our experiments the inlet CO concentrations were kept low enough (about 0.3 vol. %) to ensure near-isothermal opera tion. Furthermore, a large excess of 0 (2 vol. %) was em ployed; thus we need to consider only the conservation of CO in the mathematical model. While the diffusion-reaction model was found to be adequate in analyzing the steady state behavior of the CO-Pt system (9), in this study we will use a transient model which also includes the accumulation of CO over the cata l y t i c surface. The importance of including surface phenomena in the tran sient model of porous catalyst particles has been pointed out, e.g., by Sheintuch and Schmitz (J_2). Experimental work by Lehr et a l . (13) and by Denis and Kabel (14, 15) seems to support this argument. Elnashaie and Cresswell ΤΤβ, 17.) also employed a mathematical model which accounts for adsorption, desorption, and surface reaction in studying porous catalyst pellets. The balance equation for CO in the intrapellet gas phase is 2
1
L 2 3r
[ D ( r ) r |f 2
] - a(r) R
(1)
a
where R represents the net rate of CO adsorption on the Pt ac tive sites. The conservation of adsorbed CO over the Pt surface can be expressed, in terms of i t s surface fractional coverage Θ, as a
ι de Ν s dt
(2)
where Ν represents the CO concentration over the active sites corresponding to a complete monolayer coverage, and R is the rate of the surface reaction. For our computations, N was s
s
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
464
CHEMICAL REACTION ENGINEERING—HOUSTON
-9 2 taken to be 2 x 1 0 mol C0/cm Pt based on the assumption of 1:1 stoichiometry between Pt surface atoms and CO molecules. The most general case requires solving Eqs.^(l) and (2) simultaneously, with the given rate expressions R and R . In the present study, however, the chemisorption process on the Pt surface is assumed to rapidly equilibrate according to the Langmuir isotherm. This assumption seems reasonable because CO adsorption on Pt is a fast, non-activated process (18, 1 9 ) , and the desorption rate also appears to be reasonably fast at our reaction temperatures [around 200°C or higher (18, 20, 21)]. It is convenient to eliminate Ra between Eqs. JT) and J2) to yield a
s
a
From the Langmuir isotherm relationship de _ / "
d t
8Θ
^
(
8C
w
Κ
M
_
χ
Κ
~ ( Τ
}
+
Kc )
3C 2
( A \
3 t
and thus Eq. (3) becomes Κ [
e
P
( r )
+
\*w
,
,2
J If = h ÏF
A
c
(5)
IF J - ^)«
S
It should be noted that in deriving Eq. (4), 0 adsorption on Pt was assumed to be negligibly small compared to CO adsorption. The dynamic behavior of the individual catalyst pellets can then be simulated by solving Eq. (5) for the four different layers shown in Fig. 1. The boundary conditions for Eq. (5) are 2
ff(0)=0
(6)
R
c
C R
7
IF <> = OT c ~ - <> 3
<>
In addition, the continuity of both the flux and concentration of CO i s imposed at the zone interfaces (that i s , r = r-., r and r ^ ) . For the particular catalyst considered here, D, ε ana a are taken to be piecewise constant with the following properties: 2
D
ε
a
l
=
D
=
ρ,1 l
=
2
a
3
=
ε
D
3
> y
D
( 8 )
4
ε
ρ,2 " ρ,3 »
=
a
4
=
0
9
a
2
=
ε
( 9 )
ρ,4
f i n l t e
10
( )
where the numbers in the subscripts refer to various layers of the catalyst pellet (see Fig. 1).
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
38.
OH ET AL.
CO Oxidation in Integral Reactor
465
Independent experiments with a recycle reactor in our lab oratory (22) indicated that under similar operating conditions the maximum rate of CO oxidation a t 200°C occurs a t a CO con centration of 0.04 v o l . %. Since i t follows directly from the Langmuir isotherm that Θ = 0.5 at the CO concentration cor responding to the peak rate, the adsorption equilibrium constant can be estimated to be 3 Κ = 3.118 exp (16000/R T) , j^y (11) g
with the heat of adsorption taken to be 16000 cal/mol (23). With the assumption of chemisorption equilibrium invoked here, the^surface reaction becomes the rate determining step, and thus R in Eq. (5) b reasonabl approximated b th empirical rate expressio quate in describing the steady state behavior of CO oxidation under our operating conditions (9_). That i s , s
ft , s
k
o
T
e
x
p
H5000/R T) c c ^ q
^
Q
[1 + 4.5 χ ΙΟ Τ exp (2000/R T)c] 5
g
2
m
Q
l
C
Q
(
i
2
)
2
' cm Pt sec
12 where the pre-exponential factor k is on the order of 10 . The system of partial differential equations describing the various layers of the individual pellets [Eqs. (5) through (7)] was f i r s t reduced to a large set of ordinary differential equations in the time domain by using Galerkin's method employ ing piecewise continuous rational basis functions. Galerkin's method of this type has proven to be effective in solving com posite catalyst pellet problems (9, 1 0 ) . The numerical integration of the resulting set of ordinary differential equations presents a considerable challenge, since the system exhibits a rapid overshoot followed by a slow tran sient, as will be shown later. Due to the widely different time constants inherent in our problem, we used the GEARIB code ( 2 4 ) , which is well suited to handle such s t i f f problems. The detailed description of the numerical technique can be found elsewhere (25). The integral reactor was simulated by a cascade of axial mixing c e l l s . The Reynolds number for our typical operating condition is about 50, and the corresponding Peel et number (based on the particle diameter) is about 2 (26). If the num ber of mixing cells is chosen by N ] ] = Pe L/4R, then each layer of pellets amounts to a mixing cell (27). Since our i n tegral reactor is about 8 pellet diameters long, 8 mixing cells were used in the computations. The conservation equation for CO around the j t h mixing cell is 0
ce
Q C c ( j - l ) " c.(j) ] + 3 k V e
m
c e l l
ίψ-
[ c(R, j) - cjj)
] - 0 (13)
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
466
CHEMICAL REACTION ENGINEERING—HOUSTON
This equation allows us to determine the exit concentration of the jth c e l l , c ^ i j ) , from the known inlet concentration c ( j - l ) and the solution of the single-pellet equations. It should be noted that the accumulation of mass in the interpellet space was neglected in Eq. (13), since i t s time constant is typically 80 times smaller than that of the intrapellet transients. The external mass transfer coefficient of CO, k , of Eqs. (7) and (13) was estimated from the de Acetis-Thodos correlation, as given in Smith (]J_). œ
m
Results and Discussion It has been shown in the earlier paper (9j that isothermal CO oxidation over Pt-alumin catalyst with appreciabl intra pellet diffusion resistance state multiplicities in the conversion-temperature, conversion inlet CO concentration, and conversion-mass flow rate domains. Fig. 2 shows the steady state CO conversion as a function of reactor inlet temperature for a fixed set of concentrations (~0.3 vol. % CO, ~2 vol. % 0 ) . The details of the experimental conditions of Fig. 2 and the subsequent figures are given in Table II. Hegedus et a l . (9) pointed out that the hysteresis envelope shown in Fig. 2 corresponds to the highest and lowest stable steady state conversions, and also demonstrated the existence of several intermediate stable steady states within the envelope of the hysteresis loop. They also have shown that each of these multiple conversion levels can be achieved by a properly chosen sequence of steady state operations. 2
Table II Description of Various Experimental Conditions
k
c
Fig. 3
-
-
1.07 χ 1 0
varies
varies
212
212
0.4
0.4
0.4
0.4
2.07
2.01
2.02
2.00
0.297
0.3160.1080.316
varies
0.3210.0760.321
o
ε C
Fig. 2
0 , i n (%) 2
i n
{%)
Pulse Duration (sec) QP (g/sec)
3
0.089
0.094
Figs. 4, 5
3
0.094
Figs. 6, 7 12
1.10
χ 10
varies
0.093
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
12
38.
OH ET AL.
CO Oxidation in Integral Reactor
Ο
Increasing Τ
•
Decreasing Τ
—
01 150
I
I
I
J
L
I
Eyeball Lines to S h o w Course of Experiments
I
200
L
I 250
T
m
467
I
I
» 300
(°C)
Figure 2. Steady state hysteresis in the conversion-inlet temperature domain
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
468
CHEMICAL REACTION ENGINEERING—HOUSTON
In the present study we investigate the possibility of en hancing the reactor conversion in the regime of multiple conver sions by means of deliberate perturbations of the i n i t i a l steady state. For a l l the results reported here, the reactor was i n i t i a l l y set to operate at the lowest conversion steady state, and the reactor inlet CO concentration was perturbed by temporarily reducing the CO concentration to a lower value, while maintain ing the total flow rate, the reactor pressure, and oxygen con centration essentially unperturbed. Before each pulse, the re actor was cooled down to a temperature well below the hysteresis loop of Fig. 2 and then slowly heated up to a desired tempera ture to establish the lowest conversion state. Fig. 3 shows the steady state conversion data at various temperatures before and afte th inlet concentratio pulse In this experiment, th 0.316 vol. % to 0.108 vol be readily seen that the steady state conversion is enhanced upon pulsing in the multiple conversion regime, while the reac tor quickly returns to the original conversion level at temper atures outside the hysteresis loop (e.g., Τ · = 145°C or 299°C). It is interesting to note that the hysteresis loop of Fig. 2 can be made to superimpose reasonably well with Fig. 3 i f the latter is shifted to the l e f t by approximately 10°C along the temperature axis. This small shift of the hysteresis loop (without changing i t s shape or area significantly) seems to be associated with the d i f f i c u l t y in exactly reproducing the chem ical state of the catalyst at the beginning of each experiment. Allowing for this, the data of Fig. 3 may be taken to represent the outer boundaries of the hysteresis envelope. In order to examine in more detail the conversion enhance ment in the multiple conversion regime, we investigated the ef fects of pulse amplitude and duration at a temperature which f a l l s in the middle of the hysteresis loop in the conversiontemperature plane (see Fig. 2). Fig. 4 shows the observed time variations of CO conversion for various pulse amplitudes at Τ · = 212°C. In each case of Fig. 4, a pulse of 3 sec duration was injected at time t = 0 to the reactor which had been previ ously stabilized at the lowest conversion steady state. As ex pected, the degree of conversion enhancement was found to i n crease with increasing pulse amplitudes. Also, i t appears that the reactor already attained the highest conversion level (about 40%) with the pulse amplitude of 0.321-0.076-0.321, and thus the even larger pulse amplitude of 0.317-0-0.317 did not provide any further conversion enhancement. The computational results shown in Fig. 5 are in reasonably good agreement with the experimental data of Fig. 4, except at the early portion of the transients. It can be seen that the transient model predicts a larger overshoot followed by a some what faster stabilization to a new conversion level when com pared with the experimental data. This difference in time beΊ
Ί
η
η
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
38.
CO Oxidation in Integral Reactor
OH ET AL.
469
80 Γ
70h-
.-8 50 h-
40 h
ο 30 h Ο
20 Y
10
! 100
120
I g —*~-~~Γ^ 140
160
180
I
I
I
220
240
260
I
200
I 280
I 300
Tin (°C>
Figure 3. Steady state conversion performance with pulsing at various temperatures. Pulse amplitude = 0.316-0.108-0.316. Pulse duration = 3 sec.
70
60
50 Pulse Amplitude (vol. % CO) — 0 — 0.317
==
^ ======= ~^^_^'0.Z\1
8 40
===
^ 0 . 3 2 1 — 0.076 — 0.321 <-> 3 0 h 0.317 — 0.178 — 0.317 20
h 0.317 — 0.244 — 0.317
6
8
10
12
14
16
Time (min)
Figure 4. Effects of pulse amplitude on conversion enhancement (ex periments). Pulse duration = 3 sec. T{ = 212°C. n
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
470
CHEMICAL REACTION ENGINEERING—HOUSTON
havior may be attributed to the nonidealities of our experimental system, such as the transportation lag (about 30 sec, see Fig. 4) and signal dispersion effects between the reactor exit and the CO analyzer, and within the CO analyzer. Therefore, no attempts were made in this study to match the transient response of the early period (i.e., near t = 0) during which rapid changes in CO concentration occur. Instead, we focused our attention on the ultimate steady state which the system assumed as the result of the perturbation. Although only three different conversion levels are shown in Fig. 5, computations with other pulse amplitudes indicated that conversion enhancement to other intermediate conversion levels is also possible. For example, with a pulse amplitude of 0.317-0.174-0.317, th model predicted final CO conversio of 30.9%. We also conducted some experiments at the same inlet tem perature as before ( T j = 212°C) to investigate the effects of pulse duration. The pulse amplitude of 0.321-0.076-0.321 was used, and the experimental data are shown in Fig. 6 for various values of pulse duration. Conversion enhancement was observed for the durations of 1 sec or longer, and virtually no further enhancement was achieved when the pulse duration was increased beyond 2 sec. The simulation results shown in Fig. 7 provide a good qualitative comparison with the experimental data of Fig. 6. The curve for the pulse durations of 2 sec and 6 sec exhibits a slower response than the other curves for shorter durations. This behavior seems to be consistent with the experimental observation (Fig. 6). The computed reactor response with the pulse duration of 1.05 sec is also included in Fig. 7 to show the sensitivity of the system and to i l l u s t r a t e the existence of some additional intermediate stable steady states. It is of interest to discuss the predictions of a d i f f u sion-reaction model which accounts for no surface accumulation phenomena [that i s , the model with N = 0 in Eq. (5)]. We found that such a model was inadequate in describing the transient behavior of our system: the simulation based on the operating conditions of Fig. 6 predicted a conversion enhancement to the highest conversion level even with the very short pulse duration of 0.25 sec. In view of the small characteristic response time (about 0.1 sec) for intrapellet diffusion, surface phenomena seem to play a key role in determining the transient response of supported catalysts (12, ]± 15, 28). This, of course, does not invalidate the use of the simpler diffusionreaction model for the description of steady state behavior, as shown in our previous paper (9). To our knowledge, the present work is the f i r s t observation of conversion enhancement upon perturbations in the regime of isothermal steady state reactor m u l t i p l i c i t i e s , although transitions between stable steady states have been reported by n
s
9
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
OH ET AL.
CO Oxidation in Integral Reactor
80
Pulse Amplitude (vol % CO)
£
0,317 -
0076 -
0 317
0 317 -
0 178 -
0 317
40
Ο υ
30
20
0 317 — 0 244 — 0 317
10
2
3
Time (mm)
Figure 5.
Effects of pulse amplitude on conversion enhancement (theory). Pulse duration = 3 sec. T = 212°C. in
Figure 6. Effects of pulse duration on conversion enhancement (experi ments). Pulse amplitude == 0.321-Ό.076-0.321. T = 212°C. in
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
472
CHEMICAL REACTION ENGINEERING—HOUSTON
so r
Pulse Duration 2 sec and 6 sec
1 sec
0 25 sec
2
3 Time (mm)
Figure 7.
Effects of pulse duration on conversion enhancement (theory). Pulse amplitude = 0.321-0.076-0.321. T = 212°C. in
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CO Oxidation in Integral Reactor
OH ET AL.
38.
473
Root and Schmitz (29), and Votruba et a l . (30) for adiabatic reactor systems. Adiabatic reactor multiplicities were also i n vestigated by Aris and Schruben (3]_), computed the ultimate conversions achieved from various i n i t i a l conditions. Besides i t s practical implications in improving reactor conversion performance by deliberate inlet concentration per turbations, this study also serves to confirm the existence of the isothermal reactor multiplicities and the intermediate sta ble steady states reported in our earlier paper (9). Acknowledgement The reactor experiments were carried out by E. Miller. Nomenclature 2
3
/ a (cm Pt/cm
pellet)
l o c a l P t surface area
3
c (mol/cm )
CO c o n c e n t r a t i o n i n the i n t r a p e l l e t gas phase
c
0
(mol/cm )
n U
2
c
2
concentration
3
(mol/cm )
CO c o n c e n t r a t i o n f a r away from c a t a lyst pellet
D^c (cm /sec)
e f f e c t i v e d i f f u s i v i t y o f CO i n Zone I
k
mass t r a n s f e r c o e f f i c i e n t o f CO
m
(cm/sec)
k i n e t i c pre-exponential i n Eq. (12) Κ
CO a d s o r p t i o n e q u i l i b r i u m constant
L (cm)
length o f the intégral r e a c t o r
N
number o f mixing c e l l s
cell N (mol/cm P t ) 2
s a t u r a t i o n CO c o n c e n t r a t i o n o f a c t i v e sites
s
Pe
Peel et number gas v o l u m e t r i c f l o w r a t e
Q (cm'/sec) r
(A)
i n t e g r a l averaged pore r a d i i
macro or micro r (cm) R (cm)
pellet radial
R. (mol/cm
net r a t e o f CO a d s o r p t i o n on P t
coordinate
p e l l e t radius
P t sec) 2
R
$
(mol/cm
P t sec)
surface reaction rate gas constant
s (mVg)
BET s u r f a c e area o f support
t (sec)
time
Τ (Κ o r °C)
temperature
V
volume o f a mixing c e l l
V
cell
( α η 3
>
macro o r micro ^
3
c m
^
p e l l e t mac^o o r micro pore volumes
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
474 ε
η
μs
CHEMICAL REACTION ENGINEERING—HOUSTON pellet void fraction in Zone I
;
Λ,
3 ρ (g/cm ) gas density 3 pp (g/cm pellet) pellet density 3 P (g/cm solid) pellet solid density θ fractional surface coverage of CO Literature Cited 1. Douglas, J. M., D. W. T. Rippin, Chem. Eng. Sci. (1966), 21, 305. 2. Douglas, J . Μ., Ind. Eng. Chem. Proc. Des. Devel. (1967), 6, 43. 3. Lee, C. K. 4. Wandrey, C., A3-3. 5. Douglas, J . M., "Process Dynamics and Control," Prentice -Hall, Englewood Cliffs, N.J., 1972. 6. Bailey, J . E., Chem. Eng. Commun. (1973), 1, 111. 7. Sincic, D., J. E. Bailey, Chem. Eng. Sci. (1977), 32, 281. 8. Wandrey, C., A. Renken, Chem. Eng. Sci. (1977), 32, 448. 9. Hegedus, L. L., S. H. Oh, K. Baron, AIChE J . (1977), in press. 10. Hegedus, L. L., J. C. Cavendish, Ind. Eng. Chem. Fund. (1977), in press. 11. Smith, J . Μ., "Chemical Engineering Kinetics," McGraw-Hill, New York, 1970. 12. Sheintuch, M., R. A. Schmitz, Cat. Rev.-Sci. Eng. (1977), in press. 13. Lehr, C. G., S. Yurchak, R. L. Kabel, AIChE J. (1968), 14, 627. 14. Denis, G.H.,R. L. Kabel, AIChE J. (1970), 16, 972. 15. Denis, G.H.,R. L. Kabel, Chem. Eng. Sci. (1970), 25, 1057. 16. Elnashaie, S. S. E.H.,D. L. Cresswell, Can. J. Chem. Eng. (1973), 51, 201. 17. Elnashaie, S. S. E. H., D. L. Cresswell, Chem. Eng. Sci. (1974), 29, 753. 18. Hayward, D.O.,B. M. W. Trapnell, "Chemisorption," But terworths, London, 1964. 19. Morgan, Α. Ε., G. A. Somorjai, J . Chem. Physics (1969), 51, 3309. 20. Bonzel, H. P., J. J. Burton, Surf. Sci. (1975), 52, 223. 21. Bonzel, H. P., R. Ku, Surf. Sci. (1972), 33, 91. 22. Chou, T. S., J . C. Schlatter, unpublished results, 1976, General Motors Research Laboratories. 23. Hori, G. K., L. D. Schmidt, J . Catalysis (1975), 38, 335. 24. Hindmarsh, A. C., Lawrence Livermore Laboratory Report UCID 30130, 1976. 25. Cavendish, J . C., S. H. Oh, to be presented in 70th Annual Meeting of AIChE, New York, November 1977. 26. Froment, G. F., Adv. in Chem. Series (1972), 109, 1. 27. Wei,J.,Adv. in Catalysis (1975), 24, 57. 28. Unni, M. P., R. R. Hudgins, P. L. Silveston, Can. J . Chem. Eng. (1973), 51, 623. 29. Root, R. B., R. A. Schmitz, AIChE J . (1969), 15, 670. 30. Votruba, J., V. Hlavacek, J . Sinkule, Chem. Eng. Sci. (1976), 31, 971. 31. Aris, R., D. L. Schruben, Chem. Eng. J . (1971), 2, 179. s
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
39 Limit Cycle Phenomena during Catalytic Oxidation Reactions over a Supported Platinum Catalyst M . B. C U T L I P Department of Chemical Engineering, University of Connecticut, Storrs, CT 06268 C . Ν. K E N N E Y Department of Chemical Engineering, University of Cambridge, Cambridge, England C B 2 3RA
Oscillatory phenomen mal catalytic reaction and hydrogen oxidation over various forms of platinum catalysts. Recent research has concentrated mainly on carbon monoxide oxi dation perhaps as a result of continuing interest in automotive emission control and the rather unique aspects of this reaction. Carbon monoxide oxidation over platinum is discussed in considerable detail by Wei (1) and Carberry (2). The kinetics are unusual in that the rate i s first order with respect to carbon monoxide at low concentrations and negative f i r s t order at high concentrations. There i s general agreement with the following sequence of elementary steps involved in this react ion:
where S in step (1) represents two platinum surface atoms for a bridged adsorbed CO species and one surface atom for a linear adsorbed CO species. It i s well known that steps (1) and (2) are very nearly irreversible at low temperatures as they are the basis for platinum titration procedures which u t i l i z e hy drogen (3) and carbon monoxide (4). Unfortunately there is little agreement as to the relative importance of carbon dioxide production via the Langmuir-Hinshelwood step (3) and the EleyRideal step (4). A thorough review of multiplicity and oscillatory phenomena ©
0-8412-0401-2/78/47-065-475$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
476
by Schmitz (5) summarizes the previous work prior to 1974. Limit cycles have recently been observed for carbon monoxide oxidation by McCarthy (6) using supported platinum on α alumina pellets and by Plichta ( 7 ) 9 platinum f o i l . Gradientless reactors were used in both studies, and transients in product C0 were observed by continuous infrared analysis. Attempts at modeling the oscillations by using steps (1) (4) with idealized kinetics have not been successful. Plichta (7) obtained oscillations by considering step (1), step (2) and step (4) where the activation energy of step (4) was assumed to be linearly dependent upon the surface coverage of the adsorbed atomic oxygen. Unfortunately the resulting model did not satis factorily represent the results. Pikios (8) analyzed a kinetic scheme similar to step (1) t (3) d als d change i activation energy of to obtain oscillations Eigenberge (9)ha g approach that oscillations may result when a non-reactive species reversibly adsorbs on the catalyst surface. Thus an additional step may be considered for carbon monoxide oxidation as follows: 5 A + S t A -S Step (5) (5) -5 where A i s a species such as 0 which reversibly chemisorbs but does not react. u s i n
2
k
2
Experimental Considerations Reactor System. A general purpose reactor system shown in Figure 1 was used in this work to study catalytic oxidation re actions over supported platinum catalyst pellets. This equip ment allowed up to six precise gas mixtures to be prepared and made available for feed to the reactor. The switching valve directed a desired gas mixture flow to the reactor while another gas mixture flow was precisely measured by the bubble flow meter. A switch interchanged the reactor and flow meter streams so that the reactor could be subjected to step changes in flow and/or composition enabling a wide variety of experiments to be per formed. The reactor was made from a 304 stainless-steel cylinder 69.8 mm in diameter and 50.8 mm in length. The catalyst pellets were placed in seven 9,53 mm in diameter holes in the cylinder and were retained by screens. The two end closures were sealed by standard copper vacuum gaskets which were gold plated. A metal bellows recycle pump described by Hanson (10) was used to maintain a recycle ratio in excess of 30 to 1 so that completely mixed or gradientless reactor performance was obtained. The reactor, metal bellows pump, and recycle lines were contained in a forced convection oven held at the reaction temperature. An o r i f i c e plate in the recycle line enabled the recycle ratio to be measured by a pressure transducer. Reactor/recycle line gas volume was found to be 52 cm .
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
39.
cuTLiP AND KENNEY
477
Limit Cycle Phenomena
Inlet and outlet analyses were obtained by an on-line magnetic-deflection mass spectrometer equipped with a fast response continuous inlet system. An electronic peak select unit allowed up to four mass numbers to be continuously mon itored. Catalyst. The catalyst was 10g of 0.5% platinum by weight, deposited on the surface of 1/8 inch in diameter γ alumina pel lets and obtained from Engelhard Ltd., Cinderford, England. The properties of the catalyst are summarized in Table I. Catalyst deactivation was not observed during the experimental studies. Experimental
Results
Steady State Multiplicity During CO Oxidation. Rates were measured for various oxygen-rich feed compositions at a fixed feed flow rate of 100 cnr/min. Regions of multiple steady state reaction rates were determined by maintaining feed composition and flow rate constant and varying the reactor temperature in a programmed manner. Typical results for a 2% CO and 3% 0 in argon feed com position are shown in Figure 2. This hysierisis curve was gen erated by starting at a low temperature and obtaining rates at increasing temperatures until the temperature at which the rate jumped to the high rate. The reactor was then slowly cooled for additional rate measurements to the temperature at which the high rate was extinguished. These "jump" temperatures result when the fractional surface coverages of adsorbed carbon monox ide and oxygen undergo dramatic changes. Cutlip (11) has dis cussed these results in more detail. A l l combinations of feed compositions between 0.5 to 3% CO and 2 to 4% 0 exhibited regions of steady state multiplicity bounded by varying jump temperatures. At any temperature in the region of the two steady states, the low rate could also be established by switching to the reactor a mixture of 10% CO in argon until the catalyst was saturated with the CO, then switching to the feed mixture. Pretreatment with 5% 0 in argon until C0 was no longer pro duced gave the high rate steady state. Tnese results indicate that the i n i t i a l coverages of the platinum surface dictate the final rate in the multiple steady state region with the low rate occuring at high coverages of carbon monoxide and the high rate occuring at high coverages of oxygen. External gradients were experimentally eliminated by inc reasing the recycle ratio until the characteristic "jump" temperatures were no longer affected. Extensive calculations of interphase and intraphase heat and mass transfer also indi cate the absence of gradients. It is significant that no oscillations were observed when 2
2
2
2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
478
Figure 1.
Experimental system
Table I - Catalyst Properties Platinum Dispersion A.
H Chemisorption
46.7 ± 3.7%
B.
H Desorption
48.0%
C.
CO Titration in Situ (4)
43%
D.
Thickness of Impregnated Layer
0.03 mm
2
2
BET and Pore Size Determinations A.
Average Pore Radius
20.1 A
B.
Total Pore Volume
.23 cm /g
C.
Σ Pore Areas
212 m /g
D.
BET Area
227 m /g
Pellet Density
3
2
2
2
1.98 g /cm
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
3
39.
cuTLip AND KENNEY
Limit Cycle Phenomena
479
the reactor was operated in a gradientless manner. This may be due to the low experimental turnover rates of this work which tend to minimize undesirable gradients. A comparison of turnover rates is given in Table II. Anomalous oscillations were occasionally noted when recycle rates were low or when i t was thought that trace hydrocarbons were inadvertently added to the recycle stream from the surfaces of new metal tubing or fittings. Table II - Approximate Turnover Rate Comparison Rate (molecules site) This Work
.0
Plichta (7)
.60
Temperature (°C)
Ratio to This Work
230
60
McCarthy (6) 40 210 4000 Limit Cycles During Simultaneous CO and 1 - Butene Oxidation. Subsequent rate measurements were made for a mixture of 2% CO, 3% 0 and 1% 1-butene in argon. As this mixture was introduced to the reactor at temperatures above the previously determined multiple steady state region, very dramatic concentration oscillations were obtained as shown in g Figure 3 for a temperature of 150°C and a feed rate of 100 cm / min at NTP. This limit cycle was characterized by a periodic rapid rate of oxidation of CO and 1-butene with a period of 31 minutes yielding minima in the reactant concentrations and a corresponding maximum in product C0 concentration. The spontaneous oscillations once established were quite reproducible with only minor variations attributed to flow rate and temperature fluctuations. Gas phase temperature variations within the reactor were not detected. The effect of temperature was investigated with increments of 5°C increases from the 150°C base temperature at a fixed feed rate of 100 cm /min. At 160°C, the period and amplitudes of the oscillations were decreased as indicated in Figure 4. The time-averaged rates of both CO and 1-butene oxidation were increased, and the oscillations became more sinusoidal. At 165°C oscillation amplitudes were very small and the period was reduced to 0.78 minutes. Thus i t is apparent that temperature has a very strong influence on the oscillations. The reactor space time was also varied at the base temperature of 150°C. Figure 5 shows the oscillations obtained when the flow was reduced from 100 cm^/min to 75 cm /min at NTP. Two relative maxima per cycle are evident for a l l of the reacting species and product C0 . Further reduction of the feed flow rate to 60 cm /min at NTP yielded the complex limit 2
2
3
2
3
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
480
Figure 2.
Multiple steady states for 2% CO, 3% 0 feed at 100 cm /min NTP 2
3
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
39.
cuTLiP AND KENNEY
Limit Cycle Phenomena
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
481
CHEMICAL REACTION ENGINEERING—HOUSTON
482
cycle of Figure 6 where seven relative maxima per cycle were found. Additional experimental data are summarized in Table III in order of increasing flow rate at NTP for the 2% CO, 3% 0 and 1% 1-butene in argon feed mixture. These experimental results in the regions of oscillations indicated that at fixed reactor space time, higher temperatures resulted in period and amplitude decreases for a l l components of the reacting system. At constant temperature, space time decreases also resulted in period and amplitude decreases. The time-averaged rates of oxidation of both CO and 1-butene increased with temperature and with reduction in space time. Reactor material balances suggested that 1-butene oxidation was essentially complete to C0 and H 0. 2
2
2
Discussion of Results These oscillatory phenomena are best understood by f i r s t considering the steady state multiplicity which is observed in the absence of 1-butene. Our interpretation is that carbon monoxide is very strongly adsorbed at the lower temperatures, and thus almost completely covers the platinum surface. As the reactor tem perature is slowly increased, more and more oxygen is adsorbed. Thus the overall reaction rate increases gradually until the surface reaction of equation (3) achieves a c r i t i c a l rate causing the various elementary steps to collectively produce a high overall rate where most of the carbon monoxide i s removed from the reactor. At this point the catalyst has appreciable coverage of adsorbed oxygen, l i t t l e adsorbed carbon monoxide and a significant proportion of vacant sites. As the reactor is cooled, the high rate continues but f a l l s gradually until the rate is reduced sufficiently for carbon monoxide to again be chemisorbed in sufficient amounts to extinguish the reaction rate. A proposed expiai nation for the oscillations during the introduction of 1-butene requires significant adsorption of the 1-butene on the platinum: Β + S I B-S k-5 5
step (5)
(6)
where Β refers to the 1-butene. At low temperatures, the 1butene covers some of the platinum surface and thus increases the temperature required to i n i t i a t e the "jump" to the high rate of CO oxidation. During the "jump", CO i s removed both from the gas phase and the catalyst surface. This allows the 1-butene to adsorb on the platinum surface with some oxidation, but the adsorption eventually quenches the high rate of CO oxidation. CO then begins to adsorb on the platinum and accumulates causing the entire process to be repeated.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
39. cuTLip AND KENNEY
Limit Cycle Phenomena
483
h 3%
νΛΛΛ/\Μ V
V
I
I
I
I
I
I
ι
»
ι
l
T I M E
Figure 6.
M
,
M I N
Oscillations at Τ = 150°C and feed at 60 cm /min NTP 3
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.
94.7
100
100
6
7
8
115.8
75
5
11
75
4
100
75
3
100
60
2
10
60
1
9
Flow Rate cm3/min
Point
165
165
160
155
150
160
160
155
150
155
150
0.12
0.08
0.25
0.73
0.93
0.08
0.05
0.09
0.83
0.06
0.67
0.05
0.06
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Reactior CO Temp. % °C max. min.
0.10
0.07
0.18
0.38
0.76
0.06
0.03
0.05
0.59
0.05
0.32
avg.
1.08
1.00
1.88
2.35
2.46
1.18
0.93
1.44
2.53
1.03
2.36
max.
°2 %
0.92
0.95
0.79
0.42
0.32
0.84
0.79
0.75
0.38
0.73
0.36
min.
1.03
0.96
1.48
1.80
2.29
1.00
0.82
1.13
2.24
0.89
1.68
avg.
2. 53
2 53
2 55
2 83
2 76
2 67
2 60
2 71
2 63
2 73
2 83
max.
2
2
co %
2.43
2.51
1.93
1.23
1.04
2.43
2.53
2.32
1.13
2.57
1.23
min.
g
2.48
2.52
2.14
1.83
1.26
2.56
2.58
2.55
1.41
2.63
1.94
avg.
4
0.87
0.80
0.95
0.99
0.97
0.88
0.80
0.88
1.00
0.82
0.96
max.
4
8
0.77
0.80
0.76
0.72
0.77
0.83
0.78
0.82
0.76
0.78
0.81
min.
CH%
Table III Data f o r Feed M i x t u r e o f 2% CO, 3% 0 and 1% l - C H i n Argon
19
1
21
Period min.
0.80
0.80
0.86
0.92
0.96
0.63
0.78
1.5
15
31
0.86 0.88
0.79 0.88
0.83 1.18
0.98
0.80
0.91
avg.
1
1
1
5
1
1
1
1
2
1
7
Relative Maxima Per C y c l e
0.687
1.49
1.32
1.24
1.10
0.845
1.25
1.01
0.996
0.720
0.797
7
Time-averaged CO O x i d a t i o n gmole/g sec χ 10
1.35
1.22
0.693
0.446
0.102
1.11
1.02
0.763
0.0475
0.774
0.327
Time-Ave raged C-Hp O x i d a t i o n gmoTe/g sec χ 108
3
C/3
w m ο I a ο c
3
1
m
ζ
δ
Η
> ο
»
>
Ο
M
Ο
00
39.
cuTLip AND KENNEY
Limit Cycle Phenomena
485
An additional elementary step must be added to equations (1) - (4) and (6) to account for the surface reaction of the 1-butene. Numerical simulations with an elementary step modeling approach discussed elsewhere, Cutlip (JJ[)» have confirmed limit cycles for this group of elementary steps when combined with dynamic material balance equations for the reactor. We are continuing experimental and modeling investigations on these interesting phenomena. Conclusions 1. The multiple steady state regions for carbon monoxide oxidation in oxygen rich feed mixtures can be generated by catalyst pretreatment with which lead t high reactio rate and by pretreatmen low reaction rate. Thi plat inum has appreciable adsorbed oxygen at the high rate and significant adsorbed carbon monoxide at the low rate. 2. No oscillations were observed for carbon monoxide oxidation. This may have resulted from the low turnover rates of this work which may have enabled gradientless reactor operation to be achieved with more certainty. 3. The dramatic oscillations observed during simultaneous carbon monoxide and 1-butene oxidation can be interpreted by including reversible adsorption and surface oxidation of the 1-butene occuring simultaneously with the elementary steps describing the carbon monoxide oxidation. Activation energies of surface rate processes which vary with surface coverages need not necessarily be used in modeling the experimental oscillations. 4. Multiple steady state and limit cycle experiments may well contain valuable quantitative information regarding surface rate processes in catalytic reactions and may contribute to improved dynamic catalytic models for process optimization and control. Acknowledgements Financial support was provided by the U. K. Science Research Council, the U. S. National Science Foundation and the University of Connecticut Research Foundation. Catalyst properties were evaluated in the laboratory of J. B. Butt, Northwestern University. Abstract Isothermal kinetic studies of carbon monoxide oxidation
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
486
which included the introduction of 1-butene were made in a gradientless reactor containing 10 grams of 0.5% platinum on alumina catalyst. In the absence of 1-butene, multiple steady state regions were found for oxygen rich feed streams, but no oscillations or limit cycles were observed. The addition of 1-butene to a feed mixture which previously had given a multiple steady state region yielded very dramatic oscillations (limit cycles) which can be explained by a proposed sequence of elementary steps occuring on the platinum surface.
Literature Cited 1. Wei, J. and Becker, E. R., Adv. in Chem. (1975) 143, 116 2. Carberry, J. J., "Chemical and Catalytic Reaction Engineering," McGraw-Hill 3. Benson, J. E. an , , (1965) , 4. Wentrcek, P., Kimoto, K, and Wise, H., J. Catal. (1973) 31, 279. 5. Schmitz, R. Α., Adv. in Chem. (1975) 148, 156. 6. McCarthy, E., et at., J. Catal. (1975) 39, 29. 7. Plichta, R. J., "Oscillations in the Oxidation of Carbon Monoxide on an Unsupported Platinum Catalyst," Ph. D. Thesis, University of Illinois, 1976. 8. Pikios, C. Α., and Luss, D., Chem. Eng. Sci. (1977) 32, 191. 9. Eigenberger, G., Preprints, 4th International/6th European Symposium of Chemical Reaction Engineering, Fed. Re. Germany, April, 1976. 10. Hanson, F. V., and Benson, J. E., J. Catal. (1973) 31, 471. 11. Cutlip, M. B., Hawkins, C. J., and Kenney, C.N., Chicago Meeting, Α. I. Ch. Ε., December, 1976.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
40 Kinetic Modeling for Oscillatory Catalytic Reactions M. SHEINTUCH Department of Chemical Engineering, Technion, Israel Institute of Technology, P.O. Box 4910, Haifa, Israel R. A . S C H M I T Z Department of Chemical Engineering, University of Illinois at Urbana-Champaign, 108 Roger Adams Laboratory, Urbana, I L 61801
In a recent publicatio intrinsic oscillations i sized the potential exploitation of combined theoretical and experimental studies of oscillatory behavior for obtaining new insights into catalytic reaction mechanisms and kinetics. In the present paper, we elaborate further on the subject of formulating and analyzing kinetic models which account for oscillatory behav ior, and we present some new experimental information for the oscillatory oxidation of CO on a platinum foil. As in reference 1, the analysis here is applied to models describable by two first order differential equations. The laboratory data reported were obtained from an isothermal gradientless CSTR of void volume 460 cm3 into which there was inserted a platinum foil of area 200 cm . Continuous measurements were made of the C O concentration in the effluent stream. The experimental system is described in detail elsewhere (2, 3). 2
2
Positive Feedback and Capacity Effects. Well-known theorems of Bendixon and Poincare lead to the conclusion that sustained periodic solutions can be ruled out for a second-order differential system of the form L dx/dt = F(x) i f it is impossible throughout the parameter space for the trace of the matrix L~l J , (where J is the Jacobian of F) to change sign from negative to positive values with F(x) = 0 and with the deter minant of IT J positive. Therefore, the magnitude of the capac ity elements in L and the magnitude and signs of partial deriva tives in J are crucial in ascertaining the possibility of oscil latory states. Notice that in general there is no need for'posi tive feedback" or "autocatalycity" to exist; that is to say, it is not necessary for the existence of oscillatory states that either 3F-j_/3x-^ or 3F2/8X2 become positive. The following simpler mathematical form applies to two models to be considered here. 1
© 0-8412-0401-2/78/47-065-487$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
488
The u n d e r l y i n g k i n e t i c models and r e a c t i o n mechanisms are d e s c r i b e d l a t e r . In both models, the v a r i a b l e x-j_ represents a gas-phase c o n c e n t r a t i o n , x , a surface c o n c e n t r a t i o n , and £ i s a surface capacitance f a c t o r . Therefore, the f u n c t i o n F^(x-j_ X2) accounts f o r f l o w terms ( i n a CSTR species balance equation) as w e l l as chemisorption and perhaps other r e a c t i o n terms. The f u n c t i o n F (xj_, X 2 ) , on the other hand, accounts o n l y f o r surface r a t e processes. The v a r i a b l e X2 i s a " l a t e n t " v a r i a b l e , not measurable i n s i t u i n the unsteady s t a t e p r e s e n t l y . For t h i s system, the above c r i t e r i o n r e q u i r e s t h a t the quan t i t y [ 3 F / 3 x + (l/Z )dF s t a t e s t o be p o s s i b l e become p o s i t i v e ; t h a t i s , p o s i t i v e feedback must e x i s t . F u r t h e r more, i n our experimental system, i a s very s m a l l . (We e s t i mated i t s value t o be as low as 0.01.) Thus the term c o n t a i n i n g the d e r i v a t i v e 3F2/3X2 i n the above expression dominates, and our a t t e n t i o n a p p r o p r i a t e l y focused on those r e a c t i o n mechanisms and k i n e t i c models f o r which 3F2/9x2 c o u l d be p o s i t i v e and hence f o r which the l a t e n t v a r i a b l e c o u l d a c c e l e r a t e the r a t e o f CO conver sion. I t i s worth mentioning t h a t t h i s s m a l l value of & might be expected t o l e a d t o r e l a x a t i o n o s c i l l a t i o n s . Such o s c i l l a t i o n s would be t y p i f i e d by sudden jumps i n the l a t e n t v a r i a b l e X2 w i t h corresponding jumps i n the r a t e o f change o f xj_. 2
c
2
1
1
c
Q
V
c
R e s u l t s o f A n a l y s i s o f Two Models The r e s u l t s of an a n a l y s i s o f two models, h e r e a f t e r r e f e r r e d t o as models 1 and 2, fashioned from the set o f r e a c t i o n s l i s t e d i n Table I are d e s c r i b e d b r i e f l y here. Assumptions made through out are t h a t oxygen i s present i n excess i n the gas phase and t h e r e f o r e constant at i t s feed v a l u e , and t h a t the e f f e c t o f the surface capacitance i s important o n l y i n the product £ dx2/dt — a l l other terms c o n t a i n i n g surface capacitances are neglected. In model 1 i t i s f u r t h e r assumed t h a t r e a c t i o n 1 i n Table I i s i n e q u i l i b r i u m , t h a t the reverse r a t e o f r e a c t i o n 2 i s n e g l i g i b l e , and t h a t r e a c t i o n s 5* 6 and 7 do not occur. We c o n s i d e r two subcases, models l a and l b , each o f which invokes the assump t i o n t h a t the r a t e - d e t e r m i n i n g steps are chemisorption of oxygen and the formation of CO2 — the formation of CO2 o c c u r r i n g o n l y b; way o f r e a c t i o n 3 i n model l a and o n l y by way o f r e a c t i o n k model l b . The r a t e expressions and equations f o r these models are givei i n Table I . In both cases, X]_ represents the reduced concentratic o f CO i n the gas phase, and X2 the f r a c t i o n a l surface coverage by chemisorbed oxygen. Under the assumptions s t a t e d , both cases y i e l d mathematical d e s c r i p t i o n s of the form given i n equation ( l ) c
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
SHEiNTucH AND SCHMITZ
40.
Oscillatory Catalytic Reactors
TABLE I. SUMMARY OF CO OXIDATION MODELS Stoichiometric Reactions (1) A s 1+
(2)
V.
s
. _ — 2s
r
(3) 2A A 1
2
A
+
s
chemisorption of CO and CL
i
2 A +ss ~
2 s
3 +
formation of C0 W
2 A
ls 2s
(5) 2Α +A +s χ
(6) 2 A
.2A s>
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
< >' <
6 b )
where Da
(6C)
s = o P ÎTTVI Da
ex
L
J
S So the steady state u , The reaction number Β i parameter by Eq. ( 5 c ) . Provided a highly exothermic reaction occurs, a steady state may be unstable. Stability considerations [1,2,3,4] lead to the definition of the two s t a b i l i t y parameters U
D 2 a =B
[ S «1 1 aÇ""" -T^r
J μ* S 1 <>> ^ T%-—SOT" (8) U
7
Q
=B
(l _i)2 S S _S μ μ whose signs determine whether a steady state i s stable or not. A steady state is stable i f α < ο and 3 > 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 <ε<0.03
the maximum percentage e r r o r Table I:
s
B u
Within the range α > ο , β > ο < u
+ 2 0 . 5 y V - 0 . 2 By*
2
s + 0.23
0.40
c
503
10
< Β < 30
0.2
< μ* <
0.6
( ω _ _ - u> )/ 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
<
R
101 ml/h < v 3 F e
665 s
< τ
300,8 k
< T
15,2
<
+
305 ml/h
< Q
< Β
1800 s
<
305,6 k
<
27,9
H
4,2 g-mole/1
< c 2°2
< 7,5 g-mole/1
0,08g-mole/l
< c
< 0,12g-mole/l
E
H +
Cpe
3+
=
0,02g-mole/l
Fig. 8 gives an impression of the frequency and the amplitude of the measured oscillations. The oscillation of the temperature i s extremely asymmetric. The Figures 9 and 10 show a -comparison of the experimental data of the oscillation period and the temperature amplitude with the computed results. The basis of these plots is a refined mathe matical model that takes the evaporation of water into account. The main assumption is to consider the oxygen stream to be saturated with water vapour. On this condition the heat per unit time removed from the reactor is given by
Qev = \
H
*
^·V
Wlth
Ύ
76Q - °H 0 P
=
2
(
2
3
)
2
As n 2 is proportional to the reaction rate, the following ex pression for the heat balance could be derived 0
1 dv = - / . 4 Da (l-u)[l-c- (v)] · exp ^ v
ξ
0
Y
" \ W) = °'
215
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
(24)
< ) 25
C H E M I C A L REACTION
508
ENGINEERING—HOUSTON
Table II: Comparison of some representative amplitudes of temperature computer
Eq.(18)
Δ
parameters
B=10 ε=0
u =0,80 μ*=0,297
comp (a) 0,275 (0,268)
B=10 ε=0
u =0,6 μ*=0,261
2,21 (0,976)
B=30 ε=0,02075
u =0,80 μ*=0,573
(0,827)
B=30 ε=0,02075
u =0,70 μ*=0,467
B=30 ε=0,02075
u =0,65 μ*=0,445
s
s
Eq.(ZO) A
0,44
1,22
2,67
1,79
3,82 (0,9990)
2,82
3,84
4,45 (0^99973)
3,19
4,33
s
s
s
Τ 3612| T
Figure 8.
Measured oscillations of temperature and conversion
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
Figure 9. Experimental period of oscillation in comparison with computer period
( Max" MiAomp T
T
[Grad]
Figure 10. Experimental temperature difference (Tmax — Tmin) vs. computed results for the refined mathematical model
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
509
CHEMICAL REACTION ENGINEERING—HOUSTON
510
The parameter γ(ν) was determined from the temperature dependence 0 f
P
( V )
H 0 On the basis of the refined heat balance (24) and Eq.(la) a lot of computer simulations were performed that led to a good agreement between numerical calculations and experimental findings as per Fig. 9 and 10. 2
Abstract The oscillatory behaviour of temperature and conversion in a cooled continuous-flow stirred tank reactor with a f i r s t order exothermic liquid phase reaction was studied. Approximate analytical relationship were developed to predict the period and the amplitud of operation conditions experimental findings. The agreement between theoretical computations and experimen tal observations was good. Notation a modified dimensionless amplitude of temperature, Eq. (17) A dimensionless amplitude of temperature, Eq. (11) Β reaction number, Eq. (5a) c concentration Cp specific heat of reaction mixture Da Damkbhler number Eq. (5d) Ε Activation energy F area for heat transfer to the coolant (-ΔΗ) heat of reaction ΔΗ heat of evaporation k(T ) rate constant at T kw heat transfer coefficient m mass transfer coefficient fiQ2 molar flow rate of oxygen ν
0
0
Ρμ 0
water vapour
Q
heat per unit time by evaporation
2
r R Τ u u ν V ν
ey
reaction rate universal gas constant temperature degree of conversion Eq. (2) time average of u Eq. (12) dimensionless temperature difference Eq. (2) volume of the reaction phase volume flow rate
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
41. HUGO AND WIRGES
OsciUations in Stirred Tank Reactor
511
Greek symbols α 3 γ ε Θ μ μ*
s t a b i l i t y parameter, Eq. (7) s t a b i l i t y parameter, Eq. (8) dimensionless pressure ratio, Eq. (23) reciprocal of the dimensionless activation energy, Eq.(5b) dimensionless time, Eq. (2) dimensionless heat transfer coefficient, Eq. (4) dimensionless cooling parameter, Eq. (5c)
-
oscillation period
ξ ρ τ ω
dimensionless heat ratio, Eq. (25) density of the reaction mixture mean residence time dimensionless frequenc Subscripts
comp exp Ε k L Lo R s ο
from computer solution referring to experimental data entrance of reactor coolant by linearized equations by linearized equations and α = ο from regression equation steady state referring to Τ , Eq. (3)
"Literature Cited" [1] WICKE,E., "Grundlagen der chem.Prozessregelung"p.54, Editors Oppelt and Wicke,Oldenbourg Verlag, München 1964 [2] HOFMANN,H.and HOFFMANN,U., Ind.Chim.Belge (1967)32, 326 [3] GILLES,E.D., the same book as [2], p. 111 [4] UPPAL,A., RAY, W.H. and POORE,A.B., Chem.Engng.Sci. (1974) 29, 967 and (1976) 31, 205 [5] DOUGLAS,J.M.and GAITONDE,N.Y.Ind.Engng.Chem.Fund.(1967)6,265 [6] LUUS,R.and LAPIDUS,L., Chem.Engng.Sci.,(1966) 21, 159 [7] HUGO,P., Proc.4th Europ.Symp.on Chemical Reaction Engng., Brussels 1968, p. 459 [8] BEEK,J., Chem. Engng.Sci. (1977) 32, 265 [9] WIRGES,Η.-P., Dissertation TU Berlin, 1977 [10] HAFKE,C., Diplomarbeit, TH Darmstadt, 1964 [11] HOFMANN,H., Proc.Third Europ.Symp. on Chemical Reaction Engng. Pergamon Press, Oxford 1965, p. 283
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
42 Effect of Periodic Operation on the Selectivity of Catalytic Reactions A. S. AL-TAIE and L. S. KERSHENBAUM Department of Chemical Engineering and Chemical Technology, Imperial College, London S.W.7, England
In recent years ther revealed that unsteady-stat proves superior to the conventional steady-state operation. The subject has been extensively reviewed by Bailey (1) who c l a s s i fied the periodic operation according to the ratio of the cycle time to the dominant time constant of the system. In spite of the numerous publications showing the potential of such periodic operations especially in the f i e l d of complex reactions, experimental studies are v i r t u a l l y non-existent. Of the few experimental works, Renken et a l . (2) compared the performance of a tubular reactor in which a single reaction, the hydrogenation of ethylene, took place, under periodic operation and at steady state. He reported an improvement of 60% in conversion. In another publication, Renken et a l . (3) showed experimentally that periodic operation can be used to eliminate the temperature problems associated with highly exothermic reactions, e.g. the oxidation of ethylene over a s i l v e r c a t a l y s t . I n other e x p e r i mental work Unni e t a l . (4) showed that p e r i o d i c v a r i a t i o n o f reactant composition improved the r a t e o f o x i d a t i o n of SO2 over a vanadium oxide by as much as 30%. Denis and Kabel (5) studied the c y c l i c o p e r a t i o n o f a heterogeneous r e a c t o r f o r the vapour phase dehydration of ethanol and observed that adsorption/desorption played a predominant r o l e i n the t r a n s i e n t s of the system. The above-mentioned work has d e a l t p r i m a r i l y w i t h s i n g l e r e a c t i o n systems. Although much of the t h e o r e t i c a l work has i n d i c a t e d that the r e a l p o t e n t i a l of p e r i o d i c o p e r a t i o n i s i n the improvement o f s e l e c t i v i t y i n complex r e a c t i o n systems, no e x p e r i mental work has yet been reported t o confirm these f i n d i n g s . I n t h i s work an experimental i n v e s t i g a t i o n has been conducted on the e f f e c t o f c y c l i n g the i n l e t feed compositions on the performance of an isothermal heterogeneous fixed-bed c a t a l y t i c r e a c t o r i n which a complex r e a c t i o n i s t a k i n g p l a c e . The r e a c t i o n system s t u d i e d was the hydrogénation of butadiene over a commercial n i c k e l catalyst.
©
0-8412-0401-2/78/47-065-512$05.00/0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
42.
AL-TAiE AND KERSHENBAUM
Selectivity of Catalytic Reactions
513
Experimental The experimental system i s o u t l i n e d i n F i g . 1 and c o n s i s t s of three main p a r t s - a r e a c t a n t s feed system, the fixed-bed c a t a l y t i c r e a c t o r , and the gas a n a l y s i s system. A l l feed gases were s u p p l i e d by the B r i t i s h Oxygen Co.; 1, 3-Butadiene was s t a t e d to be 99.6% pure, Hydrogen and Nitrogen were 99.9% pure. Normal, t r a n s , and c i s Butènes used f o r c a l i b r a t i o n purposes were 99.8% pure. The feed gases were thoroughly mixed i n a j e t mixer before e n t e r i n g the r e a c t o r . This a l s o served to damp out any pressure waves d u r i n g p e r i o d i c o p e r a t i o n . The p e r i o d i c v a r i a t i o n of the r e a c t a n t composition was achieved by a c t u a t i n g two s o l e n o i d v a l v e s through an autotimer which gave two s i g n a l s which, i n these experiments, were 180° out of phase. The r e a c t a n t s stream a f t e r p a s s i n g through the mixer entered the preheater, which wa water bath maintained a y The r e a c t o r was made of 10 mm ID brass tube and had a length of 0.25 m. Four copper-constant thermocouples, placed a t i n t e r v a l s o f 5 cm along the r e a c t o r a x i s , were connected t o a Data Logger w i t h a punch tape output. The r e a c t o r was packed w i t h a commercial 23% N i on K i e s e l g u h r c a t a l y s t s u p p l i e d by Harshaw Chemical Company. I t was crushed to mesh s i z e 18-22 (mean d i a meter 778 microns) and d i l u t e d by an i n e r t packing of the same dimension ( d i l u t i o n r a t i o 3:2 by volume) which e f f e c t i v e l y e l i m i n a t e d any bulk temperature r i s e along the r e a c t o r . In a d d i t i o n , the feed gas always contained 60% d i l u e n t (nitrogen) which f u r t h e r reduced bulk temperature r i s e s and minimized l o c a l hot spots on the c a t a l y s t . The c a t a l y s t was found to be a c t i v e a t temperatures greater than 30°C and no a c t i v a t i o n was r e q u i r e d . I t was normally stored under a blanket of n i t r o g e n when not i n use. The e f f l u e n t stream from the r e a c t o r could be e i t h e r sent t o a wet-test meter, o r d i v e r t e d t o the vent. P r o v i s i o n s were a l s o made f o r sampling of the product stream i n a gas chromatograph during the steady-state runs o r the c o l l e c t i o n of an e f f l u e n t sample i n a s p e c i a l purpose c o l l e c t i o n chamber d u r i n g the c y c l i c runs. S i m i l a r l y there was a by-pass arrangement f o r the a n a l y s i s of the r e a c t a n t s stream f o r the s t e a d y - s t a t e runs and a r e a c t a n t c o l l e c t i o n chamber f o r the c y c l i c runs. The steady-state gas analyses were done by c o n v e n t i o n a l chromatography, but f o r the p e r i o d i c runs, the i n l e t and e x i t analyses were performed on an i n t e g r a t e d sample. Any d i s c r e t e sample a n a l y t i c a l technique such as chromatography has c e r t a i n disadvantages under t r a n s i e n t o p e r a t i o n . These disadvantages are a m p l i f i e d when one i s d e a l i n g w i t h p e r i o d i c o p e r a t i o n a t h i g h f r e q u e n c i e s , e s p e c i a l l y when the dead-time and e l u t i o n time are large compared w i t h the p e r i o d of the input s i g n a l . In t h i s work, we overcome these d i f f i c u l t i e s by c o l l e c t i n g the r e a c t o r e x i t gas over many p e r i o d s to c a l c u l a t e mean compositions. A modified water-displacement method was used; t h i s assured that the product was being c o l l e c t e d a t a constant flow r a t e , d e s p i t e v a r i a t i o n s
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
514
CHEMICAL REACTION ENGINEERING—HOUSTON
i n l i q u i d l e v e l i n the c o l l e c t i o n chamber (_6 ). The c o l l e c t e d sample was then analyzed by chromatography u s i n g a column packed w i t h 33% dimethyl-sulpholane on chromosorb P. The c o l l e c t i o n and sampling procedure was t e s t e d by comparing analyses of known compositions under non-reactive c o n d i t i o n s . The e r r o r i n the compositions was l e s s than ± 0.8%. The experimental runs were d i v i d e d i n t o two main c a t e g o r i e s , steady-state and p e r i o d i c runs. The purpose of the steady-state runs was to o b t a i n e x p e r i m e n t a l l y the value and c o n d i t i o n s o f maximum steady-state y i e l d . The y i e l d under p e r i o d i c o p e r a t i n g c o n d i t i o n s was always compared w i t h t h i s maximum achievable under steady-state c o n d i t i o n s . During each o f these runs the reactant flow r a t e s were s e t t o the r e q u i r e d v a l u e . A f t e r a l l o w i n g time f o r the system to reach the s t e a d y - s t a t e the e f f l u e n t v o l u m e t r i c flow r a t e was measured and feed gas samples wer The temperature p r o f i l e along the r e a c t o r was c o n t i n u o u s l y moni tored t o check on the i s o t h e r m a l i t y o f the r e a c t o r . Steady-state runs were conducted a t four residence time l e v e l s : 0.273, 0.352, 0.54 and 1.33 seconds. For each residence time, a s e t o f t e n runs were made a t d i f f e r e n t ^rCt+Hg r a t i o s , keeping the d i l u e n t composition (nitrogen) always constant at ^ 60%. For a l l runs, the o p e r a t i n g c o n d i t i o n s were a temperature o f 70°C (± 0.5°C) and a pressure o f 1 p s i g (1.07 b a r ) . In the case o f the p e r i o d i c runs, the f l o w r a t e s of the two r e a c t a n t s H2 and Ci^He were d i v i d e d i n t o two s e c t i o n s . A p o r t i o n of the feed of each r e a c t a n t was f e d at a constant r a t e and the balance i n a p e r i o d i c mode. The n i t r o g e n flow r a t e was maintained at ^ 60% of the t o t a l v o l u m e t r i c r a t e throughout each s e t o f c y c l i c runs. The c y c l i n g p o l i c y was such that the mean composit i o n , the o v e r a l l v o l u m e t r i c flow r a t e and residence time, temp e r a t u r e and pressure were i d e n t i c a l t o those a t the corresponding optimum steady s t a t e c o n d i t i o n s . Each p e r i o d i c run was s t a r t e d by a d j u s t i n g the flow r a t e s of the f i x e d p o r t i o n s of the r e a c t a n t s t o the r e q u i r e d v a l u e . Then the flow r a t e s o f the c y c l e d s e c t i o n s were s e t , by s w i t c h i n g i n t u r n , one of the s o l e n o i d v a l v e s , keeping the other switched o f f . The c y c l e time was s e t by programming the autotimer drum t o give the r e q u i r e d c y c l e time. A 15 minute i n t e r v a l was adequate f o r the system t o reach pseudo-steady-state. The product sample was then c o l l e c t e d , and the temperature p r o f i l e along the r e a c t o r a x i s was c o n t i n u o u s l y monitored t o check the i s o t h e r m a l i t y o f the reactor. Reactor Performance. I n the absence of d e t a i l e d economic data, the performance o f a chemical r e a c t o r can be measured i n terms o f conversion, s e l e c t i v i t y , y i e l d , or some combination o f these. The choice of a s u i t a b l e performance index w i l l depend upon the p a r t i c u l a r a p p l i c a t i o n , although maximum s e l e c t i v i t y g e n e r a l l y corresponds t o n e g l i g i b l e conversion i . e . small product-
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
42. AL-TAiE AND KERSHENBAUM
Selectivity of Catalytic Reactions
515
i o n r a t e of the d e s i r e d products. O b j e c t i v e f u n c t i o n s considered i n t h i s work were: ( i ) y i e l d ; ( i i ) s e l e c t i v i t y subject to the c o n s t r a i n t that the y i e l d i s equal to the maximum achievable a t s t e a d y - s t a t e ; ( i i i ) the d i f f e r e n c e i n production r a t e of d e s i r e d and undesired products (7). (The y i e l d i s defined here as the moles of the d e s i r e d intermediate produced per mole o f reactant fed t o the r e a c t o r ) . For the competing/consecutive hydrogénation of butadiene, the conversion, s e l e c t i v i t y , and y i e l d can be c a l c u l a t e d from experimental measurement of the mole f r a c t i o n of each component i n the e x i t and i n l e t gas streams. In a l l cases, care was taken to c o r r e c t f o r f r a c t i o n a l volume shrinkage upon r e a c t i o n , which would otherwise have introduced a systematic e r r o r i n t o the c a l c u l a t i o n . For f a i r comparison s t a t e and p e r i o d i c o p e r a t i o n must be s a t i s f i e d . The p e r i o d i c o p e r a t i o n performance index should be compared to i t s optimum steady s t a t e counterpart, as there i s no p o i n t i n using p e r i o d i c o p e r a t i o n to achieve something which can otherwise be r e a l i z e d through the conventional steadys t a t e mode of o p e r a t i o n . The same amount of r e a c t a n t s should be used under both modes of o p e r a t i o n . The same r e a c t i o n c o n d i t i o n s , e.g. pressure, temperature and residence time should apply. Theoretical The hydrogénation of Butadiene proceeds according to the f o l l o w i n g elementary steps (Bond ( 8 ) ) . C H U
6
k
"
ki + s
Q
« W
S
(C
l t
+
H
2
^ ( C , H
1
0
)
s
k -l k
(Ci»H ) 6
s
+ H
*
S !
^(C,H )
2
8
S
H
1 0
)
s
^
MC H 6
1 0
)
+ s
k (C^Hs) W
^
C^Hs + s
S
k From the mechanism i t can be seen that m a t e r i a l i s added to or depleted from the gas phase by a d s o r p t i o n / d e s o r p t i o n w i t h the exception of hydrogen which i s assumed to be consumed d i r e c t l y from the gas phase. I n f o r m u l a t i n g a t h e o r e t i c a l model f o r the system i t was assumed that the a d s o r p t i o n / d e s o r p t i o n k i n e t i c s played an important r o l e i n the dynamics of the p e r i o d i c o p e r a t i o n and these k i n e t i c s were incorporated i n t o the dynamic equations. Furthermore, i t was assumed that there was n e i t h e r bulk nor pore d i f f u s i o n a l heat and mass t r a n s f e r r e s i s t a n c e s , that the r e a c t o r was isothermal (both i n the bulk gas phase and l o c a l l y ) and that the flow p a t t e r n i n the r e a c t o r could be approximated by plug flow. Most of the above assumptions ( i . e . p l u g f l o w , bulk isothermal c o n d i t i o n s , no pore d i f f u s i o n l i m i t a t i o n s ) could be 3
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
516
CHEMICAL REACTION ENGINEERING—HOUSTON
v e r i f i e d by simple independent experiments o r by w e l l accepted c o r r e l a t i o n s . Under these c o n d i t i o n s and assuming that the a d s o r p t i o n / d e s o r p t i o n f o l l o w s the Langmuir monolayer theory, d i f f e r e n t i a l mass balances on the gas and s o l i d phases y i e l d Gas phase: 3x.
3x.
_L
+ £_JL ν at
3z
•(ΡΘ
x.k. - k .θ.)(1-ε)ρ ν ι ι - i l c
1,3,4
(1)
Hydrogen, i = 2, i s removed d i r e c t l y from the gas phase and hence ^ 3x
3x2
r
2
£
+
=
(1-ε)ρ
_s_2
ç
(2)
vp_
ν 3t
3z
Adsorbed phase: (ΡΘ x.k. - k .Θ.) + r .
3Θ.
ι
V
1 1
-11
SI
3t
(3)
where r ^ i s the r a t e o f surface r e a c t i o n o f component i , where g
0*
*-l
r Sl
r r r
=
s
2
s
3
-1
-1
+1
-1
s 0
si
S2
si
k
2
(4)
+1
ΡΘ x 51
k
1 2
ΡΘ χ 52
3 2
The a d s o r p t i o n / d e s o r p t i o n r a t e constants were e x p e r i m e n t a l l y meas ured u s i n g a chromatographic technique (9) and the surface r e a c t i o n r a t e constants were obtained independently from a n o n - l i n e a r r e g r e s s i o n o f the data from the steady s t a t e runs. The set o f coupled h y p e r b o l i c p a r t i a l d i f f e r e n t i a l equations ( l ) - ( 4 ) were solved n u m e r i c a l l y by the method o f c h a r a c t e r i s t i c s . The high degree o f c o u p l i n g i n the d i f f e r e n t c h a r a c t e r i s t i c d i r e c t i o n s r e q u i r e d that an i t e r a t i v e method be used f o r the numerical s o l u t i o n (6). Results Steady-State Runs. Four l e v e l s o f residence times were employed: 0.273, 0.352, 0.54 and 1.33 seconds. Each set o f runs was conducted over a wide range o f r a t i o of r e a c t a n t s i n the feed stream, keeping the n i t r o g e n composition constant throughout a t ^ 60%, and the water bath temperature a t 70°C. The o b j e c t i v e o f these runs was t o e s t a b l i s h e x p e r i m e n t a l l y the c o n d i t i o n s f o r optimum steady-state y i e l d , and t o determine the k i n e t i c s
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
42.
AL-TAiE AND KERSHENBAUM
Selectivity of Catalytic Reactions
517
of the r e a c t i o n s . The r e s u l t s o f these steady-state runs are presented i n F i g s . 2 to 4 i n the form of c o n v e r s i o n , s e l e c t i v i t y , and y i e l d vs. H2: Butadiene r a t i o . From F i g . 4, i t can be seen that the optimum y i e l d value f o r each residence time occurs at a given H : Butadiene r a t i o which i s s h a r p l y d e f i n e d . The values o f the conversion and s e l e c t i v i t y which correspond to the maximum y i e l d can be read from F i g s . 2 and 3. I t i s more convenient to transform these steady s t a t e data i n t o a p l o t which i s independent o f residence times and feed composition. L e v e n s p i e l (10) gave a general time-independent, p l o t f o r second-order s e r i e s - p a r a l l e l r e a c t i o n s . However, i t can be shown that such a p l o t i s a l s o v a l i d f o r Langmuir-Hinshelwood k i n e t i c s , i f the denominators are the same f o r both r e a c t i o n s . F i g s . 5 and 6 show u n i v e r s a l s t a t e y i e l d and s e l e c t i v i t times and H : Butadiene r a t i o s l e s s than 6 (runs a t the higher r a t i o s were d i f f i c u l t to reproduce because of u n c e r t a i n t i e s i n chemical analyses caused by the high d i l u t i o n ) . I t can be seen from these two p l o t s that the optimum steady-state y i e l d i s 30% and the corresponding conversion and s e l e c t i v i t y are 50% and 60% respectively. The steady-state data were a l s o used to estimate the best values o f the surface r a t e c o n s t a n t s , k and k . This was 2
2
SI
S2
.
.
achieved by a n o n - l i n e a r weighted l e a s t squares e s t i m a t i o n t e c h nique, given the e x p e r i m e n t a l l y obtained values of the a d s o r p t i o n / d e s o r p t i o n r a t e constants. These constants were subsequently used i n the s i m u l a t i o n of the c y c l i c runs. C y c l i c Runs. Having e s t a b l i s h e d the i n l e t r a t i o of H : Buta diene f o r which the s t e a d y - s t a t e y i e l d i s maximised f o r a given residence time, the c y c l i c runs were c a r r i e d out such that the mean value o f the feed compositions were as near as p o s s i b l e t o t h e i r optimum steady-state v a l u e s . The mole f r a c t i o n s of H and Butadiene were c y c l e d out of phase i n a symmetrical square wave f a s h i o n . Such symmetrical wave forms need not be the optimum p e r i o d i c o p e r a t i o n . Indeed, Farhad Pour et a l . (7) demonstrated t h e o r e t i c a l l y that i t was p o s s i b l e to o b t a i n f u r t h e r improvement i n the s e l e c t i v i t y of s e r i e s - p a r a l l e l r e a c t i o n s i n a CSTR when asymmetrical r a t h e r than symmetrical square waves are considered. T h e o r e t i c a l l y the search f o r the optimum wave modulation, o r the number of switches over one c y c l e time, can be computed by search methods o r o p t i m i s a t i o n r o u t i n e s . However, i n t h i s work we a r b i t r a r i l y l i m i t e d ourselves t o symmetrical square waves which are 180 out of phase a c c e p t i n g that such a c o n f i g u r a t i o n may, indeed, be q u i t e f a r from the optimum p e r i o d i c mode. The p e r i o d i c o p e r a t i o n was conducted over the whole range o f disturbance amplitude, λ(0-100%) and c y c l e time, τ (2-30 seconds). Two l e v e l s of residence time were employed, 0.27 and 0.54 seconds. T y p i c a l r e s u l t s f o r these p e r i o d i c runs are presented i n F i g s . 7-9 i n the form of time average conversion, s e l e c t i v i t y and y i e l d 2
2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
518
CHEMICAL REACTION ENGINEERING—HOUSTON
TO VEUT
Figure 1. Diagram of experimental system
Figure 2. Steady-state conversion of Cj,H
6
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
AL-TAiE AND KERSHENBAUM
Selectivity of Catalytic Reactions
Figure 3.
Steady-state selectivity
Figure 4.
Steady-state yield of C^H
8
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
520
• X=133S
0
10
20
Figure 5.
30
40 50 60 CONVERSION %
70
80
90
100
Composite plot of yield vs. conversion
CONVERSION % Figure 6.
Composite plot of selectivity vs. conversion
Figure 7.
Mean conversion under periodic operation
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
AL-TAiE AND KERSHENBAUM
Figure 8.
Selectivity of Catalutic Reactions
Mean selectivity under periodic operation
_
1
8
Figure 9.
— j — , — , — , — , — , — , — j _
12
16 20 CYCLE TIME s
24
28
32
Mean yield under periodic operation
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
522
CHEMICAL REACTION
ENGINEERING—HOUSTON
f o r one residence time. They are compared t o the corresponding steady-state values a t optimum y i e l d given i n the previous s e c t i o n . I t can be seen that r e l a t i v e l y high improvements i n e i t h e r y i e l d , s e l e c t i v i t y o r both can be obtained depending on the choice o f amplitude, c y c l e time and the r e a c t o r residence time. Faced w i t h t h i s wide spectrum o f improvements we must s t a t e our o b j e c t i v e c l e a r l y . Choosing y i e l d as a performance index, i t can be seen that as much as 20% improvement i n y i e l d i s p o s s i b l e depending on the choice o f amplitude, c y c l e time and residence time. On the other hand, improving the s e l e c t i v i t y alone i s meaningless, as t h i s can l e a d t o i n f i n i t e s i m a l convers ion. Consequently, f o r a meaningful comparison between steadys t a t e and p e r i o d i c o p e r a t i o should impos th c o n s t r a i n t that the r e a c t o r performanc values corresponding t optimu s t e a d y - s t a t e , i v i t i e s a t t a i n a b l e under p e r i o d i c o p e r a t i o n f o r each residence time and amplitude show that an i n c r e a s e of up to 24% can be achieved w h i l e m a i n t a i n i n g the y i e l d a t i t s optimum steady-state value. Thus, p e r i o d i c o p e r a t i o n i s capable o f improving both the q u a l i t y and the q u a n t i t y o f a d e s i r e d product over i t s best steady-state value. This i s reminiscent o f the work o f Cannon et a l . (11) who observed t h a t , depending on the choice of the l i q u i d flow time and the vapour flow time, i t i s p o s s i b l e t o improve e i t h e r the e f f i c i e n c y o r the c a p a c i t y o f a d i s t i l l a t i o n column by p e r i o d i c o p e r a t i o n . To complete the p i c t u r e over the whole range of f r e q u e n c i e s , a set o f runs was made under c o n d i t i o n s of slow c y c l i n g (τρ -> °°). In a l l cases, the conversion and y i e l d under slow c y c l i n g was always i n f e r i o r t o the optimum steady-state values This i s t o be expected as t h e i r response surfaces are concave. A t y p i c a l r e s u l t of the s i m u l a t i o n o f the r e a c t o r behaviour corresponding t o c o n d i t i o n s i n F i g s . 7-9 i s shown i n F i g . 10. These r e s u l t from the numerical s o l u t i o n o f the dynamic equations (1) - (4) w i t h the r e l e v a n t r a t e constants f o r adsorption/desorp t i o n and surface r e a c t i o n , e q u i l i b r i u m constants and c a t a l y s t c a p a c i t y obtained by independent experimental measurements (no f i t t i n g o f the p e r i o d i c data was attempted). The r e s u l t s c l e a r l y i n d i c a t e a general agreement w i t h the experimental data. The s i m u l a t i o n s are described and discussed i n d e t a i l elsewhere (6, 12). Discussion The r e s u l t s presented above i l l u s t r a t e that s i g n i f i c a n t improvement can be achieved i n the performance of r e a c t o r s w i t h complex r e a c t i o n s . Furthermore, t h i s performance could be e x p l a i n e d by p o s t u l a t i n g that the k i n e t i c s o f adsorption/desorpt ion played an important r o l e i n the system dynamics i n general and i n t h i s improvement, i n p a r t i c u l a r . N e v e r t h e l e s s , there are other models which could a l s o be c o n s i s t e n t w i t h t h i s behaviour,
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
AL-TAiE AND KERSHENBAUM
0
Figure 10.
4
8
Selectivity of Catalytic Reactions
12 16 CYCLE TIME S
20 '
24
28
Simulation of mean yield and selectivity under periodic operation
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
524
and an attempt was made to confirm that the adsorption e f f e c t s were indeed predominant. A set of step and pulse responses was performed under both r e a c t i v e c o n d i t i o n s ( i . e . w i t h both reactants present) and under non-reactive c o n d i t i o n s . I t was seen t h a t , i n both cases, the form of the responses and the mean and spread of the response curves were n e a r l y i d e n t i c a l . This i m p l i e d that the same process (adsorption/desorption) was respon s i b l e f o r the dynamics of the system under both r e a c t i v e and nonr e a c t i v e c o n d i t i o n s . Furthermore, i t appeared that l o c a l thermal e f f e c t s were not the main f a c t o r i n the improvement of perform ance, although they may have been a c o n t r i b u t i n g f a c t o r . Having p o s t u l a t e d a mechanism f o r the r e a c t o r dynamics, p o s s i b l e reasons f o r the improvement i n the r e a c t o r conversion, y i e l d and/ or s e l e c t i v i t y can be discussed q u a l i t a t i v e l y I t can be argued that under c y c l i c o p e r a t i o h o l d i n g more reactant (Butadiene at the corresponding s t e a d y - s t a t e . Hence over the hydrogen-rich h a l f of the c y c l e i t i s p o s s i b l e to hydrogenate more of the Butadiene. S i m i l a r l y , because of the strong Butadiene adsorption Butènes are desorbed before they have a chance to react f u r t h e r to Butane w i t h consequent increases i n s e l e c t i v i t y . Conclusion. The work has demonstrated e x p e r i m e n t a l l y that s i g n i f i c a n t improvement i n the y i e l d and/or s e l e c t i v i t y can be obtained by o p e r a t i n g a r e a c t o r w i t h competing/consecutive r e a c t i o n s i n a p e r i o d i c mode. The main cause of t h i s improvement appears to be the resonance induced by the a d s o r p t i o n / d e s o r p t i o n k i n e t i c s during p e r i o d i c o p e r a t i o n . Notation
k r R t ν x
i
ε
τ
s2
a d s o r p t i o n r a t e constant desorption r a t e constant surface r e a c t i o n r a t e constants t o t a l pressure net r a t e of surface r e a c t i o n r a t e of surface r e a c t i o n f o r hydro génation of butadiene, butene time l i n e a r gas v e l o c i t y mole f r a c t i o n of component i c a p a c i t y of c a t a l y s t voidage surface coverage f o r component i amplitude catalyst density molar gas d e n s i t y mean residence time p e r i o d of input disturbance
kmol/kg.s.bar kmol/kg. s kmol/kg.s.bar bar kmol/kg. s kmol/kg,s
Subscript i r e f e r s to component: 1=Ο^Η ; 2=H ; 3=0^118; 6
2
s ml s kmole/kg
3
kg/m kmol/m s s 3
^=C^IQ
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
42. AL-TAiE AND KERSHENBAUM
Selectivity of Catalytic Reactions525
Literature Cited (1) Bailey J.E., Chem. Eng. Commun., (1973), 1, 111, (2) Renken A., Helmrich H. and Schlügerl Κ., Chem. Ingr. Techn., (1974), 46, 647. (3) Renken Α . , Müller M. and Wandrey C., Proc. 4th Intl. Conf. Chem. Reac. Eng., (1976), Heidelberg, 107. (4) Unni M.P., Hudgins, R.R. and Silveston P.L., Can. J. Chem. Eng., (1973), 51, 623. (5) Denis G.H. and Kabel R . L . , A.I.Ch.E. Jl. (1970), 16, 972. (6) Al-Taie A.S., Ph.D. Thesis, University of London, 1977. (7) Farhad-pour F.A. and Gibilaro L.G., Chem. Eng. Sci., (1975), 30, 735. (8) Bond G.C., "Catalysi b Metals" Academi Press N.Y (1962) (9) Smith J.M. and Schneide (10) Levenspiel O., "Chemical Reaction Engineering", Wiley, (1972). (11) Cannon M.R., Oil and Gas J., (1956), 55, 68 (12) Αl-Taie A.S. and Kershenbaum L., in press
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
43 Dynamic Studies of Acetylene Hydrogenation on Nickel Catalysts M . R. B I L I M O R I A and J. E . B A I L E Y Department of Chemical Engineering, University of Houston, Houston, TX 77004
Several benefits including improved selectivity, increased conversion, and reduced sensitivity may in some cases be realized by intentional periodic operation of chemical reactors [1-6]. These alterations in reactor performances arise because, in dy namic operation, the governing rate processes may assume different relationships than can occur in the more constrained steady state case. Thus, in addition to revealing promising new operational policies for chemical reactors, unsteady-state reaction studies may provide valuable insights into the fundamental properties of the reaction system. This study focuses on the vapor-phase catalytic hydrogenation of acetylene to ethylene and ethane: C H + H --> C H C H + H --> C H 2
2
2
2
4
2
4
2
2
6
Bond [7], Komiyama and Inoue [8], and several others have studied this reaction sequence using nickel catalysts, and Bond et al. [9] have reported that the ethylene s e l e c t i v i t y S varies with hy drogen p a r t i a l pressure p according to h2
S = 1 - Κpnh where Κ = a constant and 2
0
(1)
Since S is a convex function of p , it appears that fluctuations h2
in p
H2
w i l l have a b e n e f i c i a l e f f e c t on ethylene s e l e c t i v i t y .
This hypothesis has been corroborated i n s i m u l a t i o n s t u d i e s based upon the k i n e t i c s o f Komiyama and Inoue [ 8 ] . Lee's c a l c u l a t i o n [10] i n d i c a t e s t h a t s u b s t a n t i a l improvements i n ethylene s e l e c t i v i t y may be obtained by c y c l i n g the feed hydrogen c o n c e n t r a t i o n to a p e r f e c t l y mixed, isothermal continuous flow r e a c t o r w i t h a ©
0-8412-0401-2/78/47-065-526$05.00/0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
43.
BiLiMORA AND BAILEY
Acetylene Hydrogénation on Nickel Catalysts 527
p e r i o d o f the order o f one-half the mean r e a c t o r residence time. Although i n t r a p e l l e t d i f f u s i o n a l e f f e c t s were considered by Lee, i t i s important t o note t h a t other dynamic phenomena which might occur w i t h i n the porous c a t a l y t i c s o l i d were t o t a l l y neglected i n h i s model. Experimental M a t e r i a l s and Methods The r e a c t i o n was conducted a t a pressure o f 108.2 kN/m^ i n a continuous-flow, s p i n n i n g basket (104.7 rad/s) s t a i n l e s s s t e e l r e a c t o r w i t h a mean residence time o f 66 s. Nearly i s o t h e r m a l o p e r a t i o n at 439 Κ was maintained by automatic on-off c o n t r o l o f a h e a t e r i n an a i r - c o o l e d j a c k e t surrounding the r e a c t o r . The gases used i n the experiment Lind b 145 Atomi absorp t i o n grade acetylene (>99.6%) (>99.99%) and p r e p u r i f i e grad n i t r o g e (>99.997%) Acetylen feed t o the r e a c t o r was maintained constant a t 0.5 cm /s, whereas the f l o w - r a t e s o f hydrogen and i n e r t n i t r o g e n were adjusted i n a complementary manner so as t o maintain t o t a l gas feed r a t e o f 5 cm /s. In p e r i o d i c experiments, t h e i n l e t hydrogen flow r a t e u ( t ) was v a r i e d i n a bang-bang f a s h i o n as f o l l o w s : 3
3
3 .625 cm /s
u(t) = ^
f o r 0 <_ t < γτ
G.250 cm /s
(2)
f o r γτ <_t < τ.
Here τ i s the length o f one c y c l e o r p e r i o d , and γ i s the f r a c t i o n o f τ f o r which the hydrogen feed r a t e i s a t the upper l e v e l . The manipulated input u i s evaluated at subsequent times according to the p e r i o d i c i t y r u l e u ( t ) = u ( t + τ)
f o r t _> 0
(3)
The mean o r time-average hydrogen flow r a t e i s 3
ïï = 0.25 + 1.375γ cm /s
(4)
and the n i t r o g e n feed f l o w - r a t e w(t) i s s p e c i f i e d by W
( t ) = 4.5 - u ( t )
3
cm /s.
(4)
These v a r i a t i o n s i n feed hydrogen and n i t r o g e n concentrations were generated without any a p p r e c i a b l e pressure f l u c t u a t i o n s and at constant v o l u m e t r i c flow by a dosing system composed o f a m u l t i channel e l e c t r o n i c t i m e r , metering v a l v e s , and s o l e n o i d valves as shown i n Figure 1. The c a t a l y s t s used i n the experiments, Harshaw NÎ-0707T ( C a t a l y s t I) and G i r d l e r G52 ( C a t a l y s t I I ) , were crushed t o a s i z e o f 0.84-1.2 mm and p r e t r e a t e d by soaking i n 5% (wt.) s o l u t i o n o f N a S 0 i n H^O f o r 24 h as recommended by 2
2
3
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
528
Komiyama and Inoue [ 9 ] . Before each run, the c a t a l y s t was a c t i vated " i n s i t u " i n a hydrogen stream at 477 Κ f o r 6 h. From time to time, the e f f l u e n t concentrations from the r e a c t o r were measured using a 0.25 cm^ sampling valve and a f l a m e - i o n i z a t i o n type gas chromatograph w i t h a Porapak Ν column and n i t r o g e n c a r r i e r at 313 K. The r e s u l t i n g peaks from the chro matograph were recorded on a s t r i p - c h a r t and i n t e g r a t e d auto m a t i c a l l y by a d i g i t a l i n t e g r a t o r . The product gas stream was a l s o monitored continuously by a v a r i a b l e - f i l t e r i n f r a - r e d ana l y z e r w i t h a flow-through c e l l , and acetylene, ethylene and ethane were detected at 3.05, 5.25 and 6.55 ( a l l pm), r e s p e c t i v e l y . The r e a c t o r i s s a i d to be i n a p e r i o d i c s t a t e when a l l the s t a t e v a r i a b l e s s a t i s f y the c o n d i t i o n x. (t) = x. (t 1
'
1
where tp i s d e f i n e d as the s t a r t - u p time r e q u i r e d to reach p e r i o d i c c o n d i t i o n s . The o s c i l l a t i n g e f f l u e n t concentrations may be damped by a surge tank (see Figure 1) to o b t a i n a t i m e - i n v a r i a n t process e f f l u e n t which may be d i r e c t l y compared to the products o f s t e a d y - s t a t e r e a c t o r o p e r a t i o n . The time-average e f f l u e n t concentrations may a l s o be c a l c u l a t e d using 1 ft +τ x. = — Ρ x.(t)dt ι τ tn
(7)
1
and sets o f instantaneous c o n c e n t r a t i o n data which span the p e r i od. These computed values were c o n s i s t e n t l y i n good agreement w i t h d i r e c t surge-tank measurements. Results and D i s c u s s i o n The experimental r e s u l t s are presented i n Figures 2 through 8. Figure 2 i s a comparison o f steady-state compositions w i t h time-average values obtained by c y c l i n g w i t h d i f f e r e n t periods f o r C a t a l y s t I . This c a t a l y s t showed n e g l i g i b l e f o u l i n g w i t h almost constant a c t i v i t y , a r e s u l t c o n s i s t e n t w i t h conventional B.E.T. s u r f a c e - a r e a measurements which gave values o f -125 129 m /g before and a f t e r r e a c t i o n . The data show that p e r i o d i c o p e r a t i o n r e s u l t s i n i n c r e a s e d conversion f o r τ=60 s, τ=180 s and τ=300 s, w i t h the maximum e f f e c t obtained f o r the longest p e r i o d . In a d d i t i o n , the data f o r τ=300 s show a s i g n i f i c a n t improvement i n both ethylene and ethane y i e l d s . This dependence on c y c l i n g p e r i o d i s q u i t e d i f f e r e n t from L e e s p r e d i c t i o n s (optimum p e r i o d ~ 1/2 mean residence time = 33 s) and suggests that the c a t a l y s t phase dynamics cannot be neglected f o r t h i s system. The instantaneous concentrâtion-time p r o f i l e s obtained dur i n g p e r i o d i c o p e r a t i o n w i t h C a t a l y s t I f o r τ=300 s are shown i n Figure 3. A l l these curves were obtained by making 15 d i s c r e t e 2
1
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
BiLiMORA AND BAILEY
Acetylene Hydrogénation
on Nickel Catalysts
INTEGRATOR
Figure 1.
Experimental reaction system highlighting cyclic feed makeup apparatus and effluent analysis equipment
Δ ACETYLENE ο ETHYLENE • ETHANE
ζ Lu 3
ο <
STEADY STATE PERIODIC TIME
007
006
05
10
15
20
25
RATIO OF Hg/CgHg IN
30 FEED
Figure 2. Steady-state (solid line) and periodic (broken lines—see legend) effluent hydrocarbon distributions for various time-average hydrogen/ acetylene feed ratios for Catalyst I
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
530
E T H A N E E T H Y L E N E - T=300S_ 77= 13/15
ACETYLENE 0.08
0
1/3
2/3
1.0
NORMALIZED
4/3
5/3
TIME
t/τ
2.0
Figure 3. Instantaneous effluent compositions for cycling with Catalyst I and a period of 300 s. Differ ent sets of data correspond to different mean hydro gen feed rates.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
43.
BiLiMORA AND BAILEY
Acetylene Hydrogénation
on Nickel Catalysts 531
measurements at d i f f e r e n t times during one p e r i o d using the gas chromatographic method already d e s c r i b e d . These data show the e f f e c t o f v a r y i n g γ f o r a constant τ. As expected, the wave-form f o r each component shows a maximum v a r i a t i o n i n amplitude f o r γ * 1/2. The wave-forms f o r γ = 13/15 show unusual d i s c o n t i n u i t i e s j u s t before the hydrogen i s switched to the lower l e v e l , and i t i s t h i s set o f operating c o n d i t i o n s t h a t gives r i s e to the l a r g e s t d i f f e r e n c e s between p e r i o d i c time-average and steady-state behavior f o r a l l three hydrocarbons. For γ = 7/15 and γ = 2/15, the p r o f i l e s i n d i c a t e that acetylene conversion continues t o i n crease f o r a short time a f t e r the hydrogen feed r a t e i s switched to the lower l e v e l . S i m i l a r overshoots are a l s o observed f o r both ethylene and ethane. These observations r e i n f o r c e the hypothesis t h a t such pheno mena are a d i r e c t consequenc c a t a l y s t phase w i t h a utes. I n an attempt to b e t t e r understand t h i s unexpected behav i o r , another s e r i e s o f unsteady-state experiments was conducted w i t h C a t a l y s t I . A step i n c r e a s e i n hydrogen feed c o n c e n t r a t i o n showed an overshoot i n the instantaneous ethylene c o n c e n t r a t i o n f o l l o w e d by a very slow approach to s t e a d y - s t a t e (see Figure 4 ) . On the other hand, a step decrease i n feed hydrogen r e s u l t e d i n a r e l a t i v e l y very r a p i d and monotonie d e c l i n e to the f i n a l steadys t a t e ethylene c o n c e n t r a t i o n . I t should be noted t h a t the sum of a l l h y d r a u l i c and mixing lags f o r t h i s system i s o f the order of 75 s and the d i f f u s i o n a l r e l a x a t i o n time (R /D ) i s much smal l e r than one second. Hence, the extremely slow response observed i n the step-up experiment and i t s asymmetry compared to the stepdown r e s u l t suggest t h a t n o n - l i n e a r dynamics o f the gas phasec a t a l y s t surface i n t e r a c t i o n p l a y a major r o l e i n unsteady reac t o r behavior. A more complete set o f experiments was done w i t h C a t a l y s t I I which gave h i g h e r absolute conversions than C a t a l y s t I f o r the same feed c o n d i t i o n s . However, t h i s c a t a l y s t , which had a h i g h e r n i c k e l content and more a c i d s i t e s than C a t a l y s t I , was found to be s u b j e c t to severe f o u l i n g . In order to keep t r a c k o f the gradual d e c l i n e i n c a t a l y s t a c t i v i t y , the sequence of experiments was mod i f i e d i n such a way t h a t p e r i o d i c experiments were sandwiched i n between s t e a d y - s t a t e experiments. Figure 5 shows a comparison o f s t e a d y - s t a t e and p e r i o d i c time-average data f o r ethane on C a t a l y s t I I . The r e s u l t s show an i n c r e a s i n g trend i n ethane s e l e c t i v i t y due t o c y c l i n g which was counter to the gradual d e c l i n e i n cata l y s t a c t i v i t y due to d r a s t i c f o u l i n g . The steady-state r e g i o n shown on t h i s f i g u r e i n d i c a t e s the a t t a i n a b l e set o f ethane com p o s i t i o n s by s t e a d y - s t a t e o p e r a t i o n throughout the e n t i r e u s e f u l l i f e o f t h i s c a t a l y s t and hence i n c l u d e s e f f e c t s which are a d i r e c t consequence of the f o u l i n g . Figure 5 c l e a r l y demonstrates t h a t i n s p i t e o f f o u l i n g , p e r i o d i c o p e r a t i o n of chemical r e a c t o r s gives r i s e to product compositions which are u n a v a i l a b l e i n any steady-state operation. 2
e
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
532
A. S T E P
INCREASE
-0.96
0.1 - 0.94 .08 -0.92 ETHANE
.06 .04
" / 1
•0 90
V
.02
ACETYLENE
0.88 0.86
0 0
1 1 240 480
1 1 1 1 1 1 720 960 1200 1440 1680 1920 ACETYLENE
f
0.1
0.96 -0.94
.08 .06 .04 .02 0
B. S T E P
DECREASE
" Ί
0.92
"J
0 90
-1\ ETHANE
-0
240 480
" 086
720 960 1200 1440 1680 1920 TIME (SECONDS)
Figure 4. The results of a step-up in feed hydro gen mole fraction (A) show overshoots and much longer transients than the reverse step-down ex periment (B)for Catalyst I
Figure 5. The shaded region shows the domain of ethane yields obtained in several different steady-state experiments at different stages of deactivation of Catalyst II. The curves show ethane yields obtained by cycling feed hydrogen concentration with different periods.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
43.
BiLiMORA AND BAILEY
Acetylene Hydrogénation
on Nickel Catalysts
533
RESPONSE TO STEP INCREASE IN FEED HYDROGEN
¥
240
480
720
960 5280 5520| ACETYLENE
RESPONSE TO STEP DECREASE IN FEED HYDROGEN
480
Figure 6. Feed hydrogen step-up (A) for Catalyst II produces a damped osciUation in effluent ethylene in contrast to a stepdown in feed hydrogen (B)
720 960 TIME (SECONDS)
NORMALIZED TIME t/τ
Figure 7. Instantaneous effluent compositions for feed hydrogen cycling with Catalyst II for nine sets of periods (τ) and mean hydrogen feed rates (di rectly related to y: see Equation 4)
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
534
^^^^
E T H Y L E N E
A E T H A N E
y
13 "15
V A C E T Y L E N E
Figure 8. Periodic effluent concentrations for three different switching fractions as measured continuously using the ir ana lyzer (τ = 180 s, Catalyst 11)
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
43.
BiLiMORA AND BAILEY
Acetylene Hydrogénation
on Nickel Catalysts 535
Step response experiments f o r t h i s c a t a l y s t show t h a t when the r e a c t o r i s subjected t o a step i n c r e a s e i n feed hydrogen, the ethylene c o n c e n t r a t i o n p r o f i l e e x h i b i t s damped o s c i l l a t i o n s , w h i l e ethane and acetylene show an overshoot and an undershoot, r e s p e c t i v e l y , f o l l o w e d by a slow monotonie approach t o the f i n a l s t e a d y - s t a t e value. On the o t h e r hand, an asymmetric response was again observed f o r a step decrease i n feed hydrogen (Figure 6 ) . Figure 7 shows the r e s u l t s o f a parametric study o f the instantaneous concentration-time p r o f i l e s obtained by c y c l i c o p e r a t i o n w i t h C a t a l y s t I I f o r d i f f e r e n t T'S and y's. A l l these curves were obtained from gas chromatographic measurements. Once more, as w i t h C a t a l y s t I , f o r γ = 2/15 and a l l three x s the p r o f i l e s tend t o overshoot the s w i t c h i n g p o i n t . As expected, f o r a f i x e d value o f γ the peaks i n the wave-forms tend to be come sharper as τ i n c r e a s e s i n the bottom row o f diagrams f e r e n t i n t h a t acetylene and ethane seem t o f o l l o w the s w i t c h from high t o low hydrogen feed r a t e f a i r l y w e l l although they tend to overshoot the reverse s w i t c h i n g p o i n t . The behavior o f ethy lene f o r these cases i s d r a m a t i c a l l y d i f f e r e n t . In the case o f γ = 13/15 a l l three components f o l l o w the high t o low hydrogen switch very w e l l , but show a considerable l a g f o r the reverse o p e r a t i o n . These r a t h e r unusual response p a t t e r n s have been confirmed by continuous i n f r a - r e d measurements (see Figure 8 ) . The r e s u l t s obtained i n these unsteady-state s t u d i e s c l e a r l y show t h a t the dynamics o f the gas p h a s e - c a t a l y s t s u r f a c e i n t e r a c t i o n cannot be neglected when determining a p e r i o d i c c o n t r o l s t r a t e g y . F u r t h e r , c a t a l y s t s u r f a c e capacitance should not gen e r a l l y be neglected when i n v e s t i g a t i n g s t a b i l i t y and c o n t r o l o f c a t a l y t i c r e a c t o r s . S i m i l a r conclusions have r e s u l t e d r e c e n t l y from s e v e r a l s t u d i e s o f s e l f - o s c i l l a t i n g isothermal c a t a l y t i c r e a c t i o n s [11]. Features observed i n dynamic experiments such as these w i l l undoubtedly c o n t r i b u t e t o improved understanding o f c a t a l y s t behavior. f
Acknowledgments We are g r a t e f u l t o Dr. Duane D. Bruns f o r h i s help i n the design and f a b r i c a t i o n o f the r e a c t o r . We are a l s o g r a t e f u l t o the N a t i o n a l Science Foundation, the C a m i l l e and Henry Dreyfus Foundation, and the U n i v e r s i t y o f Houston f o r f i n a n c i a l support to t h i s work.
Literature Cited 1. 2. 3. 4.
Bailey, Bailey, Bailey, (1972). Renken,
J. Ε . , Chem. Eng. Comm. 1, 111 (1973). J. Ε. and F. J. M. Horn, JOTA 7, 378 (1971). J. Ε. and F. J. M. Horn, Chem. Eng. Sci. 27, 109 A. et al., Proc. AIChE/GVC Mtg. Munich, p. A3-1 (1974).
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
536
CHEMICAL REACTION ENGINEERING—HOUSTON
5. 6.
Renken, Α . , Chem. Eng. Sci. 27, 1925 (1972). Renken, A. et al., 4th Int./6th Europ. Symp. Chem. React. Eng., Heidelberg, p. III-107 (1976). 7. Bond, G. C., J. Chem. Soc., p. 2705, 4288, 4738, (1958). 8. Komiyama, H. and Inoue, H . , J. Chem. Eng. Jap. 1, 142 (1968). 9. Bond, G. C. et al., Trans. Far. Soc. 54, 1537 (1958). 10. Lee, C. K., MS Thesis, Univ. of Houston (1972). 11. Sheintuch, M. and Schmitz, R. Α., Cat. Rev., in press.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
44 Multiple Steady States of a Moving Bed Reactor—Theory and Experiment K L A U S T H O M A and D I E T E R V O R T M E Y E R Institut Β fürThermodynamik,Technische Universität München, 8000 München 2, Arcisstr. 21, West Germany
A moving bed chemical is characterized b countercurrent movemen t i o n s . Furthermore heat and mass is exchanged between the two phases. Due to the solid movement the reactors are difficult to model i n laboratory experiments. The only experiments known to us are reported by weekman and Nace (1). These authors were mainly i n t e r e s t e d i n the behaviour of an isothermal moving bed reactor with respect to catalytic cracking and used f o r t h e i r experiments more or less free falling p a r t i c l e s i n a cocurrent gas stream. In the present paper model experiments are reported under defined conditions f o r gas and solid flow by counter current o p e r a t i o n . In this s i t u a t i o n the energetic feedback by the e f f e c t i v e heat conduction is increased through the countercurrent movement. I n t e r e s t i n g stability problems a r i s e concerning ignition/extinction phenomena. In p r i n c i p l e these effects are rather s i m i l a r to those encountered i n f i x e d bed reactors ( 2 ) , ( 3 ) , (4) although the s i t u a t i o n gets a new dimension by the solid movement. A s i m p l i f i e d t h e o r e t i c a l i n v e s t i g a t i o n of a countercurrent moving bed reactor was presented by Schaefer, Vortmeyer and Watson (5). The work neglects heat conduction i n both phases, the only feedback mechanism being the movement of one phase against the o t h e r . Three s o l u t i o n s were obtained f o r c e r t a i n parameter ranges. The upper and lower s o l u t i o n s were stable and the middle one unstable. I t i s i n t e r e s t i n g to note that the governing equations for a moving bed are i d e n t i c a l with the two phase model of a l i q u i d / l i q u i d spray column which was i n v e s t i g a t e d t h e o r e t i c a l l y by Luss and Amundson ( 6 ) . The aim of our work was to design a laboratory model of a moving bed reactor and to compare experimental r e s u l t s with numerically predicted m u l t i p l e steady state s o l u t i o n s of the governing equations. © 0-8412-0401-2/78/47-065-539$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
540
D e s i g n o f a moving bed r e a c t o r The most d i f f i c u l t problem was t o o b t a i n a d e f i n e d s t e a d y movement o f t h e s o l i d . A movement due t o g r a v i t a t i o n a l f o r c e o n l y r e s u l t s i n a s t i c k - s l i p f l o u ( Y o s h i d a e t a l (2)) w h i c h makes t h e d e s i r e d measurement u n c o r r e c t , i f n o t i m p o s s i b l e . T h e r e f o r e t h e c a t a l y s t p a r t i c l e s were s u r r o u n d e d by a f i n e w i r e c l o t h . T h i s t u b u l a r arrangement o f 2.5 m l e n g t h was p u l l e d m e c h a n i c a l l y t h r o u g h a s t a i n l e s s s t e e l tube ( l e n g t h H-.95 m, i n n e r d i a m e t e r 5 cm, w a l l t h i c k n e s s i n t h e r e a c t i o n s e c t i o n 0.2 mm). T h i s tube was c l o s e d a t b o t h ends. A 2k cm l o n g c e n t r a l p a r t o f t h i s tube was t h e r e a c t i o n s e c t i o n ( f i g . 1 ) . A vacuum and t h e r m a l i n s u l a t i o n t o g e t h e r w i t h a d d i t i o n a l h e a t e r s kept r a d i a l h e a t l o s s e s low The s o l i d was moved t h r o u g h t h 5 mm/min. The gas m i x t u r e e n t e r s and l e a v e s t h e r e a c t o r s h o r t l y b e f o r e and s h o r t l y a f t e r t h e r e a c t i o n s e c t i o n as i n d i c a t e d i n f i g . 1. S i n c e both ends o f t h e l o n g c a t a l y s t s t o r a g e p i p e were c l o s e d t h e gas c o u l d o n l y move t h r o u g h t h e r e a c t i o n s e c t i o n . Temperature p r o f i l e s w i t h i n t h e r e a c t i o n s e c t i o n were measured by a movable t h e r m o c o u p l e w i t h i n a t h i n a x i a l tube. In t h e r e a c t i o n s e c t i o n ethane was o x i d i z e d by a Pd-Al203 c a t a l y s t . O v e r a l l c h e m i c a l r e a c t i o n r a t e s were d e t e r m i n e d e x p e r i m e n t a l l y i n a d i f f e r e n t i a l r e a c t o r as a f u n c t i o n o f c o n c e n t r a t i o n and t e m p e r a t u r e by Simon ( 8 ) , ( 9 ) . Theory W i t h r e g a r d t o a f i x e d bed t h e moving bed r e a c t o r has two more o p e r a t i o n a l p a r a m e t e r s . They a r e t h e p r e h e a t tempera t u r e T s and t h e mass f l o w r a t e mg o f t h e s o l i d . Because o f the i n c r e a s e d number o f v a r i a b l e s c a l c u l a t i o n s had t o be made i n advance i n o r d e r t o f i n d t h e i n t e r e s t i n g e x p e r i m e n t a l range where m u l t i p l i c i t y c o u l d be e x p e c t e d . The f a l l o w i n g s t e a d y s t a t e model e q u a t i o n s were s a l v e d : 0
Energy b a l a n c e s solid:„ d Τ NT
Τ2Γ dx
-
U
d Τ
s ' s -ΈΓ c
~ hB(T -T )s
F
a i
( T )=-AH.r V
u
(1)
gas : C
F
dT" -hS
Concentration
-
PF
I*FI C. F'
s
2
F
= 0
balance
. #^ = r
t α t
(2)
dx
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
(3)
44.
THOMA AND VORTMEYER
Steady States of Moving Bed Reactor
541
Some u n d e r l y i n g a s s u m p t i o n s a r e i) piston flou ii) o n l y s l i g h t heat l o s s e s t o t h e w a l l iii) no c o n c e n t r a t i o n d i f f u s i o n . I n f a c t w i t h o u t t h e term mg.cg dTg /dx i n e q u a t i o n ( 1 ) uje have a s e t o f e q u a t i o n s which has been used s u c c e s s f u l l y by v a r i o u s a u t h o r s f o r t h e m o d e l l i n g o f f i x e d bed c h e m i c a l r e a c t o r s . A n o t h e r i n t e r e s t i n g a s p e c t can be shown by r e w r i t i n g e q u a t i o n s ( 1 ) and ( 2 ) i f heat c o n d u c t i o n and heat losses are neglected: jrîipCp nîgCgl d Tp -
^
dTp
- y - + (Irnpl c
F
- Iftgl c ) ^ s
= -
A H T
(k)
dx |ÏÎU-C
T
f
dT
F
= T - - t — L ^ S F hS dx Q
(5)
r
The f i r s t term i n e q u a t i o n (*+) r e p r e s e n t s t h e d i s p e r s i o n ( f e e d b a c k ) p r o c e s s caused by t h e c o u n t e r c u r r e n t movement o f s o l i d and f l u i d . Boundary c o n d i t i o n s 1
The a d j u s t m e n t o f t h e b e s t o t h e e x p e r i m e n t a l s i t u a t i o n i s somewhat p r o b l e m a t i c . Due t o t h e p a r t i c u l a r way how t h e gas i s f e d i n t o and t a k e n o u t o f t h e r e a c t o r t h e f l o w c o n d i t i o n w i t h i n i n l e t and e x i t c r o s s - s e c t i o n s a r e r a t h e r u n d e f i n e d . W i t h i n a zone o f a t l e a s t 1 cm w i d t h a t both s i d e s o f t h e r e a c t i o n s e c t i o n t h e r e a r e r a d i a l and a x i a l f l o w components. More d e t a i l s on t h e c o n v e r s i o n o f r a d i a l i n l e t f l o w t o a x i a l f l o w i n p a c k e d beds can be f o u n d i n a paper by S z e k e l y and Poveromo ( 1 0 ) . F o r m a t h e m a t i c a l r e a s o n s , however, c l e a r c u t b e s a r e needed. UJe t h e r e f o r e s i m p l y choose 1
i)
χ = 0
T (0) s
=
T
s
ο T CL) F
=
Τρ
ο
Ά
-
vCD
= y
0
D
These c o n d i t i o n s e x c l u d e heat f l u x e s a c r o s s i n l e t and e x i t s e c t i o n s . A more s o p h i s t i c a t e d c h o i c e o f b c s would be an e x t e n s i o n o f t h e Danckwert's c o n d i t i o n s : f
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
542
x = 0
ii)
m c s
(T
s
-T CW) = X f
s
S
f
φ)
Ο
Χ = L.
( T
T
F - F o
C L ) )
=
Γ
λ
ζτ\_
yCD = y° x = L
T ( L ) = Tp
+
F
+
O
In c o n t r a s t t o i ) now heat f l u x e s a c r o s s i n l e t and e x i t s e c t i o n s a r e i n c l u d e d . These f l u x e s p r e h e a t t h e i n f l o w i n g gas and s o l i d . C a l c u l a t i o n s w i l l show n e g l i g i b l e d i f f e r e n c e s i n t h e r e s u l t s from t h e two s e t s o f b c s f
The n u m e r i c a l p r o c e d u r S o l u t i o n s o f t h e s t a t i o n a r y model e q u a t i o n s were o b t a i n e d by the c o l l o c a t i o n method ( 1 1 ) . The f o l l o w i n g e x p a n s i o n s i n Legendre p o l y n o m i a l s f o r t h e t e m p e r a t u r e s and t h e concen t r a t i o n were assumed:
Τ (χ)
=
ς
b
Ν ^ a, P , ( x ) i=1
(6)
Ν ^ i=1
b. Ρ (χ)
(7)
Ν ^ i=1
c
1
Τ (χ) =
y(x)
=
1
1
1
1
Ρ. (χ)
(θ)
1
F o r some c a s e s an e x p a n s i o n up t o 1M = 17 was n e c e s s a r y . U s i n g e q u a t i o n s ( 6 ) , ( 7 ) , ( 8 ) t h e system o f e q u a t i o n s may be w r i t t e n i n t h e f o l l o w i n g m a t r i x form: A_
·
ξ
=
r ( f )
where ξ i s t h e s o l u t i o n v e c t o r and r c o n t a i n s t h e n o n l i n e a r p a r t s o f t h e d i f f e r e n t i a l e q u a t i o n s . The n o n l i n e a r i t y was s o l v e d w i t h a s i m p l e i t e r a t i o n p r o c e d u r e . As R e i l l y and S c h m i t z (12) p o i n t e d o u t such a p r o c e d u r e w i l l g i v e o n l y stable solutions. Calculated region of multiple
solutions
T a b l e I summarizes t h e d a t a f o r which a range o f m u l t i p l i c i t y was f o u n d by c a l c u l a t i o n . The t a b l e a l s o i n c l u d e s numbers f o r t h e v a r i o u s heat t r a n s p o r t c o e f f i c i e n t s o f e q u a t i o n s ( 1 ) and ( 2 ) . These c o e f f i c i e n t s a r e determined e x p e r i m e n t a l l y :
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
TiiOMA
Steady States of Moving Bed Reactor 543
AND VORTMEYER
sol id flow · gas flow
column catalyst
particles
m t c h a n i s m for solid movtment
496 cm
Figure 1.
Moving bed reactor
Table I : Data f o r n u m e r i c a l
calculations
383 Η 0.0D55 300 Η 2Θ5.6 kg/m / h r 0.24 m 1.39 U/m/K 0.427 0.43 cm
Tsc Vrj
lui
9
ε
Re
iil/m /K 3
1
3.95 4.82 6.16
0.33 1.66 4.12
0.007 0.99 1.06
0.41 h d e t e r m i n e d by l\lu = 0.89 Re 1048 O/kg/H a t 573 H 932 J/kg/H a t 573 H 1.29 kg/m3 a t s t a n d a r d c o n d i t i o n s 952 kg/m (1-ε?·Ρ 1012 1/m S - 1.425·10 J/kmole ΔΗ 1/22.414 kmole/m a t s t a n d a r d c o n d i t i o n s c tot 3
3
9
3
K i n e t i c d a t a from Simon ( 8 ) , ( 9 ) .
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
544
Under v a r i o u s c o n d i t i o n s t h e r e a c t i o n s e c t i o n was h e a t e d o n l y by a h o t gas s t r e a m . Temperature p r o f i l e s were measured and f i t t e d t o t h e e q u a t i o n s . The c a l c u l a t e d r e s u l t s a r e p r e s e n t e d i n f i g . 2 where t h e i n l e t gas t e m p e r a t u r e Tp i s p l o t t e d a g a i n s t the r a t i o o f " f l o w c a p a c i t i e s B = m ^ C p / m g C ^ . A l r e a d y Luss and Amundson (6) f o u n d t h i s parameter t o be t n e most i m p o r t a n t one b e s i d e s i n l e t c o n d i t i o n s when t h e y a n a l y s e d a c o u n t e r c u r r e n t l i q u i d / l i q u i d s p r a y column. I n l e t gas c o n c e n t r a t i o n y and t h e p r e heat t e m p e r a t u r e T g o f the s o l i d a r e parameters of t h e g r a p h . The shaded a r e a i s t h e range o f p r e d i c t e d m u l t i p l e s o l u t i o n s , w h i l e o u t s i d e e i t h e r we f i n d a u n i q u e upper o r l o w e r s t e a d y s t a t e . The l i m i t i n g c u r v e s marked w i t h i ) o r i i ) a r e o b t a i n e d from t h e two d i f f e r e n t s e t s o f b c ' s The e x p e r i m e n t s were p e r f o r m e seen t h a t t h e range o β = 1. The c a l c u l a t i o n s were done f o r the e x p e r i m e n t a l l y a c c e s s i b l e range o f Β and T p . 11
Q
Q
Experimental r e s u l t s The measurements were p e r f o r m e d a c c o r d i n g t o t h e c a l c u l a t e d d a t a . The f o l l o w i n g p r o c e d u r e was a d a p t e d ( f i g . 3): F o r a p r e h e a t s o l i d t e m p e r a t u r e o f Tg = 3Θ3 K e l v i n t h e r e a c t o r was s t a r t e d i n t h e l o w e r steady°state by c h o o s i n g a s u i t a b l e i n l e t t e m p e r a t u r e Tp . T h i s t e m p e r a t u r e then was g r a d u a l l y i n c r e a s e d a l o n g the p a t h 1-^2 i n f i g . 3. The r e a c t o r r e mained i n t h e l o w e r s t e a d y s t a t e u n t i l a t p o i n t 2 i g n i t i o n o c c u r s . The r e a c t o r remains i g n i t e d i f T p i s f u r t h e r i n c r e a s e d . The e x t i n c t i o n p r o c e d u r e goes a l o n g p a t h 3-^4. W h i l e l o w e r i n g t h e gas i n l e t t e m p e r a t u r e t h e r e a c t o r r e m a i n s i g n i t e d u n t i l p o i n t k i s r e a c h e d where e x t i n c t i o n t a k e s place. I f t h e e x p e r i m e n t a l r e a c t o r behaves l i k e t h e o r e t i c a l p r e d i c t i o n s t h e i g n i t i o n / e x t i n c t i o n e x p e r i m e n t s s h o u l d ex h i b i t a pronounced h y s t e r e s i s . F i g . k shows t h a t t h i s i s i n f a c t t h e c a s e . The c o n v e r s i o n o f ethane i s p l o t t e d a g a i n s t T p w i t h o t h e r p a r a m e t e r s k e p t c o n s t a n t . The numbers 1 t o k i n f i g . 3 c o r r e s p o n d t o t h o s e o f f i g . 4. F i g . 5 c o n t a i n s t e m p e r a t u r e p r o f i l e s o f t h e upper and l o w e r s t e a d y s t a t e . Due t o t h e movement o f t h e s o l i d t h e y l i e much c l o s e r t o g e t h e r t h a n one would e x p e c t from f i x e d bed r e a c t o r b e h a v i o u r . The f i n a l f i g . 6 i s c o n c e r n e d w i t h an e x p e r i m e n t a l check o f t h e c a l c u l a t e d range o f m u l t i p l i c i t y . A s e r i e s o f i g n i t i o n / e x t i n c t i o n e x p e r i m e n t s were p e r f o r m e d a t t h r e e d i f f e r e n t r a t i o s o f B {0.902, 1.09, 1.381}. The b l a c k p o i n t s i n f i g . 6 r e p r e s e n t s t a t e s where t h e r e a c t o r may e i t h e r be i n t h e upper o r l o w e r s t a t e w h i l e t h e b r i g h t p o i n t s a r e unique s t a t e s . The shaded a r e a a g a i n i s the c a l c u l a t e d one w i t h be i ) from f i g . 2. Q
0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
THOMA AND VORTMEYER
Steady States of Moving Bed Reactor
The m e a s u r i n g procedure
{
/
/
/
/
\
.
upper
state
© lower
state
m .c s
Figure 3.
s
Measuring procedure
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
546
Figure 4.
Measured conversion of ethane as a function of the gas inlet temperature T Fo
length
Figure 5.
fern]
Upper and lower temperature profiles in the region of multiplicity
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
THOMA AND VORTMEYER
Figure 6.
Steady States of Moving Bed Reactor
Measured and calculated ranges of multiplicity and uniqueness
American Chemical Society Library 1155 16th St., M.W. In Chemical Reaction Engineering—Houston; Weekman, V., et al.; Washington, O.C. 20036 ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
548
Discussion The agreement between computed and measured r e s u l t s i s good for B > 1. A t β = 0.902 l a r g e r d e v i a t i o n s a r e o b s e r v e d . T h i s may be due t o a g r o w i n g d i s c r e p a n c y between model a s s u m p t i o n s and e x p e r i m e n t a l r e a l i t y i f s m a l l e r v a l u e s o f B a r e a p p r o a c h e d . T h i s was done by k e e p i n g mg c o n s t a n t and l o w e r i n g t h e gas v e l o c i t y t o 5.5 cm/s NTP a t B = 0.902. I n the range o f low gas v e l o c i t i e s e f f e c t s o f h e a t l o s s e s u s u a l l y become more pronounced, a f a c t t h a t i s a l s o o b s e r v e d i n f i x e d bed e x p e r i m e n t s . I n o r d e r t o t e s t t h i s p o i n t o f view we have r e p l a c e d i n be i ) t h e e x i t t e m p e r a t u r e g r a d i e n t (dT /dx) = 0 by a n e g a t i v g r a d i e n t e s t i m a t e d fro measurements. The d o t t e gradient of (dTg/dx) uppe l i m i t i n g c u r v e ϊο h i g h e r gas i n l e t t e m p e r a t u r e s i s o b s e r v e d which g i v e s a b e t t e r f i t t o t h e d a t a . T h i s shows t h a t i n d e e d heat l o s s e s may be r e s p o n s i b l e f o r t h e o b s e r v e d d i f f e r e n c e s between t h e o r y and e x p e r i m e n t a t B = 0.902. s
L
Conclusions The two-phase model o f a moving bed c h e m i c a l r e a c t o r w i t h c o u n t e r c u r r e n t o p e r a t i o n was s o l v e d n u m e r i c a l l y . Due t o t h e i n c r e a s e d f e e d b a c k by t h e c o u n t e r c u r r e n t movement a b r o a d range o f m u l t i p l i c i t y was o b t a i n e d . E x p e r i m e n t s c o n f i r m e d the p r e d i c t e d r e s u l t s . T h i s work was s p o n s o r e d by t h e Deutsche F o r s c h u n g s g e m e i n s c h a f t (SFB 153). Nomenclature
J
tot
ΔΗ d h L m mg Pi r P
F
f S
l i n e a r p a r t o f t h e system o f d i f f . e q u a t i o n s i n matrix form s p e c i f i c heat o f gas ( c o n s t , p r e s s . ) J/kg/K s p e c i f i c heat o f s o l i d , J/kg/H c o n c e n t r a t i o n o f t h e gas m i x t u r e ( a t s t a n d a r d c o n d i t i o n s ) , kmole/m^. reaction enthalpy, J/kmole diameter of c a t a l y s t p a r t i c l e , m h e a t t r a n s f e r c o e f f i c i e n t , J/m^/hr/H length of the reaction section,m mass v e l o c i t y o f gas, kg/m /hr mass v e l o c i t y o f s o l i d , kg/m^/hr Legendre p o l y n o m i a l ^ r e a c t i o n r a t e , kmole/m / h r n o n l i n e a r p a r t o f t h e d i f f . equ. i n v e c t o r form s u r f a c e a r e a p e r u n i t bed volume, 1/m t e m p e r a t u r e o f t h e gas, H 2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
44. THOMA AND VORTMEYER
Tp Tg Tg Ty χ y y *o
D
Q
Steady States of Moving Bed Reactor
549
i n l e t temperature o f the gas, H temperature o f the s o l i d , H i n l e t temperature o f the s o l i d , Κ ujall temperature, Η a x i a l distance, m mole f r a c t i o n o f ethane mole f r a c t i o n o f ethane a t t h e e n t r a n c e
Greek l e t t e r s a,,
c o e f f i c i e n t d e s c r i b i n g heat l o s s e s t o t h e u j a l l J/m /hr/K 3
α
2 ε XS^f ρF PS ξ
void fractio e f f e c t i v e therma J/m/hr/K d e n s i t y o f t h e g a s , kg/m d e n s i t y o f t h e s o l i d , kg/m s o l u t i o n v e c t o r , c o n t a i n i n g the expansion c o e f f . 3
Literature cited (1) Weekman, V.W., Nace, D.M., AIChE J.,(1970),16,397. (2) Van Heerden, C., Chem.Eng.Sci., (1958),8,133. (3) Amundson, N.R., Canad.J.Chem.Engng.,(1965), 43, 49. (4) Wicke, E., Padberg, G . , Arens, H., Proc.Europ. Symp. Chem.Reaction Eng., 4th, Brussels (1968). (5) Schaefer, R.J., Vortmeyer, D., Watson, C.C., Chem. Eng.Sci.,(1974),29,119. (6) Luss, D.L., Amundson, N.R., I&EC Fund.,(1967),6,437. (7) Yoshida, S., Tamura, S., Kunii, D., Int.J.Heat Mass Transfer (1966), 9,865. (8) Simon, B., thesis, T e c h n . U n i v e r s i t ä t München (1976). (9) Simon, B., Vortmeyer, D., Chem.Eng.Sci., in Press. (10) Szekely, J., Poveromo, J.J., AIChE J.,(1975),21,769. (11) Finlayson, B.A., "The method of weighted residuals a. variational principles", Acad. Press (1972). (12) Reilley, M.J., Schmitz, R.A., AIChE J., (1966),12,153.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
45 Cell Model Studies of Radial Flow, Fixed Bed Reactors J. M .
CALO
Department of Chemical Engineering, Princeton University, Princeton, NJ 08540
The radial flow, fixed bed reacto (RFBR) originall de veloped to handle larg of ammonia. Since then, RFBRs have been used, or considered for, catalytic reforming, desulfurization, nitric oxide conversion, catalytic mufflers, and other processes in which fluids must be contacted with solid particles at high space velocities. The prin cipal advantages of the RFBR over the more conventional tubular, axial flow, fixed bed reactor (AFBR) have been outlined elsewhere (1,2). Although usually cylindrical in geometry, spherical RFBRs have also been considered (3). Perhaps the first published analysis of an RFBR was by Raskin, et al. (4), who developed a quasicontinuum distributed parameter model for a radial ammonia synthesis reactor. General conclusions were limited, however, since the model was specifically concerned with ammonia synthesis and later carbon monoxide conversion (5), where both processes are second order and reversible. However, these authors did note that "radial reactors are anisotropic", i.e., they observed higher ammonia yields for centripetal radial flow (CPRF -- periphery to the center) than for centrifugal r a d i a l flow (CFRF -- center to periphery) (4) . In the present work, a packed bed c e l l model i s used to calcu late temperature and concentration profiles i n the adiabatic RFBR for exothermic c a t a l y t i c reactions with interphase resistance to mass and heat transfer. In p a r t i c u l a r , differences between the RFBR and the AFBR, operated at the same space v e l o c i t y , are explor ed with respect to uniqueness, m u l t i p l i c i t y , and s t a b i l i t y of the steady state, p r o f i l e location, s e l e c t i v i t y i n p a r a l l e l and series reactions, and transient behavior. RFBR C e l l Model Following Vanderveen, et a l . (6), the mass and energy conser vation equations for the f l u i d and the p a r t i c l e i n the j t h c e l l for a f i r s t order, i r r e v e r s i b l e , exothermic reaction are M.(v. . - v.) - (v. - v.) =a fdv./dt) D 3-1 Ύ 3 Τ 1 1 J
© 0-8412-0401-2/78/47-065-550$05.00/0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
[1]
45. CALO
Radial Flow, Fixed Bed Reactors
551
( V J - v.) - k.v. = a ( d v . / d t )
C3]
3
(y. - y . l + 3k .v. = a.fdy./dt) [4] 3 3' 3 3 4 3 s u b j e c t t o the i n l e t c o n d i t i o n s VQ = VQ(t) = 1.0 and yo = y o ( t ) = 1.0 and a p p r o p r i a t e i n i t i a l c o n d i t i o n s (see N o t a t i o n and Vanderveen, e t a l . (β) f o r parameter d e f i n i t i o n s ) . In r a d i a l f l o w , the f l u i d i n t e r s t i t i a l v e l o c i t y , u j , i s a f u n c t i o n o f p o s i t i o n i n the bed, and hence, c e l l number, j . The interphase mass and heat t r a n s f e r c o e f f i c i e n t s vary approximately as R e (£, 1_) , and thus Mj and Hj are f u n c t i o n s o f Re® ·** which increase i n CPRF and decrease i n CFRF w i t h bed depth, k j i s a l s o a f u n c t i o n o f U j due t With the assumptio the bed (_5) , the c o n t i n u i t y equation f o r c y l i n d r i c a l geometry i n t e grates t o ur = U^Ri = U2R2; w h i l e f o r s p h e r i c a l geometry, u r = 1 1 = U2 2 I n t e g r a t i o n o f the v e l o c i t y , u = ±dr/dt (+ f o r CFRF and - f o r CPRF), from the bed entrance t o the bed e x i t y i e l d s the space time d i s t r i b u t i o n along the bed l e n g t h . R e s u l t s o f t h i s c a l c u l a t i o n r e v e a l t h a t i n r a d i a l flow the l o c a l residence time near the o u t e r p e r i p h e r y o f the bed i s increased a t the expense o f residence time near the i n n e r core o f the bed as compared to a x i a l flow a t the same t o t a l space time. The steady s t a t e temperature p r o f i l e s presented i n F i g u r e 1 were determined by an i n i t i a l value c e l l - b y - c e l l c a l c u l a t i o n f o r the same feed c o n d i t i o n s , average space v e l o c i t y , and bed depth. A l l the parameter v a l u e s are those o f Vanderveen, e t a l . (6) ex cept as otherwise noted. As can be seen, the CPRF p r o f i l e appears e a r l i e r , and the CFRF p r o f i l e appears l a t e r i n the bed than the ax i a l flow p r o f i l e as a r e s u l t o f residence time reapportionment. This " e a r l y - l a t e " phenomenon i s accentuated by d e c r e a s i n g aspect r a t i o and by s p h e r i c a l over c y l i n d r i c a l geometry a t the same aspect ratio. Uniqueness, M u l t i p l i c i t y , and S t a b i l i t y V
0 , 6
U
R
2
R
2
A l g e b r a i c m a n i p u l a t i o n o f the steady s t a t e forms o f the con s e r v a t i o n equations [104] i n the same manner as E r v i n and Luss (8) yields y. * y- -, = (M.+l)k.(y . - y.)/M. = G. (y.) 3 3-1 3 3 m3 3 3 3 3 Κ
J
,
[5]
Κ
f
where y j i s the maximum p a r t i c l e temperature i n the j t h c e l l (8}. Equation [5] can be r e w r i t t e n as m #
1 = G.CyJ/ly. - y.^)
Ξ F. (y.)
[6]
and the steady s t a t e s o f the system are determined by the i n t e r s e c t i o n o f t h e h o r i z o n t a l l i n e a t u n i t y and the f u n c t i o n F j ( y j ) . For s m a l l y j , d F j ( y j ) / d y j i s n e g a t i v e , and i f A
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
552
CHEMICAL REACTION ENGINEERING—HOUSTON
0
10
20
30
40
50
60
70
80
90
100
C e l l Number, j
Figure 1. Unique steady state temperature profiles for CPRF and CFRF ( and axialflow(P = 9kP , T — 667 K , T = 667 Κ,β = 5, M/H = 1.67) 0
a
0
0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
P
=
0.25)
45.
CALO
Radial Flow, Fixed Bed Reactors
dF. (y.)/dy. < 0 3 3
,
j
J
J
2
y.e(y
3
m,3
KJ
553 ., y. _)
3~1
[7]
J
then t h i s i s a s u f f i c i e n t c o n d i t i o n f o r uniqueness of the steady s t a t e . I f c o n d i t i o n [7] i s v i o l a t e d , then F j ( y j ) w i l l e x h i b i t extremum a t y-j
= ΙΎΙΥ_ ^
1
j [ ^'ί
where
Q
=
Ύ2
y4_J
+
+Y
j-1
±
) 2 +
ôJ/ [y^ + Ύ - y^_J 2
4Yy
j-l m,ji j-l 5
y
"Y
w
" Vj)]*
In order t o i n s u r e c o n d i t i o n [ 7 ] , the argument of Qj must be nega tive , or Inf 4 l<j
2 j-1 •
where Aj = (Mj+1)/(Hj+1). Aj v a r i e s w i t h bed p o s i t i o n i n r a d i a l flow ana can e i t h e r i n c r e a s e o r decrease w i t h j f o r CPRF o r CFRF depending on whether Mj/Hj i s g r e a t e r than, or l e s s than, u n i t y . More c o n s e r v a t i v e lower bounds f o r the RHS o f i n e q u a l i t y [9] can be obtained by s e t t i n g Aj equal t o i t s minimum value i n the bed and Y j - i = 1 : Y < 4
r
i+
( A
)J
1}
/ ( y
[ i o ]
i 1, i n e q u a l i t i e s [9] and [10] are i d e n t i c a l f o r CPRF s i n c e the minimum Aj occurs i n the f i r s t c e l l where Yj-χ = 1· o CFRF, however, the RHS of i n e q u a l i t y [9] w i l l always be g r e a t e r than the RHS of i n e q u a l i t y [10] s i n c e the l a t t e r i s the lower bound. Thus for M/H > 1, CPRF i n c r e a s e s the range of parameter space f o r which m u l t i p l i c i t y can occur, and CFRF decreases the range, as compared to a x i a l flow a t the same t o t a l space time. The opposite i s t r u e f o r M/H < 1. Again, t h i s e f f e c t becomes more pronounced f o r de c r e a s i n g aspect r a t i o and f o r s p h e r i c a l over c y l i n d r i c a l geometry at the same aspect r a t i o . C o n d i t i o n [9] i s s u f f i c i e n t but not necessary t o i n s u r e uniqueness of the steady s t a t e . I f i t i s v i o l a t e d , m u l t i p l e steady s t a t e s w i l l e x i s t i n c e l l s f o r which F j ( y j + ) > 1 > F j ( y j - ) . T y p i c a l behavior o f the F j ( y j ) curves w i t h c e l l number i s i l l u s t r a t e d i n Figure 2, which shows t h a t f o r M/H > 1, y j - l i n c r e a s e s w i t h bed depth, and y j i n c r e a s e s , but l e s s r a p i d l y , t o ym. Simultaneously, the F j ( y j ) curve r i s e s , y j - approaches yj+,^and a t some p o i n t i n the bed, yj+ = y j - Ξ y j and Fj(yj+) = F j ( y j - ) = F j ( y j , t ) ~ the t r i f u r c a t i o n p o i n t . I f j ( Y j , t ) 1* m u l t i p l e steady s t a t e s e x i s t for^some c a t a l y s t p a r t i c l e s i n the bed i n the r e g i o n where j*yj ) j(yj~)' However, i f F j ( y j ) < 1, then a l l c a t a l y s t p a r t i c l e s have a unique steady s t a t e , and the r e a c t o r p r o f i l e i s unique. F j ( y j ^ ) < 1 i s both a necessary and s u f f i c i e n t c o n d i t i o n f o r uniqueness of the steady s t a t e . In r a d i a l f l o w , j ( Y j , t ) cannot be c a l c u l a t e d a p r i o r i as i n F
m #
f t F
F
+
>
1
>
> F
/ t
t
F
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
r
554
CHEMICAL REACTION ENGINEERING—HOUSTON
a x i a l flow because the values o f Aj and k ( i n k j ) a t the t r i f u r c a t i o n p o i n t are not known. Nevertheless, i t can be shown t h a t the lowest i n t e r s t i t i a l v e l o c i t y i n the bed, i . e . , a t the outer p e r i p h e r y , y i e l d s an upper bound i n e v a l u a t i n g j ( y j , t ) - Thus, i f j ^ j # t ) u . b . I* then t h i s i s a s u f f i c i e n t , but not necessary con d i t i o n f o r uniqueness o f the steady s t a t e . The d i f f e r e n c e i n behavior between the F j ( y j ) curves f o r CPRF and CFRF i n F i g u r e 2 i s due t o the s c a l e f a c t o r e f f e c t o f (Mj+1)/ Mj and kg ( i n k j ) . These velocity-dependent terms are l a r g e r f o r CPRF and s m a l l e r f o r CFRF i n the i n i t i a l p o r t i o n o f the bed, and they cause the F j ( y j ) curves t o r i s e f a s t e r from c e l l t o c e l l i n CPRF. Therefore, i f m u l t i p l e steady s t a t e s e x i s t , the region o f m u l t i p l i c i t y w i l l be s h i f t e d toward the bed entrance i n CPRF and toward the bed e x i t i n CFRF. This e f f e c t can be b e t t e r appreciated i n F i g u r e 3, which i s a of j f o r the same c o n d i t i o n and F j ( y j - ) branches cross u n i t y and coalesce a t the t r i f u r c a t i o n p o i n t f i r s t f o r CPRF, next f o r a x i a l f l o w , and l a s t f o r CFRF. The open i n t e r v a l [ F j ( y j + ) , j ( y j ~ ) 3 i s measure o f the pa rameter space f o r which m u l t i p l i c i t y can occur. CPRF presents a l a r g e r i n t e r v a l and CFRF a s m a l l e r i n t e r v a l than a x i a l flow a t the same average space v e l o c i t y . Thus, i n g e n e r a l , CFRF suppresses m u l t i p l i c i t y and CPRF promotes m u l t i p l i c i t y as compared t o a x i a l flow a t the same average space v e l o c i t y . I n a l l the c a l c u l a t i o n s performed, however, CPRF never induced m u l t i p l i c i t y nor d i d CFRF completely suppress m u l t i p l i c i t y when compared t o the " e q u i v a l e n t " a x i a l flow case. On the other hand, the p o s s i b i l i t y t h a t condi t i o n s may e x i s t under which t h i s could occur has not been e l i m i nated. I t should be noted t h a t Hlavacek and Kubicek (1) concluded t h a t CPRF, and not CFRF, tends t o suppress m u l t i p l e s o l u t i o n s f o r the quasicontinuum a x i a l d i s p e r s i o n model without interphase t r a n s port resistance. A s t a b i l i t y a n a l y s i s o f the t r a n s i e n t equations [1-4] y i e l d s the same necessary and s u f f i c i e n t s e t o f c o n d i t i o n s f o r asymptotic s t a b i l i t y as obtained by Vanderveen, e t a l . {6), v i z . g
F
F
<
F
b._ > Ul
0
;b
D2
>
0
a
2
2
; b. b H > b _b. . + b _ ; b > D l J2 33 3I J4 33 34
0
,
[11]
except, o f course, t h a t f o r r a d i a l f l o w , M and H are f u n c t i o n s o f j . The f o u r t h c o n d i t i o n , b j 4 > 0 , i s simply c o n d i t i o n [ 7 ] , i . e . , d F j ( y j ) / d y j < 0 . Thus a l l steady s t a t e s on the p o s i t i v e slope branch o f F j ( y j ) are unstable w i t h respect t o s m a l l p e r t u r b a t i o n s . Steady s t a t e s on the h i g h and low temperature branches w i t h nega t i v e slope have a chance o f being s t a b l e i f i n a d d i t i o n they s a t i s fy the f i r s t three c o n d i t i o n s i n [ 1 1 ] . For g a s - s o l i d systems w i t h a i 4 / a 3 » 1, the f i r s t two c o n d i t i o n s i n [11] imply the slope c o n d i t i o n (§_ §_,9) . C o n d i t i o n [7] i s stronger than the slope c o n d i t i o n i f f
(l V
+ H . ) M . / ( H . ( M . + δ.)) 3 3 3 3 3 '
> 1
,
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
[12]
CALO
Radial Flow, Fixed Bed Reactors
Figure 2. Fffîj) curves as a function of cell number for CPRF and CFRF ( = 0.5). (P = 9kP , T = 667°K, T = 667% β = 7.5, M/H = 1.1183). The curves are labeled with cell numbers. P
0
a
0
0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
C e 1 1 Numbe r ,
j
Figure 3. F/$+) and F/5,—) as a function of cell number for CPRF, CFRF, and axial flow for the same conditions as in Figure 3. The CPRF and CFRF curves are dashed to F/5i,t)„.. since the Fj(yjj) are not known. &
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
45.
CALO
557
Radial Flow, Fixed Bed Reactors
which i s always s a t i s f i e d f o r M/H > l,and thus c o n d i t i o n [7] im p l i e s the f i r s t , second, and f o u r t h c o n d i t i o n s i n [11]. For M/H < 1 and 6 j - 1, i n e q u a l i t y [12] i s not s a t i s f i e d , and the slope c o n d i t i o n w i l l be s t r o n g e r . In any case, f o r a steady s t a t e on the negative slope branches o f F j ( y j ) t o be stable., the t h i r d con d i t i o n i n [11] must a l s o be s a t i s f i e d , and as has been p o i n t e d out (§_r§) ι t h i s c o n d i t i o n i s a complex expression w i t h no obvious p h y s i c a l meaning. A comparison o f r e l a t i v e magnitudes o f c o n d i t i o n [12] f o r M/H > 1 r e v e a l s t h a t r a d i a l flow tends t o d e s t a b i l i z e the bed a t the outer p e r i p h e r y and s t a b i l i z e the bed a t the i n n e r core t o a g r e a t e r extent than a x i a l flow a t the same t o t a l space v e l o c i t y . Selectivity Effects The reapportionmen gous t o v a r i a b l e volume would be expected t o a f f e c t product s e l e c t i v i t y i n s e r i e s and para l l e l r e a c t i o n s . For two p a r a l l e l f i r s t o r d e r , exothermic r e a c t i o n s , the p a r t i c l e equations [3, 4] become (v. - v.) - (k . + k .)v. = 0 3 3 ID 23 3 K
J
K
[13]
j
[14]
(Yj " Y j ) + ( 3 ^ 1 . + 3 k ) v . = 0 2
2 j
The r e s u l t s o f a t y p i c a l c a l c u l a t i o n are presented i n Figure 4. For the parameters chosen (see f i g u r e c a p t i o n ) , CPRF i n c r e a s e d the y i e l d o f R and decreased the y i e l d o f S, w h i l e CFRF acted i n the opposite sense. Thus, i n t h i s case, the y i e l d o f R v a r i e d 6.2% and t h a t o f S 6.7% simply according t o whether the r e a c t o r was operated i n CPRF o r CFRF. For two s e r i e s f i r s t order, exothermic r e a c t i o n s , the p a r t i c l e mass balance i s the same as Equation [ 3 ] , but the p a r t i c l e energy balance (Eq. [4]) becomes y
j "h
+
'ΛΛ
+
2 2?j -
&
k
0
-
[15]
where Wj i s the f r a c t i o n o f i n t e r m e d i a t e . A l s o , a d d i t i o n a l p a r t i c l e and f l u i d mass balances are r e q u i r e d f o r the i n t e r m e d i a t e . The r e s u l t s o f a t y p i c a l c a l c u l a t i o n f o r t h i s case are presented i n F i g u r e 5. As compared t o a x i a l f l o w , and f o r the parameter values chosen (see f i g u r e c a p t i o n ) , CPRF i n c r e a s e d the y i e l d o f product S and decreased the y i e l d o f intermediate R, w h i l e CFRF again acted i n the opposite sense. The y i e l d o f S v a r i e d 9.5% and t h a t o f R 77.3% simply a c c o r d i n g t o flow d i r e c t i o n i n c y l i n d r i c a l r a d i a l flow. A l s o , when the crossover p o i n t f o r R and S i s near the r e a c t o r e x i t i n a x i a l f l o w , CPRF can y i e l d a product w i t h S > R, w h i l e CFRF y i e l d s a product w i t h R > S. This occurs when the crossover p o i n t moves toward the bed entrance i n CPRF, i n c r e a s i n g S over R, and moves out o f the r e a c t o r e x i t i n CFRF, thereby i n c r e a s i n g R over S. Of course, d i f f e r e n c e s i n s e l e c t i v i t y due t o flow d i r e c t i o n i n an RFBR are extremely s e n s i t i v e t o the s p e c i f i c k i n e t i c parameters.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
558
CHEMICAL REACTION ENGINEERING—HOUSTON
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
45. CALO
Radial Flow, Fixed Bed Reactors
559
However, i t i s c o n c e i v a b l e , depending on the r e a c t i o n system, t h a t s e l e c t i v i t y e f f e c t s i n r a d i a l flow could be s i g n i f i c a n t . T r a n s i e n t Behavior When m u l t i p l e steady s t a t e s e x i s t , steady s t a t e p r o f i l e s can be determined o n l y by a t r a n s i e n t a n a l y s i s . T y p i c a l r e s u l t s o f the numerical s o l u t i o n o f the t r a n s i e n t simple c e l l equations [1-4] are presented i n F i g u r e 6. Here f l u i d temperature p r o f i l e s are presented f o r CPRF and CFRF f o r c y l i n d r i c a l geometry (p = 0.25), and a x i a l flow f o r the same average space v e l o c i t y a t 5, 15, and 30 minutes a f t e r s t a r t up. The feed and i n i t i a l c o n d i t i o n s are noted i n the f i g u r e c a p t i o n . S e v e r a l i n t e r e s t i n g features are apparent. The i n c i p i e n t p r o f i l e s a t 5 minutes are much c l o s e r t o gether than a t 30 minutes. I n each case the r e a c t i o n zone i s f o r med w i t h i n 15 minutes, an the bed e x i t . I t i s q u i t the most, and the CPRF p r o f i l e the l e a s t . I t i s a l s o i n t e r e s t i n g to note t h a t a l l the CFRF and a x i a l flow p r o f i l e s s i g n i f i c a n t l y overshoot the maximum a d i a b a t i c f l u i d temperature, y , w h i l e the CPRF p r o f i l e a l s o does but t o an almost i m p e r c e p t i b l e e x t e n t . The creep behavior i s d i r e c t l y r e l a t e d t o the degree o f temperature overshoot, s i n c e i t i s caused by c o o l i n g o f the over-temperature c e l l s t o l e s s than o r equal t o y , which, o f course, cannot be ex ceeded a t steady s t a t e . Thus i n F i g u r e 6, the a x i a l flow and CFRF p r o f i l e s continue t o creep u n t i l the c e l l s near the bed e x i t c o o l . The degree o f overshoot, and hence, p r o f i l e creep, i s a func t i o n o f the i n i t i a l bed temperature, y-jo- study was conducted i n which the i n i t i a l bed temçerature was v a r i e d keeping a l l the other parameters constant. As yjQ was increased from 1.0 t o 1.17, t h e p r o f i l e s f o r a l l three flow modes i g n i t e d c l o s e r t o the bed en t r a n c e . A l l the p r o f i l e s were s t a t i o n a r y a t 30 minutes from s t a r t up except f o r the CFRF p r o f i l e f o r yjQ = 1.17, which overshot the maximum a d i a b a t i c f l u i d temperature and was s t i l l c r e e p i n g . A l s o , for yjQ = 1.17 the CPRF and a x i a l f l o w p r o f i l e s were the c l o s e s t together, w h i l e the CFRF was f a r t h e s t from the other two and mov ing away. Thus, f o r i n i t i a l bed temperatures exceeding the feed temperature, steady s t a t e m u l t i p l i c i t y tends t o accentuate the " e a r l y - l a t e " r e a c t i o n zone phenomenon observed f o r the unique steady s t a t e p r o f i l e s . m
m
A
Conclusions In g e n e r a l , CPRF i s the b e t t e r mode o f o p e r a t i o n f o r the RFBR when m u l t i p l e steady s t a t e s are p o s s i b l e . I n a d d i t i o n t o e x p e d i t ing the approach t o steady s t a t e , the establishment o f the CPRF p r o f i l e e a r l y i n the bed i s an advantage i n cases where the r e a c t i o n zone g r a d u a l l y creeps toward the bed e x i t due t o c a t a l y s t de a c t i v a t i o n . When o n l y unique steady s t a t e s are p o s s i b l e and/or f o i p a r a l l e l and s e r i e s r e a c t i o n s , the p r e f e r r e d flow mode may depend on other c o n s i d e r a t i o n s .
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
Figure 6. Transient behavior of temperature profiles in ÇPRF, CFRF (p = 0.25), and axial flow ( = 0.25, P = HkP , T = 667°K, T = 883°K, β = 5 M/H = 1.67) P
0
a
G
0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
45.
CALO
Radial Flow, Fixed Bed Reactors
561
Notation [see a l s o Vanderveen, e t a l . (6)] Aj Fj Gj Hj
= = = =
defined i n t e x t Oj d e f i n e d by Eq. [6] R r d e f i n e d by Eq. [5] U,u dimensionless HTU f o r heat t r a n s f e r v,w k j = dimensionless r a t e constant y Mj = dimensionless HTU f o r mass transfer f
3 = (-AH)k /hfT γ = (-ΔΕ)/RgT g
0
0
= defined i n text = radius = i n t e r s t i t i a l f l u i d ve locity = r e a c t a n t mole f r a c t i o n •» T / T Q (dimensionless temperature)
oj = k j / ( l + k j ) ρ = Ri/R
2
S u b s c r i p t s and S u p e r s c r i p t j m η 0
= c e l l number = maximum = last cell = feed c o n d i t i o n s
= p a r t i c l e phase 1 = inner radius 2 = outer r a d i u s
Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9.
Hlavacek, V . , and Kubicek, M . , Chem. Eng. S c i . (1972), 27, 177. Dudukovic, M. P . , and Lamba, H. S., 80th AIChE National Meet ing, Boston (1975), paper #576. Cimbalnik, Z . , et al., 2nd CHISA Cong., Czechoslovakia (1965). Raskin, A. Y a . , et al., Theor. Found. Chem. Tech. (1968), 2, 220. Raskin, A. Y a . , and S o k o l i n s k i i , Yu. Α., Khim Prom. (1969), 45, 520. Vanderveen, J . W., Luss, D . , and Amundson, N. R., AIChE J . (1968), 14, 636. Wicke, E., Chem. Ing. Tech. (1965), 37, 892. Ervin, Μ. Α., and Luss, D . , AIChE J. (1970), 16, 979. L i u , S.-L., and Amundson, N. R., IEC Fund. (1962), 3, 200.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
46 Flow Control Operation of a Plug-Flow Tubular Reactor with High Heat Diffusivity Y U . P. G U P A L O , V . A . N O V I K O V , and Y U . S. R Y A Z A N T S E V The Institute for Problems in Mechanics, USSR Academy of Sciences, Moscow, USSR
1. Formulation of the problem I t i s known that c o n t r o l l e actors at n a t u r a l l y unstable conditions should be of i n t e r e s t i n the design of some commercial reactors because the unstable or s o - c a l l e d intermediate s t a t e s may o f f e r a d e s i r a b l e compromise between a s t a t e of very low a c t i v i t y or conversion on the one hand and a s t a t e of poor s e l e c t i v i t y on the other [1]. In the present paper the model of a t u b u l a r r e a c t o r with n e g l i g i b l e mass diffusivity and high diffusivity of heat i s considered. The dimensionless equations with the boundary and initial conditions governing the unsteady mass and heat t r a n s f e r i n the one-dimensional plug flow t u b u l a r r e a c t o r with high heat d i f f u s i v i t y can be w r i t t e n i n the form
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
46.
GUPALO ET AL.
Flow Control of Plug Flow Tubular Reactor
563
where X i s a s p a t i a l coordinate ( 0 ≤ X ≤ L), L i s a reactor length, t i s a time, c i s a concentra t i o n of r e a c t i v e species i n r e a c t o r volume, c is a feed concentration of r e a c t i v e s p e c i e s , ξ i s an ex tent, u i s flow v e l o c i t y , ε i s the r a t i o of a bulk fluid volume to a t o t a l one, Τ i s a temperatu re; V , S are a r e a c t o r volume and a surface of r e a c tor w a l l s , * g density and a heat capacity o
c
of f l u i d ;
j* , c s
Q
a
r
e
a
are a density and a heat capacity
of c a t a l y s t , T i s a feed flow temperature, h i s a heat of r e a c t i o n for reaction rate, Ε i s a gas constant, u* i s c h a r a c t e r i s t i c reactant flow v e l o c i t y * In obtaining Eqs (1.1) and (1.2) mass d i f f u s i v i t y has been neglected; high d i f f u s i v i t y of heat and f i r s t order Arrhenius k i n e t i c s f o r one step exother mic chemical r e a c t i o n has been assumed. These assump t i o n s can serve as a f a i r approximation f o r some kinds of f l u i d i z e d - b e d r e a c t o r [g] . The Eq. (1.2) can be derived f o r m a l l y by i n t e g r a t i o n over the t o t a l length of the r e a c t o r . The s o l u t i o n s of the steady-state forms of Eqs (1.1) and (1.2) can be w r i t t e n as Q
The dependence of the steady-state temperature Θ on parameter ν f o r f i x e d values of θ£ , and g obtained from Eq. (1.6) are presented i n F i g . 1, which shows that the m u l t i p l i c i t y of the steady s t a tes i n p o s s i b l e . F o r example three steady-state tem peratures correspond to the value ν = v » I t i s known that the upper and lower steady s t a t e s 0 , 0"" are s t a b l e , meanwhile the intermediate steady s t a t e i s unstable [ 3 ] · 0
e
+
2. The method of c o n t r o l Consider the p o s s i b i l i t y of s t a b i l i z a t i o n of the un^ s t a b l e intermediate steady s t a t e by the method of p r o p o r t i o n a l c o n t r o l (see, f o r example [ 4 ] ). Up t o now the theory of chemical r e a c t o r c o n t r o l was f o c u -
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
564
sed primerely upon the c o n t r o l of a s t i r r e d r e a c t o r 1^2 · The f i r s t example of the a n a l y s i s of the un stable steady s t a t e s t a b i l i z a t i o n f o r d i s t r i b u t e d pa rameter r e a c t o r was given r e c e n t l y by Oh and Schmitz
[1]· In the case under consideration the c o n t r o l l e d v a r i a b l e i s the temperature θ and the manipulated v a r i a b l e i s the flow v e l o c i t y ν . The feed back r e l a t i o n s h i p i s as f o l l o w s v ( t ) = v { l + ά [ θ ( ΐ - ΐ ) - θ|]} 0
(2.1)
4
where θ| i s intermediate steady-state temperature, f j i s a time l a g , d i s t a b i l i z a t i o In view of (2.1 tively, -g exp (- β/θ°) - θ° + 1 - exp — = : a.= 0 (2.2) v [ l + d(9°- 9|)J The r e l a t i o n s h i p (2.2) shows that i n the pre sence of c o n t r o l the upper and lower steady-state temperatures depend on parameter d and can be de termined as the i n t e r s e c t i o n points of curve 1, with l i n e s θ° = θ| + d ( v - v ) . corresponding to d i f f e r e n t values of d ( l i n e s 2-7) i n F i g . 1; The dependence of θ° on d r e s u l t i n g from Eq. (2.2) are pointed out i n F i g . 2. I t can be seen that f o r d > d the i n termediate steady s t a t e turns to be the lower one and f o r d > d± i t becomes the s i n g l e steady s t a t e . The value of d can be obtained from the c o n d i t i o n that 0
c
c
the l i n e θ° = 9Î + d ( v - v ) i s tangent to the curve 1. 0
β d
= —
?
v
0
Γβ g exp(- β/θ|) exp L E . +
I f the i n e q u a l i t y dy s t a t e condition considered as d>d_.
d >d
Ί (
2
>
3
)
takes place the s t e a -
θ° = θ| should s a t i s f y the s o - c a l l e d slope f o r s t a b i l i t y . Therefore one can expect the system of r e a c t o r c o n t r o l to be e f f e c t i v e This q u a l i t a t i v e conclusion requires r i g o -
rous approaches. In order to analyse the s t a b i l i t y of steady state under c o n t r o l , ire use the small ^pertur bation method. By s u b s t i t u t i n g Θ ( Ό = 9 ° + e ' W and ξ(χ,-ε) = ?/(x) + ξ ' ( χ , Ό i n t o Eqs (1.1)-(1.4) and (2.1) one can obtain by the Laplace transform the so l u t i o n f o r θ'(C) and ξ ' ί χ , Ό . I t can be found that a l l the s i n g u l a r i t i e s of t h i s s o l u t i o n s are poles and
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
46. GUPALO ET AL.
Flow Control of Plug Flow Tubular Reactor
565
are determined by the roots of c h a r a c t e r i s t i c equation. Y(s)
= s
2
0
0
+ a^s exp (- sv
2
1
+ a^ + [ a ^ exp (-sv°i: ) - a J s " " [ l - exp(-s)] = 0, d
6
s= p/v°
(2.4)
^ = — ^ ( 9 ·
- Θ8),
ω -
a = 2
ί ^ [ ΐ
9 a, =
b
v
d
*^
[
θ
ο
2
a
fi
=
b a> £
«—h-
-
-
b
exp(- | ) ] 0
C
1 + exp (- | ) ]
θ " -
0
, bχ exp ( - -o)
( p - i s the Laplace transform v a r i a b l e ) . The neces sary and s u f f i c i e n t c o n d i t i o n f o r s t a b i l i t y of the c o n t r o l l e d r e a c t o r to small perturbations i s that the r e a l parts of the roots of Eq. (2.4) are negative. Therefore the c o n t r o l l e d r e a c t o r are s t a b l e i f a l l the roots of the Eq. (2.4) l i e i n the r i g h t h a l f - p l a ne of the complex plane s = χ + i y . We chose the countor Γ » Γ + Q where fj i s the r i g h t h a l f - c i r c l e of large radius R with the centre l o c a t e d i n Zero point and Γ i s the part of the imaginary axis l y U R . I t can be shown that the increament of argument V(s) on Π| at R oo i s equal t o 2^r f o r any value of a · Λ
ζ
3· The i d e a l c o n t r o l i n Eq.
In the s p e c i a l case of i d e a l c o n t r o l by putting (2.4) f j , = 0 one can obtain
Y ( s ) = s 2 + fljs -
+ £ 2 ( 1 - e~ )/s s
(3.1) £,=
- a3 " 4» a
&z=
a
5
- a 6f
^3= i a
+
a
2
The f u n c t i o n ( 3 · Ό depends on s as w e l l as on three parameters & , Ω,χ . To analyse the s t a b i l i t y of c o n t r o l l e d r e a c t o r we have to f i n d thedomain i n three-dimensional space ( Çl^ Ω > ^3 ) ^ k& k η
9
2
n
w
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
c
CHEMICAL REACTION ENGINEERING—HOUSTON
566
there are no roots of V ( s ) with p o s i t i v e r e a l p a r t s . To do t h i s we consider the behaviour of the f u n c t i o n Y ( s ) on Γ , I t can be seen that the r e a l p a r t s of roots of Y ( s ) vanish f o r those values of , Ώ-ζ* Ώ which belong to the surface defined by the f o l l o wing equations 2
3
= -y
ο
2
sm y
+ a y
Ί
,
o
=
Q
3
1 - cos y
—z—
(3.2)
1 - cos y
04 y < 0 0 The a n a l y s i s of Eq ( 3 · 2 ) reveals that f o r the domain bounde
and plane Sl - - f l the increament of argument V (s) on i s equal to -2X . Therefore the t o t a l i n c r e a ment on Γ -+ i s nought and i s the s t a b i l i t y 1
ή
domain because i t contains no roots of V (s) with po s i t i v e r e a l parts. The r e s u l t s obtained permit to analyse the i n fluence of the c o n t r o l on the intermediate steady s t a t e s t a b i l i t y . The s e c t i o n of the s t a b i l i t y domains and the point A corresponding to intermediate steady temperature θ° = θ| f o r d i f f e r e n t values of parame ter d are shown i n F i g . 3 . The s e c t i o n of s t a b i l i t y domain corresponding to d = 0 i s dashed i n F i g . 3 · I t i s seen that the intermediate steady s t a t e becomes s t a b l e when d > d . I f d = d the point A achieves the boundary of the s t a b i l i t y domain. The value d can be obtained from the equation Sl^—fï^, which i s i d e n t i c a l to Eq. (2.4). Thus the intermediate steady s t a t e becomes s t a b l e when i t turns to be the lower steady-state. The numerical a n a l y s i s shows that i n the n o n l i n e a r case the value of d depends on the pert u r b a t i o n amplitude. F o r example i f d = d the i n t e r mediate steady s t a t e i s s t a b l e as the temperature perturbations are l e s s than Δ θ (see F i g . 2). 2
4. The influence of time l a g I t has been shown that i f d > d and f = 0 the c o n t r o l l e d steady s t a t e i s s t a b l e . To study the e f f e c t of time l a g on s t a b i l i t y we consider the i n crease of argument of f u n c t i o n (2.4) on f f o r d i f f e r e n t values of t
z
t
=
λ
c
5
=
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
46. GUPALO ET AL.
Flow Control of Plug Flow Tubular Reactor
567
Figure L The steady-state diagrams for several values of the parameter d. Curve 1 corresponds to the dependence of the steady-state temperature θ° on parame ter ν for fixed values of 9 ", β, and g. Curves 2-7 are lines θ° = θ ° + d(v — corresponding to different values of 0
2
f
j j
ΔΘ f\ \
1 1
J
1 ' 1
Figure 2. The dependence of the steady-state temperature θ ° on stabilization parameter d
I ι
£ 10
0
/
/
X2,
ο Ai
ΊΟ
Figure 3. The sections of the sta bility domain. The points A corre spond to the intermediate steadystate temperature 0 ° = $2°·
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
568
s t a b l e , and f o r *i = i t i s ^ u n s t a b l e . Thus t h e ^ c r i t i c a l value of delay" time exists. I f = the curve corresponding to Ϋ ( i y ) i n the Nyquist p l a ne goes through zero p o i n t . From t h i s c o n d i t i o n n e can get the system of equations f o r obtaining 'Cj â
-y
2
+ a
- a + a
4
+ [ a cos(yv°<) - a 5
sin(yv° x j )
5
cos(yv°Xi)
?
0
y|V, c o s C y v ^ ) -[a
3
1
~
C Q S y
? + a
6
1
2ί£-Σ ysin(yv°
= 0
(4.1)
Φ
S3£J:]eiii(yv^2) = Ο
+
The computing r e s u l t s of the s o l u t i o n of Eq. (4.1) i n ^ > ^T- plane are shown i n F i g . 5. The curve Î J = C Y (d) separates the i n s t a b i l i t y domain from the s t a b i l i t y domain (dashed one). I t can be seen that the c r i t i c a l value of decreases i f the s t a b i l i z a t i o n parameter d grows. Therefore the upper l i mit of d i s determined by the value of time l a g É
u
·
5 . Nonlinear a n a l y s i s The t r a n s i e n t behavior of the r e a c t o r f o r f i n i te perturbations was studied by computer simulation of Eqs (1.1)-(1.4). The curves 1 and 2 i n the F i g . 6 demonstrate the t r a n s i t i o n from the lower s t a b l e s t a te to s t a b i l i z e d intermediate one a f t e r beginning of the p r o p o r t i o n a l c o n t r o l operation at ΐ = 0. The cur ve 1 corresponds t o the case of i d e a l c o n t r o l (^
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
46. GUPALO ET AL.
Flow Control of Plug Flow Tubular Reactor
569
V
0.6
-a
-0.6
01
U
Figure 4. The curves W = ψ(ίυ) = U + iV, 0 $C y on the Nyquist plane for three values of the time lag
ι
-Λ
J
1/ 1
Figure 6. The transient behavior of the reactor temperature obtained by the computer simuhtion. Curve 1 corresponds to the ideal control (V = 0). Curve 2 corresponds to nonideal control with parameters d and r from stability domain. Curve 3 corresponds to the parameters d and T from instability domain at Figure 5. d
d
d
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
570
I t was obtained a l s o that f o r the points ( T j , d) from the i n s t a b i l i t y domain at d > d only unstable steady s t a t e e x i s t s . I n t h i s case as the numerical c a l c u l a t i o n s pointed out the sustained o s c i l l a t i o n s of the concentration and temperature are p o s s i b l e . A
6. Conclusion I t i s shown that the s t a b i l i z a t i o n can be achieved by p r o p o r t i o n a l f l o w - c o n t r o l method as long as the time l a g i n the c o n t r o l a c t i o n does not ecxeed c e r t a i n c r i t i c a l value. By numerical s o l u t i o n a r e s t r i c t i o n to be imposed on the c o n t r o l parameter f o r s t a b i l i t y of an intermediate s t a t e at given d i s t u r bance l e v e l i s defined By computer s i m i l a t i o on n o n l i n e a r system i s studied. I t i s shown that f o r zero time l a g the s t a b i l i z e d intermediate steady s t a te i s achieved without o s c i l l a t i o n s . Under imperfect c o n t r o l operation damping o s c i l l a t i o n s of concentrat i o n p r o f i l e and temperature near intermediate s t a t e can e x i s t the amplitude being dependent on the timel a g value. F o r c e r t a i n values of f l o w - c o n t r o l parameters sustained o s c i l l a t i o n s of concentration prof i l e and temperature i n the r e a c t o r are p o s s i b l e . Literature Cited 1. 2.
Oh S.H., Schmitz R.A. Chem. Eng. Commun. (1974)
1, 199.
Borodulya V.A., Gupalo Yu.P. Matematicheskie modeli himicheskih reaktorov s kipyashim sloem. "Nauka i technika", Minsk, 1976. 3. Gupalo Yu.P., Ryazantsev Yu.S. PMTF (1969) 1, 82. 4. A r i s R., Amundson N.R. Chem. Eng. Sci. (1958) 7, 121, 132, 148. 5. Schmitz Roger A. Advances in chemistry s e r i e s
(1975) 148, 156.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
47 Use of Intensity Function Representation of Residence Time Variability to Understand and Improve Performance of Industrial Reactors PHILIP T . W O O D R O W Union Carbide Corporation, Chemicals and Plastics Division, Research and Development Department, South Charleston, W V 25303
The application o established method for identifying process system f l u i d flow and mixing characteristics. Tracer data analysis v i a this theory can give valuable insight into a system's hydrodynamic charac teristics. It has been applied to understand and improve indus trial reactor performance. Two applications are discussed. Introduction Residence time d i s t r i b u t i o n theory i s appropriately applied when the experimental objective i s to account for a system's f l u i d flow and mixing behavior. This i s a v i t a l objective because to predict and/or analyze process equipment performance one must know the amount of mixing, the manner i n which f l u i d passes through the equipment, and the time that a given f l u i d element can be expected to remain i n the system. Experimentally this information can be determined by admitting a tracer into the system and monitoring its behavior as it exits the system. Common tracer input forms are the pulse and step. "System" i n this paper refers to systems with closed boundaries, i.e., a system where material can enter and exit only once. Three assumed properties, inherent i n residence time analysis, should be noted: • Stationarity. The system's average physical properties are time independent. Although i n r e a l i t y the proper ties fluctuate around some average, these time fluctua tion periods are very short compared to a p a r t i c l e ' s residence time. Hence, the system and i t s properties can be c l a s s i f i e d as quasi-steady which i s necessary to perform meaningful residence time studies. • Ergodicity. By injecting a sample with a large number of tracer molecules, the residence time density thus derived would be equivalent to the residence time density obtained from a large number of experiments using one tracer molecule. ©
0-8412-0401-2/78/47-065-571$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
572 •
Although the tracer should be experimentally distinguishable, i t must possess the same "mixing" properties as the system f l u i d . Within the scope of residence time analysis, there are two fundamental functions and an additional derivable function. Although these are defined elsewhere Ο ) , for purposes of completeness they are given here. F i r s t , is the residence time density function, f ( t ) . The physical interpretation of f ( t ) is given by the following: On viewing a particle which has just entered the system, the prob a b i l i t y of i t s leaving within a time interval (t to t + dt) is equal to f(t)dt. Mathematically f ( t ) i s constrained by:
/f(t)dt « 1
f(t) is the system response to a unit impulse of tracer material. Second, i s the integral of the residence time density or cumulative density function, F ( t ) , where t β
F(t)
1
1
Jfit'Jdt ( t is a dummy variable of integra0 tion) with F(0) * 0 and F( ) » 1 00
F(t) gives the fraction of particles possessing a residence time of t or less. F(t) i s the system response to a unit step of tracer material. There is also the compliment of F(t), F*(t), where F*(t)
« 1 - F(t)
F*(t) gives the fraction of particles possessing a residence time exceeding t. Finally, there is a function which indicates the escape probability for a particle which has stayed in the system for a period t. This function, the intensity function (2) , λ (t), is useful i f one is interested in the probability of a particle leaving a system in the time interval ( t , t + dt) given that the particle has already stayed in the system for a time t. This probability i s denoted b y X ( t ) d t and may be deduced v i a the following: let: A be the event that a particle which has just entered a system leaves in the next time interval, dt. Β be the event of the particle not leaving before t.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
47. WOODROW
Performance of Industrial Reactors
573
C
be the event that the p a r t i c l e w i l l leave i n the next i n t e r v a l , d t , given that i t has not l e f t before. In p r o b a b i l i t y terms t h e r e f o r e : P(A)
« P(B) · P(C) » P(B) · P(A/B)
In terms o f the previous d e f i n i t i o n s : P(A) P(B)
= f(t)dt « F*(t)
P(C)
= P(B/A) * λ(t)dt
Therefore : f ( t ) d t » F*(t)
X(t)dt
or: A ( t ) - f ( t ) / F * ( t ) = -d/ <£n(F*(t))) A l s o note that f ( t ) and A ( t ) are r e l a t e d transformation: dt
by the f o l l o w i n g
t f i t ) - λ ( t ) exp
1
JxU^dt ] ο
Hence, the i n t e n s i t y f u n c t i o n i s another way of e x h i b i t i n g resi dence time v a r i a b i l i t y and, as w i l l be shown i n the subsequent examples, y i e l d s flow mechanism i n s i g h t and h i g h l i g h t s d i s t i n c t features o f d i f f e r e n t d i s t r i b u t i o n s . A common approach used i n t r a n s l a t i n g the a b s t r a c t residence time data i n t o more p h y s i c a l l y meaningful concepts i s t o compare the experimental d i s t r i b u t i o n s t o d i s t r i b u t i o n s derived from i d e a l i z e d models. This approach has a drawback i n that f ( t ) and/or F ( t ) f u n c t i o n s derived from d i f f e r e n t p h y s i c a l models may appear to be q u i t e s i m i l a r . Because a large number o f d i f f e r e n t models can lead t o s i m i l a r f u n c t i o n s , the b a s i c flow system features should be e l u c i d a t e d i n more p r e c i s e terms. For t h i s reason the i n t e n s i t y f u n c t i o n , A ( t ) , i s a more e f f e c t i v e way o f e x h i b i t i n g residence time c h a r a c t e r i s t i c s rather than d e n s i t i e s or d i s t r i b u t i o n s . The i n t e n s i t y f u n c t i o n can give a d i r e c t i n d i c a t i o n o f stagnancy and/or bypassing according t o the following: • A system w i l l e x h i b i t bypassing i f a f l u i d element can s h o r t - c i r c u i t from i n l e t to o u t l e t . This would be seen by a peak i n f i t ) f o r t l e s s than the apparent mean residence time. The i n t e n s i t y function (escape
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
574
•
p r o b a b i l i t y ) would decrease over some time i n t e r v a l before the apparent mean residence time. A system w i l l e x h i b i t stagnancy i f a f l u i d element enters a region only weakly connected w i t h the r e s t of the system. This would be i n d i c a t e d by slow decay of f ( t ) f o r t greater than the apparent mean residence time. E x p e r i m e n t a l l y , t h i s may be hard to d i s c e r n . The i n t e n s i t y f u n c t i o n would show a decrease over some time i n t e r v a l a f t e r the apparent mean residence time.
Case 1 - P l a n t Scale Reactor A c e t i c a c i d i s a commodity chemical produced by Union Carbide Corporation v i th l i q u i d phas oxidatio f butane While a c e t i c a c i d i s th and e t h y l acetate are v a l u a b l e by-products. Large s c a l e gas l i q u i d r e a c t o r s are used to p r a c t i c e t h i s technology. In general the p l a n t r e a c t o r performance was i n f e r i o r i n both p r o d u c t i v i t y and s e l e c t i v i t y when contrasted to p i l o t u n i t s c a l e r e a c t o r s c a r r y i n g out the same r e a c t i o n under equivalent conditions. The i n f e r i o r performance was manifested i n high temperatures necessary to t r a n s f e r the oxygen to the l i q u i d phase f o r chemical r e a c t i o n . The higher-than-desirable temperatures adversely a f f e c t e d r e a c t i o n s e l e c t i v i t y , producing undesirable q u a n t i t i e s of non-usable by-products, e.g., carbon d i o x i d e and water. I f lower r e a c t i o n temperatures could be achieved without lowering reactant feed r a t e s , r e a c t i o n s e l e c t i v i t y would change to enhance both the a c e t i c a c i d and v a l u a b l e r e a c t i o n by-product e f f i c i e n c i e s . In a d d i t i o n , lower temperatures would decrease r e a c t o r metal c o r r o s i o n r a t e s and a l l o w more s t a b l e and flexible c o n t r o l of the r e a c t i o n system. I t was suspected that f l u i d bypassing was o c c u r r i n g i n the p l a n t r e a c t o r s which would n e c e s s i t a t e o p e r a t i o n at higher temperatures to e f f e c t oxygen mass t r a n s f e r and reaction. Residence time d i s t r i b u t i o n s t u d i e s u s i n g i d e a l i z e d r e a c t o r flow models s t r o n g l y confirmed t h i s s u s p i c i o n . Residence time t e s t i n g of the p l a n t r e a c t o r s was infeasible due to severe c o n d i t i o n s , s a f e t y c o n s i d e r a t i o n s , and the neces s i t y to determine what m o d i f i c a t i o n s could be made during an impending p l a n t shut-down. Based on these c o n s t r a i n t s , a P l e x i g l a s s c a l e model of a p l a n t r e a c t o r , p r e v i o u s l y constructed but u t i l i z e d f o r v i s u a l mixing/flow p a t t e r n s t u d i e s o n l y , was the best a v a i l a b l e apparatus to perform a d d i t i o n a l work. Because c a p i t a l c o n s t r a i n t s p r o h i b i t e d radical reactor geometry changes, e.g., L/D r a t i o , low cost m o d i f i c a t i o n of r e a c t o r i n t e r n a l s appeared to be the most expedient method f o r improving performance. An experimental p l a n was made to study
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
47. WOODROW
Performance of Industrial Reactors
575
the e f f e c t s o f i n t e r n a l s change on the residence time c h a r a c t e r i s t i c s o f the scaled-down p l a n t r e a c t o r . The e x i s t i n g i n t e r n a l c o n f i g u r a t i o n was studied as w e l l as e i g h t a l t e r n a t e c o n f i g u r a t i o n s . For each c o n f i g u r a t i o n the system was pulsed w i t h a h i g h l y conductive dye s o l u t i o n which afforded qualitative observation recording by motion p i c t u r e s and q u a n t i t a t i v e residence time d e n s i t y data acquisition by c o n d u c t i v i t y measurement. Each experiment was r e p l i c a t e d . The t r a c e r i n j e c t i o n was a pulse of such narrow width that f o r a l l i n t e n t s and purposes the system saw i t as an impulse. Hence, the output c o n c e n t r a t i o n response ( a f t e r n o r m a l i z a t i o n ) could realistically be regarded as the residence time d e n s i t y , f ( t ) . Figures 1, 2, and 3 e x h i b i t the s a l i e n t residence time study r e s u l t s . Figure 1 show three d i f f e r e n t c o n f i g u r a t i o n s p l a n t r e a c t o r and two a l t e r n a t e i n t e r n a l m o d i f i c a t i o n s (labelled A and B, r e s p e c t i v e l y ) . Figure 2 e x h i b i t s the residence time d i s t r i b u t i o n F ( t ) and Figure 3 e x h i b i t s the deduced i n t e n s i t y function X ( t ) . The i n t e n s i t y f u n c t i o n curves c l e a r l y show the suspected p l a n t r e a c t o r bypassing; some stagnancy i s a l s o i n d i c a t e d . The s l i g h t stagnancy of a l t e r n a t i v e A and the uniform behavior o f a l t e r n a t i v e Β are a l s o shown. I f i d e a l s t i r r e d tank behavior were superimposed on the p l o t i t would be a h o r i z o n t a l l i n e ( t h i s l i m i t i n g behavior i s discussed i n the second case o f i n t e n s i t y f u n c t i o n u t i l i t y presented l a t e r i n t h i s paper). Comparison of the f ( t ) and F ( t ) behaviors does l i t t l e t o i n d i c a t e which a l t e r n a t i v e i s c l e a r l y i n d i c a t i v e o f well-mixed p r o p e r t i e s . The f ( t ) curve f o r the e x i s t i n g p l a n t r e a c t o r does i n d i c a t e bypassing. The corresponding X ( t ) curve confirms the bypassing. Although a l l i n t e r n a l m o d i f i c a t i o n a l t e r n a t e s are not shown here, the i n t e n s i t y f u n c t i o n was o f equal u t i l i t y both i n differentiating between alternatives and assisting in a l t e r n a t i v e choice f o r p l a n t implementation. A l t e r n a t i v e Β was chosen as the recommended m o d i f i c a t i o n . Whereas one might f e e l that the moments o f the f ( t ) curves should give q u a n t i t i e s f o r d i f f e r e n t i a t i n g between the observed performances, they gave no s i g n i f i c a n t guidance i n t h i s case. The recommended m o d i f i c a t i o n was made i n a p l a n t r e a c t o r . Follow-up data and a n a l y s i s showed the modified r e a c t o r to a l l o w lower temperature operation at the same raw m a t e r i a l consumption r a t e s as the unmodified r e a c t o r s . Product a n a l y s i s showed a s i g n i f i c a n t l y higher c o n c e n t r a t i o n of d e s i r a b l e and hence more p r o f i t a b l e products. As a r e s u l t the remaining r e a c t o r s have been modified. The p l a n t can now produce the same commodity amount w i t h lower raw m a t e r i a l requirements o r conversely with the same raw m a t e r i a l consumptions, more product can be produced.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION
576
ENGINEERING—HOUSTON
1.0|—
ο
Existing Plant
Ι-
Δ
Alternative
0.5
Figure 1.
1.0
A
1.5
2.0
t
Salient residence time study results. Residence time density, f(t).
ο Existing Reactor
0.5
Figure 2.
1.0
1.5
2.0
t
Salient residence time study results. Resident time dis tribution F(t).
•ŒDaïuDŒom
O O D O O O O O O D
Δ
Δ
DOOOOOQOOOO ,
ο ο ο ο. Existing Reactor Δ Alternative A ° Alternative Β 0.5
Figure 3.
1.0
1.5
2.0
Salient residence time study results. Deduced intensity function λ(t).
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
47.
WOODROW
Performance of Industrial Reactors
577
Case 2 - P i l o t U n i t Scale Reactor E a r l y i n the development o f a new process, a p r o d u c t i v i t y l o s s was encountered when the process was moved from the exploratory scale reactor to a larger p i l o t unit scale reactor. A f t e r study o f many f a c t o r s , the problem was r e s o l v e d by i n s t a l l i n g a second i m p e l l e r on the p i l o t r e a c t o r mixing s h a f t . While the a c t i o n produced the d e s i r e d r e s u l t s , i t was not apparent why the one i m p e l l e r system had performed below expectations. The traditional scale-up criterion of horsepower/unit volume f o r mixed v e s s e l s had been used when moving from the e x p l o r a t o r y t o p i l o t r e a c t o r . H i s t o r i c a l l y this c r i t e r i a had proved to be s a t i s f a c t o r y . In an e f f o r t t o residence time data wa r e a c t o r s . Step t e s t i n g was used and thus the response was i n the form o f the residence time d i s t r i b u t i o n f u n c t i o n F ( t ) . F o r each system the residence time data was r e p l i c a t e d twice. Figure 4 shows the average r e s u l t s f o r the r e s p e c t i v e reactors. While there i s c l e a r l y a d i f f e r e n c e i n F ( t ) behavior, there i s no d i r e c t i n d i c a t i o n as to why the one i m p e l l e r r e a c t o r y i e l d e d about h a l f the p r o d u c t i v i t y as the two i m p e l l e r r e a c t o r . The F ( t ) data were transformed t o give the corresponding i n t e n s i t y f u n c t i o n , X ( t ) , curves shown i n Figure 5. Comparison of the curves c l e a r l y shows a d i f f e r e n c e between the two r e a c t o r s . The two i m p e l l e r r e a c t o r e x h i b i t s well-mixed behavior whereas the one i m p e l l e r r e a c t o r e x h i b i t s behavior i n d i c a t i v e o f a d i s t r i b u t e d system. This n o t i o n can be supported by examining a simple, t r a n s i e n t , d i f f u s i o n / c o n v e c t i o n flow model:
i l l Pe
a z
88
- âï
2
δζ
at
S o l u t i o n w i t h the f o l l o w i n g c o n d i t i o n s gives f ( t ) y ( z , 0) » 0 y(0, t) - 6 ( t ) lim y(z, t) finite β
Ζ ~#
initial
condition
and boundary
ζ > 0 t > 0 t > 0
oo
Pe
exp
I f one changes the i n l e t boundary c o n d i t i o n t o y(0,
t ) = H(t)
t
>
0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
578 F(t) can be derived:
Evaluation of F(t) for high values of the Peclet number, Pe, can present problems. Use of the approximations given by Abramowitz and Stegun (3) resolve computational problems. The intensity function for the diffusion/convection model is formulated by X(t) * f ( t ) / ( l - F(t)) Figures 6, 7, and 8 sho f ( t ) , F(t) X(t) different values of Peclet number. The limiting cases of Pe • <» (zero diffusivity-plug flow) and Pe 0 (infinite diffusivity well-mixed behavior) are also shown. By comparison of the intensity function results in Figure 5 to the curves shown in Figure 8, one can see directly the well-mixed behavior of the two impeller system versus the distributed behavior of the one impeller system. It was concluded that a well-mixed reactor was a necessary condition to ensure maximum productivity for the process under development. Hence, very firm mixing and f l u i d flow guidelines were established at the process development stage which reduced the risk of scale-up to plant equipment. β
Conclusions and Recommendations Based on the examples presented, i t is clear that intensity function representation of residence time v a r i a b i l i t y i s a valuable tool for understanding and discerning fluid mixing characteristics. Effective u t i l i z a t i o n of this tool requires good experimental technique. Determination of residence time characteristics and use of intensity function representation/ interpretation should be a c r i t i c a l step in the sequential development of exploratory, pilot unit and plant scale reactors. Nomenclature D L P( ) Pe V t
reactor diameter reactor length probability of event ( ) occurring axial Peclet number (VL/D ) f l u i d velocity axial diffusion coefficient dimensionless time
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
WOODROW
Performance of Industrial Reactors
1.0
Q Ο Ο Ο Ο
FM
Ο °
°
_ •
D
Q Ο Ο
0.5
8
~
·
Figure 4.
ρ ο Ο Ο Two Impellers
—
0.5
O n e Impeller
1.0
•
1
.
1
1.5
2.0
t
Residence time data. Residence time distribution function F(t).
3.0|Q Ο Ο Ο Ο Ο One Impeller
2.0
1.0Γ
ο οο οοο°° ο°
°
Ο.5
FigureS.
1.0
T
1.5
J.
w
o
Impellers
-Ι
2.0
t
Residence time data. Intensity function k(t).
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
580
0.
Figure 7.
Behavior ofF(t) for different values of Peclet number
0.5
Figure 8.
1.0
1.5
2.0
t
Behavior of k(t) for different values of Peclet number
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
47. WOODROW
y ζ 6(t-t*) H(t-t*)
Performance of Industrial Reactors
581
dimensionless c o n c e n t r a t i o n v a r i a b l e dimensionless a x i a l d i s t a n c e (Z = 1 corresponds to the bed o u t l e t ) u n i t impulse (Dirac d e l t a function) a t time t * t * u n i t step (Heaviside step function) a t time t=t*
Literature Cited 1.
2. 3.
Lapidus, L. and Seinfeld, J . Η., "Mathematical Methods in Chemical Engineering, Volume 3: Process Modeling Estimation, and Identification", pp. 289-339, Prentice-Hall, Inc., Englewood Cliffs, 1974. Naor, P. and Shinnar, R., I & EC Fundamentals (1963), 2, 278- 286. Abramovitz, M. and matical Functions", pp. 298-299, National Bureau of Standards, Washington, D. C., 1964.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
48 Oxidation of S O on Supported Molten
V O -K S O
2
2
5
2
2
7
Catalyst Kinetics under Varying Degree of Liquid Diffusion Influence
P. G R Y D G A A R D , H . J E N S E N - H O L M ,
H . LIVBJERG,
and J. V I L L A D S E N
Technical University of Denmark, 2800 Lyngby, Denmark
SO -oxidation rat conditions are presented with measurements of the composition of the V O -K S O c a t a l y t i c melt. It i s shown that all available rate data can be explained if the v content of the cata l y s t i s assumed to increase with decreasing temperature and with increasing l i q u i d d i f f u s i o n resistance and i f furthermore the a v a i l a b i l i t y of active v compounds in the c a t a l y t i c cycle i s assumed to decrease with de creasing temperature, most probably by p r e c i p i t a t i o n of some v species. 2
2
5
2
2
7
(4)
(4)
(4)
SO -Oxidation Kinetics 2
Despite persistent research efforts over the l a s t 40 years the active sulfovanadate complexes of the cata l y s t have not yet been i d e n t i f i e d . Under normal pro cess conditions the rate determining step is almost c e r t a i n l y the reoxidation of a v species Y i n (2) or (4) i n model 1 and model 2. The reduction of v spe cies X may be either (1) as proposed by Mars and (4)
(5)
Maessen [3] o r ( 3 ) as proposed by Boreskov [ 4 ] . Both (1) and ( 3 ) a r e supposed t o be f a s t e q u i l i b r i u m r e a c t i o n s , a l t h o u g h a s h i f t i n r a t e d e t e r m i n i n g step may be p o s s i b l e a t very low o p e r a t i n g temperature. S0
+ nX t S O , + mY 3 mY + \0 t nX
Model 1 :
(1)
o
^
(2)
2
Model 2:
S 0
+
n
X
2 ^ mY + | 0 o
m
Y
t
(
3
nX + S O ,
)
(4)
? ν(*0 In terms o f the degree o f r e d u c t i o n ε = — — and w i t h 2
n=m=2 the e q u i l i b r i u m constants f o r (1) anS ( 3 ) a r e
©
0-8412-0401-2/78/47-065-582$05.00/0
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
48. GRYDGAARD ET AL.
S0
K, =-^^2= (1-εΓ
1
K
P
Oxidation on Molten V 0-K S 0 2
2
7
Catalyst
S0
1 2
= 8.9-10(l-εΓ S0
583
(5)
8
1 0
1
exp(iI^)(atm- )
P
d
2
2.3-10- exp ( ^ 2 )
=
2
2
(6)
1 2
The ε d a t a used i n [3>] t o propose (5) d i d not have a s u f f i c i e n t l y l a r g e v a r i a t i o n o f p^Q t o d i s c r i m i n a t e between (5) and (6) w h i l e a t h o r o u g h e x a m i n a t i o n o f a l l a v a i l a b l e ε - d a t a i n [1] i n c l u d i n g some w i t h a 30-fold v a r i a t i o n o f p^Q p o i n t s t o (6) as the most l i k e l y e q u i l i b r i u m s t e p ? Th s t a t i s t i c a l a n a l y s i f -dat show t h a t n=m=2 i s t i o n o f i n t e g e r exponent model 2. Both (5) and (6) are based on d i f f u s i o n f r e e d a t a o b t a i n e d w i t h e i t h e r an e q u i l i b r a t e d gas phase (no o v e r a l l r e a c t i o n t a k e s p l a c e ) o r w i t h l i q u i d s d i s p e r s e d w e l l enough t o a v o i d d i f f u s i o n e f f e c t s . The v a r i a t i o n o f ε w i t h l i q u i d l o a d i n g i s shown i n F i g . 1 which i s based on [5J . L i n e C i s d e s c r i b e d by ( 6 ) . A s o l u b i l i t y o f 4-6$ i n K S 0 a t 400-600^0 i s found i n [7] and B o r e s k o v [8] i d e n t i f i e d by ESR two v(4) s p e c i e s below 480°C. The e x i s t e n c e o f c r y s t a l s o f a p r e c i p i t a t e d v(^) compound i s mentioned i n [5>6.»7.1 · 2
Y
liq
Z
Y
2
7
( 7 )
solid
P r e c i s e measurement o f the s o l u b i l i t y o f Y i s d i f f i c u l t but q u a l i t a t i v e l y we know t h a t [Y_ i n c r e a s e s below SΟ
HQ
450°C when the c a t a l y s t i s reduced by SO2, p r o b a b l y d i r e c t l y c o n n e c t e d w i t h the i n c r e a s e o f ε by (5) o r (6). A r r h e n i u s p l o t s o f the a p p a r e n t r a t e c o n s t a n t f o r S 0 - o x i d a t i o n i n v a r i a b l y show a break a t ^450*0 and t h e apparent a c t i v a t i o n energy i s o f t e n v e r y h i g h a t l o w t e m p e r a t u r e [_8,_4]. T h i s phenomenon i s c l e a r l y c o n n e c t ed w i t h the l o w e r o x i d a t i o n l e v e l o f V a t low tempera t u r e , p r o b a b l y enhanced by l i q u i d d i f f u s i o n r e s i s t a n c e and accompanied by i n a c t i v a t i o n o f v' '. To improve the low t e m p e r a t u r e a c t i v i t y o f vanadium c a t a l y s t , a p r i m a r y g o a l i f the cumbersome i n t e r a b s o r p t i o n c o n v e r t e r d e s i g n i s t o be a v o i d e d , our u n d e r s t a n d i n g o f t h e s e complex phenomena must be advanced. 2
Experimental 190 S 0 - o x i d a t i o n r a t e measurements were o b t a i n e d i n a r e c i r c u l a t i o n r e a c t o r d e s c r i b e d i n [2] . The experimen t a l s t r a t e g y i s summarized i n Table I . 2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
584
I:
ournmary
data points
1)
of
rate
measurements
1)
Vanadium cent et it
2)
1
24
2.85
Orthogonal
d e s i g n a t 480 C. 0. : V.h-V>i, :Τ^:
·?
16
2.85
Orthogonal
d e s i g n a t 480 C.
Oy
22-48%, S 0 :
9-20%, S O ^
3
19
2.85
Orthogonal
d e s i g n a t 530 C.
0:
7-16%, SO-,:
2.9-6.5%, SOy
4
16
2.85
y'40-550 C,
10 ·" t e m p e r a t u r e
.Uep.-;. and
s t a n d a r d gas
composition
5
lb
2.85
'400-480 C,
10 C t e m p e r a t u r e
s t e p s and
s t a n d a r d gas
composition
1?
1.37
3δΟ-46θ 0,
10 C t e m p e r a t u r e
s t e p s and
s t a n d a r d gas
composition
*430-570 C,
10
C temperature
s t e p s and
s t a n d a r d gas
composition
s t e p s and
s t a n d a r d gas
composition
?
?
7
20
8
12
9
8
14.2
10
8
24.2
380-450 C,
10 C t e m p e r a t u r e
11
20
21.1
Orthogonal
d e s i g n a t 480 C.
Oy.
6-16%, SO.,:
12
17
21.1
Orthogonal
d e s i g n a t 530 0.
Oy.
7.2-16*, S 0 :
21.1 7.87
2.1-ό.5%, 3 0 ^ :
2.5-6?
7-17% 2.2-6%
400-48 400-48
3-6.8%, S O ^ 2
3-7%,
SOy.
1.9-5.4% 2-5.2%
The s u p p o r t i s c o n t r o l i e d - p o r e g l a s s (CPC, E l e c t r o - N u c l e o n i c s , I n c . F a i r f i e l d , N.J.) w i t h p u r e v o l u m e 1.02 c m / g , p o r o s i t y 69%, p o r e r a d i u s 1530 A, p a r t i c l e s i z e 2 0 / 3 0 ";<-.':.. The o v e r a l l c a t a l y s t c o m p o s i t i o n i s K/V = 3-5 atom/atom. The s t a n d a r d g a s c o m p o s i t i o n i s 10.7% 0^, 4.4% S 0 , 3-6% SO^, balance N . 5
?
2)
g VjO^/100 g
?
support.
I t was c o n t r o l l e d by c o m p u t a t i o n s 12] t h a t p a r t i c l e s i z e , p o r e s i z e , and r e c y c l e f l o w w e r e c h o s e n s u c h t h a t n e i t h e r i n t e r - n o r i n t r a p a r t i c l e gas p h a s e c o n c e n t r a t i o n g r a d i e n t s were o f i m p o r t a n c e . Porous g l a s s (CPG) was i m p r e g n a t e d w i t h an a q u o u s s o l u t i o n o f VOSOn-KHSOjj, d r i e d and a c t i v a t e d f o r 2 d a y s . 1.37-24.2 g V2O5/IOO g s u p p o r t was u s e d - t h e h i g h e r l o a d i n g s by r e i m p r e g n a t i o n as d i s c u s s e d i n [2]. Two t y p e s o f m e a s u r e m e n t s w e r e made. In the first t h e t e m p e r a t u r e was d e c r e a s e d i n s m a l l s t e p s f r o m one e x p e r i m e n t t o t h e n e x t , b u t k e e p i n g c o n s t a n t gas compo sition. Some o f t h e h i g h t e m p e r a t u r e m e a s u r e m e n t s w e r e r e p e a t e d t o c o n t r o l t h a t no d e a c t i v a t i o n had occurred. I n t h e o t h e r t y p e o f m e a s u r e m e n t gas c o m p o s i t i o n was changed i s o t h e r m a l l y u s i n g the o r t h o g o n a l f a c t o r i a l d e s i g n of f i g u r e 2. The c e n t e r p o i n t s and a l s o o t h e r p o i n t s were f r e q u e n t l y r e p e a t e d t o t e s t f o r d e a c t i v a tion. D e t e r m i n a t i o n o f a f e e d f l o w and f e e d c o m p o s i t i o n t h a t y i e l d s a p r e d e t e r m i n e d r e a c t o r gas c o m p o s i t i o n r e q u i r e s an a p p r o x i m a t e k n o w l e d g e o f t h e r a t e a t t h i s composition. A few s u c c e s s i v e f e e d f l o w a d j u s t m e n t s were sometimes n e c e s s a r y t o g i v e a p p r o x i m a t e l y the de s i r e d c o m p o s i t i o n , b u t v a r i a t i o n s o f 10% r e l a t i v e w e r e
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
GRYDGAARD ET AL.
S0 Oxidation on Molten V 0-K S 0 2
2
2
2
Catalyst
7
585
Figure 1. Vanadium reduction data obtained by ESR plotted as the equilibrium constant K = (1 — e) /ê/V o 2
2
1. • 2. V 3. Ο 4. +
S
2
unsupported melt, K/V = 3.5 [5] industrial catalyst, K/V = 2.5 [5] finely dispersed supported melt, K/V = 3.5 [5] [4]
The data of series 3 and 4 are included in the regression analysis of the present investigation.
-In ρ
\
Figure 2. Orthogonal factorial de sign for reactor gas composition
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
586
a l l o w e d as l o n g as the a c t u a l r a t e and c o m p o s i t i o n were measured a c c u r a t e l y . In t h i s way the o v e r a l l o r t h o g o n a l f a c t o r i a l d e s i g n f o r the 5 v a r i a b l e s : ^2^5 tent, was p r e s e r v e d s u f f i c i e n t l y w e l l t o T, y 0. 'SO'soa v o i d u n i n t e n t i o n a l c r o s s c o r r e l a t i o n i n the s t a t i s t i cal analysis. The e f f e c t o f temperature and V 2 O 5 c o n t e n t on the r a t e i s shown i n f i g u r e 3 an A r r h e n i u s p l o t o f t u r n over f r e q u e n c y N f o r s t a n d a r d gas c o m p o s i t i o n . In c o n
3
S Q
accordance w i t h our p r e v i o u s r e s u l t s [2] NgQ is in dependent o f V 2 Ο 5 c o n t e n t below 3% ^2^5' this re g i o n t h e r e i s no l i q u i d d i f f u s i o n r e s i s t a n c e w i t h the support t h a t we have used For 20% V 2 O 5 l i q u i d d i f f u sion resistance i s a c t i v a t i o n energy E and has not p r e v i o u s l y been f u l l y r e c o g n i z e d . Above ^450°C Ε i s independent o f V^Oc c o n t e n t , changing from 24 k c a l / m o l f o r 450
n
Ô
a
t
o
o
c
Analysis of Purely K i n e t i c
Data
In the f o l l o w i n g a n a l y s i s we s h a l l t r e a t the d a t a obt a i n e d w i t h l e s s than 3% ν 0 ^ s e p a r a t e l y from the more or l e s s d i f f u s i o n r e s t r i c t e d d a t a w i t h h i g h e r V-content. I f the i n d i v i d u a l r a t e s o f ( l ) - ( 4 ) can be d e s c r i b e d by simple power law k i n e t i c s i n molar l i q u i d c o n c e n t r a t i o n s o f r e a c t i o n s p e c i e s the f o l l o w i n g a l t e r n a t i v e r a t e e x p r e s s i o n s are d e r i v e d from Model 1 and Model 2 respectively : 2
Model
1: a
k
l
e
2
a
y
s
l
S0.
S0(1-ε)
(8)
1 K
K l
N
n
- k„ ε 2 s
e
n s
i
y
U- )
so
6
m
n
- (l-e) ' (9)
«Ό, K
P
Ό*
ν*
£
m
M o d e l 2: m-n a
k
l
e
s
2
a
J
l S0,
m (10)
(1-ε) K
2
P
y
S0
( 2
1
-
£
)
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
48.
GRYDGAARD ET AL.
S0 Oxidation on Molten V 0-K S 0 2
2
2
2
7
Catalyst
587
Figure 3. Arrhenius plot of measured reaction rate with gas composition approxi mately 10.7% 0 , 4.4% S 0 , and 3.6Ψο SO . The uppermost curve is calculated by model 1 using parameter values from Table 11. 2
2
s
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
588
0
P £
ρ
2
y
S
0
P
χ
1
Vs " " 2
1
,
κ
E 2
Ρ
ρ
5
'SO*-*? i m y 0.
(11)
1
y^ are gas m o l e f r a c t i o n s . H e n r y s law c o n s t a n t s and t o t a l vanadium c o n c e n t r a t i o n are i n c l u d e d i n k^ k^, and i n the e q u i l i b r i u m c o n s t a n t s and K2 · A f r a c t i o n l - e o f the t o t a l vanadium c o n t e n t V forms an i n a c t i v e (4) . . ν phase t h a t i s p r o b a b l y i n s o l u b l e i n the melt, 5
G s
m
ν _ τ ;
4
5
[V ],. liq
+ [V ]
= ε + - C s η χ
= - C my
V
b
(12)
Τ
ε i s the degree o f
[ ν ^ ] l. i q /ε s V Τ and Ί
cannot
The
liq
m
^ a given s o l u b i l i t y
exceed
S
ε ε < S s y o v e r a l l (or observed) degree o f r e d u c t i o n ε ε
=
ο
(
[
v
(
1
+
tV
+
\ i q
(
4
]
)
s
o
l
i
d
)/V
T
(T)
T
(13) ο
= l-e (l-e) B
is (lH)
A r r h e n i u s type e x p r e s s i o n s ( w i t h parameters t o be de t e r m i n e d from the s t a t i s t i c a l a n a l y s i s ) are supposed t o h o l d f o r k-, , k , K i , K , and S . A l l e x p r e s s i o n s are c e n t e r e d a t 480 C: p
p
y
(a. exp
(^
(| -
7
| ))) 5
The computation by e i t h e r model i s done as f o l l o w s : First e i s assumed t o be 1. At steady s t a t e N =N = the a c t u a l SO2 t u r n o v e r frequency Ν and f o r g i v e n p a r a meters Ν, ε are c a l c u l a t e d u s i n g e i t h e r ( 8 ) , ( 9 ) or ( 1 0 ) , (11). I f £<Sy no p r e c i p i t a t i o n o f v ' ^ ' o c c u r s and the solution i s correct. I f ε>θ then εε =S p r o v i d e s an e x t r a e q u a t i o n which combinea w i t h the p r e v i o u s equa t i o n s g i v e s Ν, ε and ε f o r ε <1. s s L e a s t squares a p p l i e d t o d i f f u s i o n f r e e r a t e d a t a , s e r i e s 1-6 o f T a b l e I , was combined w i t h supposedly d i f f u s i o n f r e e vanadium r e d u c t i o n d a t a ( s e r i e s 3 and 4 o f P i g . 1 ) . Both r a t e d a t a and r e d u c t i o n d a t a were ob t a i n e d w i t h K/V = 3.5 and e s s e n t i a l l y the same tempera t u r e - and gas c o m p o s i t i o n range. 31 r e d u c t i o n d a t a and 105 r a t e d a t a are i n c l u d e d i n the r e g r e s s i o n . Parameter v a l u e s t h a t m i n i m i z e d SS.Q were determined. s
SSQ
1
= SSQ +SSQ N
e
Σ
1
[
1
η
^
2
^ o b s ^ ^ p r e d ^ ' 3
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
GRYDGAARD ET AL.
48.
S0
Oxidation on Molten V 0-K S 0
2
2
+ Σ [1η(ε ). . - 1η(ε ) . Λ ^ o'i,obs o'i,pred
2
2
7
Catalyst
2
589
(16)
c· i s c o n s t a n t f o r s e r i e s j , but may v a r y between s e ries. I t i s i n c l u d e d i n the r e g r e s s i o n a n a l y s i s (ex cept f o r s e r i e s 1 where C-^ΞΙ) s i n c e s m a l l s y s t e m a t i c v a r i a t i o n s (±10%) are e x p e c t a b l e due t o v a r i a t i o n s i n c a t a l y s t sample i m p r e g n a t i o n and a c t i v a t i o n . Both f o r model 1 and 2 a l a r g e number o f (m,n) v a l u e s were t r i e d , b u t m=n=2 were the b e s t w i t h a r e s i d u a l comparable t o the e x p e r i m e n t a l e r r o r . The r e s u l t s are shown i n T a b l e I I . The minimum SSQ i s o b t a i n e d o n l y when ( 1 ) o r ( 3 ) i s c l o s e t o e q u i l i b r i u m , a v e r y s a t i s f a c t o r y r e s u l t s i n c e t h i s was p r e v i s a g e d from t h e observations which lea As a consequence a-j_ k^ cannot be d e t e r m i n e d w i t h any degree o f c o n f i d e n c e . Model 1 appears s l i g h t l y b e t t e r t h a n model 2. The r e a son i s t h a t the S 0 ^ i n h i b i t i o n even f a r from e q u i l i b r i um w h i c h i s o b s e r v e d i n the r a t e d a t a (see T a b l e I I I ) i s e x p l a i n e d i n model 1 t h r o u g h i t s i n f l u e n c e on Κ-·, . I t i s however, w e l l p o s s i b l e t h a t S 0 ^ a f f e c t s the f o r ward r e a c t i o n r a t e o f ( 4 ) i n a manner w h i c h i s n o t e x p l a i n e d by the r a t e e x p r e s s i o n ( 1 1 ) , and a d i s c r i m i n a t i o n between the two models cannot be made on the b a s i s of our r a t e data. !£r* Irrv-it (-•: parameter*.-
f o r model
1 a n d < '; i t h n=n=2.
ε k
h
?.o
g mole (gatomV)sec Model
Model 2
"ode 1
1)
1
and
kcal/moie
β
2
0.39*0.15
26.1+3
0.72*0.13 1.20±0.2
(0.37±0.06)exp[ ( 132U012000) (i - ^ )
>1000
0.6ύ±0.^ί
27.8+5
0.66±0.15 1.59±O.H
(5.6±H . 0 ) e x p [ ( 12000±3000) (| - ^ ) ] i a t m " )
Ε
yo
1
l i m i t s are included
>100
ς
Model
6
?a c o n f i d e n c e
y kcal/mole
Standard error
SSQ£
SSQN
0.^8*0.05
7.2±2
11
0.6
O.b
0.35±0.03
i4.0±3
13
0.6
l.u
k,, α,, a
?
becomes i n d e t e r m i n a t e
since the f i r s t
]
1
step i s close t o equilibrium.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
590
The e q u i l i b r i u m c o n s t a n t s and Kp o f Table I I a r e n o t d i r e c t l y c o m p a r a b l e w i t h t h o s e i n 15) a n d ( 6 ) , s i n c e t h e l a t t e r p a i r i s based on measured e and i n c l u d e p r e c i p i t a t e d V"(^'. A t h i g h Τ w h e r e no v ' ^ ' i s p r e c i p i t a t e d t h e agreement i s v e r y good f o r K]_. F o r ε <1 K o o f (6) i s somewhat h i g h e r t h a n i n T a b l e I I a n d K-^ o f (5) a f a c t o r 5 l a r g e r t h a n t h e c o r r e s p o n d i n g v a l u e s from Table I I i n t h e whole temperature range. Q
3
T a b l e I I I : E s t i m a t e d p a r a m e t e r s i n a power l a w r a t e expression: N=k y y y . D a t a f r o m s e r i e s 1, a
b
Q
S
c
Q
S
Q
3 , 11, a n d 12 o f T a b l e I . 2σ c o n f i d e n c e l i m i t s a r e shown.
480 V
2°5
a
b
c
b
a
c
Content
2.85? 0.74±0.12 0.50±0.08 -0.51±0.10 0.86±0.08 0.53±0.08 -o.300.06 21.1% 0.77±0.08 0.40±0.08-0.37±0.06 0.8l±0.l6 0.50±0.l4 -0.18±0.10 The o b s e r v e d c h a n g e o f E a t 450°C i s w e l l p r e d i c t e d b y b o t h m o d e l s ( f i g u r e 3) a f a c t t h a t g i v e s c r e d e n c e t o t h e p o s t u l a t e d p r e c i p i t a t i o n o f a V ( t ) compound. The p r e d i c t e d p r e c i p i t a t i o n i s shown o n f i g u r e 4 w h i c h a g r e e s r e m a r k a b l y w e l l w i t h t h e ESR m e a s u r e m e n t s o f [8], assuming t h a t , line B o f t h e r e f e r e n c e corresponds t o p r e c i p i t a t e d v'^'. With t h e standard gas composition o f o u r m e a s u r e m e n t s a s o l i d p h a s e a p p e a r s b e l o w 470°C, a n d a t 380°C o n l y 1/3 o f t h e V i s d i s s o l v e d . Calcula t i o n s w i t h S = l made i t e v i d e n t t h a t n e i t h e r o f t h e t w o m o d e l s c o u l d be u s e d i f t h e p r e c i p i t a t i o n ( o r i n a c t i v a t i o n ) m e c h a n i s m was n o t i n c l u d e d . Prom T a b l e I I t h e solubility S a t 480°C i s .48 ( m o d e l 1) a n d .36 ( m o d e l 2) a n d t h e t e m p e r a t u r e d e p e n d e n c e o f S i s s m a l l . S i n c e a VpOc-, 3.5-KpSp0 m e l t c o n t a i n s 17% v a n a d i u m (calcu l a t e d a s V 0 J t h e s o l u b i l i t y o f V ^ ) a t 480 'C i s ^17 S % o r 8% ( m o d e l 1) a n d 656 ( m o d e l 2 ) . Both r e s u l t s a g r e e v e r y w e l l w i t h t h e o b s e r v e d s o l u b i l i t y (^4-6%) i n a
!
f
f f
y
7
C
2
5
y
[71. We c o n c l u d e t h a t a t w o s t e p m e c h a n i s m ( l ) - ( 2 ) o r ( 3 ) - ( 4 ) c o m b i n e d w i t h a p r e c i p i t a t i o n s t e p (7) e x p l a i n s the a p p a r e n t l y c o n f l i c t i n g e x p e r i m e n t a l o b s e r v a t i o n s provided the data are e s s e n t i a l l y d i f f u s i o n free. Kinetics
o f The L i q u i d
Diffusion
Regime
X-ray microprobe i n v e s t i g a t i o n and s c a n n i n g e l e c t r o n m i c r o s c o p y show t h a t a b o v e 3~5% V^Otr p a r t o f t h e m e l t agglomerates i n t h e pore s t r u c t u r e t o form macroscopic
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
48.
S0 Oxidation on Molten νβ.-Κββ
GRYDGAARD ET AL.
ε,ε ,ε 0
2
Catalyst
7
8
ι 400
—ι
π
1—•
1—
500
600Τ °C
Figure 4. Prediction of vanadium reduction and precipitation of V for standard gas composition using model 1 with parameter values from Table II. (4)
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
591
CHEMICAL REACTION ENGINEERING—HOUSTON
592
c l u s t e r s [1>£>£3· T h e s e c l u s t e r s o f s i z e ^ 0 . 0 2 5 mm a r e c o m p l e t e l y i n a c t i v e , and t h e measured a c t i v i t y i s r e l a t e d e x c l u s i v e l y t o a w e l l d i s p e r s e d l i q u i d phase out side the c l u s t e r s . A d d i t i o n o f f u r t h e r melt t o t h e support leads t o growth o f t h e i n a c t i v e c l u s t e r s and a c t u a l l y t o a decrease i n a c t i v e regions. This ex p l a i n s why E i s i n d e p e n d e n t o f V ^ O r c o n t e n t a b o v e 450°C. T a b l e I I I compares t h e k i n e t i c s o f c a t a l y s t s w i t h s m a l l and l a r g e ^ O t - content. The r e a c t i o n o r d e r s f o r t h e o v e r a l l r e a c t i o n a r e e s s e n t i a l l y t h e same w h i c h supports the theory that the r e a c t i o n occurs i n a w e l l dispersed part o f t h e c a t a l y s t independent o f l i q u i d loading. The i n f l u e n c e o f V 0 ^ c o n t e n t o n b e l o w 450°C i s remarkable and i t p o i n t the melt w e l l d i s p e r s e s m a l l V2O5 c o n t e n t a t l o w t e m p e r a t u r e . Since ε o f the c l u s t e r s i s h i g h e r t h a n i n t h e r e s t o f t h e m e l t due t o the i n f l u e n c e o f l i q u i d d i f f u s i o n r e s i s t a n c e on ε ( f i g u r e 1) a r e l a t i v e l y l a r g e r amount o f v a n a d i u m w i l l p r e c i p i t a t e i n t h e c l u s t e r s . Consequently vanadium w i l l d i f f u s e from t h e a c t i v e p o r t i o n o f t h e melt i n t o t h e c l u s t e r s . T h i s may e x p l a i n t h e u n e x p e c t e d l o w a c t i v i t y a t low temperature f o r VpO^ r i c h c a t a l y s t s . We c a n n o t y e t g i v e a q u a n t i t a t i v e t r e a t m e n t o f t h e d i f f u s i o n phenomena s i n c e o u r k n o w l e d g e o f r e a c t i o n a n d l i q u i d d i f f u s i o n parameters and e s p e c i a l l y o f t h e l i q u i d d i s t r i b u t i o n f u n c t i o n i s q u i t e i n c o m p l e t e [1]. The f o l l o w i n g q u a l i t a t i v e treatment does, however, prove t h a t ε may i n c r e a s e s i g n i f i c a n t l y w i t h f i l m t h i c k n e s s i f we a s s u m e a 3 - s t e p m e c h a n i s m , w h e r e a s n e i t h e r ( 1 ) (2) n o r ( 3 ) - ( 4 ) c o u l d l e a d t o a s i m i l a r c o n c l u s i o n s i n c e b o t h assume a f a s t r e d u c t i o n s t e p w i t h C being t h e same i n t h i c k a n d t h i n f i l m s . Assume t h a t a
y
S0
+ 2X t 2Y,
2
2Y t 2Z + SC> , 3
2Z + J0
2
t 2X
(17-19)
2
ζ ρ Ύ
3
\ x
J
x
2
/e q
Σ-
k3
T
=
± — 1
(22)
Ύ-,ΎοΚ 1 2 ρ 1
χ i s t h e c o n c e n t r a t i o n o f a v ( 5 ) s p e c i e s and ( y , z ) t h e c o n c e n t r a t i o n o f two d i f f e r e n t species. kj_ a n d k- a r e f o r w a r d a n d r e v e r s e r e a c t i o n r a t e constants. Abbreviate p , p , and p b y s , s ^ , a n d o. f
S
Q
S
Q
Q
2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
48.
GRYDGAARD ET AL.
S0
Oxidation
2
on Molten
l
X 2 S
2 =
2 - V l ^
R
2
2
Δ
Ζ
νΐ* -Λ 1*2 % 2
k
l
N
6
Z
2
2
k
°
6
7
Catalyst
593
obs =
observed averaged rate/volume 2
2
(23) to (25)
Assume the l i q u i d phase k i n e t i c s k
V 0-K S 0
>
=
X
~ i 2 3
R
obs
R
obs
2 =
(23)
liquid
( 2 4 )
(
2
5
)
Gas s o l u b i l i t i e s and t o t a l vanadium content V a r e i n c o r p o r a t e d i n t o the r a t e c o n s t a n t s . Thus x+y+z=l. The c o n s t a n t s 6^ and 6 a r e T
2
k Δ
1
k,
9
=ΐξ
A
N
D
Δ
(
2 =
2
6
)
S i n c e k and k-j a r es they a r e much g r e a t e r than k . Thus ο 2 /δ^>>1 ^ 6]_ << 1. x , y , z s , and s^ a r e assumed t o be c o n s t a n t through the f i l m and o n l y t h e forward r e a c t i o n o f ( 1 9 ) i s assumed t o be d i f f u s i o n l i m i t e d due t o extreme low s o l u b i l i t y o f 0 . The e f f e c t i v e n e s s f a c t o r η i s i n t r o d u c e d t o account f o r d e p l e t i o n o f 0 i n t h i c k f i l m s . (23) to (25) are e a s i l y solved to give 1
a n <
2
5
2
2
2
χ = 1/(1
+ /â(l+/b)),
s
y = χ/Ε,
(
1 +
δ
5
( 1 +
"
-§7>
Δ
2
γ
ι
3
1^2 3
3 1^2 3
2
+ S
δ
(28)
Ύ
Γ
(ι
δ
2 - y χ
2 3
'
Yl
(27)
0
2
ζ = x/âb
_ :ζ__
γ
2 3 - | 7 2 ) +δ
ι " ν η ο 2
(29)
2
Υ
We wish t o study t h e case where r e a c t i o n ( 1 7 ) i s almost in equilibrium i n thin films. T h i s means t h a t the f i r s t term i n ( 2 3 ) >> the l a s t term o f ( 2 5 ) or S > > 6 Y S i n c e a l s o 6 << 1 ( 2 8 ) - ( 2 9 ) can be reduced t o 2
2
V
0
1
δ
Sp
Ί
(30) 1 1 2 3 2 ° S i n c e a i s p r a c t i c a l l y independent o f η t h e same simple expression f o r a i s obtained i n t h i c k films while b changes from a =
- φ Ύ
and
b =
r
5
Y
S
+
δ
η
2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
594
CHEMICAL REACTION ENGINEERING—HOUSTON
δ
b(n = l )
ι
^ —=-r 6 o~
to
b(n^O) = Y
2
2
6 /6
2
Ί
(and -*± -^τ -) ô 2 o*
9
1 2 3
since
S
1.
«
I t i s seen t h a t b and c o n s e q u e n t l y ζ may i n c r e a s e s i g n i f i c a n t l y from t h i n f i l m s (where zMD) t o t h i c k films. As a consequence r e a c t i o n (18) which i s f a r from e q u i l i b r i u m i n t h i n f i l m s i s p r a c t i c a l l y i n e q u i librium for thick films. Thus i n t h i c k f i l m s (17) t o (19) c o l l a p s e t o Mars and Maessen s model ( l ) - ( 2 ) . In t h i n f i l m s (18) and (19) can be combined and the model i s i d e n t i c a l to Boreskov p r e t s Y as an adduc f
List
of
Symbols
c^ C ,C χ
C o r r e c t i o n parameter f o r r a t e d a t a o f s e r i e s i Molar l i q u i d c o n c e n t r a t i o n , mole /cm3 y
E ,E-^,E ,E a
k
A c t i v a t i o n energy, k c a l / m o l e
2
3
R a
l ^2
Κ ,Κρ v Κ
"te constants,
mole/(gatomV)/sec
E q u i l i b r i u m constants (5005/Τ-4.743) atm . -\, gas phase u 10 c o n s t a n t f o r S02+|02 -> SO^
η
2
ΊΠ
p
Ν,Ν^,Ν^,Ν^^
T u r n o v e r f r e q u e n c y , moles/(gatomV)/sec
p,p^
Pressure, p a r t i a l pressure,
Rg
Gas
S ,S y
SSQ,SSQ ,SSQ £
Τ V"
atm
constant
Solubility
y Q
N
Sum
of
defined i n
1
1 ε ε C
9
1
d.
1
Eq.13
o f squares d e f i n e d i n E q . l 6
Temperature T o t a l c o n c e n t r a t i o n o f vanadium (gatomV) /cm* α ,α ,β ,3 Power law exponents T
e q u ·i lτi bκr i u· m
in liquid,
0
d
Degree of reduction i n the liquid phase [V ' L . /V, T o t a l f r a c t i o n o f vanadium r e d u c e d t o ' The The ff rr aa cc tt ii oo nn ooff tt oo tt aa ll vanac vanadium c o n t e n t which i s d i s s o l v e d i n the l i q u i d v
ο Q
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
48. GRYDGAARD ET AL.
S0
2
Oxidation on Molten V 0-K S 0 2
2
2
7
Catalyst
595
Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9.
V i l l a d s e n , J. and L i v b j e r g , H., "Supported Liquid phase c a t a l y s t s " , C a t a l . Reviews, Chem.Eng. (1978) L i v b j e r g , H., Jensen, K . P . , and V i l l a d s e n , J., J. Catalysis (1976) 45 216 Mars, P. and Maessen, J.G.H., J. Catalysis 10 1 (1968) Boreskov, G . K . , Polyakova, G . M . , Ivanov, Α.Α., Mastikhin, V . M . , Dokl.Akad.Nauk. (USSR) 210(3) 626 (1973) (Engl. t r a n s i , p. 423) Mastikhin, V . M . , Polyakova, G . M . , Z y u l k o v s k i i , Y., Boreskov, G . K . , Kinetics and Catalysis (USSR) 14 1219 (Engl. t r a n s l . ) (1970) H ä h l e , S. and (USSR) 12(5) 127 Holroyd, F . P . B . and Kenney, C . N . , Chem.Eng.Sci. 26 1971 (1971) Boreskov, G . K . , Davydova, L.P., Mastikhin, V.M., Polyakova, G . M . , Dokl. Akad. Nauk. (USSR) 171(3) 648 (1966) (Engl. transl. p. 760) Jensen-Holm, H . , Ph.D. Thesis, Technical U n i v e r s i ty of Denmark, Lyngby, To appear 1978.
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
INDEX A Absorbance sample cells, gas-phase .. 12 Absorbed radiation 276 Absorption 10,57 without reaction, mass transfer in .. 329 Acetic acid 574 Acetic anhydride hydrolyse, isothermal run of 42 Acetylene 527, 535 conversion 531 hydrogénation of 526 Acid, acetic 574 Acrylonitrile-methyl methacrylat (ANMMA) 17 Activation energy 34,490 of CO-consumption 32 of hydrocarbon formation 32 rate equation parameters 22 values of the 507 Active monlith, entrance effect in 80 Adiabatic calorimetry, accumulaton method .. 37 methanator 63,70 pilot plant data 290 reactor multiplicities 473 run 90,91 Adsorbed species, spectra 3 Adsorber-reactor 50, 52 specifications 53 use of 59 Adsorption effects binary 59 of multicomponent 51,57 of water on ieri-butanol 58 in heterogeneous catalysis 50 mechanism, Langmuir-Hinchelwood 283 reaction studies 57 studies, transient 55 types of reaction heat 63 of water on alumina 56 Advantage of parallel passage reactor 70 Agitation rate on performance, effect of 452 Agitation tests 451 Air-lift fermentors 154-157 Algorithm, Gears 103 Algorithm, Newton-Raphson 88
Alumina adsorption of water on 55, 56 cobalt-molybdenum on 448 dehydration of feri-butanol on 57 dehydration of 2-propanol over 10 Ammonia, catalytic synthesis of 550 Amplitude, stability diagram 504 Amplitudes of temperatures 505 Analysis equipment, cyclic feed makeup apparatus, effluent 529 Analysis, Semenov-type dimensional.. 173 Analytical evaluation of the plugging time 228
continuous culture 166 effluent analysis equipment, cyclic feed makeup 529 Arab Light naphtha 287, 288 Argon 314,477 feed mixture 482 Aromatic sulfonation 327 Aromatics 288 Arrhenius diagrams for reaction rates 31 equations 165 expressions 588 kinetics 563 law of 500 parameters, kinetic 318 plot ( s ) 30, 77,310,583, 586,587 Ash-free coal 307 Asynchronousmotor 17 Autoclave, back-mixed catalyst 293 Auto-oxidation system 350 Autothermal operation 86 Axial conduction 101,249 dispersion 426-428 coefficient 308 model 242-246,307,359 distributions 115-118 flow 554-557 in packed beds 541 steady state temperature profiles 552 mixing 304,338-340,343 effect of diameter on 342 gas flow rate on 342 packings on 345 plates on 345
599
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
600
CHEMICAL REACTION ENGINEERING—HOUSTON
mixing (continued) of liquid in packed bubble col umns of large diameter 337 of liquid in perforated plate col umns of large diameter 337 Peclet numbers 242,249 profiles 360 temperature for different thermal conductivities 102 thermocouple 412 velocity field development 76 Axisymmetric jets 6
Β Back-mixed catalyst autoclave 293 Backmixing model, countercurrent .... 400 Bacterial growth, kinetical analysi of unbalanced 16 Bacterial growth, steady state of 172 Bacterial time lag 172 Balance equation, mass 430 mass 64,66 on transport cell, force 419 Barocel pressure transducer, datametrics type 53, 531 Base metal catalyst, oxidation of carbon monoxide over a 83 Basket reactor, multiphase kinetic studies with a spinning 447 Basket stainless steel reactor, continuous flow spinning 527 Batch culture 164 Batch operation 431-433 Batch reactor, recirculating 6 Beam, reference cell ir 6 Bed(s) axial flow in packed 541 catalytic reactor, fixed 513 catalytic reactor, isothermal heterogeneous 512 freely bubbling 400 gas in a bubbling fluidized 436 height 441 variations of composition with 442-445 volumetric gas flow and 439 parameters 412 reactor(s) catalyst effectiveness factor in trickle387 cell model studies of radial flow, fixed 550 design of a moving 540 fixed 539 fluidized563 Gulf-patented segmented 304 modeling the slugging fluidized .. 400
reactor(s) (continued) moving 543 performance equations for trickle389 trickling fixed 447 round-nosed slugging 401 slugging fluidized 404 Behavior of the reactor for finite perturbations, transient 568 Bench-scale heat flow calorimeter 37-40,43 Bench-scale reactors 303 Bendixon theorems 487 Benzene 288,315-322, 327,334 composition profiles, paraffin and .. 288 to maleic anhydride, oxidation of .. 440 molar concentrations of 323 production of maleic anhydride from 215 with S 0 , sulfonation of 327 /styrene, molar concentrations of .. 321 sulfonation of 328-334 Benzenesulfonic acid 327 Big Horn coal, kinetics of catalytic liquefaction of 303 Binary adsorption effects 59 Binder-Schmidt method 67 Biomass, production of 153 Biot number 393,396 Biphenyl 451 Boric acid 348 Boundaries, R A 175 Boundary condition(s) 66,88,104,541 finite bed 247 infinite bed 241 Bubble column (s) 337,341-343,360 C0 -interphase mass transfer in a 359 design, determination of fluid dynamic parameters in 372 gas 401 phase 440 size 380 Bubbling fluidized bed, gas in a 436 Bubbly flow regime 373, 374 Butadiene 524 hydrogénation of 515 Butane 524 oxidation of 574 terf-Butanol dehydration 57, 58 Butanol, hydrogénation of 2-butanone into 2414 Butanone 411-414 1-Butene oxidation 479, 482 Byproducts, diversity of 350 3
2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
601
INDEX
C CH-oxidation process, improvement of the 349 Calcium sulfate 225 Calorimeter, bench-scale heat flow 37-40,43 Calorimetry adiabatic accumulation methods .... 37 differential scanning 181 isoperibolic accumulation method .. 37
Candida tropicalis
154
Capillarity 417 Caprolactam, preparation of 348 Carbon dioxide formation of 488 gas phase mole fraction of 367 interphase mass transfer in a bubble column 35 liquid phase partial pressure of 369 Carbon monoxide 30, 482 and 1-butene oxidation, limit cycles during simultaneous 479 concentration s ) ....117,118,463,468,492 consumption 32, 35 conversion 27 dependence of selectivity on 28 rate of 492 hydrogénation 26 inhibition by chemisorption 490 multiple steady states for 2% 480 oxidation 83, 465,466,476, 491 in an integral reactor 461 over platinum 475 steady state multiplicity during .. 477 Carbon oxides, methanation of 63 Caribbean residues 255-262 Carrier solvent 307 Catalysis adsorption in heterogeneous 50 of P ( O C H ) isomerization 44 Ziegler 140,149 Catalyst(s) activity 29,255 coked 210 HDS 208 age, relative 258,260 autoclave, back-mixed 293 basket, annular 449 basket, reactor development— 450 bed concentration changes 68 concentration profile in the 67 diffusion coefficient in the 66 temperature 414 catalytic oxidation reactions over supported platinum 476 cobalt-molybdate ( C O M O X 1661) 207,210 3
3
Catalyst ( s ) ( continued ) copper chrome "aero ban" 84 deactivation 29 by fouling 201 mechanism of 255 through pore mouth plugging .... 254 dynamic studies of acetylene hydrogénation on nickel 526 effectiveness 387,393,394 hydrogénation of 2-butanone on a ruthenium 411 industrial 585 Kieselguhr 513 life in a stirred-tank reactor 260 limit cycle phenomena 475 manganese-containing 26 oxidation of carbon monoxide over
molten V 0 - K S 0 582 particles 417 deactivation of a single 255 pellets 389,391,462 performance 29,35 poisoning in monolithic 110 pretreatment 35 properties 195,462 Pt-alumina 463,466 reaction rate on the 217 thermal conductivity of porous 189 utilization, selection of system to determine maximum 428,429 wetting 387,388,427 zeolite cracking 288 Catalytic cracking 440 decomposition of hydrogen peroxide, nitric acid 505 hydrogénation of acetylene, ethylene, ethane, vapor phase .. 526 liquefaction processes 303, 306 mufflers 550 oxidation reactions over supported platinum catalyst 475, 476 partial oxidation reactions 215 reactions effect of periodic operation on the selectivity of 512 kinetic modeling for oscillatory .. 487 vapor-phase 293 reactor, fixed bed 513 reactor, isothermal heterogeneous fixed-bed 512 recycle reactor, single-wafer 13 reformer, fixed bed 283 synthesis of ammonia 550 Catalyzed reaction, tube wall 74 Catalyzed reactors 98 2
5
2
2
7
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
602
CHEMICAL REACTION ENGINEERING—HOUSTON
Column(s) Cell(s) bubble 337,341-343,360 aromatic sulfonation in a stirred .... 327 C0 -interphase mass transfer in model studies of radial flow, a bubble 359 fixed-bed reactors 550 design 372 number 555,556 of large diameter 337 after a shift in temperature 169 liquid/liquid spray 539 fractional yield as function of 558 Comparison with experimental data Centripetal radial flow, ammonia for sulfation of fully calcined yields for 550 limestone 231 Channels, effect of multiple 103-107 Complex gas phase reactions, develChemisorption, C O inhibition by 490 opment of reaction models for .... 313 Chemisorption of oxygen 488 Composition(s) Chlorination of saturated Arrhenius plot of reaction rate hydrocarbons 440 with gas 587 Chromatograph with bed height, variations 442-445 flame ionization type gas 528 effluent 530 gas 315, 513 gas-liquid 20 Chromatographic method, gas paraffin and toluene 288 Chromatography 514 profiles 288 Churn turbulent regime 373,374,379 paraffin and benzene 288 Closed (batch) modes of operation .... 4 steady state 528 Coal Computer ash-free 307 -aided development of the cyclokinetics of catalytic liquefaction hexane oxidation process 348 of big Horn 303 digital 7 moisture-free 307 IBM/1800 6 particle dissolution, mechanism of . 303 interface, spectrophotometer6 solvation 304, 310 program description 54 Cobalt-molybdate catalyst simulation 569 ( C O M O X 1661) 207 typical temperature oscillation Cobalt-molybdenum on alumina 448 from 501 Cocurrent cooled reactors 218 Concentration s ) anol 349 -countercurrent movement 539 anone 348-349 flow 216,364 axial distribution 117 gas-liquid tube reactor 329 balance 540 operation 86 benzene 323 reactors 220, 222 carbon monoxide 463, 468, 492 runs 90,93 against D a number, residual iodine 128 system 215 ethylbenzene 323 tube reactor, aromatic sulfonation ethylene 323,531 in a 327 ethylene/styrene 321 Coefficient gas phase 366 axial dispersion 308 glucose 165-171 diffusion 66, 77 hydrogen feed 531 gas-liquid mass transfer 311 hydrogen/styrene 321 gas phase dispersion 379,381 integral reactor 21 heat transfer 8, 9, 45, 89, 241,249,498 oscillation of 568 liquid phase dispersion 379,380 perturbation, single inlet 461 mass transfer 365-367 polymer 143 temperature 53 profile(s) 67,72,230,235,261 Coil design equations, cracking 271 ethylene 535 Coke 201,258 pulses in the regime of isothermal catalyst activities 210 multiplicities, transient deposition 207,209 response to 461 Collocation method 542 of a rectant species 441 orthogonal 67, 103 -residence time curves 20 of solution, perturbation/ 232 2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
603
INDEX Concentration ( s ) ( continued ) of styrene/benzene 321 styrène 323 sulfur 255 valualdehyde 295 vanadium 255-259,588 Conductivity 101,102 axial 249 model for prediction of the r a d i a l . . . 247 molecular 248 of a pellet, thermal 191 of porous catalysts, thermal 189 radial 250 static 249 thermal 190,194,195,315 turbulent 248,249 Conductometer 192 Configurations, mixed flow Constant matrix, selectivity rat Constant, realtime activity rate 283 Consumption, C O 32,35 Contacting efficiency 395,397 Continuity equation 271 steady state 73 Continuous culture 164 Continuous flow stirred tank reactor 125,337,498 Continuum heat transfer models, homogeneous 239 Controlled reactor, stability of 565 Convection 273 flow model, diffusion/ 577 Convective transport of vorticity 74 Conversion 515, 517 acetylene 531 enhancement, effects of pulse on 469-472 of ethane 544,546 measured oscillations of temperature and conversion 508 nitric oxide 550 plot of selectivity vs 520 plot of yield vs 520 rate of C O 492 selectivity, yield 514 vs. space velocity 68, 69 time-averaged 505 Convertor, concentration and velocity profiles in the entrance region of a monolithic 72 Coolant, flowrate of 220 Coolant pass reactors 221 Copolymer approximate kinetic form ( C P A F ) 181,182 Copolymer systems, simulated R A boundary for 178 Copolymerization 149,173 Copper ...^ ^ 191 chrome "aero ban" catalyst 84 Corrsin's expression 130
Countercurrent backmixing model cooled reactors flow movement, cocurrent operation reactor reactor-heat exchanger run system trickle-bed reactor Cracking furnace, thermal Crossflow monoliths Curve, hysteresis Cycle(s) experimental limit limit multipeak
372 400 218 216,363 539 86 215,220 90,92 222 414 274 83-85 477 493 500,506 494
simple 494 simulated limit 493 during simultaneous C O and 1-butene oxidation 479 three-peak 494 Cyclic feed makeup apparatus effluent analysis equipment 529, 533 form, new model mechanistic 403 runs 517 Cyclohexane conversion 349,352 Cyclohexane oxidation 354-356 process, computer-aided development of the 348 Cyclohexanol 348 Cyclohexanone 348 Cyclohexylhydroperoxide intermediate, decomposition of the 349 Cyclohexyl radicals 350 Cyclone reactor 328-334 aromatic sulfonation in a 327, 333 selectivity in the 333 D Damkohler ( D a ) number 75-79,128 Dammitol, oxidation of 292, 294 Danckwert conditions 541 Data, fixed bed kinetic 59 Data, kinetic 586 Datametrics type 531 barocel pressure transducer 53 Davidson, model of Hovmand and 408,409 de Acetic—Thodos correlation 466 Deactivation 204,206 by fouling, catalyst 201 mechanism of catalyst 255 poisoning mode of 202 pore mouth plugging mode of ... 202, 254 of a single catalyst particle 255
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
604
Diffusion (continued) Decomposition of hydrogen peroxide, pore 226 nitric acid, catalytic 505 process 420 Decomopsition reactions of hydro regime, kinetics of the liquid 590 carbons, thermal 313 resistance 225 Dehydration liquid 592 of ieri-butanol on alumina 57, 58 zone, interface 327 of 2-propanol over alumina 10 7 Dense-phase gas 401 Digital computer 17 Dense phase voidage 438 Diphenyl (Dow Therm) Diphenyl sulfone 327 Density 307,308,426-428 function, residence time 572 Dispersion, axial Dissolution, mechanism of coal parameters 167 particle 303 residence time 576 Distribution(s) Deposits correlation of straight-chain coke 207 hydrocarbons, product 34 on the desulfurization activity, of emission breakthrough and inter effect of metal 262 geometries 201,20 metal sulfide 25 integral reactor 21 Derivative-free simplex method of oxygen 118 (Nelder and Mead) 22 of poison deposition 115 Design product 30 data from a bench-scale heatflow residence time 576-580 calorimeter 37 theory, residence time 571 factors 4 D N A contents 166-171 model, validity of a 359 Dolomite, absorption of S 0 by 225 of a moving bed reactor 540 Dufort and Frankel method 67 of multitubular reactors 214 Dynamic orthogonal 584 lag 41 central-composite 293 methods 195,196 factorial 585, 586 process 248 Desulfurization 255, 262-266, 550 catalyst deactivation through pore mouth plugging 254 Ε dibenzothiophene 451 Early late reaction zone phenomenon 559 effect of metal deposition on 262 Effective conductivity 248 and H uptake 433 Effectiveness factor 114,395,397 kinetics 447 411 Development, axial velocity field 76 Efficiency, wetting 113 Diameter on axial mixing, effect of . . . 342 Eigenfunction expansion Elliptic differential equations 74 Diameter ratio, heat transfer in packed beds 238 Emission breakthrough at different axial positions 117 Diazo-decompositions temperatureEnergy programmed run 42 activation 34,490 Dibenzothiophene 448 balances 173,540 desulfurization 451 of CO-consumption, activation 32 in white oil 447, 452 consumption 153,159 Differential equation 271 equations, elliptic 74 of hydrocarbon formation, equations, stiff 315 activation 32 reactors 10,15 values of the activation 507 scanning calorimetry ( D S C ) 38,181 thermal analysis ( R T A ) 38 Equation(s) Arrhenius 165 Diffusion continuity 271 coefficient 66 cracking coil design 271 of ethylene in air 77 with the Damkohler number 76 —convection flow model 577 elliptic differential 74 influence, liquid 582 energy 271 limitation region 77, 80 2
2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
605
INDEX
Equation ( s ) ( continued ) intrinsic rate mass balance mass transport Michaelis-Menten Monod of motion, Navier-Stokes for oxidation of ethylene pressure drop radical reaction reaction rate with the Schmidt number steady-state continuity Stokes-Einstein for trickle-bed reactors, performance tubeside reactor Wilsons Equilibrator, external hydrogen Equilibrium constant Equilibrium flash Equipment, experimental Escape probability for a particle
416 430 73 164 164 72, 73 80 271 350 414 76 492 73 331 389 21 35 428 585 430 238 572
Experiments, results of loop reactor .... 21 Exponential model 297 Expression, Corrsin 130 Expression, Lennard-Jones 77 Extinction temperature 98,101
F Factorial design, orthogonal Factorial design for reactor gas composition Fan, flywheel/ Feed concentration, hydrogen makeup apparatus effluent analysis equipment, cyclic mixture, argon
586 585 51 531 529 482
teristics or 431 Feedstocks 255 Fermentation 153,154 Fermentors air-lift 154-157 comparison of various 160 Escherichia coli 164 loop 154,159,160 Ethane 535 mechanically stirred 154-156 conversion of 544 performances of various 153 cracking furnace 271 Fick's law 64 gas inlet temperature, measured 439 conversion of 546 "Fines" content 247 Ethane yields 531 Finite bed boundary condition Ethyl acetate 574 Finite perturbations, transient behavior of the reactor for 568 Ethylbenzene 315-322 273 decomposition 320,321 Fire box heat transfer 26, 63 molar concentrations of 323 Fischer-Tropsch synthesis pyrolysis of 313-316 Fixed-bed adiabatic methanator 70 Ethylbenzyl 316 catalytic reactor 513 disintegration of the 318 catalytic reformer 283 Ethylene 207,316-322 kinetic data 59 concentration 531 reactor(s) 539 profile 535 cell model studies of radial flow .. 550 ethane, vapor phase catalytic trickling 447 hydrogénation of acetylene 526 reforming pilot plant, isothermal .... 287 hydrogénation of 512 155 molar concentrations of 323 Flat-blade turbine 220 oxidation of 77,80,440 Flexibility consideration in the design of styrene, molar concentrations of .... 321 multitubular reactors 214 Evaluation of the plugging time, analytical 228 Flow ammonia yields for centripetal Exchanger radial 550 heat 353 axial 554-557 monolithic reactor-heat 83, 89 behavior, fluid 571 systems, simple heat 215 cocurrent 216 Exit profile 144 control operation 562 Expansion, gas 438 countercurrent 216,363 Experimental methods 190 diagram, process 454 Experimental study of velocity and fixed bed reactors, cell model concentration profiles 72 studies of radial 550 Experiments, L P A 317
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
606
CHEMICAL REACTION ENGINEERING—HOUSTON
Flow (continued) increases with gas velocity and "fines" content, interstitial 439 laminar 72 methods, heat 37 model, diffusion/convection 577 modes, M R H E 87 modes of operation, open 4 in packed beds, axial 541 patterns in typical ir-cell reactors .... 5 plug 72 polymerization of E P D M polymer, laminar 140 radial 553,554 inlet 541 rate of coolant 220 rate, heat 38 reactor(s) catalyst utilization in a trickl for hydrotreating heavy oil, trickle 425 isothermal continuous 526 plug 428 trickle 431 recycle 584 steady state temperature profiles, axial 552 velocity profile analytic solution for nonuniform viscous 149 Fluid(s) field 216 flow behavior 571 interstitial velocity 551 mixing behavior 571 Newtonian 73, 74 nonNewtonian 149 Fluid dynamic parameters in bubble column design, determination of 372 Fluid dynamic properties 362 Fluidized-bed reactor 563 model(s) 436,438 modeling the slugging 400 Fluxes, heat 273, 277 Force balance on transport cell 419 Formation of C 0 488 Formation rate, straight chain paraffins 33 Foulant deposit geometries 201, 202 Fouling from interactions of pore structure and foulant deposit geometries 201 Fourier law 190 Frankel, Dufort and, methods 67 Frequency factors, rate equation parameters .... 22 spectral 8 stability diagram with curves of equal 502 2
G Gas (es) 63,310 analysis system 513 bubble 401 in a bubbling fluidized bed 436 chromatograph 315,513 flame ionization type 528 method 531 composition, Arrhenius plot of reaction rate with 587 composition, orthogonal factorial design for reactor 585 dense-phase 401 exchange 401,402 rate 441 expansion 438, 440 flow
rate, molar 360 inlet temperature, measured conversion of ethane 546 linear velocity 375-380 -liquid chromatograph 207 interface 428 mass transfer 387 coefficients 311 reactor(s) 351-353 systems 373 tube reactor, cocurrent 329 phase absorbance sample cells 12 absorption, double-beam compensation for 10 concentration 366 dispersion coefficient 379,381 equilibrated 583 intrapellet 463 mole fraction of C 0 367 profile 365 reactions 4, 447 development of reaction models for complex 313 temperature variations 479 profiles 368,369 -solid mixing 51 noncatalytic reactions 226 reactions, pore plugging model for 225 systems 554 solubilities 593 temperature, inlet gas 544 velocity and "fines" content 439 Gears algorithm 103 Geometries, nature of the interaction of the pore structure and foulant deposit 201,202 2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
INDEX
607
Glass tubular reactor 207 Global rates 3 Glucose concentration 165-171 Glucose consumption rate 170 Graetz problem 89 Grain models 225 Grain size, variation of 225 Grignard-reagent, formation 44, 45 Growth in batch and continuous culture 168 kinetical analysis of unbalanced bacterial 163 rate 163 reciprocal plots between the specific 167
specific
165,169
at varying temperatures, specific Gulf-patented segmented bed reactor
166
transfer (continued) property, temperature dependence of radiative Henry's law 362, Heptanes Heterogeneous catalysis, adsorption in Heuristic approach to complex kinetics Hexanes Hinschelwood equation, Langmuir— .. Hinschelwood, kinetic models, Langmuir— Homogeneous continuum heat transfer models
47 273 588 288 50 292 288 209 57 239
Homopolymerization
Hougen and Watson kinetic models .. Hovmand and Davidson, model of 408, 409 32,34 Hatta numbers 125 Hydrocarbon(s) chlorination of saturated 440 Hazards, assessment of thermal 43, 45 distribution, steady state, and Heat periodic effluent 529 of adsorption 57 thermal decomposition reactions of 313 types of reaction 63 trace 479 balances in matrix notation 273 306 capacities 41 Hydrocracking reactions 307 diffusivity, flow control operation Hydrodesulfurization 254-261,387 of a plug-flow tubular reactor of residual oils 255 with high 562 of thiophene 207 evolution, rate of 41 exchanger 353 Hydrodynamic entrance effect 89 monolithic reactor— 83, 89 Hydrofluorination of U 0 440 run Hydrogen 288,307, 448 cocurrent reactor93 cycling, feed 533 countercurrent reactor92 donor reactions 306 for the pellet-filled reactor90 equilibrator, external 428 systems, simple 215 feed concentration 531 flow mole fractions of 517, 532 calorimeters 37-40 peroxide, nitric acid, catalytic control principles 38 decomposition of 505 methods 37 reduction of ores 440 rate 38 styrene, molar concentrations of 321 flux (es) 277 -styrene ratio 319 methods, linear 190 sulfide 448 nonradiative 273 uptake, desulfurization and 433 profile 271 Hydrogénation of reaction 41 of acetylene, ethylene, ethane, transfer vapor phase catalytic 526 coefficient 45, 89, 241, 249,498 of butadiene 515 control, method of 38 of 2-butanone 411,414 data 247 carbon monoxide 26 fire box 273 of ethylene 512 mechanism 218, 250 of α-methylstyrene 414 models, homogeneous continuum 239 on nickel catalysts, dynamic in packed beds of low studies of acetylene 526 tube/particle diameter ratio 238 solvent 311 parameters 15 in trickle-bed reactor, butanone 413 H
2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
608
Hydrolyse, isothermal run of acetic anhydride 42 Hydrotreating heavy oil, trickle flow reactors for 425 Hyperbolic model 295-298 Hysteresis 53,101 in the conversion-inlet temperature domain 467 curves 99-101,477 in wall-catalyzed reactors 98 I I B M model, equivalence between the SA model and the 133 Ideal mixing ( C S T R ) 14 Ignition point apparatus ( Ή Ρ Α ) , therma temperatures 98,10 zone 101 Industrial reactors, performance of .... 571 Infinite bed boundary condition 241 Information System, (TIS) Technological 352 Infrared beam, reference cell 6 cell-reactors 3-5,10 spectrometer 7 spectrophotometer 4-6 Initiator limitations 175 Instrumentation, thermal 37 Integral reactor 15,17, 462 advantages of 22 carbon monoxide oxidation in an .... 461 concentration 21 experiments 20 temperature distribution 21 Integration constant determination 66 routine, Rung-Kutta variable step size 103 rule, Simpson's 286 Intensity function 576-580 representation of residence time variability 571 Interface axial distribution of fractional active sites at fluid-solid 115 gas/liquid 428 liquid/solid 428 spectrophotometer-computer 6 Interstitial flow increases with gas velocity and "fines" content 439 Iodine concentration against D a number 128 Iodine consumption 126 Ionization chamber, electron impact .. 314 Ionization type gas chromatograph, flame 528
Iron 191 Isobutene 359 Isomerization, of P ( O C H ) 44 Isoperibolic calorimetry, aceumullation method 37 Isotherm, Langmuir 464, 465 Isothermal conditions 388 continuous flow reactor 526 fixed-bed reforming pilot plant 287 heterogeneous fixed-bed catalytic reactor 512 multiplicities 461 reactor 72 reforming reactor profiles 289 run 42-44 Isotropic transport 420 3
3
J Jet stirring Jones expression, Lennard-
136 77
Κ Ketone aqueous solution 412 methyl ethyl 574 vapor pressure 421 Kieselguhr catalyst 513 Kinetic(s) 41 activity 282 effect of catalyst pretreatment on 35 Arrhenius 563 parameters 318 of catalytic liquefaction of Big Horn coal 303 data 586 fixed-bed 59 desulfurization 447 determination of the realtime activity 287 design data from a bench-scale heatflow calorimeter 37 form ( C P A F ) , copolymer approximate 182 heuristic approach to complex 292 of the liquid diffusion regime 590 measurements 3,15, 26 modeling for oscillatory catalytic reactions 487 models 57-59,453,488-490 nonlinear 301 parameters 22 penultimate effect 175 phi-factor 175 reforming model 282 resistance 225,230 selectivity 282
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
609
INDEX Kinetic(s) (continued) studies with a spinning basket reactor, multiphase S 0 oxidation Kummer's hyper geometric function .. Kutta variable step size integration routine, Runge2
447 582 113 103
L L91 L I N S E I S equipment 191 L P A experiments 317 LP91 L I N S E I S conductometer 192 Lag dynamic 41 influence of time 566 temperature 57 time 568 Laminar flow 7 polymerization of E P D M polymer .. 140 Langmuir -Hinschelwood adsorption mechanism 283 equation 209 kinetic models 57 isotherm 464, 465 monolayer theory 516 LaPlace-transformation 340 Late reaction zone phenomenon, early559 Law of Arrhenius 500 Law, Fick's 64 Law, Fourier 190 Law, Henry's 362,588 Law, Michaelis-Menten 126 Layer diffusion, product 226 Least square, nonlinear 309 Legendre polynomials 542 Lennard-Jones expression 77 Limestone, absorption of S 0 by calcined 225 Limestone, comparison with experimental data for sulfation of fully calcined 231 Limit cycle(s) 506 experimental 493 frequency of 500 phenomena during catalytic oxidation reactions over a supported platinum catalyst 475 simulated 493 Limtiation region, diffusion 77, 80 Linear heat flux methods 190 regression methods 295 statistical methods 292 velocity, gas 375-380 Liquefaction of Big Horn coal, kinetics of catalytic 303 process (es) 303-306 2
Liquid diffusion influence 582 regime, kinetics of the 590 resistance 592 distribution in a trickle-bed 417 full upflow reactor 428 -gas chromatograph 207 -gas systems 373 interface, gas/ 428 - l i q u i d spray column 539 - l i q u i d systems 373 phase deviation from plug flow 387 dispersion coefficient 379,380 mass transfer coefficient 367
geneous 388 -solid interface 428 -solid transport 393 velocity dependence of reaction rates 415-418 Loop fermentors 154-160 Loop reactor 15-18 advantages of 22-25 data with pilot plant experiments, comparison of 24 design of 17 experiments, results of 21
M Macromixing 126 Macromolecular content 163—165 Magnetic deflection mass spectrometer 477 Maleic anhydride from benzene, production of 215 Maleic anhydride, oxidation of benzene to 440 Manganese-containing catalysts 26 Mass balance 64-66 equation 430 spectrometer, magnetic deflection .. 477 spectrometer, time of flight 314 transfer 8,153,154 in absorption without reaction .... 329 in a bubble column, C0 -interphase 359 with chemical reaction, regime of 327 coefficient 8,9,365-367 effects 306 factors 57 interphase 428 limitations 428 parameters 15 performance 8 rates 13 representation of reactants 418 2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
610
CHEMICAL REACTION ENGINEERING—HOUSTON
transfer (continued) on selectivity, influence of 327, 328 in stirred cell reactor during sulfonation 329 in a trickle-bed reactor, mathe matical model of 420 transport to the catalyst bed, con centration changes caused by .. 68 transport equation 73 Material balances 405,406 Matrix eigenvalues of the selectivity 284 eigenvectors of the selectivity 284 notation 283 heat balances in 273 selectivity rate constant 285 truncation on catalyst effectiveness effect of 39 Measurement(s) heat flow 38 kinetic 1,15,26 transient rapid response 50 Mechanical stirring, relative efficiency of 134 Mechanically stirred fermentors ...154-156 Mechanism(s) heat transfer 218, 250 of interaction 125 reaction 488 Mechanistic model 404, 408,409 Melt 585 Menten's equation, Michaelis126,164 Metal catalyst, oxidation of carbon monoxide over 83 deposition on the desulfurization activity, effect of 262 removal in a stirred-tank reactor .... 260 sulfide deposits 258 Methanation 63,70 Methane 316 Method(s) ASTM 193 collocation 542 dynamic 195,196 experimental 190 linear heat flux 190 regression 295 statistical 292 perturbation 564 collocation 232-235 Rung-Kutta 315 static 190,195 steady state 339 thermal 37 Thomas 143 two-plate 191 unsteady state 339 water displacement 513
Methyl ethyl ketone 574 Methylstyrene, hydrogénation of α- .. 414 Michaelis-Menten's equation .125,126,164 Micro-methods 38 Micromixing 8 effects 126 experimental parameters for 127 phenomena in continuous stirred reactors 125 time(s) 129-131,134 Mid-Continent naphtha 287, 288 Middle East residues 255,261, 262 Mini-pilot reactor 37 Minimum lifetime 259-262 Mixed flow profiles 220 Mixed flow reactor 219 axial 304,337-345 behavior, fluid 571 gas-solid 51 radial 304-306 (STR), ideal 14 Model(s) axial dispersion 242, 307, 359 axially dispersed plug flow 239 for complex gas-phase reactions, development of reaction 313 countercurrent backmixing 400 diffusion/convection flow 577 dual site 455 evaluation of 243 exponential 297 fluidized bed reactor 436, 438 for gas-solid reactions, pore plugging 225 homogeneous continuum heat transfer 239 Hougen and Watson kinetic 57 of Hovmand and Davidson 408, 409 hyperbolic 295-298 kinetic 59,453,488, 490 Langmuir—Hinschelwood kinetic .... 57 of the liquid distribution in a trickle-bed 417 of mass transfers in a trickle-bed reactor 42C mechanistic 403, 404, 408, 40S Monod's 17C nonlinear kinetic 301 one-dimensional dispersion 372 "parallel bundle" 202 plug flow 242-244 pore plugging 226,231, 233, 23S pore structure 20c for prediction of the radial conductivities 241 pseudomonomolecular kinetic reforming 282
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
INDEX
611
Monad's (continued) for reaction in partly wetted catalyst pellets 391 "shrinking aggregate" 130 slugging fluidized bed reactor 400 621 spectrophotometer 6 studies of radial flow, fixed bed reactors, cell 550 time-averaged 408, 409 trickle-bed reactor 411 two-phase 400-403,539 dispersion 359 "wedge layering" 202 Modeling for oscillatory catalytic reactions, kinetic 487 Modulus, Thiele 34, 99,125 Moisture-free coal 307 Molar concentrations 321-32 Molar gas flow rate 360 Mole fraction 515 of C 0 , gas phase 367 feed hydrogen 532 of H 517 profiles for different thermal conductivities 102 Molecular conductivity 248 Molten V 0 - K S 0 catalyst, oxida tion of S 0 on supported 582 Monod's equation 164 Monod's model 170 Monolith(s) channels 72,103 entrance effect in active 80 catalysts, poisoning in 110 convertor, concentration, and velocity profiles 72 pellet-filled 83-85 physical dimensions of crossflow .... 84 reactor (active wall) 72 reactor-heat exchanger 83, 89 Monomer disappearance 143 Monomer sensitivity limitations 175 Monte Carlo integrations 275 Movement, cocurrent-countercurrent 539 Moving bed reactor, design of a 540 Multi-component adsorption, effects of 51, 57 Multiphase kinetic studies with a spinning basket reactor 447-449 Multiplicity 551 during C O oxidation, steady state .. 477 measured and calculated, ranges of 547 phenomena 499 steady state 98 and uniqueness, regions of 545 upper and lower temperature profiles region or 546 in wall-catalyzed reactors 98 Multitubular reactor(s) 215 Mutta technique, Runge90 2
2
2
5
2
2
2
7
Ν Naphtha 306 Arab light 287,288 Mid-Continent 287,288 Nigerian 287 Naphthalene 8 sublimation rate of 9 Navier-Stokes equation of motion ...72,73 Nelder and Mead, derivative-free simplex method 22 Newton-Raphson algorithm 88 iteration 114 method 103 procedure 273 Newtonian fluid 73,74
catalysis, dynamic studies of acetylene hydrogénation on .... 526 content 531 Nigerian naphtha 287 Nitric acid, catalytic decomposition of hydrogen peroxide 505 Nitric oxide conversion 550 Nitrogen 425 Noncatalytic homogeneous liquid phase reaction 388 Noncatalytic reactions, gas-solid 226 Nonisothermal behavior in chain addition copolymerization 173 Nonisothermal histories 180 Nonlinear kinetic models 301 Nonlinear least square 309 Non-Newtonian fluids 149 Nonradiative heat fluxes 273 Nonselective poisoning 110-111,115 cell 555,556 fractional yield as function of cell .. 558 Nusselt 99 Peclet 248, 249,308, 338-344,578-580 Prandtl 248 Reynolds 243-249, 465 wall biot 249, 251 Nylon-6 348 Nyquist plane 566-569
Oil(s) dibenzothiophene in white flush furnace heavy fuel trickle flow reactors for hydrotreating heavy vaporized white One-dimensional dispersion model ....
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
310 447 307 306 306 425 448 448 372
CHEMICAL REACTION ENGINEERING—HOUSTON
612
Packed bed ( s ) ( continued ) Operating time on catalyst perform axial flow in 541 ance, effect of 29 of low tube/particle diameter Operation on the selectivity of ratio, heat transfer in 238 catalytic reactions, effect of periodic 512 Packed bubble columns of large diameter, axial mixing of Ores, hydrogen reduction of 440 liquid in 337 Organism and growth medium 163 Packing efficiency 346 Orthogonal central-composite 345 design 293 Packing on axial mixing, effect of 339,344 Orthogonal collocation 67,103 Pall rings 288 Orthogonal design 584-586 Paraffin composition profiles Paraffin formation rate, straight chain 33 Oscillation ( s ) 202 amplitude of temperature 503 "Parallel bundle" model Parallel passage reactor asymmetric behavior of the advantage of 70 temperature 503 dimensions of 65 of concentration 568 methanation in a 63 at different temperatures 480-483 experimental period in compariso with computed period 50 Parallel reaction mechanism 309 from computer simulation, typical temperature 501 Parameter(s) cross-correlations 247 in a stirred tank reactor, theoretical and experimental study of heat transfer 15 mass transfer 15 self-sustained 498 of a pseudomonomolecular kinetic of temperature and conversion .508,568 reforming model, realtime Oscillatory catalytic reactions, activity 282 kinetic modeling for 487 RA . 175 Oscillatory phenomena 482 search technique, Rosenbrock's 287 Oxidation 99,173 of anol to anone 348 Parametric sensitivity 30 of benzene 217, 440 Partial pressure of carbon monoxide .. of butane 574 Particle(s) catalyst 417 1-butene 482 diameter ratio, heat transfer in carbon monoxide ...83,465,466,476,491 packed beds of low tube/ 238 cyclohexane 354, 356 diffusional resistance through the of dammitol 292, 294 pores of the 225 efficiency 352 escape probability for a 572 of ethylene 77,80, 440 size 584 in an integral reactor, carbon monoxide 461 Particulate phase, piston-flow region of 405 kinetics, S 0 582 Peclet Pe number 242,248,249, 308, limit cycles during simultaneous 338-344,578-580 C O and 479 over platinum, carbon monoxide .... 475 Pellet(s) catalyst 462 process, computer-aided develop -filled crossflow monolith 83-85 ment of the cyclohexane 348 mathematical model for reaction in process, improvement of the C H - .. 349 partly wetted catalyst 391 reactions 63 partially wetted catalyst 389 catalytic partial 215 thermal conductivity of a 191 section by means of T I S F L O , Penultimate effect kinetics 175 simulation of a plant 352 420 of sodium sulfite 154 Percolation theory of S 0 512,582 Perforated plate columns of large diameter, axial mixing of liquid steady state multiplicity during C O 477 in 337 tubular reactor for xylene 19 Oxygen 477, 488 Performance of industrial reactions .... 571 Periodic effluent concentrations 534 Ρ Periodic effluent hydrocarbon distri P ( O C H ) isomerization 44 butions, steady state and 529 Packed bed(s) 248,250 Periodic operation 520-523 2
2
3
3
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
INDEX
613
Permeability 437 Perturbation(s) collocation method 232-235 of the initial steady state, deliberate 468 method 564 single inlet concentration 461 solution for small times 229 transient behavior of the reactor for finite 568 Phase deviation from plug flow, liquid 387 Phase, equilibrated gas 583 Phenomenon, early-late reaction zone 559 Phi-factor kinetics 175 Physical component, azimuthal 73 Physical dimensions of crossflow monoliths 84 Pilot plant, adiabatic data 29 Pilot plant, isothermal fixed-bed reforming 287 Pilot-reactor, mini37 Pilot unit scale reactor 577 Piston-flow region 404-406 Plane, Nyquist 566-569 Plant experiments, comparison of loop reactor data with pilot 24 Plant oxidation section by means of T I S F L O 352 Plant reactor 25, 574, 575 Plant scale reactor 574 Plastic powders, nonporous 193 Plate(s) on axial mixing, effect of 345 efficiency 346 method, modified 194 Platinum 477 -alumina catalyst 463, 466 carbon monoxide oxidation over .... 475 catalyst, catalytic oxidation reactions over supported 475, 476 Plot(s) Arrhenius 310,583,586 of conversion vs. space velocity 69 for oxidation of ethylene, Arrhenius 77 of reaction rate with gas composition, Arrhenius 587 of selectivity vs. conversion 520 between the specific growth rate, reciprocal 167 of yield vs. conversion 520 plug flow 72, 425 of liquid 387, 388 model 242-244 axially dispersed 239 reactor 254,337,428 tubular reactor with high heat diffusivity 562 Plugging, pure pore mouth 202-205, 254 Plugging time, analytical evaluation of the 228
Poincaré theorems Poiseuille profile, laminar Poison (ing) deposition mode of deactivation in monolithic catalysts nonselective pure selective Polymer concentration Polymer molecular weight Polymerization Polynomials, legendre Pore blockage diffusion
487 72 115 202 110 110-111,115 205 111-115 143 173 140,173 542 232 226
desulfurization 254 mouth plugging, pure 202, 205 plugging model 225,226,231-235 for gas-solid reactions 225 size 584 structure and foulant deposit geometries 201, 202 internal 391 model 203 of the particle, diffusional resistance through the 225 Porosity changes 225 Powders, nonporous plastic 193 Prandtl's number, (Pr) 45,248 Precipitation 591 Pressure apparatus 314 of C 0 , liquid phase partial 369 of carbon monoxide, partial 30 change, system response to 56 drop equation 271 ketone vapor 421 response characteristics 55 transducer 53 transient for ferf-butanol catalytic dehydration, adsorption-reaction 58 Probability for a particle, escape 572 Problems, stability 539 Product, diffusional resistance through the solid 225 Product gas, recirculation cold 63 Profile(s) analytic solution for nonuniform viscous flow, velocity 149 axial 360 flow, steady state temperature .... 552 in the catalyst bed, concentration .. 67 composition 288 concentration 230,261 description of measured 366 2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
614
CHEMICAL REACTION ENGINEERING—HOUSTON
Profile(s) (continued) for different thermal conductivities, mole fraction 102 in the entrance region of a monolithic convertor 72 ethylene concentration 535 exit 144 gas 368,369 gas phase 365 heat flux 271 initial velocity 144 inlet velocity 144 isothermal reforming reactor 289 laminar Poiseuille 72 mixed flow 220 in multiple channels, radial temperature 107 paraffin and benzene compositio region of multiplicity, upper lower temperature 546 solid temperature 116 steady state 559 temperature 144, 239,240, 246,514, 540 transient behavior of temperature .. 560 tubeside temperature 220 tube wall temperature 271 Program description, computer 54 2-Propanol 4 Propanol, aeration of 377, 378 over alumina, dehydration of 10 Properties of catalysts 195,462 Properties, fluid dynamic 362 Proportional control 563 Pseudomonomolecular kinetic reforming model, realtime activity parameters of a 282 Pseudosolubility 153 Pulse amplitudes 468-471 Pulse duration on conversion enhancement, effects of 468-472 Pulsing at various temperatures 469 Pump, metal bellows recycle 476 Pyrolysis of ethylbenzene 313-316 Pyrosulfonic acid 327-329
Q Qualitative trends of the hysteresis curve Quartz
99 314
R Radial conductivity 247-250 dispersion effects 363 distribution of fractional sites 116 distribution of poison deposition .... 115 flow 550-554 inlet 541 mixing 304-306
Radial (continued) Peclet numbers 242 temperature profiles in multiple channels 107 Radiation 273,276 Radiative heat transfer 273 Radical reaction equations 350 Raphson algorithm, Newton88 iteration, Newton114 method, Newton103 Rasching rings 339 Rate(s) . on axial mixing, effect of gas flow .. 342 of C O conversion 492 constant(s) effect of coke deposition on
reaction 310 realtime activity 283 of conversion 38 determination of, reaction 22 equation(s) 23 intrinsic 416 parameters, activation energies and frequency factors 22 reaction 414 as a function of product sulfur, reaction 454 with gas composition, Arrhenius plot of reaction 587 gas-exchange 401,441 glucose consumption 170 growth 163 intrinsic 3 mass transfer 13 molar gas flow 360 of oxidation of S 0 over vanadium oxide 512 on performance, effect of agitation 452 reaction 457 shear 149 static global 3 of sublimation 8, 9 superficial liquid velocity dependence of reaction 415,418 transient global 3 Ratio, recycle 17 Reactant(s) feed system 513 mass transfers, representation of ... 418 nonvolatile liquid 388 species, concentration of a 441 system reaction, single 57 Reaction(s) adsorption 3 to the catalyst bed, concentration changes caused by 68 2
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
INDEX
615
Reaction(s) (continued) catalytic partial oxidation 215 conditions, adsorption at 57 development of reaction models for complex gas phase 313 effect of periodic operation on the selectivity of catalytic 512 equation(s) with the Damkohlen number 76 radical 350 with the Schmidt number 76 first-order irreversible 388 first-order steady-state chemical .... 402 gas-phase 4,447 gas-solid noncatalytic 226 heat adsorption, types of 63 of hydrocarbons, thermal decomposition 31 hydrocracking 306,30 kinetic modeling for oscillatory catalytic 487 in the liquid phase, micromixing phenomena in continuous stirred reactors 125 mass transfer in absorption without 329 mechanisms 309,488 models for complex gas phase reactions, development of 313 noncatalyst homogeneous liquid phase 388 oxidation 63 in partly wetted catalyst pellets 391 pore plugging model for gas-solid 225 rate(s) 457 Arrhenius diagrams for 31 of carbon monoxide, reduced 30 on the catalyst 217 constants 310 determination of 22 equation 414 as a function of product sulfur ... 454 with gas composition, Arrhenius plot of 587 superficial liquid velocity dependence of 415, 418 temperature dependency 30 regime of mass transfer with chemical 327 selectivity 574 studies, adsorption 57 over supported platinum catalyst 475, 476 tube wall catalyzed 74 vapor-phase catalytic 293 zone phenomenon, early-late 559 Reactor(s) adsorber50-53,59 backmixed 309 bench-scale 303 coated tube 63
Reactor(s) (continued) cocurrent 218-222 gas-liquid tube 329 components 51 conditions during comparisons of trickle and batch operations .... 432 configurations, comparison of 217 continuous flow spinning basket stainless steel 527 continuous flow stirred tank 337,430,498 coolant pass 221 countercurrent 218-220,414 cyclone 328-334 design features 17, 51, 540 development 50,450 differential 10,15 evaluation 50 fixed bed 513,539 fluidized-bed 563 gas-liquid 352,353 glass tubular 207 Gulf-patented segmented bed 304 -heat exchanger 83,89-93 honeycomb 77 impinging jet infrared cell-recycle .. 3 ir cell 4, 5,10,11 inlet temperature 282,288 integral 15-17,22, 462 internal recycle 26 isothermal 72,512,526 laboratory 16 liquid full upflow 428 loop 15-25 mini-pilot 37 mixed flow 219 model(s) fluidized 436-438 gas-liquid 351 multitubular 215 slugging fluidized bed 400 trickle-bed 411 monolithic (active wall) 72 moving bed 543 multiphase spinning basket 449 multiplicity wall-catalyzed 98 multitubular 215 parallel passage 63-70 performance of industrial 571 pilot unit scale 577 plant 474,575 plug flow 254,337,428 prototypes, cell 9 recirculating batch 6 recirculation 583 selectivity in 331-333 single-wafer catalytic recycle 13 spinning basket 448 stirred cell 328-334
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
616
Reactor(s) (continued) trickle-bed 414-416,447 trickle flow 431 tube 15-17,219,334,512 Realtime activity kinetics 287, 288 Realtime activity parameters 282,283 Recirculation reactor 583 Recycle flow 584 pump, metal bellows 476 ratio 17 reactor impinging jet infrared cell3 internal 26 single-wafer catalytic 13 Reduction of ores, hydrogen 440 Reduction, vanadium 585, 591 Regime, kinetics of the liquid diffusion 59 Residence time 337, 516, 527 analysis 571 curves, concentration20 data 573-579 density 572-579 distribution 339-341,571, 576-580 Residue, Caribbean 255-262 Residues, Middle East 255-262 Resistance, kinetic 225,230 Resistance, liquid diffusion 592 Reynolds number 8, 45, 89, 243-249, 465 Rings, Pall 339,344 Rings, Rasching 339 Rosenbrock's parameter search technique 287 Rotameters 507 Run(s) 90-93 cyclic 517 Runaway analysis ( R A ) 175-183 Runge-Kutta methods 315 technique 90 variable step size integration routine 103 Ruthenium catalyst 411 S Scanning calorimetry, differential 181 Scans, steady-state spectral 12,13 Schmidt method, Binder— 67 Schmidt number 75, 76 Selective poisoning 111-115 Selectivity of catalytic reactions, operation on the 512 on C O conversion, dependence of .. 28 vs. conversion, plot of 520 conversion, yield 514 in the cyclone reactor 333
Selectivity (continued) effects 557 of catalyst pretreatment of 35 ethane 531 influence of mass transfer on 327,328 matrix 284 under periodic operation 521-523 rate constant matrix 285 reaction 574 steady state 519 in stirred cell reactor 331 of straight chain hydrocarbons 34 in the tube reactor 333 Semenov-type dimensional analysis ... 173 Sensitivity analysis 353 limitations, monomer 175
Shear rate 149 Sherwood numbers 99 Shrinking aggregate model 130 Simplex method (Nelder and Mead), derivative-free 22 Simpson's integration rule 286 Single reactant system reaction 57 Single-wafer catalytic recycle reactor 13 Sliding thermocouple 412 Slugging fluidized bed reactor 400, 404 Sodium hydroxide 339 Sodium sulfite, oxidation of 154 Solid contact and mixing gas51 interface, fluid— 115 interface, l i q u i d 428 reactions, pore plugging model for gas225 systems, gas— 554 thermal conductivity 101 transport, l i q u i d 393 Solvation, coal 304-310 Space velocity conversion vs 68, 69 Spectra, surface 3, 6 Spectral scans, steady-state 12,13 Spectrometer ir 3-7 magnetic-deflection mass 477 time of flight mass 314 Spinning basket reactor 447-449 stainless steel, continuous flow 527 Spray column, liquid/liquid 539 Stability 551 of controlled reactor 565 diagrams 501-504 domain 567-569 parameter 564 problems 539 steady state 499, 566
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
617
INDEX Stainless steel reactor, continuous flow spinning basket 527 Start-of-cycle reactor inlet temperatures 282 Static conductivities 249 global rates 3 methods 190,195 process 248 surface spectra 3 Steady state for 2% C O , multiple 480 compositions 528 continuity equation 73 conversion of C H 6 518 conversion performance with puls ing at various temperatures .... 469 diagrams 56 equation 492 gas analyses 513 hysteresis in the conversion-inlet temperature domain 467 methods 339 multiplicity 98, 466, 477 profiles 559 runs 517 selectivity 519 spectral scans 12,13 stability 499,566 temperature 532, 563-567 yield of C M 519 Stirred cell reactor 328-334 aromatic sulfonation in a 327-329 selectivity in 331 Stirred tank experiments 262 reactor 4, 430 catalyst life in a 260 continuous flow 125, 337, 498 metal removal in a 260 self-sustained oscillations in a . . . 498 Solubilities, gas 593 Stokes-Einstein equation 331 Stokes equation of motion, Navier- ...72, 73 Styrene 315-323 -acrylonitrile ( S A N ) 175 -methyl methacrylate ( S M M A ) .... 175 Sulfite, oxidation of sodium 154 Sulfide deposits, metal258 Sulfonation aromatic 327 of benzene 327,334 experiments 329-333 mass transfer 329 Sulfovanadate complexes 582 Sulfur 425 concentration 255 dioxide absorption of 225 4
4
8
dioxide (continued) oxidation kinetics over vanadium oxide, rate of oxidation of reaction rate as a function of product trioxide Sulfuric acid Synthesis of ammonia, catalytic Synthesis, Fischer-Tropsch
Technological Information System (TIS) Temperature(s) amplitude, stability diagram of
582 512 454 327-332 359 550 26,63
352 504
distribution of Ο 118 cell number after a shift in 169 coefficient of sensitivity 53 comparison of some representative amplitudes of 505 control of methanation reactors 63 conversion of ethane gas inlet 546 and conversion, measured oscilla tions of 508 dependence of "heat transfer property" γ 47 dependency, reaction rate 30 for different wall thermal conductivities 101,102 distribution, integral reactor 21 domain, steady state hysteresis in the conversion-inlet 467 extinction 98 ignition 98 inlet gas 544 lag 57 in multiple channels, wall 105-106 oscillation of 480-483, 501-503, 568 profile( s ) 144, 219-221, 240, 246, 514, 540 axial flow 552 in multiple channels, radial 107 radial 239 region of multiplicity, upper and lower 546 transient behavior 560 tube wall 271 solid 116 tubeside 220 programmed run, diazo-decomposition's 42 reactor inlet 282, 288 shift on growth, effects of 168 specific growth rate at varying 166 steady-state 469, 463-567 transient behavior of reactor 569 variations, gas phase 479
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
CHEMICAL REACTION ENGINEERING—HOUSTON
618
Termination models 174 Theorems, Bendixon 487 Theorems, Poincaré 487 Theory Langmuir monolayer 516 percolation 420 residence time distribution 571 true volume ideal two-phase 438 two-phase 436 Thermal conductivity 190-195,315 mole fraction profiles for different 102 of a pellet 191 of porous catalysts 189 solid 101 temperatures for different wall 101,102 cracking furnace 271-274 data 4 decomposition reactions of hydrocarbons 313 design data from a bench-scale heatflow calorimeter 37 energy balance 173 hazard(s) 43-45 ignition 173 ignition point apparatus 182 instrumentation 37 liquefaction processes 303 methods 37 phenomena in chain addition copolymerization 173 runaway ( R A ) 173,182 Thermocouple ( s ) 17, 53, 57 axial 412 Cr/Al 238 sliding 412 Thiele modulus 34,99, 125 Thiophene 207 Thodos correlation, de Acetis466 Thomas method 143 Time analysis, residence 571 -averaged conversion 505 -averaged model 408,409 curves, concentration-residence 20 data, abstract residence 573 density function, residence 572 distribtuions, residence 339 of flight mass spectrometer 314 lag 568,569 bacterial 172 influence of 566 residence 337,527 testing of the plant reactors, residence 574 Toluene 288,315,316 Transfer, mass 8,13-15,153,154, 388 in absorption without reaction 329 in a bubble column, C0 -interphase 359 2
Transfer, mass (continued) with chemical reaction, regime of .... 327 coefficient 311,365-367 effects 306 gas-liquid 387 representation of reactants' 418 on selectivity, influence of 327,328 in stirred cell reactor during sulfonation 329 in a trickle-bed reactor 420 Transformation, LaPlace340 Transient analysis 559 Transient behavior of reactor temperature 568-560 Transition, R A 179,183 Transport to the catalyst bed, concentration
equation, mass 73 isotropic 420 liquid-solid 393 of vorticity, convective 74 Trickle-bed reactor 416 butanone hydrogénation in 413 catalyst effectiveness factor in 387 countercurrent 414 model 411 of the liquid distribution in a 417 of mass transfers in a 420 performance equations for 389 Trickle flow and batch operation, comparison of 432, 433 reactor 431 catalyst utilization in a 425 Tropsch synthesis, Fischer63 Truncation on catalyst effectiveness, effect of matrix 393 Tube -particle diameter ratio 238 reactor 334 aromatic sulfonation in a cocurrent 327 cocurrent gas—liquid 329 selectivity in the 333 wall-catalyzed reaction 74 wall temperature profile 271 Tubeside temperature profiles 220 Tubular reactor(s) 15-19,63,512 glass 207 with high heat diffusivity, flow control operation of a plug-flow .... 562 limitations 149 polymerization in a 140 Turbulant conduction 248,249 Two-phase model 359,400-403, 539 Two-phase theory, true volume ideal.. 438 Two plate method 191
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
619
INDEX
U U 0 , hydrofluorination of Upflow reactor, liquid full Utilization, experimental system for determining maximum catalyst.... 2
440 428 429
V2O5-K2S2O7 catalyst, oxidation of S 0 on supported molten 582 Valualdehyde 294-298 Vanadium 255-259, 588, 592 oxide, rate of oxidation of S 0 over 512 removal 261-263 reduction 585, 591 Vapor phase catalytic hydrogénation 526 Vapor phase catalytic reaction Vapor pressure, ketone 42 Variability, intensity function representation of residence time 571 Vector, vorticity 73 Velocity conversion vs. space 68,69 dependence of reaction rates, superficial liquid 415-418 in the entrance region of a monolithic convertor 72 field development, axial 76 and "fines" content, interstitial flow increases with gas 439 fluid interstitial 551 gas linear 375-380 profiles 75,144,149 Viscous flow, velocity profile analytic solution for nonuniform 149 2
2
Wall biot number 242,249-251 -catalyzed reaction 74 -catalyzed reactors 72,98 thermal conductivities 101 Water displacement method 513 Water on ierf-butanol adsorption, effect of 58 Watson kinetic models, Hougen and 57 "Wedge layering" model 202,211 Wetted catalyst pellets 391 Wetted slab 394 Wetting efficiency 411 external 390,391 incomplete catalyst 427 internal 390
X Xylene, aeration of 377,378 Xylene oxidation, tubular reactor for 19
Y Yield vs. conversion, plot of conversion, selectivity ethane as function of cell number, fractional under periodic operation, mean and selectivity under periodic operation
517 520 514 532 558 521 523
Ζ
W Wafer catalytic recycle reactor, single-
13
Zeolite cracking catalysts Ziegler catalysis Zone, ignition
In Chemical Reaction Engineering—Houston; Weekman, V., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
288 140,149 101
