CO2 Solutions Inc.
`Exhibit 2015
`Akermin, Inc. v. CO2 Solutions Inc.
`IPR2015-00880
`Page 1 of 55
`
`

`
`ACQUISITIONS EDITOR
`MARKETING MANAGER
`PRODUCTION EDITOR
`SENIOR DESIGNER
`ILLUSTRATION COORDINATOR
`ILLUSTRATION
`COVER DESIGN
`
`Wayne Anderson
`Katherine Hepburn
`Ken Santor
`Kevin Murphy
`Jaime Perea
`Wellington Studios
`Bekki Levien
`
`This book was set in Times Roman by Bi-Comp Inc. and printed and bound by the
`Hamilton Printing Company. The cover was printed by Phoenix Color Corporation.
`
`This book is printed on acid-free paper.
`
`The paper in this book was manufactured by a mill whose forest management programs
`include sustained yield harvesting of its timberlands. Sustained yield harvesting principles
`ensure that the numbers of trees cut each year does not exceed the amount of new growth.
`
`Copyright O 1999 John Wiley & Sons, Inc. All rights reserved.
`
`No part of this publication may be reproduced, stored in a retrieval system or transmitted
`in any form or by any means, electronic, mechanical, photocopying, recording, scanning
`or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States
`Copyright Act, without either the prior written permission of the Publisher, or
`authorization through payment of the appropriate per-copy fee to the Copyright
`Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (508) 750-8400, fax
`(508) 750-4470. Requests to the Publisher for permission should be addressed to the
`Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY
`10158-0012, (212) 850-6011, fax (212) 850-6008, E-Mail: PERMREQ@WILEY.COM.
`
`Library of Congress Cataloging-in-Publication Data:
`Levenspiel, Octave.
`Chemical reaction engineering 1 Octave Levenspiel. - 3rd ed.
`p.
`cm.
`Includes index.
`ISBN 0-471-25424-X (cloth : alk. paper)
`1. Chemical reactors.
`I. Title.
`TP157.L4 1999
`6601.281-dc21
`
`97-46872
`CIP
`
`Printed in the United States of America
`
`Page 2 of 55
`
`

`
`Preface
`
`Chemical reaction engineering is that engineering activity concerned with the
`exploitation of chemical reactions on a commercial scale. Its goal is the successful
`design and operation of chemical reactors, and probably more than any other
`activity it sets chemical engineering apart as a distinct branch of the engi-
`neering profession.
`In a typical situation the engineer is faced with a host of questions: what
`information is needed to attack a problem, how best to obtain it, and then how
`to select a reasonable design from the many available alternatives? The purpose
`of this book is to teach how to answer these questions reliably and wisely. To
`do this I emphasize qualitative arguments, simple design methods, graphical
`procedures, and frequent comparison of capabilities of the major reactor types.
`This approach should help develop a strong intuitive sense for good design which
`can then guide and reinforce the formal methods.
`This is a teaching book; thus, simple ideas are treated first, and are then
`extended to the more complex. Also, emphasis is placed throughout on the
`development of a common design strategy for all systems, homogeneous and
`heterogeneous.
`This is an introductory book. The pace is leisurely, and where needed, time is
`taken to consider why certain assumptions are made, to discuss why an alternative
`approach is not used, and to indicate the limitations of the treatment when
`applied to real situations. Although the mathematical level is not particularly
`difficult (elementary calculus and the linear first-order differential equation is
`all that is needed), this does not mean that the ideas and concepts being taught
`are particularly simple. To develop new ways of thinking and new intuitions is
`not easy.
`Regarding this new edition: first of all I should say that in spirit it follows the
`earlier ones, and I try to keep things simple. In fact, I have removed material
`from here and there that I felt more properly belonged in advanced books.
`But I have added a number of new topics-biochemical
`systems, reactors with
`fluidized solids, gadliquid reactors, and more on nonideal flow. The reason for
`this is my feeling that students should at least be introduced to these subjects so
`that they will have an idea of how to approach problems in these important areas.
`iii
`
`Page 3 of 55
`
`

`
`i~ Preface
`
`I feel that problem-solving-the process of applying concepts to new situa-
`tions-is essential to learning. Consequently this edition includes over 80 illustra-
`tive examples and over 400 problems (75% new) to help the student learn and
`understand the concepts being taught.
`This new edition is divided into five parts. For the first undergraduate course,
`I would suggest covering Part 1 (go through Chapters 1 and 2 quickly-don't
`dawdle there), and if extra time is available, go on to whatever chapters in Parts
`2 to 5 that are of interest. For me, these would be catalytic systems (just Chapter
`18) and a bit on nonideal flow (Chapters 11 and 12).
`For the graduate or second course the material in Parts 2 to 5 should be suitable.
`Finally, I'd like to acknowledge Professors Keith Levien, Julio Ottino, and
`Richard Turton, and Dr. Amos Avidan, who have made useful and helpful
`comments. Also, my grateful thanks go to Pam Wegner and Peggy Blair, who
`typed and retyped-probably what seemed like ad infiniturn-to get this manu-
`script ready for the publisher.
`And to you, the reader, if you find errors-no, when you find errors-or
`sections of this book that are unclear, please let me know.
`
`Octave Levenspiel
`Chemical Engineering Department
`Oregon State University
`Corvallis, OR, 97331
`Fax: (541) 737-4600
`
`Page 4 of 55
`
`

`
`Contents
`
`Notation
`
`/xi
`
`Chapter 1
`Overview of Chemical Reaction Engineering
`
`I1
`
`Part I
`Homogeneous Reactions in Ideal
`Reactors I11
`
`Chapter 2
`Kinetics of Homogeneous Reactions
`I13
`2.1 Concentration-Dependent Term of a Rate Equation
`2.2 Temperature-Dependent Term of a Rate Equation
`2.3 Searching for a Mechanism 129
`2.4 Predictability of Reaction Rate from Theory 132
`
`I14
`I27
`
`Chapter 3
`Interpretation of Batch Reactor Data
`3.1 Constant-volume Batch Reactor 139
`3.2 Varying-volume Batch Reactor 167
`3.3 Temperature and Reaction Rate 172
`3.4 The Search for a Rate Equation
`I75
`
`I38
`
`Chapter 4
`Introduction to Reactor Design 183
`
`Page 5 of 55
`
`

`
`vi Contents
`
`Chapter 5
`Ideal Reactors for a Single Reaction 190
`5.1 Ideal Batch Reactors
`I91
`52. Steady-State Mixed Flow Reactors 194
`5.3 Steady-State Plug Flow Reactors 1101
`
`Chapter 6
`Design for Single Reactions I120
`6.1 Size Comparison of Single Reactors 1121
`6.2 Multiple-Reactor Systems 1124
`6.3 Recycle Reactor 1136
`6.4 Autocatalytic Reactions 1140
`
`Chapter 7
`Design for Parallel Reactions 1152
`
`Chapter 8
`Potpourri of Multiple Reactions 1170
`8.1 Irreversible First-Order Reactions in Series 1170
`8.2 First-Order Followed by Zero-Order Reaction 1178
`8.3 Zero-Order Followed by First-Order Reaction 1179
`8.4 Successive Irreversible Reactions of Different Orders 1180
`8.5 Reversible Reactions 1181
`8.6
`Irreversible Series-Parallel Reactions 1181
`8.7 The Denbigh Reaction and its Special Cases 1194
`
`Chapter 9
`Temperature and Pressure Effects 1207
`9.1 Single Reactions 1207
`9.2 Multiple Reactions 1235
`
`Chapter 10
`Choosing the Right Kind of Reactor 1240
`
`Part I1
`Flow Patterns, Contacting, and Non-Ideal
`Flow
`I255
`
`Chapter 11
`Basics of Non-Ideal Flow 1257
`11.1 E, the Age Distribution of Fluid, the RTD 1260
`11.2 Conversion in Non-Ideal Flow Reactors 1273
`
`Page 6 of 55
`
`

`
`Contents Yii
`
`Chapter 12
`Compartment Models 1283
`
`Chapter 13
`The Dispersion Model 1293
`13.1 Axial Dispersion 1293
`13.2 Correlations for Axial Dispersion 1309
`13.3 Chemical Reaction and Dispersion 1312
`
`Chapter 14
`The Tanks-in-Series Model 1321
`14.1 Pulse Response Experiments and the RTD 1321
`14.2 Chemical Conversion 1328
`
`Chapter 15
`The Convection Model for Laminar Flow 1339
`15.1 The Convection Model and its RTD 1339
`15.2 Chemical Conversion in Laminar Flow Reactors 1345
`
`Chapter 16
`Earliness of Mixing, Segregation and RTD 1350
`16.1 Self-mixing of a Single Fluid 1350
`16.2 Mixing of Two Miscible Fluids 1361
`
`Part 111
`Reactions Catalyzed by Solids 1367
`
`Chapter 17
`Heterogeneous Reactions - Introduction 1369
`
`Chapter 18
`Solid Catalyzed Reactions 1376
`18.1 The Rate Equation for Surface Kinetics 1379
`18.2 Pore Diffusion Resistance Combined with Surface Kinetics 1381
`18.3 Porous Catalyst Particles
`I385
`18.4 Heat Effects During Reaction 1391
`18.5 Performance Equations for Reactors Containing Porous Catalyst
`Particles 1393
`18.6 Experimental Methods for Finding Rates 1396
`18.7 Product Distribution in Multiple Reactions 1402
`
`Page 7 of 55
`
`

`
`viii Contents
`
`1465
`
`Chapter 19
`The Packed Bed Catalytic Reactor 1427
`Chapter 20
`Reactors with Suspended Solid Catalyst,
`Fluidized Reactors of Various Types 1447
`20.1 Background Information About Suspended Solids Reactors 1447
`20.2 The Bubbling Fluidized Bed-BFB
`1451
`20.3 The K-L Model for BFB 1445
`20.4 The Circulating Fluidized Bed-CFB
`20.5 The Jet Impact Reactor 1470
`Chapter 21
`Deactivating Catalysts 1473
`21.1 Mechanisms of Catalyst Deactivation 1474
`21.2 The Rate and Performance Equations 1475
`21.3 Design 1489
`Chapter 22
`GIL Reactions on Solid Catalyst: Trickle Beds, Slurry
`Reactors, Three-Phase Fluidized Beds 1500
`22.1 The General Rate Equation 1500
`22.2 Performanc Equations for an Excess of B 1503
`22.3 Performance Equations for an Excess of A 1509
`22.4 Which Kind of Contactor to Use 1509
`22.5 Applications 1510
`
`Part IV
`Non-Catalytic Systems
`
`I521
`
`I523
`
`Chapter 23
`Fluid-Fluid Reactions: Kinetics
`23.1 The Rate Equation 1524
`Chapter 24
`Fluid-Fluid Reactors: Design 1.540
`24.1 Straight Mass Transfer 1543
`24.2 Mass Transfer Plus Not Very Slow Reaction 1546
`Chapter 25
`Fluid-Particle Reactions: Kinetics 1566
`25.1 Selection of a Model 1568
`25.2 Shrinking Core Model for Spherical Particles of Unchanging
`Size 1570
`
`Page 8 of 55
`
`

`
`Contents ix
`
`25.3 Rate of Reaction for Shrinking Spherical Particles 1577
`25.4 Extensions 1579
`25.5 Determination of the Rate-Controlling Step 1582
`
`Chapter 26
`Fluid-Particle Reactors: Design 1589
`
`Part V
`Biochemical Reaction Systems
`
`I609
`
`Chapter 27
`Enzyme Fermentation 1611
`27.1 Michaelis-Menten Kinetics (M-M kinetics) 1612
`Inhibition by a Foreign Substance-Competitive and
`27.2
`Noncompetitive Inhibition 1616
`
`Chapter 28
`Microbial Fermentation-Introduction and Overall
`Picture 1623
`
`Chapter 29
`Substrate-Limiting Microbial Fermentation 1630
`29.1 Batch (or Plug Flow) Fermentors 1630
`29.2 Mixed Flow Fermentors 1633
`29.3 Optimum Operations of Fermentors 1636
`
`Chapter 30
`Product-Limiting Microbial Fermentation 1645
`30.1 Batch or Plus Flow Fermentors for n = 1 I646
`30.2 Mixed Flow Fermentors for n = 1 1647
`
`Appendix 1655
`
`Name Index 1662
`
`Subject Index 1665
`
`Page 9 of 55
`
`

`
`Chapter 19
`
`The Packed Bed Catalytic
`Reactor
`
`Reactant gas can be made to contact solid catalyst in many ways, and each has
`its specific advantages and disadvantages. Figure 19.1 illustrates a number of
`these contacting patterns. These may be divided into two broad types, the fixed-
`
`bed reactors of Fig. 1 9 . 1 ~ ~ b, and c and the fluidized-bed reactors of Figs. 19.ld,
`e, and f. The moving-bed reactor of Fig. 19.lg is an intermediate case which
`embodies some of the advantages and some of the disadvantages of fixed-bed
`and fluidized-bed reactors. Let us compare the merits of these reactor types.
`1. In passing through fixed beds, gases approximate plug flow. It is quite
`different with bubbling fluidized beds where the flow is complex and not
`well known, but certainly far from plug flow, and with considerable by-
`passing. This behavior is unsatisfactory from the standpoint of effective
`contacting and requires much more catalyst for high gas conversion, and
`greatly depresses the amount of intermediate which can be formed in series
`reactions. Hence, if efficient contacting in a reactor is of primary importance,
`then the fixed bed is favored.
`2. Effective temperature control of large fixed beds can be difficult because
`such systems are characterized by a low heat conductivity. Thus in highly
`exothermic reactions hot spots or moving hot fronts are likely to develop
`which may ruin the catalyst. In contrast with this, the rapid mixing of solids
`in fluidized beds allows easily and reliably controlled, practically isothermal,
`operations. So if operations are to be restricted within a narrow temperature
`range, either because of the explosive nature of the reaction or because of
`product distribution considerations, then the fluidized bed is favored.
`3. Fixed beds cannot use very small sizes of catalyst because of plugging and
`high-pressure drop, whereas fluidized beds are well able to use small-size
`particles. Thus for very fast reactions in which pore and film diffusion may
`influence the rate, the fluidized bed with its vigorous gas-solid contacting
`and small particles will allow a much more effective use of the catalyst.
`4. If the catalyst has to be treated (regenerated) frequently because it deacti-
`vates rapidly, then the liquid-like fluidized state allows it to be pumped easily
`from unit to unit. This feature of fluidized contacting offers overwhelming
`advantages over fixed bed operations for such solids.
`
`427
`
`Page 10 of 55
`
`

`
`428 Chapter 19 The Packed Bed Catalytic Reactor
`
`in
`
`Coolant-
`in
`
`t Gas in
`
`(a)
`
`t
`
`Reactant
`gas in
`
`(b)
`
`Packed bed, first stage,
`small amount of catalyst
`
`Gas in
`
`( c )
`
`Reactant
`gas in
`
`( d )
`
`t
`
`Regenerator (shown
`as a f l u ~ d ~ z e d bed)
`
`Regenerated
`catalyst returned to
`the f l u ~ d ~ z e d bed
`
`Regenerator
`gas
`
`(e)
`Figure 19.1 Various types of catalytic reactors.
`
`Page 11 of 55
`
`

`
`Chapter 19 The Packed Bed Catalytic Reactor 429
`
`Catalyst
`i.
`
`in
`
`Gas out
`
`Fluidized
`
`bed
`
`~i ng bed -
`M o\
`of
`solids
`
`Sidestream to
`regenerator
`
`Bucket elevator or
`hydraulic lift to raise
`catalyst to top of reactor
`
`Catalyst to
`regenerator
`
`~ e a c t a n t fl '
`(f)
`Figure 19.1 (Continued.)
`
`gas in
`
`@
`Reactant f u
`gas in -
`
`With these points in mind, let us proceed to Fig. 19.1. Figure 1 9 . 1 ~ is a typical
`packed bed reactor embodying all its advantages and disadvantages. Figure 19.lb
`shows how the problem of hot spots can be substantially reduced by increasing
`the cooling surface. Figure 1 9 . 1 ~ shows how intercooling can still further control
`the temperature. Note that in the first stage where reaction is fastest, conversion
`is kept low by having less catalyst present than in the other stages. Units such
`as these can all be incorporated in a single shell or can be kept separate with
`heat exchanges between stages.
`Figure 19.ld shows a fluidized reactor for a stable catalyst which need not be
`regenerated. The heat exchanger tubes are immersed in the bed to remove or
`add heat and to control the temperature. Figure 19.le shows operations with a
`deactivating catalyst which must be continually removed and regenerated. Figure
`19.lf shows a three-stage countercurrent unit which is designed to overcome the
`shortcomings of fluidized beds with regard to poor contacting. Figure 19.lg shows
`a moving-bed reactor. Such units share with fixed beds the advantages of plug
`flow and disadvantages of large particle size, but they also share with fluidized
`beds the advantages of low catalyst-handling costs.
`Many factors must be weighed to obtain optimum design, and it may be that
`the best design is one that uses two different reactor types in series. For example,
`for high conversion of a very exothermic reaction we may well look into the use
`of a fluidized bed followed by a fixed bed.
`The main difficulties of design of catalytic reactors reduce to the following
`two questions: (1) How do we account for the nonisothermal behavior of packed
`beds? and (2) How do we account for the nonideal flow of gas in fluidized beds.
`Consider a packed bed with heat exchange (Figs. 1 9 . 1 ~ and 19.lb). For an
`exothermic reaction Fig. 19.2 shows the types of heat and mass movement that
`will occur when the packed bed is cooled at the walls. The centerline will be
`hotter than the walls, reaction will be faster, and reactants will be more rapidly
`consumed there; hence, radial gradients of all sorts will be set up.
`
`Page 12 of 55
`
`

`
`430 Chapter 19 The Packed Bed Catalytic Reactor
`
`Walls cooled
`to 100"
`
`I
`
`Reactant
`flows inward
`
`Product
`flows outward
`
`Depletion of reactant
`Heat flows
`at centerline
`outward
`Figure 19.2 The temperature field in a packed bed reactor for an exother-
`mic reaction creates radial movement of heat and matter.
`
`The detailed analysis of this situation should include the simultaneous radial
`dispersion of heat and matter, and maybe axial dispersion too. In setting up
`the mathematical model, what simplifications are reasonable, would the results
`properly model the real situation, would the solution indicate unstable behavior
`and hot spots? These questions have been considered by scores of researchers,
`numerous precise solutions have been claimed; however, from the point of view
`of prediction and design the situation today still is not as we would wish. The
`treatment of this problem is quite difficult, and we will not consider it here. A
`good review of the state-of-the-art is given by Froment (1970), and Froment and
`Bischoff (1990).
`The staged adiabatic packed bed reactor of Fig. 1 9 . 1 ~ presents a different
`situation. Since there is no heat transfer in the zone of reaction the temperature
`and conversion are related simply, hence the methods of Chapter 9 can be applied
`directly. We will examine numerous variations of staging and heat transfer to
`show that this is a versatile setup which can closely approximate the optimum.
`The fluidized bed and other suspended solid reactor types are considered in
`the next chapter.
`
`Staged Adiabatic Packed Bed Reactors
`With proper interchange of heat and proper gas flow, staged adiabatic packed
`beds become a versatile system, which is able to approximate practically any
`desired temperature progression. Calculation and design of such a system is
`simple, and we can expect that real operations will closely follow these predic-
`tions.
`We illustrate the design procedure with the single reaction A + R with any
`kinetics. This procedure can be extended to other reaction types without diffi-
`culty. We first consider different ways of operating these reactors, and then
`compare these and point out when one or other is favored.
`
`Staged Packed Beds (Plug Flow) with Intercooling.' The reasoning in Chapter
`9 shows that we would like the reacting conditions to follow the optimal tempera-
`
`' This section follows directly from pp. 215-235 of Chapter 9. Hence it is suggested that the reader
`familiarize himself with that section before proceeding here.
`
`Page 13 of 55
`
`

`
`Chapter 19 The Packed Bed Catalytic Reactor 431
`
`I Exothermic reversible I
`
`I Exothermic irreversible I
`
`I Endothermic /
`
`I
`
`Optimum 4 T,,,
`
`Optimum
`
`Figure 19.3 Sketch showing how staged packed beds can closely approach the optimal tempera-
`ture progression.
`
`ture progression. With many stages available this can be closely approximated,
`as shown in Fig. 19.3.
`For any preset number of stages the optimization of operations reduces to
`minimizing the total amount of catalyst needed to achieve a given conversion.
`Let us illustrate the procedure for two-stage operations with reversible exothermic
`reactions. The method of attack is shown in Fig. 19.4. In this figure we wish to
`minimize the total area under the 11-6 versus X , curve in going from X , = 0
`to X , = some fked or required conversion. In searching for this optimum we
`have three variables which we can set at will: the incoming temperature (point
`T,), the amount of catalyst used in the first stage (locates point b along the
`adiabatic), and the amount of intercooling (locates point c along the bc line).
`Fortunately, we are able to reduce this 3-dimensional search (5-dimensional for
`
`Area measures
`
`Figure 19.4 Optimum two-stage packed bed reactor.
`
`Page 14 of 55
`
`

`
`432 Chapter 19 The Packed Bed Catalytic Reactor
`
`three stages, etc.) to a one-dimensional search where Ta alone is guessed. The
`procedure is as follows:
`1. Guess Ta.
`2. Move along the adiabatic line until the following condition is satisfied:
`
`This gives point b in Fig. 19.4, thus the amount of catalyst needed in the
`first stage as well as the outlet temperature from that stage. Especially in
`preliminary design it may not be convenient to use the criterion of Eq. 1. A
`simple alternative is a trial-and-error search. Usually two or three carefully
`chosen trials keeping away from low rate conditions will yield a good
`design, close to the optimum.
`
`3. Cool to point c which has the same rate of reaction as point b; thus
`
`(-ra)leaving a reactor = ( -ra)entering the next reactor
`
`4. Move along the adiabatic from point c until the criterion of Eq. 1 is
`satisfied, giving point d.
`5a. If point d is at the desired final conversion then we have guessed T, cor-
`rectly.
`5b. If point d is not at the desired final conversion try a different incoming
`temperature T,. Usually three trials will very closely approach the op-
`timum.
`
`For three or more stages the procedure is a direct extension of that presented
`here, and it still remains a one-dimensional search. This procedure was first
`developed by Konoki (1956a) and later, independently, by Horn (1961a).
`Overall cost considerations will determine the number of stages to be used,
`so in practice we examine 1, then 2, etc., stages until a minimum cost is obtained.
`Let us next consider the two other cases of Fig. 19.3. For irreversible exothermic
`reactions the criterion for optimal operations has also been presented by Konoki
`(1956b). For endothermic reactions the optimal criterion has yet to be developed.
`In all these cases a trial-and-error search keeping far from the regions of low
`rates is recommended.
`
`Staged Mixed Flow Reactors. For very high recycle the staged recycle reactors
`approach mixed flow. As shown in Fig. 19.5, in this case the reactors should
`operate on the line of optimum temperature progression, the best distribution
`of catalyst among the stages being found by the maximization of rectangles (see
`Figs. 6.9-6.11). In effect we need to choose the distribution of catalyst so as to
`maximize area KLMN which then minimizes the shaded area in Fig. 19.5.
`
`Staged Packed Beds with Recycle. Here we have a flexible system which can
`approach mixed flow and as such is able to avoid regions of low rates. Figure
`
`Page 15 of 55
`
`

`
`Chapter 19 The Packed Bed Catalytic Reactor 433
`
`Figure 19.5 Optimum two-stage mixed flow reactor set up (infinite recycle
`for staged packed beds).
`
`19.6 illustrates two-stage operations with a recycle ratio R = 1, and a feed
`temperature Tf. Extension to three or more stages follows directly.
`Konoki (1961) presents the criterion for optimal operations; however, in pre-
`liminary design a few good guesses will suffice to closely approach optimal opera-
`tions.
`In recycle operations the heat exchangers can be located in a number of places
`without affecting what goes on in the reactor. Figure 19.6 illustrates one of these;
`other alternatives are shown in Fig. 19.7. The best location will depend on
`
`Figure 19.6 Optimum two-stage packed bed reactor with recycle. The
`conversions shown represent a recycle ratio R = 1 in both stages.
`
`Page 16 of 55
`
`

`
`434 Chapter 19 The Packed Bed Catalytic Reactor
`
`\I
`Tf
`Figure 19.7 Different location for the heat exchangers while keeping
`the same reactor conditions as in Fig. 19.6.
`
`* T
`
`convenience for startup, and on which location gives a higher heat transfer
`coefficient (note that the exchanger arrangement of Fig. 19.7a has a higher
`through-flow of fluid than the arrangement of Fig. 19.7b).
`
`Cold Shot Cooling. One way of eliminating the interstage heat exchangers is
`by properly adding cold feed directly into the second and succeeding stages of
`the reactor. The procedure is shown in Fig. 19.8. The criterion for optimal
`operations of such an arrangement is given by Konoki (1960), and, in somewhat
`different form, by Horn (1961b). They found that the extent of interstage cooling
`is given by Eq. 2, and this is shown in Fig. 19.8.
`With cold shot cooling the calculation of reactor volumes by the 11-ri versus
`X , curve beco~lles more complicated because different amounts of feed are
`involved in each stage. We can also cold shot cool with inert fluid. This will
`affect both the 11-ri versus XA and T versus XA curves.
`
`Choice of Contacting System. With so many contacting alternatives let us sug-
`gest when one or other is favored.
`1. For endothermic reactions the rate always decreases with conversion; hence
`we should always use plug flow with no recycle (see Chapter 9). For exother-
`
`Page 17 of 55
`
`

`
`Chapter 19 The Packed Bed Catalytic Reactor 435
`
`Qin
`
`Figure 19.8 Cold shot cooling eliminates interstage heat exchangers.
`
`mic reactions the slope of the adiabatic line determines which contacting
`scheme is best. The rest of these comments concern this case of exother-
`mic reactions.
`2. All else being equal, cold shot cooling has the advantage of lower cost
`because interstage heat exchangers are not needed. However, cold shot
`cooling is only practical when the feed temperature is very much below the
`reaction temperature, and, in addition, when the temperature does not
`change much during reaction. These conditions can be summarized as fol-
`lows:
`Cold shot cooling is practical when
`
`Two situations, one when cold shot cooling is practical, the other when it
`is not, are shown in Fig. 19.9.
`
`Figure 19.9 Situations where cold shot cooling could be helpful and where it should not
`be used.
`
`Page 18 of 55
`
`

`
`436 Chapter 19 The Packed Bed Catalytic Reactor
`
`3. For exothermic reactions if the slope of the adiabatic line is low (large
`temperature rise during reaction) it is advantageous to avoid the low temper-
`ature regime where the rate is very low. Thus use high recycle approaching
`mixed flow. On the other hand, if the slope is high (small temperature rise
`during reaction) the rate decreases with conversion and plug flow is to be
`used. Typically, for pure gaseous reactant the slope of the adiabatic is small;
`for a dilute gas or for a liquid it is large. As an example, consider a reactant
`having C, = 40 Jlmol K and AH, = - 120 000 Jlmol and inerts with C, =
`40 Jlmol . K:
`For a pure reactant gas stream
`
`For a dilute 1% reactant gas stream
`
`For a 1-molar liquid solution
`
`The adiabatic lines for these cases are sketched in Fig. 19.10 and illustrate
`this point.
`
`Use plug flow
`
`Plug vs. mixed flow
`
`0
`
`K
`
`
`
`0
`
`5
`1
`Extremely low
`rates here
`Figure 19.10 Sketch showing why plug flow is used for steep adiabatic
`lines, and mixed flow (packed beds with large recycle) for lines with
`small slope.
`
`Page 19 of 55
`
`

`
`
`
`v_£39853mudnouawwm
`
`oomomvcowommoom
`
`MEsEm<58.2x.as:owuno_..EN1m.mime
`Aoo«_R::ms96n.«
`
`mn_s_vmv.NMh5.._uo._mnoEm_tacomE._.NOH<l
`1<9?nf.<234ooodw-u_m<.mMW<.
`m.:3méoe_~_u.~.~
`
`W292W2;
`
`
`
`
`
`
`
`
`
`m.m5mE.:.ohm_mm1D83HI.m.O
`
`Page 20 ofgg
`
`Page 20 of 55
`
`
`

`
`438 Chapter 19 The Packed Bed Catalytic Reactor
`
`4. For exothermic reactions in staged reactors the above discussion can be
`summarized as follows:
`
`use plug flow.
`For a dilute gas (or a solution) requiring large preheating to bring
`
`Preliminaries for a Set of Problems Dealing with a Single Packed Bed Reactor
`A single catalytic packed bed reactor is to be designed to treat 100 molls of
`reactant A and produce product R. Feed gas enters at 2.49 MPa and 300 K, the
`maximum allowable temperature is 900 K unless otherwise noted, the product
`stream is wanted at 300 K, and the thermodynamics and kinetics of the exothermic
`reaction are given to us in Fig. 19.11. Prepare a sketch showing the details of
`the system you plan to use:
`
`type of reactor: plug, recycle, or mixed ( m recycle)
`amount of catalyst needed
`heat duty ahead of the reactor, at the reactor itself, and after the reactor
`the temperature of all flowing streams
`
`Example 19.1 treats one case, Problems 19.13 to 19.16 treat four other cases.
`In all these problems assume that
`
`we are dealing with ideal gases.
`Cp = 40 Jlmol . K for all materials, and at all temperatures. This means (from
`Example 9.1) that AH, has the same value at all temperatures.
`
`DESIGN OF A SINGLE ADIABATIC PACKED BED SYSTEM
`
`Work out a good design for 80% conversion of a feed consisting of 1 mol A and
`7 mol inert.
`
`First determine the slope of the adiabatic line. For this note that 8 moles enter1
`mole of A. Thus
`
`Cp = (40 Jlmol - K) (8) = 320 JI(mo1 of A + inerts) . K
`
`Thus the slope of the adiabatic is
`
`Page 21 of 55
`
`

`
`Chapter 19 The Packed Bed Catalytic Reactor 439
`
`Drawing various adiabatics in Fig. 19.11 it seems that the one shown on Fig.
`E19.la looks best. So now tabulate XA versus ll(-ra) from Fig. 19.11. This gives
`
`Plotting ll(-ra) versus XA gives Fig. E19.lb. This tells right away that a recycle
`reactor should be used. Thus
`w - x~ - 0.8(6 X 8) = 38.4 kg. slmol
`F~~ -;a
`
`The recycle ratio, from Fig. E19.lb is R = 1.
`
`Figure E19.la,b
`
`The feed is available at 300 K, but enters the reactor at 600 K (from Fig.
`E19.la), so it must be heated. Thus
`
`Page 22 of 55
`
`

`
`440 Chapter 19 The Packed Bed Catalytic Reactor
`
`The product stream leaves the reactor at 800 K and must be cooled to 300 K, thus
`
`We show our recommended design in Fig. E19.1~.
`
`Figure E19.1~
`
`Preliminaries for a Set of Problems Dealing with Two Packed Bed Reactors in
`Series
`
`Two catalyst filled packed bed reactors are to be designed to process 100
`molls of reactant A so as to produce product R. Feed gas enters at 2.49 MPa
`and 300 K, the allowable T,,, = 900 K, unless otherwise noted, T,, = 300 K,
`the product stream is wanted at 300 K, and the thermodynamics and kinetics of
`the exothermic reaction are given to us in Fig. 19.11. Prepare a sketch of your
`recommended design and on it show
`
`the flow arrangement selected: plug, recycle (give R value), or mixed (when-
`ever R > 5). Do not consider injection of cold fluid between stages unless
`the problem states that you are permitted to do so.
`weight of catalyst needed in each stage.
`location and duty of heat exchangers.
`temperature of the flowing streams.
`
`DESIGN OF A TWO ADIABATIC PACKED BED SYSTEM
`
`Work out a good design for 85% conversion of a pure A feed to two packed beds.
`
`I
`
`First determine the slope of the adiabatic line and draw it lightly on Fig. 18.11.
`
`Page 23 of 55
`
`

`
`Chapter 19 The Packed Bed Catalytic Reactor 441
`
`A
`1.0
`
`Optimum
`/
`
`Equilibrium
`
`0.66 ---------------<
`---------
`+
`
`XA
`
`+ 4 ~ +
`
`4++ * -
`
`+
`
`+ 4 c e -
`
`Adiab$iL +
`1
`+ ++-+
`Slope = -
`2000
`
`Figure E19.2a
`
`(a)
`
`This gives a very shallow adiabatic, as sketched in Fig. E19.2~. The rate continu-
`ally increases as you move along this adiabatic, thus use a mixed flow reactor
`operating at the optimum.
`To minimize the amount of catalyst needed Chapter 6 says use the method
`of maximization of rectangles, so tabulate XA versus ll(-r;),,,
`
`And use the method of maximization of rectangles as shown in Fig. E19.2b.
`Then from the performance equation
`
`we have
`
`and
`
`W
`shaded area
`- = (XA) ------ -
`- (in Fig. E19.26
`(-r:)op,
`Fo
`
`W , = FA, (area), = 100 (2.376) = 237.6 kg
`
`W2 = FA, (area), = 100 (3.819) = 381.9 kg
`
`Page 24 of 55
`
`

`
`442 Chapter 19 The Packed Bed Catalytic Reactor
`
`Locus of
`optima
`
`-J-+
`1 .o
`
`XA
`
`(6)
`
`Figure E19.2b
`
`Now to heat exchange:
`For the first reactor. If we want to cool the feed before introducing it into the
`first reactor we'd have to cool it to
`
`which is well below absolute zero. This is impossible. So we have to cool it
`somewhere inside the recycle reactor loop as shown in Fig. E19.2~. But wherever
`you put the exchanger the amount of heating or cooling needed is the same.
`So to go to 66% conversion at 820°C the amount of heat needed per mole of
`A is
`
`(820 - 300)40 + 0.66(-80000) = -32 000 Jlmol
`
`heat in
`
`heat out
`
`But for 100 molls of feed
`
`Q , = (32 000 J/mo1)(100 molls) = -3.2 MW (cooling)
`
`For the second reactor. To go from X , = 0.66 at 820 K to X , = 0.85 at 750
`K requires, per mole
`(750-820) 40 + (0.85 - 0.66) (-80 000) = -18 000 Jlmol
`
`So for 100 molls
`
`I
`
`Q2 = (- 18 000)(100) = - 1.8 MW (cooling)
`
`Page 25 of 55