The Industrial Practice of Chemical Process Engineering

The Industrial Practiceof Chemical Process Engineering Samuel W. Bodman The MJ.T. Press Massachusetts I nstitute of Technology Cambridge, Massachusetts, and London, England Copyrigt © 1968 by The Massachusetts Institute of Technology Printed and bound i the United States of America by The Maple Press Company, York, Pensylvania. All rights resered. No part of this book may be reproduced or utilized in any form or by any meas, electronic or mechanical, including photocopying, recordig, or by any iformation storage ad retrieval system, without permission in writig from the publi s her Library of Congress catalog card number: 68-18232 Preface With study of the engineering sciences now a dominant factor in the curricula of many academic engineering departments, only limited time is available for the creative application of thcoretical fudamentals to practical chemical processing problems. I particular, the study of process design and financial evaluation is often either disregarded or given only cursory attention. As a result, the young engineering graduate frequently encouters dificulties in becoming acclimated to the environent of a commcrcial organization and in ma.ximizing the benefits which can be gcnerated from his technical background. In order to prepare its studcnts more fuly for the challenges of industrial work, the M.I. T. Chemical Engineerng Department has developed two specific programs. First, tht department's School of Chcmical Engineer­ ing Practice exoses graduate students to actual problems i an industrial environment uder the direct and close supervision of a faculty member. This program has been in operation for over fifty years and has proven to be an effective contributor to a student's total academic experience. To com­ plemcnt the Practice School program, a senior-ycar synthesis course in process design has been developed. Professor Thomas K. Sherwood summarizcd his original work in the development of the M.I. T. process desig course in his teli "A Course in Process Design". The course, as conceived by him, is based upon a series of design cases; for each case the student is reuired to devise and analyze process schemes that might lead to the solution of the design problem. The present text seeks to combine some aspects of te Practice School program with elements of Professor Sherwood's case-study approach to in­ strction i engineering design. It is hoped that the result of this combiation will not only be useful as a text for academic process design instrction but will also serve as a reference book for te youg engieer embarkig on a career i idustr. iii iv Preface An introductory chapter briefly describes te interaction and inter­ dependence of market researh, process desig, and financial evaluation functions in commercializing a chemical prduct. Methods of planing and analyzig laboratory experiments, of utiizig market and financia infor­ mation, and of preparig and presenting a chemical process desig are discussed. The introduction is followed by a series of si case studies in engineerig desig, tyical of those encountered by a youg engineer i his initial idustrial assigments. The need for accurate aaysis and correla­ tion of laboratory data is given great emphasis. Secondly, the need for devisig creative and practical solutions to prcessig problems is given some discussion. Finally, each case illustrates methods of combining tech­ nical and finacial inforation to provide a realistic evaluation of a proposed process. Each case is concluded wit a recommended design as well as suggestions for furer work that would be required in subsequent, more detailed, design efforts. A great deal of emphasis has been placed on the use of the digital computer i the aalysis and presentation of desig problems; computer programs are presented for three of the cases discussed. These progras and others lie tem have proven to be particularly stimulatig when used in a "computerized classroom, " wherei the student ca communicate directly wit the machine. In preparing porions of the text, it has been assumed that the reader has at least some kowledge of te FORTRN codig language. The present volume was written while the author sered as Director of the Boud Brook Station of M. I.T.'s School of Chemical Engieerig Practice. This station is located wth the Organic Chemical Division of the American Cyanamid Company, Boud Brok, New Jersey. The data used in the prep­ aration of Chapter 3 were gathered by a student group as a part of a project at the Bund Brook Station. The author is grateful to American Cyanamid for its permission to use these data as well as for the company's hospitality during the 1965-66 and 1966-67 academic years. Many individuals have contributed substatially to the case studes sumaried i this book. First of all, thas are due to Professor Thomas K. Sherwood, who has continued his gidance in the instrction of chemical process desig at M.I.T. It was he wo origially suggested the preparation of the present text, ad Chapters 2 and 4 are based almost entirely on desig cases developed by him for his process design courses. Sincere appreciation is el'ressed to Professor Robert York of Corell University for his gidance i the economic evaluation of chemica projects ad for his instrctive re­ view of portions of the present text. Professors C. J. King and Scott Lynn of the University of Califoria i Berkeley were kind enough to review the entire text of tis book. Their comments were particularly significant i givig additional breadth and meaig to several of te case studies. Dr. Howard Kehde and his colleages at Dow Chemical Compay, Midland, Michigan, very kidly reviewed the cases concered with styrene production; their comments provided an invaluable dimension to those cases by bringng to bear the knowl­ edge ad sophistication of a major producer of styrene monomer. Professor Giles R. Cokelet of Califora Institute of Technology provided a valuable commentary on te sulfur transporation case. Professor R. G. Thorpe of Corell University originally acquainted the author with some of the difficulties Preface v assoiated wth te vacuu fractionation of styrene-ethylbenzene mitures; this inforation was most usefl in th preparation of Chapter 6. The data used as a basis for Chapter 3 were gathered uder te direction of Professor Michael Modell of M.I. T.; his cooperation in making this in­ foration avaiable is greatly appreciated. Several forer teaching assist­ ants and students at M.I. T. contributed substantialy to the development of computer progras for Chapters 5, 6, and 7. I this respect, specia thaks are due to Robert L. Blumberg, Bruce Crocker, Avelino R. Rodrigez, and Robert L. Sandel. Machie computations for this book were perfored at the M.I. T. Computation Center. The author gratefully ackowledges the financial suppor of a research initiation grat from the Rohm ad Haas Compay which was instrmental in the preparation of tis text. The autor wshes to express his tanks to Messrs. Georges F. Doriot, Henry W. Hoaglad, William H. Congleton, John A. Shane, ad Miss Droty E. Rowe of American Research and Development Cororation. Their gidace durig te past four years in various aspects of finacial aalysis ad business j udgment contributed substantially to the present work. The greatest source of encouragement ad assistace in the preparation of tis mauscript has come from the author's wife Betsy. Without her many very thoughtfu ad skillful contributions, this work could not have been com­ pleted. S. W. Bodma Cambridge, Massachusetts March, 1968 Contents Preface iii 1. Introduction 1 2. Reactor Desig, Optiization, and Control i the Production of Monochlorobcnzene 18 3. Process Improvement for Liquid-Liquid Extraction of Fcnway AcW 51 4. Catalytic Reactor Desig for Benzene Hydrogenation 75 5. Evaluation of New Methods for Sufur Trasporation 100 6. Vacuu Fractionator Desig for the Purification of Styrene Monomer 125 7. Process Desig and Evaluation for te Production of Styrene Monomer 151 Appendi 199 Index 229 1. Introduction The industrial practice of chemical engineering design requires the application of many talents and skills. By the definition of his pro­ fession, the process design engineer in the chemical industry imple­ ments the work of the chemist and development engineer in providing mechanical and structural specialists with a realistic description of the required equipment. Sherwood (44) has recently described the following functions which must be performed to span the gap between bench-scale chemistry and the operating plant: 1. Recognition of an economic opportunity 2. Conception of a plan or design 3. Preliminary analysis of the design 4. Completion of a final design 5. Implementation of construction and operation These functions are useful indicators of the stages through which a design must pass and of the various scales of thinking which are re­ quired of the design engineer. The foregoing list is quite helpful in placing each individual job in the perspective of the over-all effort which is required. I the analysis of a design project, it is to be re ­ membered that an economic evaluation for the entire proj ect must be completed after each step in the design; in the absence of a favorable evaluation after each step, the time and effort required by the next step cannot be justified. To complete the transition from laboratory conception to operating plant successfully, the design engineer in industry must call upon a wide background not only of technical fundamentals but also of finan­ cial and social understanding. For example, knowledge of geographi­ cal factors may be important in selecting a proper plant site, while a grasp of corporate finance and economics may be a prerequisite to a proper evaluation and presentation of the economic benefits to be gained from a speciic chemical project. Clearly an understanding of the operation of modern computation eqUipment is now an essential part of the training of a design specialist. In addition to having a 1 2 Chapter 1 broad technical background, the successful design engineer must con­ tinually develop talents in analyzing his own technical performace and in evaluating the efforts and contributions of other people. The present text describes the type of technical and economic background necessary for the successful completion of a chemical process design. These fundamentals will be summarized briefly in the present chapter. This introduction is followed by a series of de­ sign case studies that serve to illustrate important aspects of indus­ trial chemical engineering design. The cases selected for presentation illustrate not only different types of engineering projects but also vriations in the requ;.red de­ gree of completion for a design. Cases requiring chemical reactor design, separation equipment design, and pipeline sizing and optimi­ zation are included. One of the most dificult aspects of these design cases, or for that matter of any realistic technical problem, is that of defining the real nature of the problem, i. e. , deciding what is re­ quired. One of the more common failings of a technical program re­ sults from a tendency to answer a question that has not been asked or to complete work that has not actually been requested. This dificulty is particularly prevalent in design work, where many different types and degrees of effort may be required. The case studies here pre­ sented illustrate industrial problems and are summarized in the form of memoranda. In some instances the data were obtained from the literature, while other cases represent actual industrial problems where the data originated in a company laboratory and where the in­ dicated result constitutes the actual solution presented to manage­ ment. In each of three cases cited, the design analysis is summarized in the form of a computer program which is reproduced in the text. Re­ sults generated by each program are employed to evaluate the econo­ mics of a design as a function of the important process variables. However, results for all possible combinations of these variables have not been obtained, and the computer programs are presented in order that they may be further exloited to refine the economic evaluation of the projects to which they apply. These programs have been found particularly useful when applied in a computer classroom-a situation in which a class can "communicate" directly with digital computation equipment. The use of a computer to evaluate in detail a chemical process represents one extreme of the situations that might be encountered by a typical industrial design group. At the other extreme is the situation where no detailed design or economic evaluation is required and only a modest number of calculations is needed to establish the most liely coniguration for the ultimate design. In the cases of the latter type which are presented in this volume a consideration of limit­ ing cases and the use of shortcut methods in preparing the calculations prove to be most helpful. By presenting a series of cases having not only a vried technical content but also a varied degree of required sophistication, this text attempts to illustrate some of the concepts associated with the suc- II/troductiol/ 3 cessful completion of an industrial process desig. By definition, process design is involved with the application of technical principles to the available experimental information in order to produce a work­ able manufacturing process. As such, design cases have traditionally been examined individually with relatively little emphasis on a consis­ tent set of principles necessary for the proper understanding and successful execution of general c1.asses of problems. To some degree, such a set of prinCiples can be established; as a gide in maing the ensuing case studies meaningful beyond their own particular boun­ daries, the following set of principles may be considered: 1. Determination of design requirements 2. Comprehension of market conditions 3. Evaluation of experimental data 4. Establi�hment of critical design parameters-simulation and optimization 5. Evaluation of process economics 6. Presentation of design results The present introduction does not purport to be a thorough review of each subject listed. Only a cursory discussion of each point is of­ fered, together with a review of a few pertinent references. Neither should the reference citations mentioned be considered as a complete literature review; they are merely those that have proved useful in working with young chemical engineers encountering their first in­ dustrial design problems. DETERMNATION OF DESIGN REQUIREMENTS The sophistication of a process design must be tailored to meet the requirements of the individual situation. As mentioned before, the use of data-processing equipment allows the designer more freedom than ever before to investigate various combinations of system parameters. Indeed, one of the major functions of the present text is to demon­ strate the utility of machine computations in studying various aspects of a process design. Nevertheless, the advent of modern computers makes it quite easy for the user to pass through the point of diminish­ ing returns. A great deal of objective thining is required to avoid solving problems merely for the intellectual satisfaction gained from the solution. As in all aspects of engineering for industry, if the value of the programming and computer time used is not exceeded by the value of the design improvement gained, then both engineering and computer time have been misspent. To determine the possible need for a detailed design calculation, it is most useful to analyze limiting aspects of a desig situation by means of Simple hand calculations. Computations for limiting cases 4 Cliapter 1 are often quite straightforward, since simplifying assumptions can usually be made. For exmple, if a laboratory reactor has been oper­ ated adiabatically between two temperature levels, the results of such an experiment can be scaled directly to a commercial-scale adiabatic unit operating between the same two temperature levels. Compari­ son of this result with that obtained by assuming an isothermal opera­ tion at the lower temperature level sets the extremes between which nonisothermal designs must fall. By noting the variations in the im­ portant design parameters as the design is shifted from one limit to aother, one can assess the need for maing more detailed and often more time-consuming calculations at intermediate conditions. Such a calculation procedure is illustrated by Chapter 4, in which a reactor for the hydrogenation of benzene is designed. The need to make a comparison of limiting conditions would seem obvious; nevertheless, this simple technique is often overlooked, resulting in an unnecessary exenditure of engineering and/or computer time. One of the most valuable talents that can be developed by the de­ sign engineer is an ability to perform the Simple calculations neces­ sary to establish the limiting cases of a design, where the most dif­ ficult technique is often that of making the appropriate assumptions in order to simplify the calculations. This ability usually must be developed through may years of exerience, and the novce often finds it quite dificult to achieve. It is to be appreciated, however, that the ability to perform a simple but meaningful analysis of a prob­ lem does not develop automatically with experience. A conscious ef ­ fort must be made to compare the results evidenced in the final opera­ ting plant with the assumptions made in the early stages of the deSign. Only by such a feedback and by comparison can the quality of sub­ sequent estimates be upgraded. The need for limiting-case calculations cannot be overemphasized; such calculations should be applied as early as possible in the con­ Sideration of any chemical project. More and more effort is being made today and will be made in the future to provide the research manager with a quantitative estimate of the probability for the tech­ nical and economic success of a particular research project. Clearly a major ingredient in such an estimate must be a preliminary fore­ cast of the capital and operating costs for the project. This type of estimate is necessarily based on little or no data, and the computa­ tions must result from some sort of limiting-case analysis. Thus the ability to perform such an analysis is valuable not only i establishing preliminary limits on the process variables but also i determining whether the probability for financial success justifies the expenses involved in the bench-scale and pilot-scale experimental work. In this light, the deSign engineer should enter into consideration of a chemical project at the bench stage. I his initial calculations do not show a high probability for financial success, the very existence of the bench work should probably be reconsidered unless external Circumstances, such as a raw-material position, are more important than economic factors. Similarly, as work proceeds through bench and pilot-scale development, discussions between development groups and a process design engineer may be very important, particularly in Introductioll 5 coordinating technical progress with the efforts of market research groups. COMPREHENSION OF MKT CONITIONS Cooperation between the desig engineer and the market research and development groups is of critical importance. One of the most essential pieces of information required for the completion of pro­ cess design calculations is an estimate of both present and future market demands for the product under consideration. In many cases the ability of a design engineer to analyze technical information and to provide an accurate scale-up to commercial equipment will have only a modest influence on the economics of the final operating plant. O the other had, an accurate sales forecast for a product is usually quite critical to a realistic prediction of the ultimate financial per­ formace of the operating unit. For example, a 20 per-cent error in a kinetic constant or heat­ transfer coefficient may be damped out at that stage in the calcula­ tions in which the over-all process economics are considered. How­ ever, a similar percentage error in a market forecast may well be amplified as it is transmitted through the calculations leading to an economic evaluation of the project. Sources of market information run all the way from government reports to the annual reviews published by the various trade journals. Most important, however, are the personal dscussions of salesmen with customers, and it is this type of interaction which forms the best basis for sales forecasts. Typically, the sales forecasts will be pre­ pared in the very early stages of process development, but they are subject to rapid and substantial deviations as the market research work proceeds. It is essential that the process design group be con­ tinually kept inormed on the status of the maket estimates. Only in this way can a final desig be produced which will be justified by present and future market estimates. Finally, it should be remember­ ed that plant construction is usually finished two years or more after the desig plans are completed. If economic conditions are favorable, the need often arises to expand the plant facilities even before con­ struction is complete. This factor further emphasizes the need for accurate market forecasting procedures. Because of the difficulty i gathering and processing meaningful raw data, the chemical engineering literature has historically given only scant attention to the subject of marketing. More recently, the availability of the electronic computer has made feasible the collec­ tion and assessment of market information sufficiently broad and ac­ curate to allow the development of useful marketing theories as ap­ plied to the chemical industry. A corresponding increase in research and publication activity in this area has been evidenced. Of particular note is a series of papers presented at a 1965 Arerican Institute of Chemical Engineers symposium in which the interaction of research, marketing, and design efforts was discussed (9,1 1,13,21,12). These papers were prepared by men familiar with all aspects of product 6 Chapter 1 commercialization in the chemical industry, and the series provides an excellent exposition of the advantages to be gained and the prob­ lems encountered by efforts to coordinate marketing and research programs. The papers are particularly valuable in illustrating the various methods by which an engineer can assure that an adequate market picture will be obtained and that a correspondingly accurate financial evaluation will be achieved. Another compendium of papers dealing with chemical marketing has been published by the American Chemical Society (l). This book, which contains twenty contributions, serves as an excellent background source for the specialized areas of marketing. For example, the roles of product advertising, applica­ tions research, and product delivery methods are given detailed treat­ ment. There is a very definite need for a complete review of recent chemical marketing literature. Such a review, preferably carried out by someone with a strong background of industrial marketing expe­ rience, would not ony clarify the situation for the student but would also hopefully lead to better market analysis techniques for the in­ dustry as a whole. EVALUATON OF EXPEIMENAL DATA I the manufacture of a particular chemical, the required process steps generally follow the sequence shown below: 1. Preparation of reactants 2. Carrying out of reaction(s) 3. Heating or cooling of reaction products 4. Separation of reactants from products and puriication of products Almost without exception, the design engineer is required to base his analysis of each step upon laboratory data generated by other in­ vestigators or obtained from the literature. For those having only a modest exosure to the chemical literature, Mellon (32) has provided a very useful guide to the proper methods to be used in searching the literature. In using literature data for the engineering analysis of a process operation, it is critical to develop an appreciation for the fuality of the information to be used. For example, data reported may years ago may have been obtained before sufficient theory had been developed to allow a proper analysis and presentation of the ex­ perimental information. In the absence of such a theory, early ex­ perimenters sometimes failed to measure a variable necessary for proper analysis. Obviously, the exerimental equipment available in the early engineering laboratories was not as sophisticated as that currently available; it is therefore important to develop an apprecia­ tion for the strengths and failings of various types of laboratory ap­ paratus. Difficulties with the proper interpretation of published data are frequently compounded by industrial censorship of process informa­ tion. The suppression of technical information is obviously necessary IntroducLion 7 to protect the commercial value of a process. However, from a tech­ nical viewpoint, censorship often requires the engineer to make a "reasonable" assumption in order to be able to proceed with his analysis. A good example of the censorship of industrial information is pro­ vided by MacMullin (30), who discusses the distribution of reaction products for the chlorination of benzene. He presents data that estab­ lish the distribution of the various chlorinated compounds as a func­ tion of the total amount of chlorine reacted. This information is of course not sufficient for the design and evaluation of a manufacturing process, since the kinetic parameters for the reactions are not dis­ closed. In order to complete a design, reasonable values of the chemi­ cal kinetic constants must be assumed; such a procedure was follow­ ed in preparing Chapter 2, in which various processes for the chlorin­ ation of benzene are discussed. When it is necessary to proceed in this manner, it is most desirable to obtain literature information from as many different sources as possible. By comparing and combining all available information, one is often more likely to establish a realis­ tic basis for a design. I fact, the technique of gathering and compar­ ing information from a number of sources is frequently useful in many aspects of a process design. Before investing the time and effort required even by a prelimin­ ary design calculation, it is prudent to assess the validity and con­ sistency of the laboratory findings upon which the design is to be based. This assessment is most easily accomplished by comparing the data directly with appropriate literature information. For example, the general accuracy of a set of vapor-liquid equilibrium data for a mixture of two components may be checked most directly by com­ paring them with those for the same two com)ounds but for other con­ ditions of temperature and pressure. I such data are not available for the desired compounds, the relative volatility computed from the laboratory result might be compared with that calculated for an ideal mixture by using Raoult's law. It may also be inform'tive to compare the relative volatility with that for other compounds having Similar chemical structures. Finally, the thermodynamic consistency of the data should be assessed by invoking one form of the Gibbs-Duhem equation. Similarly, by plotting the observed solubility of a solid in a liquid versus the reciprocal of absolute temperature on semilog paper, one should obtain a straight line from whose slope the heat of solution can be computed. A comparison of this heat of solution with heats of solution or heats of fusion for chemically similar compounds yields a check on the validity of the experimental data. An analogous tech­ nique applied to chemical kinetic data or chemical equilibrium data would yield an activation energy or a chemical enthalpy change that could then be compared wit literature values. Table 1-1 has been prepared to summarize the methods for assess­ ing the validity of those types of data most often encountered in com­ pleting design projects for the chemical process industries. It is to be emphasized that this table is not a summary of design methods but merely a set of criteria by which to judge the quality of technical 8 Chapter 1 data to be used in carrying out a design. The references shown are not m�ant to be comprehensive; moreover it is clear that the table vastly oversimplifies the types of operations carried out in the chemical industry as well as the theoretical and technical background necessary for the completion of even a simple design problem. Nevertheless. the information summarized has proved very useful in applying the results of theoretical considerations to engineering prob­ lems of practical significance. Naturally, in many instances it is both desirable and necessary to supplement the elementary methods described in Table 1-1 by using some of the more advanced the ore - tical developments. The utility of the information summarized in Table 1-1 naturally varies significantly from one segment of the chemical process in­ dustrv to another. For example, the organic chemical industry makes great use of extraction and leaching processes, and the simple tech­ nique of plotting solubility data on semilog paper to obtain a heat of solution can prove to be of great and frequent utility. Once confidence in the exerimental data is developed, the design calculations to op­ timize the number of extraction or leaching stages can proceed quite smoothly. Wen theoretical correlation of process inormation is impossible, the use of a factorially designed exerimental technique may be of great value. The use of statistically designed experiments is parti­ cularly valuable in reducing the required amount of exerimental and analytical effort to solve a problem for which there is little or no theoretical basis. The following references, arranged by Koehler, provde an excellent introduction to the application of statistical con­ cepts to a variety of problems encountered in the chemical industry. Besides a discussion of statistical designs in the analysis of labora­ tory and pilot plant data (7,23), the series also effectively presents the advantages to be gained by the application of statistical techniques to in-plant exerimentation (22), to the use of computers in data re­ duction (41), to the selection of appropriate production-line control charts ( 17), and to the general improvement of quality-control methods (26). When a sound theoretical basis for a process design is limited, the use of statistical methods can provide a highly useful foundation for the necessary design and evaluation calculations. One last point frequently overlooked is the need for preparing an adequate error analysiS. If the probable error as computed for the experimental technique used is approximately equal to the random deviation of the data about a correlating line, then it can be assumed with a high degree of confidence that all sources of error have been properly established and accounted for. Such an analYSis lends a great deal of confidence to the use of the data in a design, particularly when the exenditure of a large capital investment is required. ESTABLISHMENT OF THE CRTICAL DESGN PARMETER­ SIMULATON AN OPTIMZATION In his text, Sherwood (41) states quite appropriately that the de­ signer must be willing to make assumptions. Once sufficient informa- T a b l e 1 - 1 . U s e f u l M e t h o s o f E v l u a t i n g a d C o r r e l a t i n g C h e m i c a l E n g i n e e r i n g E x e r i m e n t a l D t a P r o c e s s O p e r a t i o n R e q u i r e d D e s i g n P a r a m e t e r F l u i d t r a n s p o r t a t i o n F r i c t i o n f a c t o r F l u i d h e a t i n g o r c o o l i n g H e a t - t r a n s f e r c o e f f i c i e n t C h e m i c a l r e a c t i o n C h e m i c a l - k i n e t i c c o n s t a n t C h e m i c a l - e q u i l i b r i u m c o n s t a n t C a t a l y t i c c h e m i c a l E f f e c t i v e n e s s f a c t o r r e a c t i o n M a s s - t r a n s f e r c o e f f i c i e n t f r o m f l u i d t o c a t a l y s t p e l l e t s u r f a c e S l u r r y r e a c t i o n M a s s - t r a n s f e r c o e f f i c i e n t ( r o m l i q u i d t o c a t a l y s t p e l l e t s u r f a c e S p a r g e d r e a c t i o n M a s s - t r a n s f e r c o e f f i c i e n t a t t h e b u l k l i q u i d s u r f a c e M a s s - t r a n s f e r c o e f f i c i e n t f r o m a g a s b u b b l e t o b u l k l i q u i d A b s o r p t i o n S o l u b i l i t y o f g a s i n a l i q u i d B o i l i n g o r V a p o r p r e s s u r e c o n d e n s a t i o n D i s t i l l a t i o n V a p o r - l i q u i d e q u i l i b r i u m ( r e l a t i v e v o l a t i l i t y ) T r a y e f f i c i e n c y C r y s t a l l i z a t i o n S o l u b i l i t y a n d s u p e r s o l u b i l i t y E x t r a c t i o n D i s t r i b u t i o n ( p a r t i t i o n ) c o e f f i C i e n t B a s e s f o r E v a l u a t i o n o r C o r r e l a t i o n o f D a t a 1 / 2 = F ( N H e ) j / = F ( N H e ) A r r h e n i u s c o r r e l a t i o n v a n ' t H o f f c o r r e l a t i o n T h i e l e m o d u l u s j o = F ( N l e ) k L = F ( D . N . D p . l . A p ) k L = F ( D , N k L a = F ( D , N , V s ) H e n r y ' s l a w o r R o u l t ' s l a w C l a u s i u s - C l a p e y r o n e q u a t i o n G i b b s - D u h e m e q u a t i o n M u r p h r e e e f f i c i e n c y r e l a t i o n s h i p C l a p e y r o n - t y p e c o r r e l a t i o n N e r n s t ' s l a w L i t e r a t u r e R e f e r e n c e s ( 3 - 1 ) ( 3 1 ) ( 6 ) ( . 5 2 ) ( 1 0 ) ( 1 0 ) ( 1 9 ) ( 2 7 ) ( 5 ) ( 2 1 ) ( 5 2 ) ( 3 7 ) ( 3 7 ) ( U ) ( 1 · 1 ) � - � c � < - - . g � 10 Chapter 1 tion is available to analyze a process completely and accurately, typically the financial incentive for completing the design will be sub­ stantially diminished. However, i order to mae appropriate pre­ liminary assumptions, the designer must develop the capability of isolating the variables that are critical to the determination of the over-all economic performance of the process. Frequently a pre­ liminary design calculation is required to establish the identity of the most important design variables. Such a case is illustrated in Chapter 4, in which the hydrogenation of benzene is considered. For the more common process operations, the critical variable frequently is well known; e.g. , in the design of a distillation column, the reflux ratio usually serves as a m0st sensitive index of the pro­ cess economics. I the first analysis of a unique or a highly complex design, the determination of the most critical variables often is left to the judgment of the engineer. Typically, when a multivariable de­ sign is approached, a base case is selected by arbitrarily establish­ ing "reasonable" values for many of the process variables that are believed to be least critical in determining the process economics. The variables thought to be most critical are allowed to vary, and a preliminary economic evaluation and optimization of the design are completed. Then variations from the base case are considered by allowing variations in the parameters that had previously been fixed. As show in Chapter 7, in which the economics of styrene production is considered, the use of a digital computer can greatly facilitate the evaluation of the base case and the variations from this case that are significant. As illustrated in the same chapter, it is essential to re­ turn to the original set of assumptions in order to establish the effect of each assumption on the over-all economics of the process. It is also important to realize that in dealing with a multi variable design problem, several local minima may exist; a certain amount of judg­ ment must be exercised in determining whether a local or an over­ all minimum has been achieved. The calculation procedure described suffers from the lack of an organized approach to the problem, and a great many decisions must be reserved for the judgf�nt of the engineer. In certain types of de­ sign problems, a more quantitative approach to the logic required for a design calculation may be achieved by applying the technique of linear programming. This method has application in design cases that result in linear algebraic relationships. Happel's very useful text on chemical process economics (18) includes a brief description and an example of linear programming techniques. It is important to note that many chemical economics problems are highly nonlinear and that in such instances linear programming techniques are not directly applicable. However, by linearizing the appropriate analytical expres­ sions, linear programming techniques may be helpful in establishing the general nature and relative importance of the cost functions under study. A significant portion of modern chemical engineering research has focused on the development of advanced methods for process optimization as applied to individual sections of a process as well as to the over-all design result. Particular emphasis has been placed Introduction 11 on the optimization of chemical reactor systems; much of this work is well summarized by Aris (5, 6), Denbigh (15), and Kramers and Westerterp (28). One of the more important of modern optimization techniques is that of dynamic programming, i which the last of a series of staged operations is first optimized; the last two stages are then optimized as a single unit. One stage is added on in a stepwise fashion, working backward until the optimum conditions for the entire process are established. This method has obvious application in the aalysis of continuous stirred-tank reactor systems (5 ). The cal­ culus of variations has been shown to have particular value in the op­ timization of tubular reactors; the method is especially useful in the case of adiabatic reactions (15). In addition to the aforementioned, the method of "steepest ascent" has also proved useful i the optimization of reactor systems (20). This technique allows one to approach an optimum as closely as desired by successive quantum changes in the process variables until the design parameter in question (e.g. , yield) is optimized. Concurrent with the development of optimization methods has been the establishment of new techniques to simplify and minimize design computational effort. Rosen (38) has presented a machine computa­ tion method for performing process material balances, and Rvicz and Norman (36) have reported a more flexible program incorpora­ ting both heat and material balances. Sargent and Westerberg (39) have developed a general-purpose approach that is very helpful in organizing the programming work required for the computer simula­ tion of a chemical process. More recently, Lee, Christensen, and Rudd (29) have made a very significant contribution in the study of multi vriable design problems where assumptions are required to proceed with the design. These investigators have established a method that allows the preassign­ ment of values to a selected set of design variables in such a way as to minimize the computational effort. This work is one of the first signs of a trend in the chemical engineering profession to make more effective use of computers in the analysis of process design problems. EVALUATON OF PROCESS ECONOMCS When the chemist undertakes a fundamental research project in the laboratory, he frequently has only a limited notion of the ulti­ mate applications and possible financial success of his product. This sort of freedom has proved invaluable in developing a creative atmos­ phere for the development of new products. However, once a chemical project emerges into applied research or development, each subsequent step in the project should be evluated finanCially before the work for that stage is undertaken. In this manner, projects having a low proba­ bility for an acceptable finacial return can be " weeded out" at an early stage, and more technical effort can be applied to developing those products which are most likely to realize the greatest economic return. One of the critical fWCtions of the design engineer tor any other person responsible for evaluating the process economics) is to keep 12 Chapter 1 abreast of the latest technical developments in a new product and to interpret these developments in the light of their ultimate effect on the profit potential . For example, if the production yield of a new product is increased by carrying out the reaction step i a particular solvent, the cost for separating the product from the solvent must be estimated. It may be that the cost of recovering the product over­ shadows the savings generated by the use of the solvent. I such is the case, the course of the early process research and development for the product will have to be altered accordingly. The actual form of a financial evaluation varies widely within the industry; and because of the obvious commercial Significance of evalu­ ation techniques, little meaningful information is available i the literature. However, some general references are available which have proved very useful in orienting chemists and engineers to the problems associated with a financial evaluation. I first approaching an economic evaluation, one of the major dif­ ficulties encountered by the technically trained person is that of understanding financial terminology. The work of Beattie and Vivian (10) greatly mitigates this problem; it provides a detailed compilation of the definitions for most terms common to financial analysis as applied in the chemical industry. In addition, the importance of using consistent terminology is well illustrated. In its simplest form, the financial evluation of a chemical project provides an estimate of the capital required for the construction of the manufacturing facility and a forecast of the costs required to operate the proposed process. By deducting the total operating costs and income taxes from the anticipated sales revenues, the net opera­ ting income for the project can be established. In addition to the an­ nual dollar income volume, profitability may also be exressed as the fraction of the capital ivestment needed to establish the antici­ pated return. The philosophy giding the analysis of corporate ven­ tures in the chemical industry is well summarized in an A.I.Ch. E. publication (2). Each company has its own peculiar raw-material position to pro­ tect, its own process know-how, its own accounting system, and its ow plans for future exansion. As a result, the identical proposed project may meet different fates, depending upon the company that considers it. For example, consider an American company that is domestically selling products that are facing competition from identi­ cal products manufactured in Europe. The European concern might be accounting for the cost of its goods on an incremental basis, Le., a basis in which depreciation and overhead costs are allocated entirely to the domestic portion of production while the production deSignated for export is burdened only with direct expenses. Clearly in such a situation the European firm might find itself in a very advantageous competitive situation even after the transportation costs are taken into account. Thus a difference in cost-accounting techniques can cause a vast disparity in the commercial market place. Similar ex­ amples are available where difference in raw-material position and process know-how lead to substantial commercial implications. Introduction 13 Some of the more standard methods which may be used in account­ ing for chemical project costs are elucidated by several texts (ls, 35, 43,50). It should be noted that each company has its own required minimum return on investment for a project; for obvious reasons these figures are necessarily held in confidence. However, in the ab­ sence of external circumstances (e.g. , raw-material position), an estimate of 8 to 10 per cent is probably a realistic lower limit on the return on invested capital required for project apPJoval. Much higher return percentages are obviously desirable and are frequently ob­ tained. The mathematics involved in evaluating the economics of a chemi­ cal project becomes quite involved when the current values of the various cash flows into and out of the project are considered. In a significant article, Souders (47) has produced an exemplary discus­ sion of this issue together with an interesting comparison of the ef­ fects of various profitability criteria on the ultimate investment de­ cision. For the reader interested in a more complete background i the fundamentals of engineering economics, this paper also includes a short but useful bibliography of definitive works in this field. One of the great difficulties in providing an accurate financial eval­ uation lies in the fact that both the market price and the demand for individual products as well as the general development of the national economy are dynamic functions. The financial performance of a plant should be examined as a function of both short-term, high-frequency variations and of long-term, gradual growth or decline in the dollar volume of product sales. Schenk (,12) presents a brief discussion and a useful example of such a study. He pOints out that the economics of a chemical project are most strongly affected by variations in the selling price. Following after the selling price, and in order of im­ portance, variations in the sales volume, sales exenses, and capital investment have been found the most critical factors afecting the re­ turn on investment. The need for adequate price and sales forecasting is well illustrated by his discussion. An examination of the inluence of variations in selling price, sometimes called a risk analysis, is frequently a required component in the final presentation of the finan­ cial evaluation of a new chemical project. Twaddle and Malloy (19) provide a useful discussion of the effects of long-term demand, selling price, and capacity variations on the economic return to be antiCipated for a given chemical project. Various methods of graphically illustrating the economic performance of a plant are well illustrated in this reference. I particular, it is effectively demonstrated that accounting for time variations in demand and price has a dramatic effect on the optimum plant size and may radically influence the decision whether the plant should be built at all. A major deterrent to the proper financial evaluation of preliminary designs arises from the paucity of reliable capital-cost information for process equipment. Chilton's excellent compilation (12) provides a useful background to the problems of cost estimating and to the proper methods of cost data correlation. The correlations contained in his text are quite adequate for preparing preliminary cost esti- 14 Chapter 1 mates; however, it is recommended that other sources (-1,50) be con­ sulted in order to verify cost estimates. In particular, the price estimates for the larger pieces of equipment should be checked by using two or three ditferent references. When the design reaches its final stages, it is normal practice to contact suppliers in order to verify the estimates for all Significant pieces of equipment. PRESENTATION OF DESIGN RESULTS Regardless of the quality of the technical work that has contributed to the design and evaluation of a chemical project, the total effort may be valueless unless it is properly presented to those who must make the ultimate investment decision. I particular, the need for lucid technical writing has long been recognized as an important issue, and several excellent texts are available for this purpose (25,33,48). Generally, a lack of quality in a technical report can be traced to a lack of effort in preparing and polishing the report rather than to a lack of knowledge of grammar, style, or proper report organization. Often the results of a technical effort must be presented orally. For the speaker who must summarize a mass of technical informa­ tion in a short time, the American Institute of Chemical Engineers has prepared an excellent booklet (3) which summarizes the important points to remember in preparing the presentation. It is particularly valuable in pOinting out the most effective m2thods of using slides and other visual aids. The texts of Atwood (8), Flesch (16), and Weaver (51) serve as valuable references to the more general aspects of pre­ paring and executing oral presentations. SUMMRY The foregoing sections provide a brief introduction to some of the more important issues that confront the industrial deSign engineer in the practice of his profession. Some of the pOints discussed sug­ gest various types of formal training necessary to the successful execution of design work. Other issues suggest specific approaches to design problems which have been found useful. In particular, the appropriate application of electronic computation equipment to aid in the design calculations requires more than ever before the use of engineering talents to comprehend and analyze the computed results. The following chapters provide a series of design case studies where­ in the important aspects of industrial design practice are brought to bear on realistic problem situations having commercial Significance. NOTATION a Interfacial surface area D Diffusion coefficient D p Catalyst pellet diameter f Friction factor jD Mass-transfer j-factor jJ Heat-transfer j-factor IlL Liquid-phase mass-transfer coefficient N Rotational speed of impeller NRe Reynolds number Vs Superficial gas velocity J Dynamic viscosity Ap Density difference between solid and liquid REFERENCES Introductioll 15 1. American Chemical Society, Chemical Marketing in the Competi­ tive Sixties, Advances in Chemistry Series, No. 24, Washington, D.C. (959). 2. American Institute of Chemical Engineers, Venture Analysis, A.I.Ch.E. Publication Department, New York960). 3. American Institute of Chemical Engineers, Guide for Writers ad Speakers, A.I.Ch.E. Publication Department, New York (196� 4. Aries, R. S., and R. D. Newton, Chemical Engineering Cost Esti­ mation,McGraw-Hill Book Co., Inc., New York (1955). 5. Aris, R., The Otimal Design of Chemical Reactors, Academic Press, New York (1961). 6. Aris, R., Introduction to the Analysis of Chemi�al Reactors, Prentice-Hall, Inc., Englewood Cliffs, N.J. (1965). 7. Atkinson, A. C., Cher. Eng. 73, No. 10, 149 (1966). 8. Atwood, R. L., When You Tal, Atwood Corporation, Melrose, Mass. (1959). 9. Bare,B.M.,Chem. Eng.P�£61,No.10,26 (1965). 10. Beattie, R. D., and J. E. Vivian, Cher. Eng. 60, No.1 (1953), re­ printed in reference 12, p. 24. 11. Bradley, J. W., Cher. Eng. Progr. 61, No. 10, 15 (1965). 12. Chilton, C. H., Cost Engineering in the Process Industries, McGraw-Hill Book Company, Inc., New York (196). 13. Craver, J. K., Cher. Eng. Progr. 61, No. 10, 24 (1965). 14. Denbigh, K. G., The Principles of Chemical Equilibrium, Cam­ bridge University Press, Cambridge (1961). 16 Chapter 1 15. Denbigh, K. G., Chemical Reactor Theory, Cambridge University Press, Cambridge U5). 16. Flesch, R. The Art of Plain Talk, Harper Brothers, Inc., New York (1946). 1 7. Freund, R. A., Cher. Eng. 73, No.3, 70 (1966). 18. Happel, J., Chemical Process Economics, John Wiley & Sons, Inc., New York (1958) . 19. Harriott, P.,A.I .Ch.E.J.8, 93 ( 1962). 20. Horn, F.,and U. Troltenier, Cher. Ing.-Tech. 32, 382 (1960). 21. Hougen, O. A., K.A. Watson, and R. A. Ragatz, Chemical Process Principles, Part I, John Wiley & Sons, Inc., New York (1954). 22. Hunter, J. S., Cher. Eng. 73, No. 7, 111 (1966). 23. Hunter, W. G., and A. C. Atkinson, Cher. Eng. 73, No.12 , 159 (1966). 24. Kennel, W. E., Cher. Eng. Progr.61, No.10, 20 (1965). 25. Kobe, K.A. , Cemicl Engneering Reports: How to Search the Literature and Prepare a Report, Inter science Pblishers, Inc., New York (1957). 26. Koehler, T. L., Cher. Eng. 73, No.1, 81 (1966). 2 7. Kozinski, A. A., and C. J. King, A.I.Ch.E.J. 12,109 (1966). 28. Kramers, H., and K. R. Westerterp, Elements of Chemical Reactor Design and Oeration, Academic Press, New York (1963). 29. Lee, W., J. H. Christensen, and D. F. Rudd, A.I.Ch.E.J.12, 1104 (1966). 30. MacMullin, R. B., Cher. Eng. Progr.44, No. 3,183 (1948). 31. McAdams, W. H., Heat Transmission, McGraw-Hill Book Company, Inc., New York (1954). 32. Mellon, M. G. Searching the Chemical Literature, American Chemical Society Publications, Washington, D.C. (1964). 33. Nelson, J. R., Writing the Technical Report, McGraw-Hill Book Company, Inc., New York (194 7). 34, Perry, J. H., Chemical Engineers' Handbook, McGraw-Hill Book Company, Inc., New York (1950). 35. Peters, M. S., Plant Design and Economics for Chemical Engin­ eers, McGraw-Hill Book Co., Ic., New York (1958). 36. Ravicz, A. E., and R. L. Norman, Cher. Eng. Progr. 60, No. 5, 71 (1964). 37. Robinson, C. S., and E. R.Gilliland, Elements of Fractional Dis­ tillation, McGraw-Hill Book Company, Inc., New York m 38. Rosen, E. M., Cher. Eng. Progr. 58, No. 10, 69 (1962). Introduction 17 39. Sargent, R. W. H., and A. W. Westerberg, Trans. Inst. Chem. Eng. 42, T190 ( 1964). 40. Satterfield, C. N., and T. K. Sherwood, The Role of Diffusion in Catalysis, Addison-Wesley Publishing Co .. Inc .• Reading. Mass. (1963). 41. Savitzky, A., Chem. Eng. 73, No.5, 99 (1966). 42. Schenk, G., Chem. Eng. Progr. 61, No. 10, 16 ( 1965). 43. Schweyer, H. E., Process Engineering Economics, McGraw-Hill Book Company, Inc., New York (1955). 44. Sherwood, T. K., A Course in Process Design, The M.I.T. Press, Cambridge, Mass. (1963). 45. Sideman, S., O. Hortassu, and J. W. Fulton, Ind. Eng. Chem. 58,32 ( 1966). 46. Smith, J. M., Chemical Engineering Kinetics, McGraw-Hill Book Company, Inc., New York (1956). 47. Souders, M., Chem. Eng. Progr. 62, No.3, 79 (1966). 48. Souther, J. W., Technical Report Writing, John Wiley & Sons, Inc., New York (1957). 49. Twaddle, J. J., and J. B. Malloy, Chem. Eng. Progr. 62, No. 7, 90 (1966). 50. Vilbrandt, F. C., and C. E. Dryden, Chemical Engineering Plant Design, McGraw-Hill Book Company, Inc., New York (1959). 51. Weaver, R. M., The Ethics of Rhetoric, Henry Regnery Co., Chicago, Ill. (1953). 52. Weber, H. C., and H. P. Meissner, Thermodynamics for Chemical Engineers, John Wiley & Sons, Inc., New York (1957). 2. Reactor Design, Optimization, and Control in the Production of Monochlorobenzene Th¡s cusc dccIs ¡t¡Ih Ihc døs¡gn oJ u j+occss /o+ Ihc chIo+¡¡icI¡oii o) bø¡izø¡iø. In¡!¡uI c¡ii¡·lms¡s ¡s ]Iucød on I|ic ¡·+o¡·c+ co++øInI¡on o] Iubo+uIo+¡ dnIc IhuI dcsc+¡bc Ihc lincI¡cs o] I|ic Ih+øø s+qucnI¡uI chIo+¡nc!¡oii +øncIions. 3c:ø+uI ¡·+occss schciii+s, iii c!ud¡ng boIh buIch cnd coiiI¡iiitous o¡·c+uI¡ons, u×c cxcm¡iicd um| cnch ¡s o¡·I¡iii¡zød ccono- m¡cnII¡. Thc mosI u!I+ucI¡c ¡·+ocøss ¡s scIøcIcd b| ii¡cuiis oJ ø:umin- iiig IIc +øsuII s o] I|ic /¡nunc¡uI c:I¡tuI¡oii. I¡iicII¸, Ihø Ihc+mcI s!cb¡I- ¡I) oJ /lic o¡·I¡¡iiitIìi ¡:¡occss is ¡n:øsI¡gcIcd ciid /hc Jøsigii ¡s iìiod¡/¡ød u]¡·+o¡·+¡nIcI¸ i¡i o+dø+ Io c¡isu+c s!nbIc o¡c+c!¡on. TIic c|n¡·Ic+ ¡·+o:idcs u¡i o]]o+I¡tn¡!¡ ]o: I|ic ¡n:ø¡iI¡on uiid cucI¡s¡s o/ t+¡oits ]+occss sc|cmcs. 3cic+cI cIIeItcI¡:ø dcs¡gns u+ø u:u¡IcbIø tt|iic|i m¡gJI o//c+ cc+Iu¡n ud:iiIugcs o:ø+ !Iosc cuscs coiisidc+cd in I|c ¡·+cscii! IøxI. Thcsc cIIc+iuIícs qui!c ¡·+o¡·c×I¡ could /o+iii !|c bcs¡s /o+ Jit×I|ic+ døsigns c¡id ccoiioi¡i!c c:/itnI¡oiis. T|ic ø]]øcIi:+ncss oJ IIi¡s c|m¡·!c+ |i¡¡igcs oii IIø dc!c+:inu!¡oii o] Ihc c]]+o¡·+iuIc døסgn ¡·n+ciiicIø+ sucu /huI I|c ccoiion¡cs oJ t+¡oits I¡¡·øs o] ++ucIo+ dcs¡giis cnii bc coiii¡·c+cd ¡¡i u mcuii¡ug/uI un). Aja Pharmaceutical Company Secaucus, New Jersey To: J. A. Smith, Engineer !roH: W, Allen, Manager of Technical Operations Ajax has often thought of maing its own monochlorobenzene in­ stead of purchasing this intermediate from the outside. Since the "Chlorpan-A" production is now shut down, there are three reactors that might be made available for chlorinating benzene, You are re- 18 Reactor Desigl l , OjJtilllizatiOll, alld COl/trol 1Ü quested to evaluate the feasibility of this proj ect under the assump­ tion that both benzene and chlorine would have to be purchased. The three reactors are equipped with coils for heating and coolig and with gas distributors to assure that the chlorine is well dispersed so as to keep the liquid saturated with chlorine. The reactors are necessarily operated at atmospheric pressure. Each has a reflux condenser, a chlorine gas recycle system, an agitator, and 550 sq ft of cooling surface in the form of a double helical coil of O. 5-in. o. d. tubing. With the agitator in operation, over-all heat transfer coef ­ ficients of 1 50 Btu/(hr) (sq ft) (OF) have been obtained for benzene at 60°C with cooling water in the coil . During operation, with chlorine being fed, each reactor will hold 400 gallons of liquid. Adequate dis­ tillation capacity is available to separate the unconverted benzene and the chlorinated products: technical -grade monochlorobenzene and a miture of di- and trichlorobenzenes. It is anticipated that this latter miture cannot be sold and that it will have to be di scarded. The kinetics of the liquid-phase chlorination of benzene have been investigated by the Research Department; their results confirm the literature reports that the chlorination of benzene, monochlorobenzene, and dichlorobenzene is in all cases first -order and irreversible, based on rate equations in which mole fractions (instead of moles per unit volume) are employed. The laboratory tests were carried out in a 2- liter flask equipped with a reflux condenser that returned everything but excess chlorine. The liquid was well agitat ed by the bubbling chlorine, which was fed through a fritted glass bubbler. Small amounts of ferric chloride were used as a catalyst. The results of the laboratory tests are summarized as follows: Mole Fraction Time Mole Fraction Benzene NGnDCh1C1CDCD2EDE ~ (hrs) 40"C ãã"C T0"C 40"C 55°C 70°C 0 I I 1 0 0 0 0. 3 0.ö3 0. 35 0. 5 0.4ö 0. 49 1. 0 0.91 0.öö 0.2I 0.09 0. 32 0. 60 2. 0 0.ß3 0.44 0.0ã 0.Iß 0. 53 0. 51 4. 0 0. 70 6.0 0. 56 0. 09 0. 43 0. 75 12. 0 0. 3 1 0. 63 0. 59 Evidently, the formation of trichlorobenzene is so small that it may be neglected. The possibility of using the three existing reactors for batch chlorinations has already been examined, and it seems clear that some form of continuous operation would be preferable. Your study ZÔ Chapter Z should be restricted to continuous operation for a maximum of 7000 hrs/year. The maximum operating temperature is 70°C; higher tem­ peratures lead to excessive vaporization and strain the capacity of the condensers. We need 8 million lbs of monochlorobenzene per year; we have no way of selling additional production at more than an un­ acceptable distress price. The attached cost figures are approximate but should be adequate for the purpose of your analysis. Specifically, you are asked to evalu­ ate the possible financial return to be achieved by producing mono­ chlorobenzene. U addition, you are to specify the optimum manner in which the process should be run. Data ß0Assumptions Chemical costs and net sales and use values: Chlorine Monochlorobenzene (b. p. 1 32°C) Dichloro-trichlorobenzene mix (b.p. 1 74-208°C) Benzene (b.p. 80°C) $0. 045/lb $0. 1 05/lb negligible $0. 034/lb Recovery costs (total, including both fixed and operating costs) : Monochlorobenzene Benzene (s.g. O. 88) Dichloro- trichlorobenzene mix Oerating costs, each reactor: Reactor heating and/or cooling Labor and supervision Chlorine recycle $0. 01 0/lb $0. 01 5/lb zero (waste) $2 . 40/hr $2. 90/hr $4. 00/hr Total fixed charges on each reactor, including piping, controls, and auxiliaries: $14, OOO/year. As an approximation, assume that the molal volume of each of the products is the same as that of benzene and that there is no volume change on mixing these liquids. Physical Data Product Benzene (liquid) Monochlorobenzene (liquid) Dichlorobenzene (liquid) Chlorine (gas) HCI (gas) ÀL | ¡ Btu/{lb mole) (°I) Al Formation at 2 5°C 33. 4 3 5. 6 3 8. 4 8. 1 6. 96 1 1 , 700 gcal/mole 2, 500 -4, 900 (average) -22, 063 Reactor Design, Optimization, and Control Z1 Sggested Nomenclatre: / Heat-transfer area available in each reactor, sq ft a Cost for benzene converted to MCB, dollars/year ó Cost for benzene converted to DCB, dollars/year L Cost for chlorine converted to MCB, dollars/year d Cost for chlorine converted to DCB, dollars/year e Cost for separating and recycling benzene, dollars / year J Direct operating costs for the three reactors, dollars/year ) Flow rate to a reactor, lb mol es/year Ê Cost of recovery of MCB, dollars/year Ì/ Fixed charges on the three reactors, dollars/year k 1 Reaction- rate constant for monochlorination reaction, hour-1 k 2 Reaction- rate constant for dichlorination reaction, hour - 1 I g _ k_.Y_/ )¿ with Ì�_ evaluated at temperature Tn' dimensionless I 2n /�2 N R / ) ,with /'2 evaluated at temperature T_,dimensionl ess I_ R/ ) ¿ dimensionless N R Moles in each reactor, lb mol es 0, Sensible heat absorbed by the cold entering benzene feed stream, Btu/hr { c Rate of heat transfer to the cooling water in a reactor, Btu/hr Ü » Total rate of heat generated by the chemical reactions in reactor n, Btu / hr Û Recycle rate of benzene, lb moles/hr l Time, hr T Temperature, oK T e Temperature of cooling water, °C T n Temperature of reactor n, °C T R Temperature in a reactor, °C Ü Over-all heat transfer coefficient, Btu/(hr) ( sq ft) (OF) 7 Mole fraction of benzene in reactor n, dimensionless Å Ö Mole fraction of monochlorobenzene i n reactor n, dimensionless x__ Mole fraction of dichlorobenzene i n reactor n, dimensionless tI Enthalpy of chlorination reaction, cal/ g mole of chlorine tT T R -T e ,oC J Oerating time, hr/year ZZ Chapter Z PRELIMNAY DESIGN ANALYSIS The reactors are to be operated continuously; it is therefore clear that the flow rate to be employed will be an important operating variable. The reactors may be operated with series flow through the three, or piped for two, or all three, in parallel. Recycled benzene can be returned to the first reactor or distributed to all three. Each reactor may be operated at a different temperature. The reactor system will be desiged by first examining several diferent process schemes where each reactor is operated at the same speCified temperature. Once the proper process flow pattern has been established, variation in the operating temperatures of each reactor will be considered. Finally, the stability of the optimum reactor system will be examined. At first thought, one might conclude that the maximum permissible temperature should be employed in order to obtain high reaction rates. The best choice of temperatures will be considered after the laboratory data have been analyzed and the best reactor flow pattern has been selected. ANALYSIS OF THE LABORTORY KNTC DATA Before studying the different possible reactor flow plans, the chemical kinetics for the chlorination reactions must be derived by referring to pertinent literature references [b) and by examining the available laboratory data. The chemical reactions to be considered are C6H6 ' Cl2 _ C6H5CI ± HCI C6H5CI + Cl2 * C6H4Cl2 * HCl C6H4Cl2 ¬ Cl2 _ C6H3Cl3 + HCI The original memorandum indicates that the rate equations for these reactions may be written as GX_ ¬ l:_x_ ( 2. 1 ) J/ ''µ = k ¡× ¬ ¬ k ;^µ ( 2. 2) d/ Formation of trichlorobenzene is to be neglected, and the mole frac­ tion of dichlorobenzene, Å__ will be assumed equal to Í ¯ A ¯ Ä Õ • The laboratory-batch data are to be compared with integrated forms of the two rate equations, in order that the rate constants may be evaluated for use in optimizing the operation of the three reactors. Reactor Design, Opti mization, and Control 23 The desired relations between ¹ ¬ , ×@ _ and t are easily obtained: CX ¬� = k _¹ ¬ , ¹ ¬ " < « I Í (x_ = 1 . 0 at t = 0) dl Solving this last, with the conditions × @ = 0 at t = 0: k ¹ " 1 (< « ¶ Í ¯ c°¿¹) `1 ¯ ^ 4 ( 2 . 3) (2. 4) Values of ^ _ are most easily obtaied from the laboratory data by plotting x ¬ vs. l on a semilogarithmic graph and drawing best straight lines through the pOints for each of the three temperatures. Even with k_ known, ther e is apparently no way to plot the data on 7 so as to evaluate k 4 by drawing a best straight line through the exerimental points. Accordingly, Eq. 2.4 is solved by trial to obtain values of R¿ corresponding to each data poit, and these are simply W 0 M C.I ¬ C.|Æ00l 30 80 ¯8Uþ8f0lUf8¸¨Û � ¯ L J O W Figure 2-1 . First-order kinetic con­ stants for benzene chlorination. (Symbol s L and. represent values computed from exerimental data. ) Z4 Chu]Ic: 2 averaged a t each temperature. The rate constants so obtained are as follows: 40°C 5 5°C 70°C Ì�_ hr- 1 0. 0965 0. 41 2 1. 55 k 2 , hr- 1 0. 0045 0. 055 0. 4 5 Figure 2 -1 shows these results graphically and may be used t o inter palate between data pOints. Figre 2 -2 is a check on the calculations; the data are compared with curves calculated by the use of Eqs. 2 . 3 and 2. 4 and the tabulated rate constat s. Ü lÕ 1Im6¡ hOurS |Z l9 lb Figure 2 -2. Concentration profiles for chlorina­ tion of benzene. (Solid lines are computed from Eqs. 2. 3 and 2. 4. ) Legend Symbol Mole Fraction Temperature, OC L 7 A 40 ¬ 7 A 5 5 A 7 A 70 ¯ 7 8 40 ^ 7 8 5 5 • 7 8 70 SELECTION OF A REACTOR FLOW ÏÏ Five different flow plas will be studied, employing the three reactors given in the problem statement to determine the optimum Reactor Desigll, Optimizati oll , und Control 3ô production costs. These process cases are: I. Three reactors i series, recycle to the first 2. Three reactors i series, recycle to the second 3 . Three reactors i series, recycle to the third 4. Three reactors i n parallel 5. Batch operation The batch process will be studied so as to compare its optimum pro­ duction costs with the production costs for the four continuous opera­ tions. The five process plans listed here are not the only possible alternatives. However, by first investigating these several cases it should be possible to determine those type s of process schemes which merit further consideration. The combination of sparged chlorine and mechanical agitation may be assumed to maintai the liquid well stirred in each reactor and to j ustiy the assumption that the composition of the effluent stream i s the same as that of the reactor contents. Each reactor i s a CSTR ( continuous stirred tan reactor) , and the operation can be analyzed by the methods outlined by Denbigh ¦) and described in several chemical engineering texts. Since the volume change on reaction i s very small, the total moles I_ present i n each reactor may be as­ sumed to be the same and constant. To permit the selection of an optimum flow pattern each reactor will be assumed to operate at 55°C. The effects of variation i tem­ perature will be inve stigated at a later stage. Case I: Tree Reactors i Series with Recycle to te First The first scheme to be analyzed i s represented by the flowsheet of Fig. 2-3 . In order to achieve the most useful result, the process show i n thi s figure will be analyzed i n a generalized fashion. The general results may then be applied easily to any specific situation. W6zeæ recjcM !t ¹z T ¹ ¹at ¹az ¹æ mtm Å § î ¹ sz ^0 ¹ fæ0 Î Cbwíæ Cb|otìm Cbkrìæ Figure 2 - 3 . Block flowsheet of continuous stirred­ reactor system for the chlorination of benzene. 0ìcbkto- 0M trìcb|oo~ w6ze6e ZÓ Chapter Z Let F represent the rate (lb moles/hour) of feed of benzene to the first reactor, including recycle. The analysis then proceeds as fol ­ lows: First Reactor Í 7 " @ J " 1 ¹ :1 where Í ] " ~ Ì! g W 8 / !,with k g based on the temperature 1 " in the nth (in this case, the first) reactor. ι µ1 ~ �t \² 1 ²@_ ¬^; ¹ µ ¡| 11 ~ �� (1 K ¡ 1 | (1 7 ";±' Second Reactor ³ 1 X æ q :2 - 1 +K1 2 ( 1 +Ku) ( 1 +K 1 2 ) Î\¹ µ; ~ × µ¡| ~ ^ 8 \º¡ × ,; ¬ º; × µ; | I ¡ ; ^µ; = (1 Í¿¸| (1 Í ¡ ; | (1 ¹ ;; | Third Reactor ^ ¹,¡ I ¡¡ 1 ( 2. 5) Reacto1' Dcsi¿¡, O]lim¡zcl.`oii,and ConLml 27 Ü all three reactors are operated at the same temperature (T 1 7 T 2 ¬ T3) , these exressions for x A 3 and x B 3 reduce to and 1 À ~ ¯¯ - [1 +K 1 ) 3 Costs (2. 6) (2. 7) ( 2. 8) The annual costs for the required production rate of 8 million lbs/year of monochlorobenzene are expressed D terms of % and 7• 400 K 62. 3 ^ 0. 88 _ 37 6 lb Ì � - . mo es 7. 48 K 78 J 8 Y 1 06 71 , 000 -- - hr/year 1 1 2. 6 FXB3 F XB3 where J must be less than or equal to 7000. ( a) Benzene for monochlorobenzene: 8 Y 1 06 Y 78 1 1 2 . 6 K 0. 034 = $1 89, 000/year [b) Benzene for dichlorobenzene: $1 89, 000 X C 3 !year x B 3 38 Cltc[·Icr 3 (c) Chlorine for monochlorobenzene: 8 K 10 6 Y 71 Y 0. 045 7 $227, 400/year 1 1 2 . 6 [J) Chlorine for dichlorobenzene: $227, 400 Y 2 ( � ¨ s ) = $454, 800 � C3 /year ^ ¤ s ^ ¤ s (e) Benzene recycle costs: 8 K 10 6 Y 78 (x »s ) ²+s / - 0. 015 = $83, 100 - year 1 1 2. 6 ^ ¤ s ^ ¤ s () Operating costs, direct: ( 2. 40 + 2 . 90 + 4. 00) Y 3 Y J = $27.90 e/year (�-) Monochlorobenzene recovery: 8 K 10 6 Y 0. 01 = $80, ODD/year (/) Fixed charges: 3 Y 14, 000 = $42, ODD/year By summing items a through h¸ the total annual operating cost for this process is established; this parameter is a function of J¸ 1¡ T ¸ and T_¬ The total costs will evidently pass through a minimum as the feed rate Ï is varied. At low flow rates, with J approaching 7000, the conversion is high and the cost of chlorine and benzene for the un­ wanted dichlorobenzene becomes large. At very high flow rates the conversion is low and the cost of benzene recycle becomes excessive. For the particular case when all the reactors are operated at 55°C, Eqs. 2 . 7 and 2. 8 may be applied. U this instance: (0. 412) ( 37. 6) 1 5. 5 [ 1 = 7· ! ! (2. 9) ( 0. 055) (3 7. 6) 2. 07 Í 4 7 ! ! ( 2. 1 0) Using Eqs. 2. 7 to 2 . 1 0, calculations have been carried out in order to optimize Case I when all the reactors are operated at 55°C. The re­ sults are summarized in Table 2-1 . Table 2-1 indicates that a minimum annual cost is achieved for Case I when the feed rate is about 55 Ib moles / hr and the reactor sys­ tem is operated approximately 2660 hrs/year. It is to be noted that the minimum in the total cost curve is a very broad one. Therefore, T a b l e Z ¬ 1 . R e s u l t s o f t h e D e s i g C a l c u l a t i o n s f o r C a s e Ï D e s i g p a r a m e t e r s ! 1 0 2 0 3 0 4 0 5 0 1 1 1 . 5 5 0 . 7 5 5 0 . 5 1 6 0 . 3 8 7 0 . 3 1 0 ' ; 0 . 2 0 7 0 . 1 0 3 0 . 0 6 9 0 . 0 5 1 8 0 . 0 4 1 4 ^ A 3 0 . 0 6 0 3 0 . 1 7 9 0 . 2 8 8 0 . 3 7 4 0 . 4 4 6 ´ B 3 0 . 5 8 6 0 . 6 5 2 0 . 6 1 4 0 . 5 6 0 0 . 5 1 0 ´ 0 g 0 . 3 5 4 0 . 1 6 9 0 . 0 9 8 0 . 0 6 6 0 . 0 4 4 0 1 2 , 1 0 0 5 , 4 4 0 3 , 8 6 0 3 , 1 7 0 2 , 7 8 0 C o s t s , d o l l a r s / y e a r a + c + g + h 5 3 8 , 4 0 0 5 3 8 , 4 0 0 5 3 8 , 4 0 0 5 3 8 , 4 0 0 ó 4 9 , 0 0 0 3 0 , 2 0 0 2 2 , 3 0 0 1 6 , 3 0 0 d 1 1 8 , 2 0 0 7 2 , 6 0 0 5 3 , 6 0 0 3 9 , 2 0 0 Û 2 2 , 8 0 0 3 9 , 0 0 0 5 5 , 5 0 0 7 2 , 7 0 0 J 1 5 2 , 0 0 0 1 0 8 , 0 0 0 8 8 , 5 0 0 7 7 , 6 0 0 T o t a l 8 8 0 , 4 0 0 7 8 8 , 2 0 0 7 5 8 , 3 0 0 7 4 4 , 2 0 0 6 0 7 0 1 0 0 0 . 2 5 9 0 . 2 2 1 0 . 1 5 5 0 . 0 3 4 5 0 . 0 2 9 6 0 . 0 2 0 7 R 0 . 5 0 2 0 . 5 4 9 0 . 6 4 9 � � ¯ 0 . 4 6 4 0 . 4 2 4 0 . 3 3 8 ~ ¯ " 0 . 0 3 4 0 . 0 2 7 0 . 0 1 3 C � 2 , 5 4 0 2 , 4 0 0 2 , 1 0 0 Þ > ` . ¯ � ~ 5 3 8 , 4 0 0 5 3 8 , 4 0 0 5 3 8 , 4 0 0 � . ~ . 1 3 , 8 0 0 1 2 , 1 0 0 7 , 3 0 0 m ~ ~ 3 3 , 4 0 0 2 9 , 0 0 0 1 7 , 5 0 0 ~ . g 9 0 , 0 0 0 1 0 7 , 3 0 0 1 5 9 , 3 0 0 C 7 1 , 0 0 0 6 7 , 0 0 0 5 8 , 6 0 0 ¤ ¯ 7 4 6 , 6 0 0 7 5 3 , 8 0 0 7 8 1 , 1 0 0 g ~ o ~ � < JÔ Chapter 2 wide variations in the operation of the three reactors for this pro­ cess can be tolerated since the total conversion cost is only slightly afected. This characteristic should mae it convenient to schedule other products for manufacture in the same three reactors. It i s now appropriate to proceed with the investigation of Case s II and Il, so that the effect of other types of recycle can be ascertained. Case Ü. Three Reactors i Series, Recycle to the Second This process case is the same as that shown in Fig. 2-3, except that the recycle stream is now mixed with the product from the first reactor. The combined stream is fed at a rate of [!+ R) lb moles/hr to the second reactor. The analysis of this case proceeds as follows : First Reactor The material balances follow directly from Case I, whereby: Second Reactor A material balance on benzene around the junction of the recycle and the line between reactors 1 and 2 gives F X @ J d R - ( F ¬ R )x Al Solving for A @ __ the composition of the stream entering the second reactor, one obtains where Í g = R/F. A benzene balance around the second reactor re­ sults in which may be rewritten as ReactoY Design, O/J/iJllizatiol1, and Control J1 S1D1l01 material balances for monochlorobenzene yield K_ K Í ¡ X ; - ¤ - [J ! ; ! ¡ } ; ±JK_} [J K ; I ¡ } ; K_ � [J Í_} [JK ; } (1 K ; Í ¡ } Third Reactor Material balances on benzene and monochlorobenzene around the third reactor re sult in 1 q K3 [J K ¡ } K ¡ . < 3 - (1 q K1) (1 + Kl q K3) 2 ( 1 !_ì ¡ } ; K1(1 q K3) ��� B 3 (1 ¬K 2 q K3 ) 2 (1 q Kl ¬K3) (1 q K 1) Kl (1 ¬K3) q (1 ¬ K1) (1 q K 2 ) (1 ¬ K 2 * Ka ) 2 !_ [J! ¡ } ¬ � � [J Í_}±J ! ¿ Í ¡ } ; ±J Î_ ! ¡ } ! Í ¡ ±J Î ¡ } �� � ±JÍ_Í ¡ } ; ±J Í ; Í ¡ } [2,JJ} [ 2,J2) One more relation may be obtained by noting that for the recycle R ¯ [! R¡ ¹ ¬ ¡ Therefore, and [2,Jß} 3Z Chu[/cr3 Equation 2 . 1 3 can be solved by trial and error so that one may obtain 1¡ as a function of 1 ¡ . The only remaining equation needed is that which relates the flow rate and conversion to J. 71, 000 J = [! R}\ µ¡ (2. 1 4) The economic evaluation of Case II is now carried out directly, since Eq. 2. 1 3 allows the proper value of R to be chosen for each feed rate so that the required annual production can be achieved. The method of computation and the results of the se calculations are sum­ marized in Table 2 -2. Case Ï! Three Reactors i Serie s_ Recycle to the Third This case also may be visualized by using Fig. 2 -3. The same proce ss scheme is used as H that figure, but here the recycle stream i s combined with the product from the second reactor ad the com­ bined stream is fed to the third reactor. The analysis for this case is exactly analogous to that for Case II. Its result is and 1¸ À ¬ -"~~~ ~~~~~~ µ¡ ¬ (1 1 ¡ } ; (1 "¡ + Í ¡ } (1 Í ; Í ¡ } Í ¡ 1 ¡ +-- ---- (1 ¯' ¿ '¡ } (1 '; ' ¡ } ' +-~ ~~ "~"" (1 ± ' ¡ } ; (1 1 ; } (1 '; 1 ¡ } '1 ( 2. 1 5) ( 2. 16) where 1 ¡ ¬ R,!. A material balance on the recycle stream yields 1 Í ~ ¡ ¬ (1 +͸} ¡ ¬ (1 + ' ¡ } ; ¬ 1 (2. 1 7) In a manner similar to that of Case II, a value of Í_ is selected, and the calculations for the economic evaluation of Case III follow direct­ ly from Eqs. 2. 1 4 to 2 . 17. These computations are summarized in Table 2-3 . T a b l e Z . Z . R e s u l t s o f D e s i g C a l c u l a t i o n s f o r C a s e Ü D e s i g P a r a m e t e r s K _ 0 . 2 0 . 3 0 . 4 0 . 6 K 1 , E q . 2 . 1 3 1 . 0 3 0 . 8 7 0 . 7 7 0 . 6 6 K 2 ~ 0 . 1 3 4 K 1 0 . 1 3 9 0 . 1 1 6 0 . 1 0 3 0 . 0 8 8 2 ) ¯ 1 5 . 5 / K 1 1 5 . 0 1 7 . 8 2 0 . 1 2 3 . 5 R ~ ! K _ 3 . 0 5 . 3 4 8 . 0 1 4 . 1 x _ _ , E q . 2 . 1 1 0 . 1 6 7 0 . 2 3 1 0 . 2 8 7 0 . 3 7 7 x µ ¡ ¸ E q . 2 . 1 2 0 . 6 4 0 0 . 6 2 2 0 . 6 0 7 0 . 5 5 1 x c _ 0 . 1 9 3 0 . 1 4 7 0 . 1 0 6 0 . 0 7 2 Ú ¸ E q . 2 . 1 4 6 , 1 6 0 4 , 9 5 0 4 , 1 6 0 3 , 4 3 0 C o s t s , d o l l a r s / y e a r Ü + L 7 _ 7 h 5 3 8 , 4 0 0 5 3 8 , 4 0 0 5 3 8 , 4 0 0 5 3 8 , 4 0 0 ó 5 7 , 0 0 0 4 5 , 0 0 0 3 3 , 0 0 0 2 5 , 0 0 0 d 1 3 7 , 0 0 0 1 0 7 , 6 0 0 7 9 , 4 0 0 5 9 , 4 0 0 L 2 1 , 6 0 0 3 0 , 9 0 0 3 9 , 3 0 0 5 6 , 8 0 0 J 1 7 2 , 0 0 0 1 3 8 , 0 0 0 1 1 6 , 0 0 0 9 5 , 5 0 0 T o t a l 9 2 6 , 0 0 0 8 5 9 , 9 0 0 8 0 6 , 1 0 0 7 7 5 , 1 0 0 0 . 8 1 . 2 2 . 0 0 . 6 0 0 . 5 3 0 . 4 7 0 . 0 8 0 2 0 . 0 7 1 0 . 0 6 3 2 5 . 8 2 9 . 3 3 3 . 0 R � 2 0 . 7 3 5 . 1 6 6 . 0 � ¯ o 0 . 4 4 4 0 . 5 4 7 0 . 6 6 7 ¨ C 0 . 5 0 1 0 . 4 1 9 0 . 3 1 5 � v 0 . 0 5 5 0 . 0 3 4 0 . 0 1 8 � ' 3 , 0 5 0 2 , 6 3 0 2 , 2 8 0 � � . i ' 5 3 8 , 4 0 0 5 3 8 , 4 0 0 5 3 8 , 4 0 0 � 2 1 , 0 0 0 1 5 , 0 0 0 1 0 , 8 0 0 g ' 5 0 , 0 0 0 3 7 , 0 0 0 2 6 , 0 0 0 5 � 7 3 , 5 0 0 1 0 8 , 4 0 0 1 7 5 , 8 0 0 ¯ � 8 5 , 0 0 0 7 3 , 5 0 0 6 3 , 7 0 0 " ¯ 7 6 7 , 9 0 0 7 7 2 , 3 0 0 8 1 4 , 7 0 0 ~ ~ ~ T a b l c Z ~ 3 . Ü B î 8 0 Í L 8 Í @ L 8 C U î Í 0 B 8 Í 0 I C a æ Ü D e s i g p a r a m e t e r s K l K 3 , E q . 2 . 1 7 F = 1 5 . 5 / K _ H = K 3 F K 2 = 2 . 0 7 / F x B 3 ' E q . 2 . 1 6 X A 3 ' E q . 2 . 1 5 x C 3 0 ¿ E q . 2 . 1 4 0 . 5 0 . 6 8 . 3 3 1 . 8 9 3 1 . 0 2 5 . 8 2 5 8 . 0 4 8 . 8 0 . 0 6 6 8 0 . 0 8 0 3 0 . 1 0 1 0 . 3 1 3 0 . 8 9 3 0 . 6 5 5 0 . 0 0 6 0 . 0 3 2 2 , 4 3 0 3 , 0 4 0 C o s t s , d o l l a r s / y e a r u ± ( ± _ ± ² 5 3 8 , 4 0 0 5 3 8 , 4 0 0 ò 1 1 , 5 0 0 1 9 , 5 0 0 d 2 7 , 0 0 0 4 6 , 4 0 0 Ü 7 3 5 , 0 0 0 1 7 4 , 0 0 0 J 6 7 , 8 0 0 8 4 , 8 0 0 T o t a l 1 , 3 7 9 , 7 0 0 8 6 3 , 1 0 0 0 . 7 0 . 8 0 . 9 8 0 . 6 3 3 2 2 . 2 1 9 . 4 2 1 . 8 1 2 . 3 0 . 0 9 3 3 0 . 1 0 7 0 . 4 4 0 0 . 5 1 4 0 . 4 9 5 0 . 3 8 7 0 . 0 6 5 0 . 0 9 9 3 , 6 6 0 4 , 3 6 0 5 3 8 , 4 0 0 5 3 8 , 4 0 0 2 8 , 0 0 0 3 7 , 0 0 0 6 7 , 2 0 0 8 7 , 6 0 0 9 3 , 5 0 0 6 2 , 5 0 0 1 0 2 , 2 0 0 1 2 1 , 7 0 0 8 2 9 , 3 0 0 8 4 7 , 2 0 0 ~ + ¯ Æ � 0 . 9 1 . 0 1 . 2 1 . 5 ~ ¯ ^ 0 . 4 4 7 0 . 3 3 3 0 . 2 0 9 0 . 1 2 0 | 1 7 . 2 1 5 . 5 1 2 . 9 1 0 . 3 7 . 7 5 . 1 7 2 . 7 0 1 . 2 4 0 . 1 2 0 0 . 1 3 3 0 . 1 6 0 0 . 2 0 1 0 . 5 5 9 0 . 5 8 9 0 . 6 0 3 0 . 5 8 6 0 . 3 0 8 0 . 2 5 0 0 . 1 3 3 0 . 1 6 6 5 , 0 9 0 5 , 8 8 0 7 , 5 5 0 1 0 , 5 0 0 5 3 8 , 4 0 0 5 3 8 , 4 0 0 4 5 , 0 0 0 5 4 , 0 0 0 1 0 8 , 4 0 0 1 2 9 , 2 0 0 4 5 , 7 0 0 3 5 , 5 0 0 1 4 2 , 0 0 0 1 6 4 , 2 0 0 8 7 9 , 5 0 0 9 2 1 , 3 0 0 Reactor Design, Optimization, uHd Conh'ol JJ Case Ï: Three Reactors in Prallel Ü the three reactors are operated in parallel with an equal flow to each, the analysis follows directly from the conside ration of the first reactor in Case I. The results are and 1 7 ~ m 1 +K 1 (2. 1 8) (2 . 1 9) Here, K 1 and K 2 are evaluated using a value for ! which corresponds to the total rate of feed including recycle to each reactor. It may therefore be written that m 8 ¥ ÍÛ Þ 23, 1ÛÛ J = - = M 3( 1 1 2 . 6)Fx Õ FX B (2. 2Û) From Eqs. 2. 1 8 to 2 . 20 the computations for the evaluation of Case IV follow directly and are shown H Table 2 -4. Case V: Batch Reaction If the chlorination were carried out batchwise in three reactors simultaneously, the same analysis used t o interpret the labratory data would apply. Thus, Eqs . 2. 3 and 2 . 4 may be used to calculate the extents of both reactions as functions of time. A pseudo feed rate to the reactors may then be computed as 3 N R 1 1 2. 8 F = * = = Í l (2.21 ) where l represents the time each batch is allowed to react. Ü the time for loading and unloading is considered negligible, the annual reactor usage follows directly as o Y ÅÛ Þ 63 0e J= = - ( 1 1 2.6)Fx B x B (2. 22) From Eqs. 2 . 3 , 2 . 4, 2. 2 1 , and 2 .22 the ideal operating cost s for the hat.rh rpart.nr havp hppn C.alr1I1at.pr anr arp !ummari7.pr in Tahlp Z~ñ. COMPARISON OF THE FVE REACTOR CASES The results of the designs for the five reactor cases are com­ pared in Fig. 2 -4, which shows the annual operating cost for the ¯ 8 D Î 0 3 ¬ 4 . Ü 0 8 0 Î Í 8 D Î D s i L 8 Î C 0 Î 8 î Ì D D 8 Î D I L 8 8 0 Ï Y D e s i g p a r a m e t e r s F 1 0 1 5 3 0 3 0 K l 1 . 5 5 1 , 0 3 3 0 . T T 5 0 . 5 1 6 K 2 0 . 3 0 T 0 . 1 3 8 0 . 1 0 3 0 . 0 6 9 x A 0 . 3 9 3 0 . 4 9 3 0 . 5 6 3 0 . 6 5 9 x B 0 . 5 0 3 0 . 4 4 8 0 . 3 9 5 0 . 3 1 8 X c 0 . 1 0 6 0 . 0 5 9 0 . 0 4 3 0 . 0 3 3 J 4 , T 3 0 3 , 5 3 0 3 , 0 0 0 3 , 4 8 0 C o s t s ! d o l l a r s / y e a r Û * L * _ * h 5 3 8 , 4 0 0 5 3 8 , 4 0 0 5 3 8 , 4 0 0 5 3 8 , 4 0 0 ò 3 9 , 8 0 0 3 4 , 8 0 0 3 0 , 1 0 0 1 3 , T 0 0 d 9 6 , 0 0 0 5 9 , 8 0 0 4 8 , 4 0 0 3 3 , 0 0 0 c 6 4 , 6 0 0 9 1 , 5 0 0 1 0 8 , 3 0 0 1 T 3 , 0 0 0 J 1 3 3 , 0 0 0 9 6 , 3 0 0 8 3 , 9 0 0 6 9 , 3 0 0 T o t a l 8 T 0 , 8 0 0 8 1 3 , 8 0 0 T 9 9 , 1 0 0 8 3 6 , 3 0 0 ~ ¯ ¯ ~ % ~ 4 0 6 0 � " 0 . 3 8 T 0 . 3 5 9 l 0 . 0 5 1 8 0 . 0 3 4 5 0 , T 3 0 . T 9 5 0 . 3 6 4 0 , 1 9 9 0 . 0 1 6 0 , 0 0 6 3 , 3 4 0 1 , 9 T 0 5 3 8 , 4 0 0 5 3 8 , 4 0 0 1 1 , 5 0 0 5 , T 0 0 3 T , 6 0 0 1 3 , 8 0 0 3 3 6 , 5 0 0 3 3 3 , 0 0 0 6 3 , 5 0 0 5 5 , 0 0 0 8 6 6 , 5 0 0 9 4 4 , 9 0 0 T a b l e 2 - 5 . R e s u l t s o f D e s i g n C a l c u l a t i o n s f o r C a s e N D e s i g p a r a m e t e r s l ¿ h r s 1 2 2 . 5 3 4 5 6 ) ¿ E q . 2 . 2 1 1 1 2 . 8 5 6 . 4 4 5 . 1 3 7 . 6 2 7 . 2 2 2 . 5 1 8 . 8 À ¿ E q . 2 . 3 0 . 6 6 3 0 . 4 3 4 0 . 3 5 6 0 . 2 9 1 0 . 1 9 2 0 . 1 2 8 0 . 0 8 3 R � ¹ µ ¸ E q . 2 . 4 0 . 3 2 7 0 . 5 3 4 0 . 5 9 5 0 . 6 4 5 0 . 7 0 6 0 . 7 3 0 . 7 3 5 - ¯ o ^ L 0 . 0 1 0 0 . 0 3 2 0 . 0 4 9 0 . 0 6 4 0 . 1 0 2 0 . 1 4 2 0 . 1 8 2 . d ¸ E q . 2 . 2 2 1 , 9 2 5 2 , 3 6 0 2 , 6 5 0 2 , 9 3 0 3 , 5 7 0 4 , 3 1 0 5 , 1 5 0 ¯ � v º ¯ ` C o s t s , d o l l a r s / y e a r < a + l + ¿ + I 5 3 8 , 4 0 0 5 3 8 , 4 0 0 5 3 8 , 4 0 0 5 3 8 , 4 0 0 5 3 8 , 4 0 0 5 3 8 , 4 0 0 5 3 8 , 4 0 0 ¯ � ~ b 5 , 8 0 0 1 1 , 3 0 0 1 5 , 5 0 0 1 9 , 7 0 0 2 7 , 2 0 0 3 6 , 9 0 0 4 6 , 7 0 0 � . ~ . ^ u 1 3 , 9 0 0 2 7 , 3 0 0 3 7 , 3 0 0 4 4 , 7 0 0 6 5 , 4 0 0 8 9 , 8 0 0 1 1 2 , 3 0 0 � ~ . c 1 6 8 , 0 0 0 6 7 , 6 0 0 4 9 , 8 0 0 3 7 , 5 0 0 2 2 , 6 0 0 1 4 , 5 0 0 9 , 5 0 0 g J 5 3 , 7 0 0 6 5 , 9 0 0 7 3 , 8 0 0 8 1 , 6 0 0 9 9 , 5 0 0 1 2 0 , 0 0 0 1 4 4 , 0 0 0 � � T o t a l 7 7 9 , 8 0 0 7 1 0 , 5 0 0 7 1 4 , 8 0 0 7 2 1 , 9 0 0 7 5 3 , 1 0 0 7 9 9 , 6 0 0 8 5 0 , 9 0 0 ¯ � � ~ � Jo Cliu]lc+ 3 t ¯ i90P ¬ i ' §80 ��� § .^ ! Figure 2- 4. Economic evaluation of five design cases. chlorination reaction plotted as a function of F. Cases I and V provide substantial savings over the other suggested methods. At low F vlues the operating costs for Cases I, II, ÜÏ¿ and V are al­ most equal because of the long residence times at low flow rates which lead to low recycle costs for all processes. At these values the method of recycle is therefore relatively unimportant. The dominating variable charges at low flow rates are those for raw material s lost in conversion to dichlorobenzene. and these are approximately the same for all cases. Several chemical engineering texts [1,5) point out that as the num­ ber of reactors H a series of CSTR's is increased the resulting con­ version-re sidence time relationship gradually approache s that for a batch or plug-flow reactor. Thus, the maximum conversion at any specified time will be achieved in a batch reactor ¦for all but zero or negative -order reactions) , because the concentration driving force for the reaction is fully utilized in either a batch or a plug-flow reactor. In a CSTR the reactant concentration in the feed is diluted when this stream is mixed with material that has already partially reacted. Thus, the rate of reaction would be maximized in the feed stream where the concentration of reactants is highest; however, the full effect of thi s concentration driving force i s lost when the stream is diluted. U line with this reasoning, Fig. 2 -4 reveals that the batch reaction achieves the least exensive operation. However, its economics are closely approximated by those for Case I. Ü the number of CSTR's were increased to more than three, the cost-versus-flow- rate curve would gradually drop and would approach that for Case V asympto­ tically as the number of CSTR's is increased to ifinity. Even in the case of three CSTR's the curves for Cases 1 and 5 show in Fig. 2-4 gradually approach each other at high feed rates, where the recycle costs dominate. Actually in the present economic analysiS the curve for Case V should be considered only as a theoretical limit, since labor and Reaclor Dfsigll , Opt imi:atioll, and Cont rol 39 time for loading, unloading, and operating the reactors have been neglected. These factors undoubtedly would be very signiicant in contributing to the total cost of operating a batch reaction system. Thus, Case Ï represents the optimum practical reactor flow plan for the present analysis. It is convenient to thin of Case V as a limit that might be approached if the number of reactors were increased indefinitely. Figre 2-4 shows that there i s only a minor advantage to be gained by using more tha three reactors. As mentioned previously, the high raw-material costs cause all five cases to be very uneconomical at low flow rates and high resi­ dence time s. The curve shown for Case II nearly coincides with that for Case V for a considerable distance as F is inc reased. Even­ tually, however, the increasing recycle charges caused by incom­ plete use of the recycle stream in Case II lead to significantly in­ creased total costs and a re sulting sharp minimum in the curve. A similar, and even more striing, effect is observed when Case III i s compared with Cases V and Ï. Case IV corresponds exactly to the operation of a single CSTR having three times the volume of the individual reactors Wder con­ sideration in the present problem. For reasons mentioned previously, the loss of the beneficial effects of staging the reactor volume would be exected to lead to higher recycling costs. This effect is observed i n Fig. 2-4, where Case IV i s show t o be one of the least desirable systems studied. The operation of three reactors in series with recycle to the first is thus the most economical of the process schemes considered. Figure 2-4 indicates that neither the operation of parallel reactors nor the use of recycle to an intermediate point leads to improved re­ sults. Thus it may be concluded that Case I, as shown in Fig. 2-3 represents the optimum arrangement that can be obtained with three reactors. At this point, it is well to emphasize that a great deal of unnec­ essary calculation has been presented in order to provide a com­ parison of various modes of reactor operation. Clearly, Cases II and ÏÛ could have been eliminated at the outset on a qualitative basis; such a decision would have been entirely in accordance with te sug­ gestion of Chapter Í that computational effort be minimized. Never­ teless, the comparative results summrized i n Fi g. 2-4 are valuable in illustrating the effect of various types of recycle. All the methods considered have been restricted to isothermal operation of the reactors. It now becomes appropriate to investigate the effect of temperature variations. This subj ect wll be treated using the reactor system shown in Fig. 2-3 as a basiS for calculation. EFFECT OF REACTOR TEMPERATUE ON PROCESS ECONOMCS Calculations of the type shown in Table 2-1 have been carried out for the case of three reactors in series with recycle to the first. Figre 2 - 5 summarizes the results of these calculations and presents 9Ü Chapte 3 Fæ ml0 f,Ð m8/N �� m % ðð M CC 55 M M ff Æ FF Æ U _,¡x¡ % % M M 55 55 M M Æ Æ M M Figure 2-5 . Effect of temperature on the economics of chlorination. the annual costs as functions of feed rate for five cases in which the temperatures in all reactors are the same. The optimum feed rate and the minimum annual costs are approximately as follows: 2_ = 2 ; ¯ 2 ¡ !, lb moles/hr 60°C 80 Costs, dollars/year 945, 000 773, 000 744, 000 743, 000 760, 000 It is found, however, that the required production rate of 8 million lb per year cannot be achieved at 40°C for any feed rate. The cost curves are flat and the annual costs relatively insensitive to temperature and feed rate. This is significant, since operation at higher than optimum feed rate could make the equipment available for some other operation a large part of the year without adding very much to the cost of the monochlorobenzene. OPTIMUM TEMPERTURE SEQUENCE Figure 2-1 indicates that the activation energy for the unwanted second reaction is far greater than that for monochlorobenzene for­ mation. I t follows that for maximum yield of monochlorobenzene the temperature should decrease as t he reaction proceeds. The tempera­ ture can be relatively high in the first reactor, since there is little monochlorobenzene present to be further chlorinated. It should then be reduced as monochlorobenzene accumulates; yet the requi red pro­ duction rate must be achieved in no more than 7000 hr /year. It is evident that there is an infinite number of possible combina­ tions of 7_¿ 7_,and 7¿ each 70°C or less, which could be specified, and it would seem probable that one of these might reduce dichloro­ benzene formation appreciably and result in an annual cost less than the $ 743, OOO/year calculated for operation of all these reactors at 60°C. One possible combination is Tl * 70°, 7 ; 7 60°, and 2 ¡ * 50°C. From Eqs. 2 . 5 and 2 . 6 a minimum annual cost of $ 750, 000 at a feed Reactor Døs¡gu, Optimization, alld Control 4Ì rate of about 1 1 0 lb moles/hr can be calculated. Figure 2-5 compares the results of this combination with those for isothe rmal operation. Pursuit of further combinations of reactor temperatures is clearly a j ob for a computer, since the possibilities are too numerous for slide- rule calculation. Formulation of the problem for a digital com­ puter is relatively simple, since the cost exressions are not com­ plicated. The rate constant s must be expressed as functions of tem­ perature, either by empirical polynomials or by Arrhenius-type equations. The value s of III and k 2 shown in Fig. 2-1 are found to be linear in l/T on a semilogarithmic graph, and may be exressed by 6_ 7 5.1 Y 101 2 e-19 6 00fRT 1 2 ¬ 2. 9 K 1 0 2 0 e - 3 2 6 00/RT where T is now in oK. (2. 23) (2 . 24) An incomplete computer search of temperature sequence s in­ dicates that there is little to be gained by temperature variations, even though total anual costs in the vicinity of $73 5, 000 to $740, 000 can be attained. The principle that the temperature should be reduced as the reaction proceeds i s sound [ see Denbigh (4) , Chapter 5], but the obj ect is now minimum cost rather than maximum yield. The cost data applicable to the present analysis are such as to give very flat optima in the economic evaluation curves. The selection of an optimum temperature sequence is a classic for the more advanced optimization techniques mentioned in Chapter 1 . A more sophisticated approach to the selection of reactor tempera­ tures would provide a worthwhile exosure to some of the se modern techniques . SUMMAY OF THE REACTOR DESIGN The minimum total annual cost for MCn production is approxi­ mately $740,000; this includes purchased chemicals, recycle and pro­ duct recove ry, operating labor, and fixed charges, and would result in an annual saving of $ 1 00, 000 as compared with use of monochloro­ benzene purchased at $0. 1 05/lbø Otimum operation is at abut 60°C with a benzene feed rate (including recycle) of 80 lb moles/hr ( 14. 2 gallons/min) . Oerating at this temperature and flow rate should make it possible to produce the requi red amount of mono ­ chlorobenzene in only 1770 hr /year. A slight gain could be made by operating successive reactors at lower temperatures, but the possible cost reduction would not appear to j ustify the more complicated control system that would be needed. The total annual cost is relatively insensitive to feed rate and would increase to only about $775, ODD/year if the feed rate at 60°C were doubled and the yearly operating hours cut from 1 770 to 1 290. This means that the eqUipment could be made available much of the year for some other use . 42 Chapter 3 It should D pOinted out that the pi'oduction of dichlorobenzene represents a substantial cost for chemicals. Its recovery and puri ­ fication would not be very difficult, and the proposed process would look very much more attractive i a market could be found for a few hundred thousand pounds per year. HEAT-TRSFER A REACTOR-STAILITY CONSIERTIONS With the basic nature of the process established, it is essential that the reactor cooling system be examined in some detail. The adequacy of the cooling medium and the available heat-transfer area must be ascertained before the reaction equipment can be recommen­ ded for MCB production. L equal importance, the possibility that the reactor operation might be unstable under the proposed operating conditions should be inve stigated. To compute the rate of heat release in each reactor, the following enthalpy changes of the chlorination reactions must be calculated from the thermodynamic data on the reactants and products: ( a) C6H6 ¬ C12= C6HsCI ¬ HCI 1 1.70 ¬ 0 = 2 . 50 -- 22. 06 ¬ DÏ DÎ= -31 . 26 Kcal (ò) C6HsCI ¬ Cl2 ~ C6H4Cl2 ¬ HCI 2 . 50 + 0 = -4 . 90 - 22 . 06 - DÏ DÏ = -29 . 46 Kcal The rate of heat evolution in a single reactor may now be computed as Q_ ~ 3 1 , 260 ( 1 . 8) (NJ1 x A ) ¬ 29, 460 ( 1 . 8) (NRk1xB ) = 2, 1 20, 000 k 1 xA + 2, 000, 000 /:_x_ Btu/hr (2. 25) At the suggested f eed rate of 80 l b moles/hr with each reactor at 60°C, the liquid compositions, found from Eqs. 2. 5 through 2. 8, are as follows : ¹. ¹ µ Mole fraction Mole fraction First reactor 0.760 0. 228 Second reactor 0. 578 0. 389 Third reactor 0.440 0. 501 Evdently the total moles of chlorie reacting are greatest in the first reactor ( 1 ¬ O. 760 ¬ O. 012 ¯ 0. 252 in the first, O. 76 ¬ O. 578 + 0. 033 - 0.01 2 ¯ 0. 203 in the second, and 0. 578 - 0. 440 + 0. 059 - 0. 033 ¯ O. 1 64 in the third) . Sice the enthalpy decrease per mole Reactor Design, Optimizatioll, and Control 43 of chlorine is about the same for each of the two steps of the chlorin­ ation sequence, it is clear that the cooling load is greatest in the first reactor. At 60°C, k l is 0. 65 hr-1 and k 2 is 0. 1 1 3 hr- 1 ; therefore Q_ ~ 2, 1 20, 000 (0. 65) (0. 76) + 2, 000, 000 (0. 1 1 3) (0. 228) ~ 1 , 1 00, 000 Btu/hr The benzene, if fed at 20°C, would absorb (60 - 20) ( 1 . 8) (80) (33 . 4) ~ 1 93, 000 Btu/hr. The heat to be removed from the first reactor is then 1,1 00, 000 - 1 93,000 ¯ 907, 000 BtU/hr. The feed to the second reactor absorbs no heat, but the heat trans­ fer to the cooling coil is still less than in the first reactor ( see Ap­ pendix) . Excess chlorine passing to the condenser provides some re­ flux cooling, but this will be neglected in order to make a conservative estimate of the adequacy of the cooling coil s . Under the assumption that cooling water i s available at 75°F and that a temperature rise of 40°F may be allowed, the appropriate tem­ perature driving force for heat transfer is computed as A T ave ~ 60 ( 1 . 8) + 32 - 90 ~ 50°F The ܬ product required in the first reactor is then given by 907, 000 ( V A)required = ~ 1 8, 1 00 Btu/(hrWF) 50 but the avilable ܬproduct was specified as \'^¹ava);aµ), ~ (1 5 0) ( 550) ~ 82, 500 Btu/(hrW F) The coil is evidently more than adequate to hadle the cooling load for cooling water averaging 90°F. There remains the question of reactor stability. Will a smal upset, causing the temperature to rise slightly, so increase the reaction rate (and hence the rate of heat evolution) that the cooling coil cannot re­ turn the temperature to the control point of 60°C? If the temperature does not return, the rate of heat evolution will continue to icrease, and the contents will boil over. There is a serious safety hazard due to benzene and chlorine, and also the possibility of damage to the equipment. Ü the reactor is inherently unstable, it may still be pos­ sible to provde controls so as to maintain it at 60°C. Exenses for control eqUipment will of course be much lower i the operation is inherently stable. If the rate of heat release goes up because the temperature rises, the increased cooling due to the larger temperature difference for heat transfer should cause the temperature to return to the desired 60°C. To determine whether this will happen, the heat release in the first reactor is calculated as a function of temperature. At 50°C, for example, Í_ and ! corresponding to a feed rate of 80 lb moles/hr are 0.1 2 1 and 0.01 21 , respectively; thus, 7 @ _ i s 0. 892 and A _ is 0. 1 07. 4J Chc[Icr2 The heat release Q¸, calculated by the procedure described earlier, i s then 494, 000 Btu/hr. Part of the heat generated by the chemical reaction is used to pre­ heat cold benzene feed, and the rest must be transferred to the cool­ ing medium. Let 2¿ represent the temperature of the liquid in the reactor, and assume the benzene to be supplied at 20°C. The heat absorbed by the feed is then g_ 7 (80) ( 33. 4) [1.B) \ 7_¬ 20) ¯ 4, 820 [T_ ¬ 20) Btu/hr The diference Q1 ¬ g_ represents the heat to be transferred to the cooling coil. At 50°C, for example, this amouts to 494, 000 - 4, 820 ( 50 - 20) ~ 3 88, 000 Btu/hr. Corresponding values at other tempera­ tures versus 2_ are shown as line I on Fig. 2-6. The points used in plotting this line have been calculated from values of Ü _ obtained from Eq. 2. 25, with values of x__ and À _ for steady-state operation of the first reactor at F 7 80. o ¸ s ± L x ¯ � Feed tc¹e · 8D!b moIes/hr Qµqn¹::y � pIo¹¹eo | U· - ºr Vr ºr ||I U > ºr n ºc B ºc C ºc 0 ºc � |.0f ¡ os~ s· r r r 4o so co ¬60C\0t l0Uµ0l0\ut6 t "L ro Figure 2-6. Stability diagram for the reactor system shown in Fig. 2- 3. ºo The rate of heat transfer to the cooling coil is given by {¿ = Í/ [ 7_ - 2¸} ¯ 1 50 ( 550) ( 60 ¬ 2_ | [J. 8) ~ 1 48, 500 ( 60 ~ T¸) Btu/hr Reactor Design, Optimization, and COll trol 4ô where T¿ is the mean temperature of the cooling water or brine. Ï { ¿ is to be equal to (Ql ¯ {¸ ) at 600e, T_ must be given by 907, 000 1 ~ 60 ¯ ~ 60 - 6. 1 ~ 53. goe ¿ 1 48, 500 Line ¬ on Fig. 2 - 6 represents the cooling rate g_ for a T¿ value of 53. goe and a varying value of Tl ' The reactor is stable at 600e (point P) by the Van Heerden criter­ ion (7) with the specified U. product of 82, 500 and with a cooling fluid temperature of 53. goe. A small temperature rise, say from 60 to 61 °e, would increase the cooling rate more than it would the net rate of heat generation. Accordingly, the temperature would drop back to 600e. The opposite will happen H the temperature drops slightly below 600e. It may seem surprising that reactor instability can be prevented by using warm water for cooling; intuitively one might thin that cold brine would be needed. At 600e the net heat generation increases roughly 8 per cent per degree increase in T u • To maintain stability, the cooling rate must increase at least 8 per cent per degree. With U1 fixed, the cooling rate is proportional to 2_ ¯ T_ ,which must then increase at least 8 per cent per degree. The ÒT must therefore not be greater than about 1 2°e. For an elaboration of this point, see Boynton, Nichols, and Spurlin (3) . U case cold water were supplied for cooling ¦ e. g., *c ¬ 20°C), the cooling line g_ would pass through the 60° point Í U the U¬ product had a value of 22, 600 instead of the available 82, 500 Btu/hr OF. Line J on Fig. 2 -6 represents the 0 ¿ cooling line in this situation. The operation is now seen to be unstable at 600e, since an increase in reactor temperature from 60 ÍD 61°e would cause the rate of heat generation to increase more than the rate of cooling: The reaction would " run away. " At this point it seems clear that the stability question has been disposed of: The criterion of stability discussed by Van Heerden [ ¯) and many other writers i s satisfied. At the operating point J¡ the cooling line ¬ is steeper than line I, the curve representing the net rate of heat generation. The latter curve, however, represents [Q_ ¯ {¸ ) under steady-state conditions at T 8 • In calculating Q_,the compositions employed were obtained from the equations for steady­ state operation at each T u • As reaction proceeds isothermally, the benzene disappears and Q_ decreases. It follows that ¦ Q_ ¯ 0 , ) would be greater at 61 °e U the liquid composition remained at the steady­ state value at 600e as the temperature climbed than if it changed to the new steady-state value at 61° e. Since the composition change may be exected to lag behind the transient temperature change, the steady­ state criterion of stability that has been employed is not reliable. The error, U any, in employing the steady-state values of reactant con­ centrations in the calculations is in the unsafe direction. This point is discussed at length by Bilous and Amundson (1), who derive the relation between composition and temperature as T u changes 46 Chapter 2 slightly from a control point. For a simple irreversible first-order reaction there is another criterion which must be met in addition to that of Van Heerden U stability is to be assured. For the pair of sequential first-order reactions encountered in benzene chlorinations there are three stability criteria. The analysis is somewhat complex and its use may not be necessary. Since the benzene concentration is decaying and the second reaction is slow, the worst that can happen is that the steady- state composi­ tion at 60° remains unchanged as the temperature increases. Under such conditions the reactor is stable U the slope of the cooling curve ¬ at 60°C is greater than that of the ( Ql ~ q¿) curve, when the latter is found using the 60° steady- state values of À @_ = O. 760 and x B 1 = 0. 228. From Eq. 2. 25 , Q 1 7 2, 1 20, 000 (0. 760 Il l) ¬ 2, 000, 000 (0. 228 k 2 ) and since then, g_ = 4820 ( Tn - 53. 9) o (Q ¬ ç¿ ) dkl dll 1 = 1 , 61 0, 000 ¯ ¬ 456, 000 ¯ 2 ~ 4820 o TR dTR dTR dink 1 dl nll 2 = 1 , 61 0, 000 k 1 -¬ 456, 000 k 2 ¬- 4820 dT R dTR = 1 , 61 0, 000 (0. 65) ( 1 9, 600) RTf + 456, 000 ( 0. 1 1 3) (32 600) RT� - 4820 o (Q ~ q ) _ = 93, 000 ¬ 7, 650 ¯ 4820 = 95, 830 Btu/(hr} ( OC) . o T R This value is to be compared with the slope of the cooling curve, which is U1 * 1 50 Y 550 Y 1 . 8 = 1 48, 000 Btu/¦hr) (OC) . Evidently the reactor will respond t o temperature transients even U composition does not change from its steady- state value at 60°C. Any change in composition with temperature will be in the direction of greater thermal stability. Reae/or Dcs/¿n, Opt i mizatiol l , uIlu COll t rol 47 Since U¬ is the same in each reactor, the cooling lines for the second and third reactors will have the same slopes as that for the first reactor. These are shown as lines C and D on Fig 2 -6 . The mean coolant temperatures in the three reactors are seen to be 53 . 9, 54.0, and 55. 1 °C. The mean temperatures for reactors I and II are approximately equal, because the lower reaction rate in the second reactor is almost exactly balanced by the lack of a cooled feed stream in the second reactor. In order to avoid confusion, curves ¬ and L have been superimposed in Fig. 2 -6. In designing the process, part of the cooling water leaving the first reactor can be used in the second reactor and part of that from the second can be used in the third. Part of that leavng the third can then be mixed with cold water so as to provide warm water to cool the first reactor. Ü the temperature rise of the cooling water i the first reactor is 1 0°F, some ( 1 , 1 00, 000 - 1 93. 000)/1 0. or 90. 700 lb/hr will be needed. Ï all of this were to be put through a single O. 5 -in. coil with O. 4-in. Ld., the mean water velocity would be 460 ft/sec. This is obviously excessive, and it will be necessary to connect the coil so as to handle a number of water streams in parallel short coil sections. There are many questions to be exlored further µ the project is pursued. Regarding stability, it i s evident that a factor of safety could be introduced by operating at 55° instead of 60°C. Figure 2 -6 shows that the slopes of the cooling line and the heat-generation curve would then differ markedly at the control point. Operation of all reactors at 55° instead of 60°C would increase the annual costs by only a very slight amount (see Fig. 2 - 5) . The subject of control has not been discussed. What contingencies must the control instruments handle? Power failure? Loss of cooling water? Unexected increase in catalyst activty? Variation in feed rate? Perhaps the quickest way to stop a runaway is to cut the chlo­ rine supply. But H cooling water were cut off, would the di ssolved chlorine continue the reaction far enough to bil over benzene? All of these questions should be treated in some detail before the final de­ sign is approved. Consideration of these types of problem during the design phase of a project can save many hours of difficulty during plant start -up and subsequent operation. SUMARY OF HAT-TRANSFER A STAILITY CONSIERATIONS It has been show that the cooling coils in the existing reactors are adequate t o tae care of the heat of reaction under the conditions of the proposed operation at 60°C and a feed rate of 80 lb moles/hr of benzene. However, stability considerations indicate that operation at 5 5°C and at a somewhat reduced feed rate would be preferable, even though the total annual costs would be slightly increased. Water can be used as a cooling medium, but it is essential to em­ ploy relatively hot water for this purpose. Ï the temperature dif ­ ference between reacting liquid and water is small, the increased rate of cooling due to a small increase in reactor temperature may be 4o C|c]Iø+ 3 made larger than the increase i rate of heat generation. This will cause the temperature to fall and to stabiliz e at the control tempera­ ture. The use of hot water as a cooling medium would undoubtedly cause scaling problems. The possibility of using treated water or some other heat-transfer medium should be evaluated. Since the average temperature difference must be small [!1 OF) , the water temperature can ri se only perhaps l O°F in passing through the coil. This means that the water rate must be rather high, and it will be necessary to modify the coil connections so that several coil sections can be used in parallel . Finally, if the proposed proj ect is to be undertaen, a careful study to determine the best type of control equipment will be necessary. Reactor Design, Optimization, and Cont rol 49 APPENI ¯L LܣϯÏÜ Z Result s of Slide -Rule Calculations of Mole Fractions Benzene and Monochlorobenzene (xA and xB ) and of Heat of Reaction Q (Btu/hr) (Each reactor ope rated at the same temperature) ) ( lb noles / hr) 40 60 80 100 1 20 40°C xA1 0. 909 0. 943 0. 958 0. 965 0. 970 xB l 0. 082 0. 057 0. 043 0. 035 0. 029 Q 1 1 87, 000 1 94, 000 1 96, 000 1 97, 000 1 98, 000 XA2 0. 832 0. 899 0. 91 6 0. 931 0. 942 xB2 0. 1 5 8 0. 1 1 0 0. 085 0. 069 0. 058 Q 2 1 71 , 000 1 85, 000 1 88, 000 1 91 , 000 1 93, 000 x A3 0. 762 0. 841 0. 877 0. 900 0. 91 3 xB3 0. 226 0. 1 60 0. 1 24 0. 1 01 0. 085 Q 3 1 57, 000 1 73, 000 1 80, 000 1 85, 000 1 88, 000 50°C xA1 0. 804 0. 861 0. 892 0. 91 1 0. 925 xB l 0. 1 90 0. 1 3 7 0. 1 07 0. 088 0. 072 Q 1 450, 000 478, 000 494, 000 502, 000 5 1 0, 000 x A2 0. 646 0. 741 0. 795 0. 83 1 0. 856 xB2 0. 339 0. 2 53 0. 201 0. 1 67 0. 1 42 Q 2 3 70, 000 41 8, 000 445, 000 464, 000 475, 000 x A3 0. 520 0. 63 8 0. 71 0 0. 757 0. 792 x B3 0. 454 0. 3 5 1 0. 283 0. 238 0. 205 Q 3 307, 000 3 6 7, 000 402, 000 426, 000 443, 000 60°C XA1 0. 621 0. 71 1 0. 760 0. 804 0. 850 XB 1 0. 343 0. 2 71 0. 228 0. 1 88 0. 1 63 Q 1 933, 000 1 , 040, 000 1 , 1 00, 000 1 , 1 48, 000 1 , 1 92, 000 xA2 0. 385 0. 506 0. 578 0. 645 0. 689 xB2 0. 523 0. 445 0. 3 89 0. 332 0. 294 Q 2 648, 000 797, 000 885, 000 963, 000 1 , 01 6, 000 x A3 0. 239 0. 360 0. 440 0. 5 1 9 0. 5 72 JÜ Chapt er 3 Ï ( lb moles/ hr} 40 60 80 1 00 1 20 × µ¡ 0. 61 6 0. 553 0. 501 0. 439 0. 396 V ¡ 468, 000 620, 000 71 9, 000 81 6, 000 876, 000 70°C × ¬ ¡ 0. 408 0. 504 0. 580 0. 632 0. 674 × µ ¡ 0. 41 6 0. 384 0. 345 0. 3 1 5 0. 286 VI 1 , 71 4, 000 2, 004, 000 2, 2 1 8, 000 2, 3 63, 000 2, 477, 000 ׿; 0. 1 66 0. 25 8 0. 336 0. 406 0. 453 × µ; 0. 462 0. 494 0. 487 0. 468 0. 444 ¬; 963, 000 1 , 293, 000 1 , 543, 000 1 , 755, 000 1 , 888, 000 x ~ ¡ 0. 068 0. 1 31 0. 1 95 0. 252 0. 305 x µ¡ 0. 3 93 0. 484 0. 5 1 8 0. 527 0. 5 1 9 V¡ 5 77, 000 866, 000 1 , 1 06, 000 1 , 3 03, 000 1 , 469, 000 REFERENCES 1 . Bilous, L. ¡ and N. R. Amundson, A. I . Ch. E.J. l, 5 12 ( 1 95 5) . 2. Boynton, D. E. , W. B. Nichols, and H. M. Spurlin, Ind. Eng. Cher. 51, 489 ( 1 959) . 3. Chermin, H. A. G. , and D. W. Van Krevelen, Chem. Eng. Sci. Î9¡ 58 (1 961 ) . 4. Denbigh, K. G. , Chemical Reactor Theory, Cambridge University Press, Cambridge {1965} . 5. Kramers, H. , and K. R. Westerterp, Elements of Chemical Reactor Design and Operation, Academic Press, New York {193} . 6. MacMullin, R. B. , Chem. Eng. Progr. 99¡ No. 3, 1 83 ( 1 948) . 7. Van Heerden, C. , Ind. Eng. Cher. 4 5, 1242 ( 1 9 53) . 3. Process Improvement for the Liquid­ Liquid Extraction of Fenway acid Tlds case is based uj)OIl [abomtoJ)' data obtained ill (II industrial laboratory />riOl" to lite design of a contillllOus extractiol! /n'ocess. Tile names of tile actual c/lemicals being cOllsidered lI(u'e been c/I(ed for /mr/JOses of comme1'cial security. Some discussioll is directed to­ lW1"d IIle use of faclorially designed eX/.erimellts ill gatherin and analyzing cltemical engineering data. The im/J01"t(IIICe of utilizing tile /Jroper /01'111 of inde/Jelldent variables ilZ tile fOl'lnulalioll of designed eX/Je1"imelll s is also em/J/Ulsized Tile design computations in lids clla/Jte1' lead /0 a classical/ill(l­ cial emluatioll in ll'hicll ca/.ital and operating costs are balallced in the determination of all optimum design. III tills case only a prelimi­ nary desigl/ is required, al/d liberal use of appmximations greatly simplies the calculation effm'l. An ol'er-all underslandillg of lite process economics is obtained by all allalysis of a limiting case in zcliell all illfillite lIumber of ext1'aclion slages is used. Fenway Chemical Company Bston, M:!!lrhu!ptt! To: Michael Higgins, Group Leader From: William Sullivan, PreSident As you know, the company is currently operating a batch process for the production of Fenway acid salt in our Back Bay plant. First, Fenway acid is produced by sulfonating Fen-aromol-A with mono­ chlorosulfonic acid. This reaction is carried out in a stirred-tan reactor containing an aromatic solvent. Sodium hydroxide is then 51 52 C/wple y 3 added to the mixture to produce the stable sodium salt of Fenway aCid; this neutralization is necessary to prevent hydrolysis of the sulfonate group. The salt is extracted into water and then amidated to the sodium salt of Brighton acid, the desired end product. Since the aromatic solvent lowers the yield of the amidation step, it must be removed before the reaction can proceed. Moreover, a highly pure aromatic solvent is necessary for the recycle to the sul­ fonator, because water reacts with the monochlorosulfonic acid. This separation is at present achieved by a cumbersome and costly series of washing and stripping operations carried out on each batch of pro­ duct. Since the batch extraction process is currently operated at pea capacity and increases in product demand are anticipated, it is de­ sired to investigate the possibility of a continuous extraction opera­ tion. Your design group is requested to complete a preliminary pro­ cess design that will allow the extraction of Fenway acid to be carried out on a continuous basis. The present batch operation is carried out at 70°C, with a PH in the aqueous phase of 8. Since only a preliminary design is requested, you may wish to restrict your attention to these same conditions. However, the manuacturing technical group has ob­ tained sufficient data to allow consideration of temperatures between 20° and 70°C and of pH values from 8 to 12. The plant has available several agitated kettles that could easily be adapted to a continuous mixer-settler operation for the proposed extraction. Since this eqUipment is currently idle, you are requested to direct at least some attention to a continuous mixer-settler opera­ tion; however, any ideas you may have about other types of processes would also be appropriate. The design requirements for other sections of the process specify the following: 1. Feed to the continuous extraction and purification system (after addition of NaOH to form the acid salt): Aromatic solvent 3, 000 lb/hr Fenway acid salt 680 lb/hr (Plus negligible water which accompanies the NaOH) 2. Product of the continuous extraction and purification system (to be fed to the amidation reactor) : Aromatic solvent 5. 6 lb/hr Fenway acid solvent 666. 0 lb/hr Water I, 995. 0 lb/hr The following sections summarize the data relevant to your design, which have been gathered by the plant technical group. Molecular Weights Although both the Fenway acid and the aromatic solvent are com­ posed of mixtures of several components, the following average mole- Process im/JYocemellt for Liquid-Liquid Extractioll 53 cular weights may be ascribed to these compounds: Compound Sodium salt of Fenway acid Aromatic solvent Water Suggested Nomenclature Molecular weight 246 123 18 A Refers to the sodium salt of Fenway acid B Flow rate of the bottoms or product stream, lb moles/hr C Capacity of a process unit, cu ft D Diameter of a fractionating column, in. f Fugacity, atm F Feed rate to a fractionating column, lb moles/hr J Distribution or partition coefficient, dimensionless L Liquid flow rate in a fractionating column, lb moles/hr nz Mass flow rate of a process stream, lb/hr; or quantity of material present, lb. n Molal flow rate of a process stream, lb moles/hr; or quantity of material present, lb moles S Refers to the aromatic solvent T Temperature, °C V Vapor flow rate, lb moles/hr or lb/hr W Refers to water x Mole fraction in a liquid phase y Mole fraction in a vapor phase ( Per cent of the total Fenway acid salt appearing i the aqueous phase " Activity coefficient Superscripts o Refers to a component in its standard state 54 Chapter 3 Subscripts AS Refers to component A in the solvent phase A w Refers to component A i the aqueous phase D Refers to the solvent content of the bottoms stream from a frac- tionating column s Refers to the aromatic solvent sw Refers to the aromatic solvent in the aqueous phase s s Refers to the aromatic solvent in the organic phase v Refers to the solvent content of the overhead product from a fractionating column w Refers to water ws Refers to water in the organic phase ww Refers to water i the aqueous phase Mutual Solubility Data The mutual solubilities at 20°C of the pure aromatic solvent and water were obtained from the International Critical Tables. They are Water in solvent: 0. 24 g/100 g Solvent in water: 0. 19 g/100 g Liquid-Liquid Equilibrium Data An exerimental program was carried out to establish the relative solubility of Fenway acid in the water and the solvent phases. A 23 factorial program was carried out; the factors and setting levels for these exeriments are as follows: Factor Levels Temperature 20° and 70°C pH 8 and 12 W:S weight ratio 1. 0 and 2. 15 The data obtained from these exeriments are summarized in Table 3-1. Process IlIlprOl'elllelll for Liquid-Liquid Extradioll 55 Table 3-1. Results of the Liquid-Liquid Exraction Studies Experiment I: 20°C;PH = 8; 1l1 w /m s = 2. 15 Aqueous phase Organic phase Component K g mole mole fro K g mole mole fro A 35. 90 0. 146 0. 00818 3. 66 0. 0149 0. 0125 W 318. 6 17. 70 0. 991 0. 585 0. 0325 0. 0272 S 1. 94 0. 0158 0. 00089 141. 2 1. 148 0. 960 356. 4 17. 86 1. 00 145. 4 1. 195 1. 00 Experiment II: 20°C;PH = 8; m w / m s = 1. 0 Aqueous phase Orgaic phase Component � g mole mole fro .I g mole mole fro A 13. 10 0. 0533 0. 00405 3. 10 0. 0126 0. 00617 W 236. 0 13.10 0. 995 0. 991 0. 0550 0. 0269 S 0.873 0. 0071 0. 00054 242. 8 1. 975 0. 967 m 250. 0 13. 16 1. 0 246. 9 2. 043 1. 00 Exeriment III: 20°C;PH = 12; m w /m s = 2. 15 Aqueous phase Organic phase Component � g mole mole fro K g mole mole fro A 33. 4 0. 136 0. 00798 3. 42 0. 0139 0. 0114 W 304. 5 16.90 0. 991 0. 546 0. 0304 0. 0249 S 1. 21 0. 00985 0. 00058 144. 4 1. 175 0. 964 . ¬ 339. 1 17. 05 1. 00 148. 4 1. 219 1. 00 Experiment IV: 20°C;PH = 12; m w /m s = 1. 0 Aqueous phase Organic phase Component � g mole mole fro , g mole mole fro A 18. 39 0. 0748 0. 00565 4.33 0. 0176 0. 00874 W 237. 0 13. 15 0. 993 0. 844 0. 0468 0. 0233 S 0. 563 0. 0046 0. 00035 240. 0 1. 950 0. 969 256. 0 13. 23 1. 00 245. 2 2. 014 1. 00 56 Chapter 3 Table 3 -1. Results of te Liquid-Liquid Extrction Studies (cont.) Exeriment V: 70°C;PH = 8; ml V /ms ~ 2. 15 Aqueous phase Organic phase Component � g mole mole fro I g mole mole fro A 42. 0 0. 171 0. 00972 4. 33 0. 0176 0. 0147 W 313. 0 17. 40 0. 989 0. 537 0. 0298 0. 0250 S 3. 09 0. 025 0. 00142 141. 0 1. 145 0. 960 -- 358. 1 17. 60 1. 00 145. 9 1. 192 1. 00 Exeriment V: 70°C;PH = 8; 111w/n1 S = 1. 0 Aqueous phase Organic phase Component � g mole mole fro I g mole mole fro A 14. 10 0. 0573 0. 00440 5. 50 0. 0224 0. 0107 TV 234. 0 13. 00 0. 995 1. 150 0. 0640 0. 0306 S 0. 825 0. 0067 0. 00051 246. 0 2. 00 0. 958 248. 9 13. 06 1. 00 252. 6 2. 086 1. 00 Experiment VII: 70°C;PH = 12; ml V /ms = 2. 15 Aqueous phase Organic phase Component � g mole mole fro g- g mole mole fro A 39. 2 0. 159 0. 00845 3. 20 0. 0130 0. 0108 IV 336. 0 18. 65 0. 990 0. 480 0. 0267 0. 0222 S 2. 35 0. 0191 0. 00101 143. 0 1. 163 0. 967 -- 377. 5 18. 83 1. 00 146. 7 1. 203 1. 00 Exeriment VI: 70°C;PH = 12; n1 w /m s = 1. 0 Aqueous phase Organic phase Component £ g mole mole fro K g mole mole fro A 14. 65 0. 0596 0. 00474 4. 76 0. 0193 0. 00943 W 225. 0 12. 50 0. 995 1. 19 0. 0661 0. 0323 S 1. 18 0. 00960 0. 00077 241. 0 1. 960 0. 958 240. 8 12. 57 1. 00 246. 9 2. 045 1. 00 Process 11ll/)rOl'emellt for Liquid-Liquid Extraction 57 The Statistics Department has analyzed these data uSing a standard computer program and has obtained the following correlating equation: { = 86. 11 + 9. 82 (: : - 1. 56) - 0. 425 (pH - 10) + 0. 0215 (T - 45) + O. 478 ( m W - 1. 56) (pH - 10) 's + 9. 25 X 10-3 (: s w ¯ 1. 56 ) (T - 45) - 8 X 10-3 (pH ¯ 10) (T 45) + 5.05 x 10-3(: - 1. 56 ) (pH - 10) (T - 45) (3. 1) where mw/m s represents the ratio of the mass of water to the mass of solvent in each batch extraction and { denotes the percentage of the total Fenway acid which is found in the aqueous phase. According to the statistics group, this equation is valid within 90 per cent confidence limits for the ranges of the variables over which the data were taken. Vapo r-Liquid Equilibrium Dat Vapor-liquid equilibrium data were obtained for aqueous solutions contaiing various amouts of aromatic solvent and Fenway acid. These data showed that Fenway acid is vrtually nonvolatile at the temperatures of interest in this problem (approximately 105°C). Data were obtained not only for mixtures containing various amounts of Fenway acid but also for mixtures havng different values of pH in the aqueous phase. As shown in Fig. 3-1, the relative volatility of the sol ­ vent mixture is quite unaffected by the variations in PH and acid con­ centration, and all the data may be correlated by a single line. Cost Correlations ad Desig Instructions The following approximate cost-correlation equations may be use­ ful in evaluating the economics of any of the process designs to be considered: 1. D = 0. 47 (V)1/ 2 2. Cost of distillation tray = $16(D) 3. Cost of reboiler = $470(V ) O. 2 4 4. Cost of condenser = $15(V) O. 6 58 C/apter 3 0.008 I 0.0 7_S)mbl 4 d 0.006 c- • W 0.00 5 Ys 0.004 0.0 3 0.00 2 I 'AW 0_0117 0.0197 0.0117 0.0197 / 0.0 1 / / 0.0002 IpH :/ 8 / 8 12 12 / V / V . + 0.0004 0.0006 0.0008 0.001 'SW Figure 3 -1. Vapor-liquid equilibrium data for solvent-water mixtures containing Fenway acid salt. 5. Cost of miing tank = $150(C) o.6 6. Cost of settling tank = $40(C )O. 7 7. Cost of liquid pumps = $300(m)O .07 where D = distillation column diameter (in.) , V = vapor rate (lb/hr), C = capacity of item (cu ft), m = mass flow rate (lb/hr) , 8. Cost of controls for a mixer-settler combination = $3,000/ extraction stage. It is to be noted that these equations yield estimates for the uninstal­ led equipment costs. The installed equipment cost may be approxi­ mated by multiplying the uninstalled cost by four. Altough the residence time in the mixer-settler equipment will eventually have to be ascertained by a detailed mass transfer analy­ sis, the following approximate values may prove useful for prelimin­ ary desig calculations: mixer residence time = 10 minutes, settler residence time = 20 minutes. At these values of residence time, an over-all stage efficiency of 100 per cent may be assumed. Reference (7) may be consulted for a discussion of the factors that may affect the efficiency of mixer-settler units. An average specifiC gravity of 1. 18 for the two-phase mixture may be used in computing the required equipment capacity. Low-pressure steam is available at $0 . 80/1000 lb, and cooling­ water charges are approximately $0.02/1 000 gallons. The cooling water is available for 80°F, and it is desired to maintain the tempera­ ture rise of the cooling water at values below 40°F. PYocess ImpYOl'eIllCII/ foy Liqllid-Liqllid Extractioll 59 PREPATION OF A PRELMIARY DESIGN Exmiation ad Evalution of Exerimental Data Before proceeding with an analysis of preliminary process de­ signs, an examination and evaluation of the exerimental data is in order. One important factor in determining the process economics will be the extent to which water and the aromatic solvent are mutual­ ly soluble. The mutual solubilities will be particularly critical, since the final product specifications allow only a small amout of solvent in the aqueous extract that is fed to the amidation reaction step. Any excess solvent must be removed, and this should probably be accom­ plished by a stripping or distillation process. The original memorandum indicates that at 20°C water is soluble in the solvent to the extent of 0. 24 g/100 g and the solvent is soluble in water to the extent of 0. 19 g/100 g. Ater converting these values to a molar basis, it is useful to compare the mutual solubilities of the pure solvents with those obtained from the liquid-liquid extraction studies in which the acid salt was present. This comparison is imple­ mented i Table 3-2. Table 3-2. Mutul Slubilities of Water and the Aromatic Slvent Exeriment Temp.oC pH nl w /m s x sw x ws Pure solvents 20 7 0. 00028 0. 0161 (lit. values) I 20 8 2. 15 0.00089 0. 0272 II 20 8 1.0 0. 00054 0.0269 II 20 12 2. 15 0. 00058 0.0249 IV 20 12 1.0 0. 00035 0. 0233 V 70 8 2. 15 0. 00142 0. 0250 VI 70 8 1. 0 0. 00051 0.0306 VII 70 12 2. 15 0. 00101 0. 0222 VII 70 12 1. 0 0. 00077 0. 0323 The data at 20°C reveal that the presence of the acid salt and the variations in pH have only a modest effect on the mutual solubilities of the two solvents. At constant temperature, the variations in pH and salt concentration do not appear to produce any Signiicant or consis­ tent changes in the mutual solubilities. The scatter in the data ob­ tained at 70°C may arise from difficulties in maintaining accurate temperature control at the higher levels of temperature. For the pur­ pose of a preliminary design, the effects of PH and salt concentration will be neglected, and average values of the mutual solubilities will 60 CI/pter 3 be assumed to apply at each temperature level. These mean values of x s w and x w s are as follows: Temperature xsw x ws 0.00059 0.0256 0.00093 0.0275 After the design has been completed, it will be important to inves­ tigate the effect of variations in the values of x sw and xws on the estimated process economics. If variations of the magnitude shown in Table 3-2 are found to affect the estimated financial return signifi­ cantly, a more exact exerimental determination of the mutual solu­ bilities would be required. Consideration of the Liquid-Liquid Equilibrium Data The application of factorial experiments is a very powerful tech­ nique in obtaining and correlating experimental data for design work. Using statistical methods, a great deal of information may be gathered by expending only a minimum of exerimental time and effort. These methods are particularly helpful when the theoretical basis of a pro­ cess operation is poorly understood. References (J, 3, 4,5) serve as an excellent introduction to statistical designs and their application to practical chemical engineering problems. By use of statistical methods, Eq. 3. 1 has been derived as the proper correlating equation for the exerimental results show in Table 3-1. This equation relates the fraction of the total Fenway acid found in the aqueous phase to variations in the temperature, pH, and amounts of solvent present. Its use in carrying out design calculations presents two very Significant difficulties. First, the validity of the equation is limited to the ranges of the variables for which the ori­ ginal data were obtained. It is quite possible that the design specifi­ cations will require the application of the correlating equation well beyond the range of variables for which the data were taken. For ex­ ample, the ratio of water to solvent was varied by only a factor of 2 in the laboratory exeriments, and it is unliely that the optimum con­ tinuous process would happen to correspond to solvent flow rates in this range. Application of the equation outside these limits would be quite risky and could lead to highly erroneous conclusions. The second difficulty, somewhat related to the first, results from the poor selection of variables that were used in setting up the ex­ perimental design and in expressing the experimental results. The selection of temperature and pH as variables appears to be reasonable; however, the use of the ratio mw/ms has no reasonable basis, and the quantity ( does not appear to be an appropriate form of the response variable. For example, if very large values of 1I1W/1I1S (outSide the range of the original data) were inserted in Eq. 3. 1, values of ( > 100 per cent could be obtained. This sort of physical impossibility might Process Improvement for Liquid-Liquid ExlYaclion 61 have gone unnoticed i the equation had been combined with other alge­ braic expressions. In view of these observations it is worthwhile to search for a more satisfactory basis of expressing the experimental results before proceeding with the design considerations. In a thermodynamic system in which a solute is distributed between two immiscible solvents, equilibrium will be obtained when the chemi­ cal fugacity of the component in one phase becomes equal to the fugac­ ity of the same component in the other phase. Wen this concept is applied to the present case, which in turn may be exanded as fA�'AlVxAlV fAos 'AS xAS Therefore, at equilibrium one obtains (3. 2) Now fO, the fugacity of a component in its standard state, is independent of composition, and at constant temperature Eq. 3. 2 may be written as (3.3) In dilute solutions, the activity coefficients may be assumed to be in­ dependent of concentration, and a further simplification is effected, whereby (3.4) The quantity] is termed the distribution or partition coefficient, and Eq. 3. 4 is conventionally know as Nernst's law. It proves quite use­ ful in correlating the results of liquid-liquid extraction exeriments. It is to be recognized that the distribution of Fenway acid between the two phases is not determined solely by physical phenomena. Since a neutralization reaction is also takig place, the simple form of Eq. 3.4 is not strictly applicable. However, as an initial approximation, it may result in a data correlation that will be useful for preliminary design calculations. Casting the data of Table 3-1 in the form suggested by Eq. 3. 4 results in the data listed in Table 3-3. They indicate that the parti- 62 Clapter 3 Table 3-3. Liquid-Liquid Exerimenta Data Expressed in the Form of a Partition Coefficient Experiment Temperature,OC pH K = X A W/X AS I 20 8 0. 655 II 20 8 0. 656 II 20 12 0. 699 IV 20 12 0. 647 V 70 8 0. 661 V 70 8 0. 411 VI 70 12 0.782 VIII 70 12 0. 503 tion coefficient is independent of pH and the relative amounts of sol­ vent. The average value of the partition coeficient at 70°C is 0.590, while that at 20°C is 0.663; only a 10 per cent variation is found over a 50°C variation in temperatre. This is probably not satistically sigiicant in view of the scatter in the data at the higher temperatre level. Therefore, Eq. 3-1 may be discarde, and the liquid-liquid extraction data may be exressed in terms of a single average value for the partition coefficient, 0.63. Since the partition coefficient has been found to be quite invariant over a wide range of exerimental conditions, the designer may use this value conidently for vrtually any desig condition. This broad application would not have been possible i the design calculations were to be based on Eq. 3-1. The results of this discussion emphasize the need for god judg­ ment i the selection of the proper method for correlatig exeri­ mental data. The use of statistically desiged exriments is an i­ vluble aid, but it is not a substitute for a meanigul analysis of a problem. I should b pited out tat the results of the ty show i Table 3-1 are convntionally correlated in the form of a tringlar diagram as illustrated by Hougen, Watson, and Ragatz (). However, i the present situation the concentrations of te solute are s small that a triaglar diagram would be neither meaningul nor useful. Vapor- Liquid Equilibrium Data The vapor-liquid equilibrium data appear to be well presented and properly correlated. Figure 3-1 should be directly applicable to the design calculation. In particular, the relative invariance of the rela­ tive volatility with changes in pH and Fenway acid concentration is a very convenient feature of the data and will grea tly reduce the re­ quired computational effort. Process Improvemellt for Liquid-Liquid Extractiol/ 63 PRELIAY PROCES DESGN CALCULATIONS To produce a Fenway acid product having the specified purity, a process must accomplish the following obj ectives: 1. Extract the acid salt from the aromatic solvent. 2. Remove the aromatic solvent from the aqueous acid salt solution prior to the amidation step. Since the original memorandum specified that a continuous mixer­ settler design should be conSidered, a process of the type shown in Fig. 3-2 should be appropriate. In this design scheme, the feed stream containing the crude Fenway acid salt is mixed with recycle and auxil­ iary water, and the combined stream is metered continuously into the Feed stream A' 680 Ib/hr 5' 3,00 Ib/hr Organic phose RofflOQle streom (Solvent recycle) A' 141b Ihr W' S' 2,994.4lb/hr Auxillory water Organic phose Aqueous recycle Aqueous exlract Figure 3-2. Block flow diagram of a one­ stage continuous extraction process. mixer. The effluent from the mixer is separated into organic and aqueous phases in the settler. The small amount of dissolved organic solvent in the aqueous phase is removed by a stripper from which the final desired product is removed. It is important to note that the aqueous stream fed to the stripper is saturated with organic solvent, ad further that the mutual solubility of the water and solvent is quite insensitive to temperature vriations. Therefore, i a rectiying sec­ tion were added to the stripper, all the plates i such a section would contai a two-phase liquid and no enrichment could be effected. For this reason, the process will have to be designed so that the desired product purity can be achieved by using only a stripping section. The overhead product from the stripper is condensed and separated. The 64 Chapter 3 aqueous phase from the condensate settler serves as the recycle water stream and is returned to the mixer , while the organic streams leaving both the first and second settlers are combined, sent to a de­ hydration still, and returned to the sulfonation reactor. The present design will consider all aspects of the separation pro­ cess except the dehydration unit for the aromatic recycle; the costs associated with this latter operation are not expected to be signiicant. As a first consideration, a design will be analyzed that incorporates one mixer and two settlers, as shown in Fig. 3-2. Clearly the econo­ mics of the process design could be altered Signiicantly by the use of additional pairs of mixers and settlers. This concept will be ex­ amined in a later stage of the analysis. Depending upon the number of stages required by the mixer-settler operation, one might wish to consider the use of an extraction column. Again this decision will be deferred until the computations for the preliminary mixer-settler de­ sign cases have been completed and analyzed. As a further initial ap­ proximation, the process will be assumed to operate at 70°C and a pH of 8. However, j udging by the results shown in Table 3-3, variations in these parameters would not be expected to affect the economics of the process seriously. The analysis of the design shown in Fig. 3-2 proceeds in a man­ ner quite analogous to that for most separation unit operations-by the alternate application of material balance and equilibrium relation­ ships. First of all, the composition of the recycle stream may be established partially by over-all material balances on components A and S: A lost in recycle of organic solvent = 680 - 666 = 14 lb / hr S in recycle = 3, 000 - 5. 6 = 2, 994. 4 lb / hr No over-all balance in water is yet pOSSible, since the flow rate of the make-up water stream has not yet been determined. Focusing attention on the mixer-settler unit, i equilibrium is at­ tained, the relationship summarized by Eq. 3-4 may be assumed valid: ( . nAI ) xA W nAI + nsl + nl -= = 0. 63 xAS /lAS (nAS + /lws + nSS ) (3.5) The quantities designated by / l represent the molal flow rates of the streams leaving the mixer-settler combination. As a first approximation, the mutual solubilities of water and solvent may be assumed to be negligible. The validity of this approximation will be determined by a second iteration on the calculation. Equation 3. 5 may be rewritten as: (3. 6) Process Improvement for Liquid-Liquid Extraction 65 where n ss = 3,000/123 = 24. 4 lb moles/hr nAW = 666/246 2. 71 n AS = 14/246 = 0. 057 Therefore, nww = 2. 71 ( 429 - 1) 0. 63 = 1, 841 lb moles/hr or mww = 33,200 lb/hr With this initial approximation it is possible to account for the mutual solubilities of water and solvent. In the analysis of the exeri­ mental data taken at 70°C, the following mutual solubility values were established: Xs w = O. 00093 xws = 0. 0275 Now the following values may be computed: nsw = 0. 00093 (2. 71 + 1,841 + 1sw) � 1. 72 lb moles/hr 111 sw = 212 lb/hr nws = 0.0275 (24. 4 + 0. 057 + nws ) I l ws = (24.46) (0. 0275) /0. 9725 = 0. 692 lb moles/hr mw s = 12. 5 lb/hr With these values, the final material balance on the process may be established: n ss = 24. 4 - 1. 72 = 22. 7 lb moles/hr n ww = 1841 - 0. 692 = 1840 lb moles/hr The auxiliary water stream may now be determined approximately by an over-all material balance as: Aux. water � 1995 + 12. 5 = 2007 lb/hr = 111.6 lb moles/hr and the recycle water is established as Recycle water = 1,841 - 111. 6 = 1729 lb moles/hr = 31, 200 lb/hr 66 ClzapLer 3 The feed to the strippig column may now be tabulated: Component lb moles/hr lb/hr A W S 2. 71 1840 1. 72 666 33,100 212 and the vapor feed to the condenser may be approximated from a material balance calculation: Component lb moles/hr lb/hr A W S o 1729 1. 68 o 31,200 206. 4 As a further step in the calculation, an approximate material balance on the condensate settler results in: n sw = 0. 00093 (1729) ¬ 1. 61 lb moles/hr ns = 1. 68 - 1. 61 = O. 07 lb moles/hr Now that the approximate flow rates of all streams have been estab­ lished, a second iteration in the calculations should establish the flow rates with sufficient validity for a preliminary economic evaluation. First, the amount of solvent in the organic phase is recomputed, taing into account the solvent in the recycle water stream: nss = 24. 4 - 1. 72 + 1. 61 = 24. 3 lb moles/hr ^ 2990 lb/hr And the water flow rate in the aqueous phase is established as: [1 + (24. 3/0. 057) ] I l w w = - 1. 0 0. 63 2. 71 = 1, 832 lb moles/hr ¬ 33, 000 lb/hr Pursuing the calculation procedure utilized previously: I l sw ¬ 0. 00093 (2. 71 + 1,832 + IZ s w) � 1. 706 lb moles/hr In sw = 210 lb/hr (0. 0275) I l ws = (24. 3 + 0. 057) - = O. 688 lb moles/hr 0. 9725 111 W S = 12. 4 Ibs/hr Process /1II/JrOL'Clllelll for Liq/lid-Liquid Exlraction 67 Aux. water = 1, 995 + 12. 4 = 2, 007 lb/hr = 111. 6 lb moles/hr Recycle water ^ 1, 832 - 111. 6 = 1720 lb moles/hr = 31, 000 lb/hr The second approximation of the feed to the strippig column is delineated i Table 3-4. Table 3-4. Feed to te Strippig Colum Component lb moles/hr ;V lb/hr A 2.71 .0014 7 666 W 1831 . 99 76 33,000 S 1. 706 . 00093 210 Total 1835.416 1. 00 The iterative procedure could be pursued, but the values tabulated do not deviate Significantly from those obtained in the first iteration. The material balance calculations have now been completed. Stripper Desig The feed to the stripper is specified by Table 3 -4, and the minimum requirement for product purity is shown in Fig. 3-2. Since most of the aromatic solvent will be taken overhead, the following molal flow rates are readily established: F = L = 1835. 4 lb moles/hr V = 1721. 7 lb moles/hr B = 113. 7 lb moles/hr and a material balance on the solvent yields 1. 706 = 1721. ty v + 113. 7X B (3. 7) Now, there are limits to the values that can be assumed by xB• The maximum tolerable value of x B is specified as 0. 0004, and from Eq. 3. 7 the corresponding value of)' v is 0. 000965. At the oter extreme, if infinite stages were used, x B would be 0 and)' v would rise to 0. 00099. Clearly this range of concentrations does not allow a sig­ nificant variation in the usage of steam; the boil-up rate is essentially fixed by an over-all stripper balance which in turn results from the specification of a one - stage extraction process. This being the case, the stripper in this instance is designed to minimize its capital cost; i.e., only one ideal stage is utilized. Based upon one stage and an L/V ratio of 1,835.4/1, 721. 7 ¬ 1.067, the McCabe-Thiele diagram for the stripper design is shown in Fig. 3 -3. 68 Glza/)ie)' 3 0.008 0.007 0.006 0.005 Ys 0.004 0.003 0.002 2) Two·s109f case L/V. 1.85 3) Oneos1oQe cose L/V. 1.067 O.OI c� 0 0008 0 01)10 Figure 3-3. McCabe-Thiele construction for the closed steam strippers used in three extrac­ tion cases. (Trial and error was used to ob­ tain an integral number of stages for each case with x B " O. 0004.) The following compositions were derived by trial and error from this figure and from Eq. 3. 7: XB = 0. 000105 Yv = 0. 000983 Qualitatively this result means that the large amount of water that must be removed and the high relative volatility of the system cause virtually all the aromatic solvent to be taken overhead in the stripper. Actually, the material balance for the mier-settler units might be modiied to include this change in flow rate, but such a computation is probably not worthwhile. SUMMAY OF TH MATEIAL BALANCE A STIPPER CALCULATIONS As mentioned before, the process shown in Fig. 3-2 may be modi­ fied by using multiple mixer-settler units. Clearly the addition of such units will decrease the required quantity of recycle water and the corresponding steam usage. Figure 3-4 shows a three-stage mier-settler process; an extension to other deSigns is obvious from this figure. Iterative material-balance calculations and stripper designs have been completed for extraction processes having one, two, and three PYocess Improveme1lt foy Liquid-Liquid Ext)-actioJl 69 Mixer· sellier NO.t Mlxer­ sertler No.2 Mixer­ sertler NO.3 Roffinote stream (Solvent recycle) Auxiliary water Aqueous recycle Aqueous extract Condensole sellier Stripper Product stream Figre 3-4. }'low diagram for a three­ stage extraction process. stages. The computations for multiple extraction stages are quite analogous to those already presented for the single-stage extraction. The calculations for the stripper designs are summarized in Fig. 3-3. In the stripper design for the two-stage extraction, a situation arises which is analogous to that encountered in the stripper design for the one-tage extraction; i.e. , the upper and low limits on Yv are nearly equivalent. As before, a stripper having one ideal stage is indicated. However, in the stripper design for a three-stage extraction process, the limits on Yv vary from O. 0049 to O. 0079, and a suboptimization is required for the rigorous determination of the desired number of stripper stages. Even so, in this instance the capital and operating costs for the stripper are so minimal that the number of stripper stages may be arbitrarily selected within the limits on ,. v set by the material balance. As such, the L/V ratio in this case has been varied by trial and error until conditions for two ideal stages have been established. As indicated in the original memorandum, a stage efficiency of 100 per cent is assumed in the mixer-settlers. In the case of the strippers, a more conservative and realistic value of 50 per cent is assumed for the over-all stage efficiency. Usig these efficiencies, one obtaino the results summarized in Table 3-5. 70 Chapter 3 Table 3-5. Results of Desig Calculations for Cases Havng One, Two, ad Three Exraction Stages Number of extraction stages, n 1 2 3 Water recycle rate, lb/hr 31,000 2,473 255 Auxiliary water, lb/hr 2,007 2,007 2,007 Total water rate, lb/hr 33,007 4,480 2,262 Vapor rate in stripper, V,lb/hr 31,000 2,480 265 Stripper overhead composition, Yv 0. 000983 0. 00160 0. 00505 Solvent content of product, xB 0. 000105 0. 00018 0. 000295 Number of trays in stripper 1 1 3 Number of pumps required 6 9 12 With this information, it is a simple matter to implement the de ­ sign criteria presented in the original memorandum and to estimate the capacities required for the mixer and settler units and for the stripping columns. The capital costs for process equipment then fol­ low directly from the cost-correlation equations available in the memorandum. After the caital estimate, the principal operating costs for these design cases may be established. The major direct opera­ ting costs are those for steam and cooling water; from the information supplied in the memo, these costs may be estimated as Steam cost ¬ 6. 4 V dollars/year C IV cost ¬ 0. 48 V dollars/year where V is the vapor rate in the stripping unit exressed i lb/hr. The results of all the preliminary economic calculations are listed in Table 3-6; it should be noted that operating costs such as labor, overhead, and maintenance are not shown. However, the maj or vriable operating costs have been taen into account, and calculations of the type shown provide a reasonable basis for comparing various process alternatives. OPTMIZATION OF THE MIER-SETTLER PROES Table 3-6 indicates that the economics of the proposed extraction process are a very strong function of the water-recycle rate. It appears that additional economies could be effected by further re­ ductions in the water flow rate with corresponding increases in eqUip­ ment capital costs. In the limit, i an infinite number of stages were used, the following implementation of Eq. 3. 6 would apply to the first Process illlprOl'emelli for Liquid- Liquid ExiYaclioll 71 Table 3-. Economic Evaluation of Processes Having One, Two, and Three Extraction Stages Numbr of exraction stges, I 1 2 3 Ca2ita cost estimate No. Item , Mier $2,130 $1,726 $2,136 , + 1 Settlers 2,880 1,500 1,600 1 Reboiler 5,640 3,060 1,800 1 Condenser 7,400 1,635 430 3(1 + 1) Pmps 3,760 5,080 6,620 Fi. 3-3 Trays 1,300 374 390 n Controls 3,000 6,000 9,000 Total purchased equipment 26, 110 19,375 22,106 Total installed equipment $104,440 $77,500 $88,424 Oerating cost estimate Depreciation, 15 per cent $15,680 $ 11, 600 $13,300 Steam, 6. 4 V 198,500 15,900 1,700 Cooling water, O. 48V 14,900 1,190 130 Total operating cost, $229,080 $28,690 $15,130 dollars/year mixer-settler stage (the stage to which the fresh Fenway acid-sol­ vent mixture is fed): 1 + (3,000/123)/(680/246) ¬ 0.63 1 + n w w/(666/246) Solving this equation shows that a minimum water flow rate of 39. 6 lb moles/hr or 713 lb/hr is required to complete the separation, even if an infinite number of stages is utilized. Since this value is less than that required in the fial product, it is clear that the amount of auxiliary water will have to be reduced when the use of larger num­ bers of stages is to be examined. In such instances, make-up water could be added to the product stream after the stripping has been com­ pleted. It may be show quite easily that, i more than three extraction stages are used, a water flow rate of less than 2007 lb/hr will be re­ quired and a corresponding decrease in the auxiliary flow must be effected. 72 ClwjJ/er 3 In order to complete the selection of the optimum process, cal­ culations have been carried out for four- and eight-stage extraction processes. For these conditions, the following results have been ob­ tained. Number of extraction stages, n 4 stages Total water flow rate, lb/hr 1565 8 stages 1000 In both systems, the water flow rate is reduced far below that re­ quired in the final product stream. The present calculations assume that the solubility of Fenway acid salt is not being exceeded. The validity of this assumption will have to b checked i any processes having a large number of stages appear economically significant. Since direct operating expenses are negligible for the four- and eight-stage operations, the fiancial evaluation for them is straight­ forward. Combining these evaluations with those summarized in Table 3-6, the process economics have been optimized according to Fig. 3-5, which shows that either a three- or a four-stage unit could be used with comparable economic results. In order to avoid any problems that may result from exceeding the solubilities of the Fen­ way acid salt, the three-stage unit is a good selection for this pre­ liminary design. ! i � � � ! � M P O � + + 4~~~ " * *¯ ¯ ¯ ° 1-(0 •• fÝÍ!Û¹!ÛÜ c.,,, I __Steam and coollng"wa,er costs Totol woler flow rote t Ib Ihr Figure 3-5. Financial evaluation of te extraction process. SUMMAY OF THE DESIGN RESULTS The results summarized in Fig. 3-5 indicate that the required separation could be accomplished by a three-stage mixer-settler process scheme. The required capital outlay would be approximately Process Improvement for Liquid-Liquid Extraction 73 $88, 000, and the computed annual operating cost for the extraction process is about $15, 000, which corresponds to $0. 003/lb of acid salt. As mentioned previously, this operating cost does not include several important items, such as labor, overhead charges, equipment maintenance, and solvent losses. I particular, the cost of solvent losses is often quite an important contributor to the operatig costs of an extraction operation. I the additional cost items were included, the resulting total conversion cost probably would approach $O. Ot/lb -a value close to those usually incurred for the type of extraction operation being considered in the present case. Since most of the additional costs are quite insensitive to the number of extraction stages, it is unlikely that the inclusion of these factors would cause a significant alteration in the optimum process design tat has been selected. Since only three mixer-settler stages are required, it is doubtful that a liquid-liquid extraction column would have any significant ad­ vantages over the proposed design. However, Table 3-6 shows that the cost for controlling the mixer-settler operation represents a large fraction of the total capital investment. This investment might well be reduced by use of an extraction column; this possibility should be examined in subsequent design calculations. Some assumptions made in the preliminary design analysis should also be investigated in later, more detailed design efforts. First of all, the residence-time values used in sizing the mixing equipment should be recalculated. The values used are thought to be reasonable, but they and the corresponding estimates for efficiency should be re­ estimated using literature values of the mass-transfer coefficients and settling times that are correlated for equipment of the type pro­ posed for the present process. Such calculations would bp !artir1l1�r­ ly important because depreCiation charges constitute a major portion of the total conversion cost. A second assumption, implicit in the siz­ ing of the mixing and settling equipment, was that little or no difficulty would be encountered in separating the phases; i.e., the two phases are not easily emulsified. Evidently no dificulty of this type was encountered in the laboratory. However, small amounts of surfactants in the plant water system could cause substantial difficulties in the commercial operation. This possibility needs to be studied thorough­ ly before finalizing the design specifications. A third assumption was that of constant mutual solubilities of the two solvents. I solvent losses prove to be an important economic factor, it may be worthwhile to establish these values more accurately. However, since both the capital and operating costs for the stripper are quite small in the optimum process, there does not appear to be much j ustification for further exerimental work at this stage in the design. In summary, it is felt that the preliminary economic evaluation calculations summarized in Fig. 3-5 have very likely established the optimum design scheme. The clarification of some of the assumptions and the inclusion of some of the costs not yet determined may alter the size of the equipment and the operatig costs for the ultimate pro­ cess. However, it is unliely that any of these factors will cause the 74 Chapter 3 optimum type of flowsheet to be greatly different from that of the three-stage unit here established. REFERENCES 1. Atkinson, A. C., Cher. Eng. 73, No. 10, 149 (1966). 2. Hougen, O. A., K. A. Watson, and R. A. Ragatz, Chemical Process Principles, Part I, John Wiley & Sons Inc. , New York (1954). 3. Hunter, J. S. , Chem. Eng. 73, No. 7, 111, (1966) . 4. Hunter, W. G. , and A. C. Atkinson, Chem. Eng. 73, No. 12, 159 (1966). 5. Hunter, W. G. , and M. E. Hoff, Ind. Eng. Chem. 59, Noø 3, 43 (1967). 6. Sherwood, T. K., and R. L. Pigford, Absorption and Extraction, McGraw-Hill Book Company, Inc. , New York (1952). 7. Treybal, R. E. , Mass Transfer Operations, McGraw-Hill Book Company, Inc. , New York (1955). 4. Catal y tic Reactor Design for Benzene H y drogenation This case examines set'eral process allemalil:es for hydrogellalillg ben wile /O j)rodllce cyclohexalle. The highly exolheYillic nature of Ihe Yeaclioll necessi/ales Ü cOllsideration of alleY/la/h'e lIlelhods of 1'e­ JJ/o1'ing /he heat of 1"eaction. While liIlle cOllsideralioll is gil.'ell to eualliatillg the ecollomics of the variolls processes considered, primar), emphasis is placed on a deterlllillation of tile imjJOrtant deS(1/ l'ari­ abIes alld on a prelimillary selection of all appropriate reactor COIl­ figuration. ExtensiL'e lise is made of illterpolatil/g betll'eell alld extra­ polatillg frolll Ü felt' des(1Z condiliolls tllal are treated ill detail. lVi/h­ ill the lim it s of tile a/>proxilllaliolls IIsed, Û prelim illary desigll scheme is selected. Cher-Fiber Cororation Houston, Texs To: Fred Schwartz, Process Desig From: Ciyde Fox, Group Leader Rc: Cyclohexane Production The planned exansion of the company's nylon production will re­ quire an additional 40 million lb/year of cyc10hexane as a raw mate ­ rial in the manufacture of adipic acid. Primary consideration is being given to the possibility of buildig a new plant to product cyclo­ hexne by the catalytic hydrogen3tion of benzene. Your Process Desig group is asked to prepare a preliminary design for the hydro­ genation process. At this early stage it would be most desirable to develop the basic equipment requirements. 1b /0 Clapler 4 For the time being it will not be necessary for you to complete an economic evaluation of the process. The Market Research group is currently negotiating with raw-material suppliers as well as with possible outside sources of cyclohexane. When this group has assem­ bled the appropriate market information, the process recommended by your group will be evaluated. In this way a decision regarding the i-house manufacture of cyclohexane can be made. The Research Laboratory has come up with a new catalyst that seems to be as good as or better than any we might buy or license. This catalyst is basically nickel on alumina and would be provided in the form of 3/16-in. pellets at a cost of $1. 40/lb (bulk density 88 lb/ cu ft). It is rugged and can be regenerated by burning off the carbon in inert gas containing abut 1 to 2 per cent oxygen. The laboratory has made a thorough study of the performance of this catalyst, using bench-scale flow reactors. The results obtained confirm the literature reports for platinum, palladium, and nickel ¦)¸4¸ ¯¿ S)¡the hydrogenation has been found to be first-order in hydrogen pressure and zero-order in both benzene and cyclohexane. The activation energy is found to be 12 Kcal /mole, confirming the literature data. Results from a representative laboratory test are attached. The reaction proceeds readily to clean and complete conversion of the benzene to cyclohexane, with only small amounts of byproducts, such as methylcyclopentane. The design problem hinges on the fact that the reaction is highly exothermic and must not be allowed to "run away." Designs must be developed to maintain stable operation at an appropriate temperature; your group is asked to determine the best approach to the deSign. The Process Development group recommends that the tempera­ ture of the reacting gases be held to a maximum of 6000K because hydrocarbon decomposition resulting in excessive carbon deposition occurs at higher temperatures. Carbon deposition also appears to result from high pressures, although high pressure helps the con­ version. For the present, plan on a maximum pressure of 150 psia. DATA A ASSUMPTIONS Summar y of a Representative Labrator y Run The reactor was a tube of 1. O-in. i.d. contaiing a ²J_-in. o.d. axial thermowell. The annulus was packed from a length of 36 in. with the 3 / 16 -in. nickel-on-alumina catalyst pellets. The reactor was wound with heating tape and the resistances so adjusted that the reactor operated adiabatically. In one representative test the hydrogen and vaporized benzene were preheated and fed to the reactor at 227°C. The benzene feed rate was 620 g/hr, and the molal ratio of hydrogen to benzene ÎH the feed was 10/1. The total pressure was 10 atm. The liquid product collected in a dry-ice and acetone trap was found to contain 0.798 mole fraction benzene and 0.202 mole fraction cyclohexane. L0!0!yÍÍC Û00CÍOI L0SÍg ¯¯ The Research Laboratory suggests that the work of Amane and Par·· ravano [J),Kassel (5)¸and Smith [/} be consulted in order to provide additional insight into the reaction kinetics for the vapor-phase hydro­ genation of benzene. In addition, the work of Smith and Meriwether (8) is helpful in that it presents results for the liquid- phase hydro­ genation. Finally, the text of Grifith and Marsh (4) provides an excel­ lent discussion of the hydrogenation mechanism H terms of the geo­ metrical characteristics of various catalysts. Mass Transfer to and Difusion Withi Catalyst Pellets It should be noted that the effects of mass transfer to the catalyst pellet surface and diffusion within the catalyst pellet have been analyzed. It has been found that neither of these afects the observed results significantly. Thermodynamic Data (From American Petroleum Institute, "Selected Values of Physical and Thermodynamic lroperties of Hydrocarbons, " Project 44, Carnegie Press, Pittsburgh, Pa.1953.) Cyclohexane Alf H¬H� T,oK Kcalg mole gcal/g mole log l O / ) 0 -20. 01 0 298 -29.43 4, 237 5.5605 400 -31. 70 7,352 -11. 2861 500 -34.08 11,425 -14.8932 600 -35. 57 16, 404 -17.4318 700 -36.59 22, 148 -19.3103 Benzene 0 24.00 0 298 19.82 3, 401 -22. 7143 400 18.554 5, 762 -19.1271 500 17.536 8, 750 -17.1521 600 16.711 12, 285 -15.9040 700 16.040 16,267 -15.0519 ¯o Claptey 4 Hydrogen 0 0 298 2,024 400 2, 731 500 3,430 600 4, 130 700 4, 832 Heats of Vaprization Benzene at 298°K: 8030 cal/g mole Cyclohexane at 298°K: 7895 cal/g mole Raw-Material Values The raw-material costs are subject to the results of current negotiations. However, the following approximate prices may be use­ ful: Benzene: $0.04/lb Hydrogen: $0.40/MSCF Oeration The process should be operated 8000 hr/year. Suggested Nomenclature Ï h All! k Activation energ for the hydrogenation reaction, equal to 12 Kcal/ g mole Equal to exp (12, OOO/RT) evaluated at absolute tempera­ ture T Temperature interval used in the evaluation of an integral by Simpson's Rule, oK Molal enthalpy of component l, g cal/g mole Molal enthalpy of a compound or element in the gas phase at any temperature when the molal enthalpy of the compound or element is taken to be zero at a temperature of OOK, g cal/g mole Isothermal enthalpy change for the formation of a pure com­ pound from its elements at any temperature, g cal/g mole Reaction rate constant, lb mole/(hr) (atm) (cu ft of catalyst bed) Ï Ñ P: Q ? Ù 1 V B W 7 LuluÎ]ÍÍC Reactor Dcsi¿~t /9 Pre-exonential factor, lb mole/(hr) (atm) (cu ft of catalyst bed) Equilibrium constant for the formation of a compound from its elements at any temperature, dimensionless Total catalyst bed length, ft Moles of hydrogen per mole of benzene in the feed stream Molal flow rate of component Í in a catalytic reactor,lb moles/hr or g moles/hr Partial pressure of component l¡ atm Rate of heat exchange between a thermodynamic system and the surroundings, g cal/hr Rate of benzene hydrogenation, (lb mole benzene reacted)/ (hr) (cu ft of catalyst bed) Universal gas constant, equal to 1. 985 g cal/(g mole) (OK) Absolute temperature, oK Volume of catalyst bed, cu ft Rate of work interaction between a thermodynamic system and the surroundings, g cal/hr Distance from the inlet of a reactor, ft Fraction of benzene converted to cyclohexane Total pressure, atm Subscripts Ö L Ï D 1 X 0 J¡´,´¡ 1:¹ Refers to benzene Refers to cyclohexane Refers to a condition in the feed stream to a reactor Refers to hydrogen Refers to a condition i the product stream from a reactor tube of length Ï Refers to a condition in a reacting stream at a distance 7 from the inlet of the reactor Refers to conditions in the feed stream to reactor 1 in Fig. 4-4 Refer to the reactors identiied by these numbers in Fig. 4-4 Superscripts , (prime) Refers to an intermediate feed stream as shown in Fig. 4-4. 80 Clwp/er 4 AALYSIS OF LABORTORY KETIC INFORMATION Before proceeding to the reactor design, it is necessary to analyze the kinetic data obtained in the laboratory. The kinetic constants ob­ tained from the analysis may then be used in the subsequent design calculations. The chemical reaction that takes place in the reactor is as follows: O + 3H2�O 4. The use of the stoichiometry of Eq. 4. . helps D tabulating the flow and enthalpy quantities in the manner shown in Table 4-1. This sort of table is useful in accurately preparing the heat and material balances necessary for the data analysis and design calculations. Table 9-1. Molal Flow Rtes ß0 Enthalpies Basis: . mole feed Compound Feed Hydrogen .... Benzene .... Cyclohexane .. Total ... At conversion . ...... .... . .... . ..... Ö Ü ..... . Molal enthalpy '' º �I H (H ¬ H+ Alj}B |l/ ¬1l + Al) J L An approximate calculation of the compressibility factor for the gas mixtures under consideration indicates that the ideal gas law may be used with negligible error. Therefore, at any position 7 in the reactor tube the partial pressure of hydrogen may be exressed as .. For the particular conditions of the laboratory exeriment, wherein a hydrogen/benzene molal feed ratio of .. was used, Eq. 4. . reduces to ¸..... ..... .¸ Í) ¬ Ü . ...... (4.3) where . denotes th� degree of conversion of benzene to cyclohexane. It is useful to evaluate the hydrogen partial pressure of the inlet and outlet streams of the laboratory reactor. Since Ö has a value of unity Catalytic Reactor Desi 81 for the feed and a value of O. 202 for the product stream, the hydrogen partial pressures are computed as P F ~ 0.9091 Ü atm P _ _ ¯ O. 9091 - 0.2727 (0. 202) Ü ¯ 0.903 Ü atm 1. 0 - 0.2727 (0.202) Since the hydrogen partial pressure vries only slightly through the reactor, an average value of O. 9061 may be used for PJ and may be assumed to be constant for purposes of calculation. In order to proceed with an analysis of the laboratory data, it is helpful to visualize the exerimental apparatus as shown in Fig. 4-1. Writing a material balance on the differential element, one obtains cNe = -dN B ~ r(dV where the reaction rate may be written as Combining Eqs. 4. 4 and 4. 5, we get -N B = kp (dV O _ ¯ kP I dV Figure 4-1. Schematic diagram of hydrogenation reactor tube. (4.4) (4.5) (4.6) As indicated in the original memorandum, the kinetic constant may be exressed by an Arrhenius exression utilizing an activation energ of 12 Kcal/g mole. Also, as noted previously, the partial pressure of hydrogen may be equated to 0. 906 Î+ Therefore, Eq. 4.6 reduces to _0.?0? q1 ?,000/u ¡ _ ~ 0.906 1ko V 0 N B F (4.7) 8² Chc[Icr 4 To proceed, the degree of conversion must be related to temperature. This relation is accomplished by writing a first-law energy balance on the portion of the reactor tube up to length X! It is to be assumed that the system is adiabatic and that there are no work interactions between system and surroundings. In addition, at steady state the time-rate variation of the internal energy of the system is zero. Therefore, the first law reduces to an eqution of the feed-stream enthalpy with the enthalpy of the partially reacted stream at any pOint H the tube. Hence, (4.8) where from Table 4-1 and 1 _ItF �F ¯ 0.9091 |Ì - It) IIF ¬ 0.0909 [H° " I[ * All,) BF N TF 1 _Iix�x = (0.9091 - 0.2727 O ) [ Ü° " It) N N T z + 0.0909 (1 " o ) (Ir - H� * Al,) B + O. 0909 O (Il" H� ¬ AII f ) (4.9) In the laboratory experiment a feed temperature of 5000K was used; the enthalpy of the feed stream is therefore computed as 1 N T F _ Hi F �l.· = 0.9091 (3430) + 0.0909 (8750 + 24,000) = 3118 + 2977 ¯ 6095 cal/g mole of feed Utilizing Eqs. 4. 8 and 4. 9, one obtains 5095 - 0.9091 [H° - H�) O = · · · 0.0909 (Il ¨ It T �I f) C - 0.0909 [H° - I[ ¬ AIlf) Ü - 0.0909 |' ¨ l[ ± AIj) Ü - 0.2727 [Ü° - I� ) (4. 10) CaIu!y!ic Reactor Design 83 Over the temperature range liely to be encountered in the laboratory or i a plant-scale reactor, the heat capacity of each component may be assumed constant and each of the enthalpy terms may be assumed to be linear in temperature. With these assumptions, O is also linear in temperature. It now becomes convenient to evaluate the numerator and denominator of Eq. 4.10 as functions of temperature; this evalua­ tion is carried out in Table 4-2. For an analysis of the laboratory reactor, only enthalpy values of 500° and 600" need be considered. However, enthalpy values at other temperatures will be useful in later stages of the design and have been included in the table. In line with the assumption of constant heat capacities, the enthalpy at 550" has been computed by averaging the values at 500° and 6000K. Table 9¬Z, Computation of Û for ß Adiabatic Hydrogenation Temperature, oK 298 500 550 600 [H ¬1�I 2,024 3,430 3,780 4, 130 µ - H� T Ij) B 27,401 32,750 34,516 36,285 (Ir - H� T Ij) c -15,773 -8,585 -6,095 -3,606 0.9091 [Il° - H �I D 3,118 3, 755 0.2727 (H - H D 935 1,126 O. 0909 (H° ¬ It) B 2,977 3,298 0.0909 (H - H� - I l ) c -780 -328 Numerator of Eq. 4.10 0 -958 Denomiator of Eq. 4.10 -4,692 -4,752 O, Eq. 4.10 0 0.2016 The fact that a value of zero is computed in Table 4-2 for Õ at 5000K is consistent with the experimental situation; the reactant mix­ ture was fed at 5000K, and at that temperature no reaction had taen place. From a first-law balance, a conversion of about 0.202 was computed at 6000K; therefore 6000K must have been the temperature of the product stream leaving the reactor. Moreover, since the molal enthalpies are assumed to be linear functions of T¸the results of Table 4-2 may be summarized as O =0.002016 [T - 500) dO = 0.002016 d1 (4.11) The results of the energy balance may now be combined with the material balance by substituting Eq. 4. 11 into Eq. 4. 7: a00 0.906 ñ ko V ¡ q i?, 000/º¯ _ T = mmmm s00 2.016 Y 10- 3 NB F (4.12) oJ Chapter 4 The left side of Eq. 4. 12 may be integrated numerically by using Simpson's rule; the calculations are shown in Table 4-3. Implementing Eq. 4.12 to obtain the pre-exponential factor, one obtais � H Ì· ('/ ] ¸ [ : 4 ¸ d.0[53 'q It 620 NBF = = O. 0175 Ib moles/hr (78) (454) 600 ¡ e12,000/R T 500 h ¤ T =· [1 500 * 160 0 * 4( fs10 *J530 * . `´ 1 590) 3 T 2 ( s20 * fS40 T ... IS 8 0)] 10 = - [201, 823 * 4(358,192) * 2(266,839)] 3 10 = - [2,168,269] 3 = 7,227, 563°K (7,227,5 63) (2.016 ^ 10- 3 ) (0.0175) ° ¬ o ¬ 9.06 (0.0153) = 1838 lb mole benzene/[hr) [cu ft of catalyst) (atm) It is interesting to determine the degree to which the rate constant varied within the laboratory reactor during the exeriment just analyzed. The following ratio is readily formulated: R [ 1 1 ] ¸ = e12,0001R 1 T k Í L P For the particular case in question, ° _ [ 600 - 500 ] = e12,00 0/1 .9 8 S (600)(500 ) k F (4.13) = e2•02 7.5 U variations in the hydrogen partial pressure are neglected, it is seen that the chemical reaction rate at the reactor outlet was more than seven times faster than that established when the feed mixture first encountered the catalyst. This sort of variation not only causes Catalytic Reactor Desig 85 difficulties in analyzing the performance of a reactor for hydrogena­ ting benzene but will also be particularly significant in the economic optimization of a commercial scale process. Table 9~ö, Evluation of the Itegral H ÏQ. 9.JZ by Simpson's Rule T 12,000/RT ¡ ¡ q i?,ooo/u ¡ 500 12.090 178,081 510 11.853 140,507 520 11.625 111,831 530 11.406 89,848 540 11.194 72,673 550 10.991 59,338 560 10.795 48,743 570 10. 605 40,330 580 10.422 33,592 590 10.246 28,169 600 10.075 23,742 GENERL DESIGN CONSIERA.TIONS Before considering the design of the complete process, it is useful to establish the constraints that must be imposed upon the composi­ tion of the gas mixture fed to the reactor. To this end, the thermo­ dynamiC data given in the original memorandum have been used to construct Fig. 4-2, which shows the effect of temperature and feed composition on the equilibrium conversion of benzene to cyclohexane. Examination of Fig. 4-2 shows that: (i) U a temperature level of 6000K is to be used to activate the reaction, equilibrium considerations suggest that at least five moles of hydrogen per mole of benzene must be included in the feed stream. (ii) From the viewoint of chemical equilibrium, the advantages of increasing the hydrogen concentration diminish rapidly after a value of Ñ ~ 5 has been reached. (iii) With a fixed pressure ceiling of 10 atm, equilibrium dictates that a few per cent of the benzene will remain unconverted if the maxi ­ mum temperature of 6000K is utilized. (iv) For total pressures i excess of a few atmospheres, equili­ brium limitations only start to become important at approximately 600oK. 80 Chapter 4 Î � 0£F 6 � ¤8 0 O.I|÷ {÷ j ¯ â L·ne • 8 C 0 £ f 6 1¸ªk n 500 7 500 5 500 5 600 W 600 7 600 5 600 5 _0.0|� m O t 0.00| -- -- --- 0.l |0 |00 .O0 |0,O0 1_ lOlol pr088ut6¸0!m Figre 4-2. Equilibrium conversion of benzene for various process conditions. Moreover, this sort of high-temperature design would require a large investment in heat-transfer area and control equipment. Thus, an economic balance should be struck that accounts for the capital costs for catalyst, reactor volume, heat transfer, and reactor control, and for the important running costs-in particular the benzene and hydrogen recycle costs. As an illustration, the reactor volume can be reduced by increas­ ing the hydrogen partial pressure in the feed. However, this gain tends to be offset by the increased operating costs for hydrogen re­ cycle. The present problem is typical of many design studies in that a number of counteracting factors have to be balanced in order to establish the over-all economic optimum. The total catalyst volume requirement will be used as the initial indication of the desirability of various types of design. Clearly other costs, such as those for heat-transfer surface, hydrogen and benzene recycle, and reactor controls, will signiicantly affect the final design selection. However, for the preliminary analysis re­ quested in the original memorandum, the catalyst volume should serve as a sensitive indication of the relative values of various types of design. ANALYSIS OF LIMITING DESGN CASES ÏDestablishing reasonable estimates for the reactor volumes requir­ ed by various process alternatives, it is desirable and exedient to utilize some approximations. First it will be assumed that the tem­ perature and feed compositions to be used will be such as to allow complete conversion of benzene to cyclohexane. The greatest error caused by this approximation will be that at 600oK, where a small per - Catalytic Reactor Design 8/ centage of the benzene will remain unconverted. This is a negligible error for purposes of establishing reactor volume, although this small percentage could greatly magnify the separation and recycle costs. Second, it will be assumed that the zero reaction-order observed for benzene H the laboratory run has application over the entire range of benzene conversions, i.e., for 0 ´ Û ´ 1. There is danger in extra­ polating a kinetic exression outside the concentration range where the data were taken; indeed, H the present case the reaction order un­ doubtedly changes in the range of high conversions. However, in the absence of more extensive experimental data, the zero-order exres­ sion will be assumed to apply. Finally, all designs presented will as­ sume the availability of pure hydrogen to be used in the feed. In many commercial installations the available hydrogen contains substantial amounts of ierts, and these have to be removed by a bleed stream on the hydrogen recycle. The flow sheets presented in this study will pro­ vide for such a bleed stream, but no consideration of hydrogen purity will be made in the design calculations. With these thoughts H mind, it is now useful to establish the re­ quired reactor volume if the laboratory reactor were scaled directly to commercial size. In this instance, the catalyst volume required for the specified production rate follows directly as ( 40 Y 106 ) ( 0.0153 ) V ¬ ° 258 cu ft 8000 X 84 0.0175 X 0.202 Under the conditions of the laboratory test, the temperature of the reaction mixture rises adiabatically from 500° to 6000K, and a total operating pressure of 10 atm is used. The hydrogen partial pressure falls from 9.09 atm H the feed gas to 9.03 atm at the exit of the reac­ tor. Clearly some advantages can be realized by operating at the maxi­ mum allowable temperature and with large excesses of hydrogen. U the limit, if a reactor were operated isothermally at 6000K, with a hydrogen partial pressure deviating only slightly from 10 atm, the following bed volume would result: and 8 ¯ 1838 q¬1 ?,000/a00) ¯ 1838 23,742 ¯ 0.0774 lb moles/(cu ft) (atm) (hr) V (40 X 106 ) ( 1 ) ¬ 77 cu ft ¯ 8000 ¥ 84 10 X 0.0774 This value constitutes the lowest attainable limit for the catalyst volume under the restrictions of the specified design criteria. 85 Chu[Icr ¬ There is no upper limit on the bed volume. However, an arbitrary upper limit can be established by specifying an isothermal operation at 5000K with a large excess of hydrogen having a partial pressure of 7.0 atm. Since the reaction rate is first order in hydrogen, 7.0 atm would appear to be a reasonable lower limit for the values of ] which should be considered in the design. Under these conditions, the bed volume is computed as and 1838 R ~ ~ 0.01033 lb moles/(hr) (cu ft) (atm) 178, 081 (10 0.0774 ) V ~ 77 - X ¯ 825 cu ft 7 0.01033 Thus by allowing the feed mixture to react adiabatically from 500° to 6000K, the bed volume is reduced from 825to 258 cuft, and a significant step has been taken i reducing the catalyst volume to its theoretical lower limit of 77 cu ft. An adiabatic reactor would not require the substantial heat-trans­ fer surface that would be necessitated by the isothermal operation. Moreover, the temperature level of the isothermal operation would require a high-temperature heat -transfer fluid (e.g., Dowtherm or Therminol) together with a specially designed boiler system. These exenses can be avoided or at least substantially reduced by maing proper use of adiabatic reactor operation. It has been demonstrated that reactor volume can be minimized by operating as closely as practicable to the maximum allowable tem­ perature. Moreover, it obviously would be advantageous to devise a design that would allow a stable, high-temperature operation without the need for large quantities of heat-transfer surface. These objec­ tives can be accomplished by the general type of design shown i Fig. 4-3. In such a design, only a portion of the benzene is fed to the inlet of the reactor. The remaining benzene enters as a liquid at regular intervals along the length of the reactor. In this way the latent and sensible enthalpy needed in bringing the benzene to reaction temperature balances a portion of the heat of reaction and serves to stabilize the reactor operation. At this point it is well to emphasize that the over-all heat-tras­ fer requirement (Btu/lb of product) is independent of whether an adiabatic or isothermal design is used. The type of design show in Fig. 4-3 has as one of its primary objectives that of reducig the cost of removing the heat of reaction; the net amount of heat cannot be changed. In the reactor desig shown, a large excess of hydrogen may be required to maintain a high hydrogen partial pressure and a cor­ respondingly high reaction rate. This practice, of course, leads to an increased requirement for hydrogen recycle and to correspondig Catalytic Reactor Design 89 0m~ µt Figure 4-3. Adiabatic reactor design. cooling, recompression, and heating expenses. The hydrogen-recycle costs can be reduced by feeding liquid cyclohexane, along with hydro­ gen and liquid benzene, at regular intervls along the reactor. The advantages of reduced recycle costs are balanced at least partially by the need for an increased reactor volume and by the increased separation costs resulting from cyclohexne recycle. Clearly an infinite variety of reactor designs may be conceived that would incorporate one or more of the aforementioned modifications. One of these, show schematically in Fig. 4-4, will be considered to demonstrate the advantages of a split liquid feed. The design shown in Fig. 4-4 maes use of five fixed-bed reactors with equal amounts of benzene fed to each reactor. The gas entering the first reactor is to be preheated to 550oK, and the temperature of the gas leaving each reactor is specified as 600oK. The total pres­ sure of the gas in each reactor is taken to be 10 atm, and the hydro­ gen partial pressure will be speciied as 7 atm at each reactor out­ let. All the benzene entering an individual reactor is assumed to be completely hydrogenated i that reactor. ^se ×a:.×:+^×: ×a,.^;,.^-a ×;,.×;,.×�s ¤;+.×;+.×�+ �� �� �� �ª ¡ H80y0|8 H, çl88d S\t80m H80y0!8 D8n28n8 ÍuSSum8d SmoII( ª Ly0lOh8x0n8 prOdu0! 6OOª× Figure 4-4. Five independent adiabatic reactors. 90 Chu[l q r d Any number of reactors could of course be used H a design of the type show in Fig. 4-4. A large number of reactors would lead to an isothermal operation at 6000K ( and to the previously calculated mini­ mum total bed volume i ¡_ were maintained near 10 atm} . However, as the number of reactors is increased, so are the piping and instru­ mentation requirements. An optimum number of reactor stages should be established for the final design, but the five-reactor system show in Fig. 4-4 should effectively illustrate the inluence of divid­ ing the fied bed into a number of individual sections. To determine the degree of this influence, the design calculations for the selected case will now be completed. DESIGN CALCULATIONS FOR THE FIVE-REACTR SSTEM As a basis for the design, it is convenient to choose (4.14) Since the benzene is assumed to react completely in each section of the reactor, it is noted that (4.15) With the basis selected, the analysis of the reactor system follows directly. First Reactor Since the benzene is assumed completely converted, a material balance is quite simple: An additional relation is obtained from the limitation imposed upon the hydrogen partial pressure: Ía Ü N IO - 3 N B O � ¬ 0.7 Nlo - 3 N B O + Nco + N B O and, from Eq. 4.14 , � I O ¬ ( 1 6/3) + (7/3) Nco (4. 16) Maing use of the enthalpy quantities given in Table 4-2 , Eq. 4.8 may be applied to the first reactor as follows: 34, 516 N B O - 6095 Nco + 3780 �I O = 4130 (�I O - 3 NBo ) - 3606 ( N cO + * BO ) or 50 , 512 - 2489 Nco - 3 50 i I O ¯ 0 Catalytic Reactor Design V1 (4.17) Combining Eqs. 4. 16 and 4.17 , values for N c , '� I O ' NCl ' and �I 1 are obtaied; these values are show in Table 4-4. Table 9¬9, Smmary of the Flow Qantities for the Adiabtic Reactor System Sown H Fig. 9~ó B asis: NBO ¯ NBI ¯ N� 2 ¯ N� 3 ¯ NI 4 ¯ 1. 0 NBl ¯ NB2 ¯ NB3 ¯ NB4 ¯ NBS ¯ Û - 0 Reactor Stream NB N c N n ͺ 1 Feed, N 1.0 14.67 39.54 7.15 Product, Nl 0.0 15.67 36.54 7.0 2 Feed, N l ' 1.0 0.966 7.58 7.15 Product, � 0.0 17.64 41.12 7.0 3 Feed, N2 ' 1.0 0.966 7.58 7.14 Product, N 3 0.0 19.60 4 5 .70 7.0 4 Feed, N 3 ' 1.0 0.966 7.58 7.13 Product, N 4 0.0 21. 57 50.28 7.0 5 Feed, N 4' 1.0 0.966 7.58 7.11 Product, Ns 0.0 23.53 54.86 7.0 Second Reactor Applying material balances around the first mixing point and the second reactor, one obtains NC2 = NCl + NB'l + N el = 16.67 + Nel �12 ¯ �I1 + �!1 ¯ 3Nn'l ¯ 33.54 + �;1 (4. 18) (4. 19) Again applying the specification on the hydrogen partial pressure and utilizing Eqs. 4.18 and 4.19 , there results 33. 5 4 T �;l Û. 7 ~ 50.21 + �!l T N e l or (4.20) An enthalpy balance on the second reactor yields the final required equation: 92 Clu[Ic: 4 (4.21) Note that the specific enthalpy quantities used in Eq. 4. 21 have been obtained from Table 4-2. As mentioned previously, it is anticipated that the use of a linear average to obtain the enthalpy values of 5500K should be quite accurate. By combining Eqs.4.18 to 4.21, the values for N dl' �:l' N_ ¿ ,and �¡ ¿ have been obtained and are tabulated in Table 4-4. Other Reactors With use of methods analogous to those just presented, the material balances have been completed for all five reactors shown in Fig. 4-3; the results are also summarized in Table 4-4. In order to proceed with te chemical kinetic calculations, it is necessary to establish the temperature at the entrance to each reac­ tor. The temperature of the feed miture entering the first reactor has been specified as 550"K, and the temperature of the product mix­ ture leaving each reactor has been fixed at 600oK. However, the tem­ peratures of the mixtures entering reactors 2 to 5 must be computed by a series of enthalpy balances. The calculations summarized in Table 4-5 serve to facilitate the estimation of the temperature at the inlet of the second reactor. The molal quantities used in Table 4-5 were taken from Table 4-4, while the enthalpy values were deri­ ved from Table 4-2. Table 9~Ô, Calculations for Estimation of the Entrace Temperatre for Second Reactor Enthalpy Quantity 1 ¯ 5500K T~ 6000K (NB1 + N;l ) lB 34,516 36,285 (NC1 + Nc�)l c -101,400 -60,000 (.n T i�/l)/ 166,800 182,500 Total enthalpy 99,916 158,785 Catalytic Reactor Design 93 With use of the assumption of liear enthalpy values, the total enthalpy of the stream entering the second reactor may be exressed as ´ _ ( N il T �2)li ¯ 158 , 785 - 1177 (600 - T ¿ ¸ _¿_¿_ l (=3 Since the flow rate, composition, and temperature of the stream leav­ ing the second reactor have already been established, the total enthalpy in that stream is computed i a straightforward manner to be 106, 400 g cal. Because the reactor is operated adiabatically with no work interactions with the surroundings, the enthalpies of the inlet and out­ let streams may be equated, and the entrance temperature for the second reactor is obtained: T ¯ 600 - ( 52 . 385 ) ¬ 555. 5°K ¿ ¸ I¿±¿T 1177 By analogous methods, the inlet temperatures for the remainig three reactors are computed as 560.2°,564.9°, and 569. 6°K for the third, fourth, and fifth reactors, respectively. An exression for the volume required in each of the five reactors is easily obtained by returning to Eq. 4.7, whereby (4.22) The temperature in each reactor must be related to the degree of conversion to complete the integral. This is easily accomplished by reference to Fig. 4-5, since it has been shown that Tis linear in Ô& With the aid of this figure, the integral in Eq. 4. 22 may be evalua­ ted either graphically or numerically. To compare the results for the two extreme situations, the integration has been carried out graphically in Fig. 4-6 for the first and fifth reactors. The two curves shown in Fig. 4-6 were integrated graphically, and the following results were obtaied: 1 Reactor 1: ¸ _12¿000/!I_g ~ 38 , 308 0 1 Reactor 5: ¸ _12¡000/Þ¯ _Q ¬ 3 1 , 168 0 Since a basis of one mole of benzene feed to each reactor has been used in the present analysiS, the appropriate value of W__ for use in Eq. 4. 22 is computed as 40 Y 106 ¬ 11. 9 lb moles/hr (8000) (84) (5) V+ Chapter 4 ÜZ Ü.9 Ü.b Ü.Ü Ì.Ü w×=,0 Figure 4-5. Temperature profiles in the five reactors. (Each curve is identified with a reactor number.) By use of this feed rate, the hydrogen partial pressure values from Table 4-4, and the values from the graphical integration, the volumes required for the first and fifth reactors may now be evaluated as follows by means of Eq. 4. 22: (11. 9) (38,308) ! t = ~ 35. 1 cu ft (1838) ( 7 .07) (11.9) (31,168) ! ¹ = (1838) ( 7.05) = 28.6 cu ft These two values are not greatly different, and it is clear that the volumes required for the second, third, and fourth reactors will be distributed approximately linearly between these two extreme values. Therefore, with reasonable accuracy, the total reactor volume for the design shown in Fig.4-4 may be computed as V ¡ ¬ % (28.6+ 35.1) = 159 cu ft . | 0 ~ º 6ס0 ^ 6×!0 5 \ 1"0' I ' " Lul0Ì]!ÍC Reactor Dcsi¿n 95 5 ` ' � 4ס0 3×J0 �..· ` ` � ` � 5 ¬ ¯ .: � 5 2.2×I0 0 0.J 02 0.3 0.4 0.6 0.6 0.7 0.6 0.9 |0 Û6gt66 0Í C00v6r5t00 t Q Figre 4-6. Curves for the graphical integration 1 of ] _12000m ¡ _ _ 0 This is a substantial reduction from the 258 cu ft that was obtained by scal ­ ing up the conditions from the laboratory experiments. Table 4 -4 shows that the hydrogen partial pressure deviates only slightly from 7.0 atm. DISCUSSION OF THE COMPUTED RESULTS Figre 4-7 provides a convenient means for comparing the results of the design calculations that have been completed. It shows reactor volume plotted as a function of the hydrogen partial pressure; results for various types of reactor operations are presented. The curves for the isothermal operations are easily computed since, for these cases, reactor volume is inversely proportional to p¡¸. The point con­ ditions for the scale-up of the laboratory run and the five-reactor de­ sign are also shown. In both of the adiabatic cases it is possible to extrapolate the results to lower pressure by assuming that reactor volume is inversely proportional to hydrogen partial pressure. This corresponds to a reduction in total pressure while maintaining a constant mole ratio in the feed. By this means of extrapolation, the enthalpy balances used in determining the two point conditions re- main valid at lower pressures. A simple extrapolation to higher hydro­ gen partial pressures is somewhat tenuous, since the limitation of 10 atm on the total pressure would require a change in the enthalpy Vb Chapter 9 balances. However, the effect of hydrogen on the enthalpy balance is probably not particularly influential, and extrapolation over a modest range of pressures, as show in Fig. 4-7, is probably warranted. '0Or 900�� sc� ¯001 _-c~ � �¬¤� borhetmoi tecc,, 6C0*8 Ü� O õ Ï s 9 |Õ AverOge hydrogen pOrIi0I µres8ure¡o!m Figure 4-7. Reactor volume as a function of hydrogen partial pressure. Up to this poit, much emphasis has been placed on the estimation of the catalyst volume necessary to produce the required amout of cyclohexane. Although catalyst and reactor capital costs may be significant factors in the economic evaluation of a design, there are other important factors that warrant detailed consideration. Oly in­ Significant cost information was given in the problem memorandum, and, in fact, an economic evluation of the reactor design was not re­ quested. With this situation in mind, other factors that will eventually have impact on the final economic evaluation will now be considered i a qualitative sense. With reference to Fig. 4-7, the advantages of a high-temperature operation in reducing the reactor volume are obvious. However, as mentioned prevously, a high-temperature isothermal operation would require large quantities of heat-transfer area; this sort of design is also vulnerable from the standpoint of possible stability problems. It is seen that the design incorporating five individual, adiabatic reac­ tors achieves nearly every possible economy in reactor volume while Catalytic Reactor Design V¯ simultaneously providing the basis for a stable reactor operation. It also should be noted that the adiabatic design requires only a minimal quantity of heat-transfer area associated directly with the reactor system. There are approaches to the heat-removal problem other than the one suggested in Figs. 4-4 and 4-5. For example, reactor temperature could be controlled by the injection of liquid water at various points in the process stream. Or intermediate waste-heat bilers could be em­ ployed between reactor sections. These alternatives are attractive in that they avoid the increased separation charges associated with recycling cyclohexane. The practicality of utilizing these alternatives' might well be considered in subsequent work. A Significant subject for a detailed economic evaluation lies in the selection of the exact type of reactor system to be used. For example, Fig. 4-7 indicates that about 170 cu ft of catalyst can be saved by using the five individual adiabatic reactors rather than the single adiabatic unit scaled up from the labratory run. Obviously this advantage is offset to some degree by the increased costs associated with building and controlling five individual reactor units. By balanCing the con­ flicting catalyst and equipment costs, an economic optimum can be established, and the proper reactor system can be selected. U addition to the designs already conSidered, Fig. 4-7 indicates that the case of a single adiabatic reactor with a feed temperature of 5500K should be investigated. This analysis will lead to a curve falling between the 5500 and 6000K isothermal curves shown in Fig. 4-7. This case would have the advantage of a single-unit construction; however, the process control requirements for the single reactor might be more difficult to satisfy than in the case of five individual reactors. The original temperature limit of 6000K resulted from the neces­ sity of maintaining catalyst activity. Figure 4-2 shows that the ther­ modynamiC limitations on the conversion per pass also become im­ portant in the same range of temperature. It would be very interest­ ing and challenging to discard the temperature limit imposed by the catalyst and to balance the effects of temperature on equilibrium and kinetics so as to achieve an optimum deSign. For example, a portion of the reactor product could be cooled and recycled; the determination of the optimum flow rate and temperature of the recycle would be a very meaningul and enlightening project. Boonstra and Zwietering [2) mention a second alternative wherein high temperatures are used in the inlet sections of the reaction rates, while the downstream sec­ tions are cooled to promote complete conversion in one pass. Dufau, çl aZ. (3) and Stobaugh [9) also provide useful discussions of the econ­ omics of various cyclohexane production methods. These references are helpful in giving perspective to the present design and in provid­ ing additional background information for subsequent design projects. With the proper reactor system selected, the next step in the de­ sign procedure should be a consideration of the recycle costs. The reduction in reactor volume achieved by increasing hydrogen partial pressure must be interpreted in light of the limitation imposed on the total system pressure. The advantages evdenced in Fig. 4-7 for Vo Chapter J higher hydrogen partial pressures must be weighed against the in­ creased recycle costs caused by rising hydrogen concentrations in the product mixture. Again an economic balance is indicated. Several factors remain which must be given consideration as the design proceeds to more advanced stages. For example, the pressure drop i each reactor unit must be established. Too high a gas velocity would lead to large pressure drops and to high rates of catalyst at­ trition. Low flow rates require a large reactor cross section and re­ sult in corresponding dificulties with bypassing and effective catalyst usage. It will be remembered that the effects of mass transfer and dif­ fusion within the catalyst pellets were not thought to D influential in the laboratory tests. The possible influence of these factors in a commercial reactor should be ascertained. For example, the pres­ sure drop in a reactor can be reduced by increasing the catalyst pel­ let size. Since a large pellet diameter increases the resistance to intraparticle diffUSion, the influence of this effect on reactor perfor­ mance would have to be ascertained. It is clear that a good deal of analytical work remains to be done before a final design can be selected. Several factors, prinCipally re­ cycle, heat transfer, and control costs, have not yet been given ade­ quate consideration. Nevertheless, the design calculations summari­ zed in Fig. 4-7 and the subsequent qualitative reasoning serve to focus attention on those designs that are most promising. The type of analysis set forth in the present design study illustrates the great advantages which are to be gained by the use of simplified models as limiting cases for a complex problem. A great deal was learned by comparing the results of a single detailed analysis of a complex adi­ abatic reactor system with the results of a straightforward analysis of an isothermal system. In deSign work, such an approach is often useful in minimizing the computational load while still obtaining the required process information. ÜÏ1ÏÜÏIL1Ü 1. Amane, A., and G. Parravano, "Advances in Catalysis" [Proc. IntI. Congress on Catalysis), A. Farkas, Ed., Vol. 9, Academic Press, New York (1957), p. 716. 2. Boonstra, H. J., and P. ZWietering, Cher. Ind. [London), 1966, p.2039p 3. Dufau, F. A., F. Eschard, A. C. Haddad, and C. H. Thonon, Cher. Eng. Progr. ÜÛ¿ 43 (1964). 4. Grifith, R. H., and J. D. F. Marsh, "Contact Catalysis," Oxord University Press, London (1957). 5. Kassel, L., U. S. Patent 2, 755, 317 (1956) [assigned to Universal Oil Products Co.). 6. Reilly, J. W., and M. C. Sze, Cher. Eng. Progr. Üó¿ No. 6, 73 (1967). Catalytic Reactoy Desil 99 7. Smith, H. A., in "Catalysis," P. H. Emmett, Ed., Vol. 5, Reinhold Publishing Corp., New York (1957), Chapter 4. 8. Smith, H. A., and H. T. Meriwether, J. Am. Chem. Soc. 71, 413 (1949). 9. Stobaugh, R. Ü.¡ Hydrocarbon Process. Petrol. Refiner. 99¿ No. 10, 157 (1965). 5. Evalu ation of New Methods for Sulfur Transportation As tle lcarld-Icide demalldfor fertilizer alld sulfuric acid has becollle more lridesjJYead, tle need for more convellient alld economical sul­ fur trans/Jortalion methods has grol('n more acute, Tllis case exalllines sel'eral allerllatiL'e tralls/Jorlatiol! melhods ill a cursory fashioll alld /Jrovides a more delailed allalysis of a /Jipeline syslem for lIle (011- t'eymlce of liquid sulfur, The pipeline ecollolllics are o/Jtimized lci/h respect to /Ji/Je diameler,line /J)'essure, number of /JIIJIl/Jilig staliolls, and insulation Illicless, A short cOIlI/mler /Jl'og/'a/ll is /J)'ol'ided to facilitate the design calculations, Tlie economics of the O/JtiIlWIll lille are com/Jared Icilll those for olher /Jossible tralls/Jorlalion techniques, LBÎCBS£8u buUuT LCDQBB§ ÏCTl LBÎCBSC8u¿ ÏCu1S1BB To, Wilbur Wolf, Chief Design Engineer From, Clyde Fox, Vice President Rc: New Methods for Sulfur Product Transportation The Exploratory Division of the company has recently discovered 8 new sulfur field near Pogo Lae. This find lies approximately 50 miles to the north of our shipping port, Port Calcaseau, and should in­ crease our company sulfur reserves by at least 15 per cent. Over the past several years, the Board of Directors has become increasingly dissatisfied with our methods of transporting sulfur. As you know, most of our inland sulfur production is now transported as a liquid to Port Calcaseau by insulated trucks and,or railroad cars. The I00 $/t/)ur Trats]orlu/iott Tcchniçucs 101 costs of such transportation methods have been rising rapidly, and the company is interested in developing new methods of delivering sulfur from the mine to Port Calcaseau. It is desired to use our new strike near Pogo Lake as a test area. The Process Design group is requested to develop a list of possible transportation methods complete with a brief description of the ad­ vantages and disadvantages of each. The Board of Directors will meet in three days, and I should like to have your list ready for presentation at that time. Only a qualitative description of several possible methods, along with your opinion regarding the probable merits of each method. is desired. U the Board agrees to proceed, we shall probably request a more quantitative study of one or more of the suggested techniques. This investigation may well grow to a scale far beyond that of the Pogo Lake project. U a good method is developed, it could well be applied by many of our foreign affiliates to transport sulfur from port cities to inland customers. For the present, however, concen­ trate your efforts on the Pogo Lae project, and assume an annual production of 375, 000 tons. GENERL CONSlDER TlONS Sulfur is conventionally produced by the Frasch process, whereby high-pressure steam is injected into a sulur-bearing ore formation. LiqUid sulfur resulting from the hot steam collects in a pool at the bottom of the well; compressed air is injected beneath the surface of the pool to lift the sulfur to ground level by a " bubble-pump" mech­ anism. Once at the surface, the liquid sulfur is pumped to a heated relay pan where noncondensibles are vented; the product is then fil­ tered to remove any carbonaceous materials present. U the sulfur well is reasonably near a shipping port, the purified product is piped to a storage area where it is cast in large solid blocks. Wen a ship­ ment from this storage is required, the solid sulfur is "mined" with explosives to produce lumps of sulfur that can be easily handled by standard power-shovel equipment. On the other hand, if the sulfur well is located some distance from a shilping port, the product is often shipped as a liquid in insulated truckS, rail cars, or ships. Thus the problem put forth involves a general consideration of methods of sulfur transportation when the source and the shipping port for the sulfur are widely separated. Upon initial conSideration, several possible transportation methods come to mind that differ from the standard techniques used in the in­ dustry. Some of these are here listed: 1. Pump liquid sulfur through 8 pipeline 2. Granulate solid sulfur and convey it pneumatically through a pipeline 3. Store solid sulfur in capsules and convey the capsules pneu­ matically through a pipeline . Slurry solid sulfur in water and pump the slurry through a pipeline 5. Transport solid sulfur on a covered conveyor belt 1Ûo Chapter b These methods represent only a portion of the possible alternatives. However, all have found application in various specific commercial situations. Each has its advantages and disadvatages; some of these will be discussed, and the more promising techniques selected for further study. Alternative No.1 The idea of pumping liquid sulur offers several possible advan­ tages. Obviously, material-handling costs will be substantially re­ duced by the elimination of solidification and granulation process steps that are required at the wellhead by the other alternatives. Clearly, however, a pipeline for liquid sulfur must be operated at a high temperature. The problems attendant to this type of operation must be given detailed consideration before such a pipeline can be considered feasible. It is interesting to note that one of the major sulfur companies has recently installed a liquid-sulfur pipeline for connecting an offshore drilling area with a major shipping port. Alternative No.2 The technique of pneumatic conveyance of granular material is quite well known, but typically Îl is used only for short distances, e. g., from one section of a plant to another. Starting up a long-distance pneumatic process might present dificulties, and the prospect of a plugged section of the line in a remote, swampy area is not particu­ larly appealing. McCabe and Smith [6) have provided an excellent dis­ cussion of the pneumatic method and have listed some of the opera­ tional problems that may be encountered. Of particular interest here, McCabe and Smith point out that erosion of the pipe walls can lead to serious difficulties. This problem is especially pertinent in our case, where many sections of the pipeline would be located in inaccessible areas. Alternative No.3 The technique of pneumatically transporting solid materials stored in capsules has been given serious consideration in applications where the solids are relatively fragile. For example, the possibility of ship­ ping encapsulated wheat from interior agricultural regions of Canada to Vancouver has been under study for quite some time. However, the advantage of protecting the material being transported would be value­ less in the sulfur transportation situation. As such, the large capital and operatig exenses of this method would probably eliminate it from consideration. Alternative No.4 The prospect of pumping a sulfur-water slurry is attractive in many respects. For example, the high temperatures ad start-up prob- Sulfur Transportatioll Techlliques 1ÛJ lems involved in a liquid-sulfur pipeline are avoided. The fact that the method is feasible is attested by the near adoption of a plan to transport coal in a water slurry from West Virginia to the great East­ ern population centers. Even more recently, some industrial concerns have given thought to the partial distillation of coal to produce a "pumpable" slurry of partially coked coal in an aromatic liquid. How­ ever, in the case of a sulfur pipeline the problems of separating and drying the sulfur would entail some economic and technical difficul­ ties. Frthermore, a water-sulur slurry would be highly corrosive to mild steel and would necessitate a more costly construction material.These problems tend to detract strongly from the advisabÎlity of this method. Alternative No. 5 At first thought, the prospect of a fifty-mile conveyor belt appears to be highly impractical. However, recent developments in conveyor technology have shown that continuous belt systems of this length are worthy of consideration. For example, the Societe des Potasses de Navar­ re, a Spanish firm, is currently using a conveyor for transportig 620 tons per hour of potaSSium ore over a distance of four kilometers [3). Cost figres for this method are available for comparison with the costs for competitive techniques. The capital exenditures for the conveyor unit were $ 400, 000, or $100 per linear meter ( 1964 costs) ; this figre includes the entire metal frame, all mechanical compon­ ents, roofing for the rubber belt, and the cost of transporting and erec­ ting all equipment. The operating costs were found to be $0.01 per ton-kilometer, including power, depreciation, maintenance, and super­ vision. CONCLUSIONS The results of the foregoing considerations are far from definitive. However, it appears that alternatives 2,3, and 4 would present more operational and start-up difficulties than would alternatives 1 and 5. Therefore, in the absence of detailed cost information about the first four techniques, qualitative considerations suggest that alternatives 2,3, and 4 be discarded in favor of alternatives 1 and 0. By comparing cost estimates resulting from preliminary designs for these latter alternatives with standard rail and truck freight rates, a reasonable assessment of the economic viability of the new transportation tech­ niques should be realized. 1ÛJ Chuµlcr Ó Calcaseau Chemical Compay Lae Calcaseau, Louisiana To: Wilbur Wolf, Chief Design Engineer Frolll: Clyde Fox, Vice President Ater considering the vrious alteratives describd in your pre­ limiary report, the Bard of Directors wishes you U prepare a more detaied desig of a liquid-sufur transportation system. It is aticipated tt a bried, jacketed pie will b used with 85 psig steam provded in te anular spce to maitain the slur i a ml­ ten state. Naturally, it wll be desirable to compae te estimted capital and runing costs for the liquid-sulr piplie wit the costs for 8 conveyor blt process ad te standrd shipping rates for rail and trck transprtation. Suggested Nomenclature D Inner diameter of sulfur pipe, inches . Oter diameter of steam pipe, inches Di Outer diameter of the insulation that surrounds the steam pipe, inches 1 Distance between sulur pumping stations, miles Ï Maximum allowable pressure in sulur pipe, psia l Thickness of the sulfur pipe wall, inches Suggested Costs 1. Steel costs $250 per tOll plus $60 per ton for delivery to site, unloading, placement, etc. 2. Engineering, surveying, etc., may be taken as $10, OOO / mile 3. Ditching, welding, installation of exansion bends, backilling, cleanup may be taen as BOOD, $ /mile 4. First cost of a pumping station is $25, 000 plus $345 per bhp 5. Labor, supervision, and salaries are $2, 600 per month for a 400-bhp station; assume $600 of this independent of station size and the rest proportional to station bhp 6. The annual maintenance cost of a pumping station may be taken as 20 per cent of the first cost of the station 7. Insulation costs $14. 70/ cu ft (istalled cost) ö. Steam costs $0. BO/ 1000 lb [total cost including fixed plus variable costs) 9. Electrical power is avilable at $0. 01 / kwh Sggested Assumptions Sulfur Transportation Teclzniques 1Ûb 1. Assume that the steam passes through an annulus 1 in. wide 2. Assume that the wall thickness of the steam lie is 0. 2 in. regardless of the value of D. This should be large enough to allow for any reasonable steam pressures and to provide the necessary structural support for the pipelie 3. The annual fixed costs of capital equipment may be taken as . . per cent of the initial instlled cost . The sulfur pumps are to be powered by electric motors; the motor-pump combination may be assumed to be . per cent efficient . The maximum allowable stress in the steel sulfur lie should be taen as . .... psi ô. The thickness of the sulfur pipe may be computed according to the standard "hoop stress" formula The Fanning friction factor may be taen as ) ^ .. . . · 8. The sulfur pipe will be buried a depth of ô feet in earth whose thermal conductivity may be taken as . .. Btu / (hr) (ft) (OF). The pipe will be insulated with material whose conductivity is . . . Btu/[hr) (ft) (OF) DESIGN OF A PIPELNE FOR TilE TRNSPORTATION OF LIQUID SULFUR As mentioned previously, several serious dificulties are envision­ ed in building a pipeline for the transportation of liquid sulfur. In particular, the problems caused by the proposed operation of the line at high temperature must be given serious consideration. Some of these dificulties and considerations will be treated very briefly, and then a preliminary process desig for the installation will be completed. The prelimiary computations should bring to light the critical parameters that should be examined more closely in subse­ quent detailed design work. Gneral Desig Coniguration The typical pipeline system consists of long lengths of buried pipe interconnected by a series of pumping stations. At each pumping station the fluid being transported is raised to its maxmum pressure and the line is designed such that the fluid pressure drops to a speci­ fied minimum value at the entrance to the station. In the present case, some means of heating the pipeline must be provided in order to main­ tain the sulfur in a liquid state. Since the pipeline will be constructed at ambient temperature, proper allowance must be made for exan­ sion of the pipe as it is heated to operating conditions. Normally, the 1Û0 Chapter Ó termal expansion problem is surmounted by the installation of ex­ pansion jOints at predetermined intervals. However, these joints are expensive, and recent development work has led to the technique of preheating (and thereby pre-expandig) sections of pipe as they are laid. The pre-exanded sections are then anchored in place and al­ lowed to cool to ambient temperature. When during start-up the pre­ stressed line is reheated to operating temperatures, the pipe assumes a completely relaxed configration. Despite its obvous importance, mechanical construction of this type will not be consi d ered in the present computations. It will be assumed that the present preliminary design will pOint up the critical parameters concerning the fluid mechanics of the system. The mechanical aspects of the preliminary design would then need to be investigated in a separate study. As pointed out in the Freeport Sulfur Handbook (3) , liquid sulfur is quite corrosive in the pre sence of small amounts of water. I our desig it will be assumed that water concentrations can be kept low and that carbon steel pipe may be used for construction. Carbon steel has been shown to be satisfactory for handling most grades of liquid sulfur product. If air pockets are allowed to build up at high pOints in the lie, an exlosion hazard could be created. However, it is anticipated that this problem will be much less acute than that encountered in oil pipelines. By proper grounding of the line (since it will be thermally insulated) and by careful design and construction practices, exlosion hazards may be effectively eliminated. Heatig ad Isulatig Techiqes Two fundamental heating methods may be considered for main­ taining the desired operating temperature: steam ad electricity. In a large-volume application such as the one under consideration, steam would undoubtedly be the less expensive source of heat, par­ ticularly in southern Louisiana where natural gas is plentiful. Thus, steam boilers could be conveniently located at pumping stations, and fuel could be made readily available. Assuming that steam is to be used as a heating medium, the logis­ tics of handling the boiler water is not immediately apparent. For example, the possibility of running a boiler-water return line along with the main pipeline should be considered. The savings generated from decreased feed-water requirements would have to justiy the additional capital exenditure. Without going into a detailed treatment of this problem it seems unliely that the savigs in water treatment would justify the increased capital. Pertient Properties of Liqid Sulfur Two available references [J,') fully delineate the properties of liquid sulur. Te primary property to be conSidered in the present design is the viscosity of the liquid. Figures 5-1 and 5-2, taen from reference (9), summarize all kown data describing the liquid phase viscosity. 0.04 � 0.03 · � . : � 0.02 : 0.0 I o \ \ ¯ ¹ ` ^ ` ` Sulfur Tral1sportati on Teclili ques 107 ` ' | . r 140 160 180 200 220 240 260 280 300 320 Temperature g°C Figure 5-1. Viscosity of liquid sulfur (low­ temperature range). ( From Tuller, reference º) 70 � 60 C W . 50 � 40 Æ D ;; 30 x : 20 10 1 �cc \ \ \ ` ` 400 500 600 Temperature 1°C Figure 5-2. Viscosity of liquid sulfur (high-temperature range). ( From Tuller, reference ') 1Ûo C/w/)/eY b Both figures show a sharp increase in liquid viscosity at a tempera­ ture of approximately 320°F. This icrease has been attributed to the rupturing of S 8 rings to form polymeric-type chains of various lengths. Above 370°F the chains are thought to break ito smaller segments; the continued chain breakage would lead to the observed decrease i viscosity. In order to avoid severe problems in the operation of the proposed pipeline, temperatures in excess of 320° F will thus have to be avoid­ ed. By using steam of a speciic pressure and degree of superheat, this temperature control can be readily accomplished. However, elec­ tric heating elements could probably not be adapted easily and inex­ pensively. References (J) and [º) contain all the iformation regarding the properties of liquid sulfur which will be necessary for the desig calculations. Assumptions to be Used U the Desig In addition to the approximations and Simplifications prevously discussed, the following assumptions will be employed to complete the preliminary design: 1. Saturated steam at 85 psig |T×a t " 327°F) will be used as heating medium, and water at 15 psig (Tsat ¬ 250°F) will be with­ draw from the annular section of the line. By this means, the sulfur will be maintained above its melting point of 246°F but below the tem­ perature range that produces the sharp viscosity increase. 2. The rate of heat loss through the isulation on the steam line will be assumed to be constant along the length of te line. 3. The fluid mechanics withi the steam annulus will not be in­ vestigated in the present study. A theoretical solution for the pres­ sure profile in the annulus would mae a relevant and interesting pro­ ject; this analysis will be required in the final design stage. Because of the simpliication used, the size of the steam annulus must be specified. Therefore, an annulus of I-in. width will be taken for all sulfur-pipe diameters. This should allow for suficient steam flow in all situations. The validity of this assumption will be checked at a later point. 4. In a pipeline system the cost of steel pipe constitutes a major capital investment. To minimize this ivestment, bth the diameter and schedule number of the pipe are varied along the length of most commercial oil and gas pipelies. For Simplicity, this practice will not be followed in the present preliminary desig, and both . and / will be assumed constant in any one design. After examination of the preliminary design results, a judgment may be made as to the neces­ sity of considering variations in . and l, Sulfur Trallsportation Tcclmiqucs 1ÛV DESIGN COMPUTATIONS The sulur pipeline is show schematically as follows: T> æ m s0¢t were te cross section of te pipe may b vsuized as: . |nsu|cliæ ³ 02 5lwm æu|0s D , D s 5u|fur pìpe Preliminary computations will be carried out in order to treat the fluid mechanics and heat-transfer aspects of this problem. After these analyses, the annual operating and fied costs for the system will be exressed as functions of . . ͸ and Ï. Maing use of this expression, the optimum set of desig parameters will be selected. Fluid Mechanics Considerations The sulfur flow rate has been fixed at . x .. lb / year or . lb,hr. Thus the velocity and Reynolds HUDDC1 are given, res­ pectively, by . ...... / ª .. . fps . ..... . . ... D Up . '0c ¯¨ P .. .. ... x- . .. . ¯ . X . . If it is assumed that the gauge pressure in the sulfur line drops to zero just as the sulfur reaches each new pumping station, the Fanning equation may be written as � . ¸·¸¸�¸ P ., . 11Õ Cho¡Icx o where ]¬ .. Implementing this equation, we have 1 ... . Ï ... . x .. .. ... �.. .. D 4 . ... . Ï . . X .. ¬ psmile of pipe Ï .� The total power for pumping is given by " ! . � H ^ .. = . 0 ... ¯ . .. . ... W= ×·´J . ... Ï ... . . . ^ . .. Ï hp (�O. . .. hp per station) The total annual cost for pumping ÎS given . . .. L_____ ¬ ¬. . . . ... ¬ ... Ï dollars /year Ï .., . ... ...... . ..... Sulfur Pipe. From the standard hoop stress formula, the wall thick­ ness of the sulfur pipe is given by .. .. l = -^ HI. .. ..... and the .., of sulfur pipe is computed as Ñ • t (D + l)(7.7) (62. 3) (5280) (50) ( ) 1 = = 1380t Î ¬ t U08 2000 (144) ....., the wall thickess in favor . Ï¿ and assuming that l ª . we have H_ ¬ ... .. . tons Steam Pipe. Assuming that . wall thickness of the steam pipe is . . we can calculate the weight of steel in the steam pipe as (0.2) .( ¬ 2.4) (7.7) (62.3) (5380) (50) � = 200(144) = 275 (D + 2.4) tns Sulfur Transportation Teclmiques 111 Total Steel. The total amount of steel is thus written as "steel = 004ô DºÍ + 275 (D ¬ 2.4) tons Heat-Transfer Considerations We have the following heat-transfer problem: `b0rth wrfæe 0t tepr0ture Tg | 0¡ . where steam is condensing on the iner wall of the steam pipe havng a diameter Ï_. For steady-state conduction from a buried pipe, McAdams [4) gives the relation Û÷ 1 4Z In- ¹ t Btu / hr where Z` Ï_ (see reference 1 for a derivation of this equation). Note that P_ is the thermal conductivity of the earth, given as 0. 40 Btu / hr-ft OF and that 2 is the total length of pipe, equal to 50 miles. Similarly, for heat transfer through the insulation, it is well known that Btu / hr Since the steady-state heat-transfer case is being conSidered, the two resistances may be summed and divided into the total driving force to yield Btu / hr 11Z Cl[pter b Taking average values of Ts as 285°F, T A as 60°F, I< 1 as 0. 40, Il ; as 0. 05, Z as 6 ft, we have Btu / hr (5.2) Total An ual Cost for the Sulfur Pipeline Making use of the foregoing analyses and the cost data given in the problem statement, the costs for the pipeline project are computed as CFixed, Steel ¬ 0. 15(310) [0. 046D 2p ¬ 275(D ¬ 2. 4)] ¬ 2. 14D2p ¬ 12, 800(D ¬ 2. 4) Cixed, Eng. ¬ 0. 15(50) (10, 000) ¬ 75, 000 CFixed,Di tehing 0. 15(800) (50) D ~ 6000 D CFixed, Pump Sta. 0.15 _ [25, 000 ¬ 345(0. 074 P)] 0Û 2000 ¸50 ¸ CLabor Pump Sta ¬ - (600) (12) ! (0. 074 P)(12) - , . L 400 L CMaint. , Pump St a .= 0. 20 ¸�¸ [25 , 000 ¬ 345(0. 074P)] C team CFixed,lnsul. Cpump Power 1. 49 K 108 1 0. 80 ¬ ¯¯ 8750 ¡288¸ ¡D; ¸1000 1000 In ¯ ¬ 8 Ìn ¯ D¸ D s 1. 04 X 106 ¸288 ¸ D. In D ; ¬ 8 In 1 D.2 - D 2 = - ' s (50) (5280) (14.70) (0.15) 4 144 ¬ 3. 18 K 103(D ; 2 - Vs2) ¬ 241 P/L (see Eqs. 5. 3J.) Sulfur Trallsportation Techniques 11Ü Summing all these costs, we obtain 7. 97 K 105 910 . L_ ~ 105, 700 ¬ 2. 14 D2p ¬ 18, 800 ¹ ¬ ¬ Ï 1 1. 04 K 106 ¬ 288 In D i ¬ 8 In� 3. 18 Y 103 (D, - Ds2) dollars / year (5. 3) Equation 0.` expresses the total annual cost of operating the pipe­ line as a function of D, Ds' Di, . and Ï. Some of these latter variables are dependent upon each other; for example, Eq. 5. 1 relates . and Ï. In addition, a I-in. steam anulus has been specified for the design. Thus, assuming a value for l of about 0. 1 in. , we get (5.4) By combining Eqs. 5. 1,5.3, and 5.4, an exression may be generated for the total annual cost as a function of D, D i , and J. Now that the appropriate cost relations have been developed, two basic courses of action may be followed. First, by selecting various insulation thicknesses a series of total cost equations may be devel­ oped for each thickness. By partial differentiation of each equation, the optimum combination of D, . and Ï may be obtained for each in­ sulation thickness. The total costs for each such combination can then be calculated and compared in order to determine the over-all optimum. However, a knowledge of the shape of the total cost curve may be even more important than the exact location of the optimum. For ex­ ample, if the total operating cost is only moderately afected by one of the variables, then the exact specification of that variable is ob­ viously not important. L the other hand, an independent variable that markedly affects the total cost curve may require more detailed ex­ amination. Thus, a second approach to the use of the cost equations would be to examine the sensitivity of the total and individual costs as the independent design parameters are varied. The two approaches just described for the cost optimization will now be applied to the present design situation. Otimization for a Speciic Isulation Thickess For the pipeline sizes likely to be encountered i the present analysis, an insulation thickness of 1. 5 in. appears reasonable. For this thickness, it may be written that D i � D ¬ 5.6 (5. 5) 1Ì4 Chuplcr b Substituting Eqs. 5. 1, 5. 4, and 5. 5 into Eq. 5.3, one obtains ³p = 183,900 ¬ 2. 14 D^p ± 37,900 D ± 2. 48 K 107 1.04 K 106 2. 18 X 1010 ± ± 5. 67 ¬ 7 I(D + 5. 6) 8 I(D ¬ 2. 6) (5. 6) By use of the methods illustrated by Sherwood [¯},Eq. 5. 6 may be dif­ ferentiated partially with respect to each independent variable and the resulting partial derivatives set equal to zero. Following this pro­ cedure to find the condition of minimum cost, one obtains and .. Ï 2. 18 X 1010 2.14 Ï^- ¬ 0 _ ^Ï A. º 1. 10 X 105 Ï ?-4 d³ / 10. 5 ×10 1 0 ¬ 4.28 DP + 37, 900 - dÏ JϨ*º 11. 9 X 107 Ï·:º 1. 04 X 106 7 ~ 8 + 5. 6 L ¬ 2.6 + """�"�""�"� = 0 [5.67 ¬ 7 In[Ï ¬ 5. 6) - 8 In[Ï ¬ 2. 5)] 2 Substituting Eq. 5. 7 into Eq. 5. 8 results in 6.08 X 105 1 1. 9 X 107 37, 900 - " Ï^: Ϩ·º 1. 04 X 106 8 7 ¬ 2. 6 Ï ¬ 5. 6 + =0 [5.67 ± 7 ln(D ¬ 5.6) - 8 ln(D ¬ 2 6) ]^ Solving this equation by trial and error, one finds Ï ¬ 4. 1 in. And, from Eqs. 5. 1 and 5. 7 J ~ 840 psi Ï = 27 miles (5. 7) (5. 8) Sulfur Transportation Teclniques 11b Taing Ï as 25 miles (to give an integral number of pumping stations) the following optimum conditions are found for a pipeline with a I-in. steam annulus covered with 111 in. of insulating material: L ~ 25 miles J ~ 990 psia D ~ 3. 9 in. By using this set of optimum design conditions, the previously derived cost equations may be applied to estimate capital and operat ­ ing expenses. These computations have been carried out and are sum­ marized in Table 5-1, an examination of which reveals several inter­ esting facts. First, it will be noted that the direct operating exenses (labor, steam, and power) are much smaller than the indirect operat - Table 5-1. Capitl and Oeratig Cost Estimates for the Otimum Pipelie Havg 11/2-Uø Insulation and Î~U. Steam Anulus Capital costs Item Steel pipe, 3. 9-in. diam Y 50 miles (sulfur) Steel pipe, 6. 5-in. diam Y 50 miles (steam) Engineering and survey Ditching costs Pumping-station costs, 2 @ $ 50,300 Insulation, I¹_-¡n thick Y 50 miles Subtotal Contingency, 20 per cent Total capital estimate Annual operating exenses Item Labor and supervision Steam costs Pumping power costs Pumping-station maintenance cost Depreciation, 15 per cent of capital Total estimated operatig cost Cost $214, 500 537,500 500, 000 156, 000 100,600 1,018, 000 2, 526,000 505, 200 $3, 031,200 Cost 23,190 161, 400 9,550 20, 100 454, 680 $668,920 11O Clwpler b ing cost [depreciation.. Since the cost optimization was carried out in order to minimize the total annual operating expense, it is clear that the optimization essentially reduces to a minimization of the capital requirement. The capital cost estimate shown in Table 5-1 shows that the cost for insulation is by far the largest contributor to the capital outlay. Since an arbitrary insulation thickness was assumed, designs using other insulation thicknesses should likewise be examied. In par­ ticular, the use of a thinner insulation layer might lead to a more economic over-all design. Gneration of Cost Otimization Curves Instead of summing all the individual cost equations to obtain a total cost relation, as in Eq. 5. 3, it is instructive to exmine the im­ portant individual costs. To accomplish this, these have been group­ ed as shown in Table . all costs included in Eq. 5. 3 have been in­ cluded in this grouping. Table 5-2. Identification of Idivdual Costs Iem FORT Symbl Dpreciatin chrge CBNG for engineering 80 srvey wrk Depreciation charge CPIPE for pipe costs and ditching work Power cost plus CPUMP depreCiation charge on pumpig station Depreciation charge CINSU for insulation Steam cost CSTM Formula T5,000 . .. .·. + .... Ï + ...... + ... 7. 97 X .. ... ¬ - Ï 3. .8 X .. Y.· .· .. . ~ 6. 76) . .. X .. ¸...¸ ¡._ In - +81n ' ²¡ D¬?. ô By applying Eq. .. to the formulas given in Table .. the following individual cost equations are derived: CENG = 75, ... CPIPE = ... Y ...· + ..... . ± 30, .. Sulfur Trans/Jorlatioll Techniques 117 CPUMP ^ Y 105 L¨¹ + 2. 48 X 107 D¯º·ª CISU ^ 3. 18 Y 103 [D¸² ÷ D² 5. 2 D ô. 7ô) CSTM ^ 1. 04 Y l06/¸ ln ¸ 2 88 ¸+ 8 In D where D : + 2. CTOT ^ CENG + CPIPE + CPUMP + CISU ± CSTM In order to facilitate computations, a FORTRAN program has been prepared using the foregoing equations; this program is listed in the Appendi. By using the computer program show in the Appendix, the individ­ ual and total costs may be computed for any specified set of deSig parameters. Retaining for the moment the assumption of a . 5-in. in­ sulation thickness, the costs for operating a sulfur pipeline have been computed as functions of pipe diameter and distance between pumping stations, with the results summarized in Figres 5-3 and 5-4. I | • 1 � � • - \ ~ - " ~ < C � ~ ¬m .. - � �ª � \ \ E . _"_ -.- � " - I 10 2 4 6 B 1 � � � � OO� � � � Sulfur-pIp dIae. Ins Figre 5-3. Individual and total costs as a function of pipe diameter for the case: (i) One-inch steam annulus (ii) One-and-one-half-inch insulation thickness (iii) Two pumpig stations 118 Chapter b • 1 • • T S • • • • • • T • s • • | 5_ Sl . J Nti c r i. " ' t _ .lIli Î To .. _I -� . ¸.C E-.. " ~ ¬« ' ¯ o 10 20 30 40 5 Dste bt_ lo stt «,mtl 6 Figure 5-4. Effect of number of pump­ ing stations on costs for Ü ° 4.0 in. and an insulation thickness of 1. 5 in. Figure 5-3 shows that the economics of constructing the pipeline is a strong function of the pipe diameter. The capital cost for insu­ lation and the steam costs are minimal, but the pumping costs and the capital costs for pipe are exceedingly high at these small diameters. As the diameter is increased, the pumping charges drop rapidly and approach an asymptote equal to the fixed charges on the pumpig station. The capital costs for pipe also decrease rapidly with increas­ ing diameter, but these costs pass through a minimum and begin to rise again. The extremely high pipe costs at small dimeters are the result of the high pressure [and correspondingly thick pipe walls) re­ quired to maintain the required sulfur flow rate. The steel required to construct steam pipe with a O. .-in. wall thickess icreases with Ï. The charge for the steam pipe eventually exceeds that for the sul­ fur pipe and causes the pipe cost curve to pass through a minimum. On the other had, Figure 5-3 shows that the steam and insulation costs increase continuously with increasing pipe diameter. The sum of all these effects causes the total cost curve to be minimized at a diameter of about 4 in. This diameter is i agreement with the result computed analytically. Further confirmation of the analytical computation is obtained from Figure 5-4, where an optimum value for L of about . miles is found. However, in this situation it is clear that the minimum in the total cost curve is very broad. This breadth certainly indicates that only a single pumping station at the inlet to the pipeline may be necessary. The minimum in the curve occurs at an 1 value of . miles, but the Sl/lfur Trw/spor/a/ion Teclmiql/es 119 minimum cost is only about $3000 per year less than the cost that would be incurred if no intermediate pumping stations were used. The preliminary cost estimate in Table 5-1 idicates that insula­ tion costs constitute a major contribution to the total cost. Calcula­ tions carried out to determine the effect of insulation thickness on the economics of the design are plotted in Fig. 5-5. An optimum in­ sulation thickness of about one third of an inch is found, with de­ creasing insulation costs being offset by icreasing steam costs as the pipe diameter is decreased. The figre shows that the balance be­ tween these factors is nearly exact and that the effect of insulation thickness having the specified conductivity is not particularly critical. It would be interesting to investigate the effect of more expensive types of insulation having lower thermal conductivities. 1 " • • • • 5 4 C 0 � " ¯ I . � ^ � P � ¯ 0 I • �I o a� o o o � o U • • • • 4 " I I . . / I ´ 05 . . . m � > > .G ... w . .. 1.0 1.5 Inahon ICln , . Figure 5-5. Effect of insulation thickness on costs for D ¬ 4.0 in.; 1 .25 miles. U consideration is limited to insulation having a conductivity of 0. 05 Btu /( hr )( tt )( q F ) , then Fig. 5-5 indicates that the use of isulation should probably be eliminated in order to simpliy construction. Cal­ culations have been carried out in order to optimize the pipe diameter for the case when only one pumping station is used [L ¬ 50 miles) and no insulation is employed. The reslts are summarized in Fig. 5-6. The elimination of insulation has only a minor effect on the over-all 120 Chc[ler b economic evaluation of the pipeline, but a new optimum pipe diameter of about 5. 0 in. has been arrived at. Therefore it may be concluded that, within the accuracy of the preliminary design calculations and the approximations that have been employed, the optimum pipeline would be 5 in. in diameter, have an uninsulated steam jacket, and be equipped with only one pumping station. 10 , Ü • Î • , 2 2 9 • 7 • • 4 , 2 , 10 o , Totol ` = �¯ ~ � Sl�om ~ �- � �~ � pe ~ (0$15 \ ¹' \ 4 Enqlneennq an survey coslS p"m "" CO5Ì5 8 12 16 20 Sulfur·pJpe dlomeler. inches - . 24 28 Figre 5-6. Indivdual and total costs as fuctions of pipe diameter for the case: (i) One-inch steam annulus (ii) No insulation (iii) One pumping station FINAL CONSIDERTION OF SULFUR -TRANSPORTATION ECONOMCS A liquid-sulfur pipeline has been desiged in order to take ad­ vantage of the comparative product-handlig ease. Several major design questions remain that must be resolved before the feasibility of such a pipeline can be ascertained. U particular, it is necessary to analyze and account for the mechanical construction that allows for thermal expansion of the pipe. Also, the fluid mechanics in the steam annulus must be studied, and the effect of variations in the an­ nulus width should be investigated in some detail. As mentioned pre­ viously, the economics of boiler-water recirculation should also be evaluated. Sulur Tmnsporlatioll Techniques 121 With the proviso that the mechanical construction problem and steam-heating design will be treated in subsequent, more detailed, investigations, the following optimum pipeline speciications result from the preliminary design: Sulfur pipe diameter 5. Ü in. Number of pumping stations 1 Insulation thickness Ü in. The cost estimate for these design conditions is given in Table 5-3. Table 5-3. Preliminary Economic Evluation of the Otimum Pipeline Havng No Isuation .. Using Oe Pumpig Sttion Capital costs Item Steel pipe, 5. O-in. diam Y 50 miles (sulfur) Steel Pipe, 7. 6-inø diam Y 50 miles (steam) Engineering and survey Ditching costs Pumping-station costs, 1 @ $40,400 Insulation costs Subtotal Contingency, 20 per cent Total capital estimate Annual operatig exenses Item Labor and supervision Steam costs Pumping power costs Pumping-station maintenance costs Depreciation, 15 per cent of capital Total estimated operating cost Cost $214,500 631,000 500,000 200,000 40,400 1,585,900 317,000 $1,902,900 Cost 9,880 286,000 2,920 8,080 285,500 $592,380 A comparison of Tables 5-3 and 5-1 shows that the estimated total capital exenditure has been reduced by about one million dol­ lars through the elimination of the insulation and the removal of the intermediate pumping station. This reduction is partially offset by an increased steam usage amounting to abut $125, OOO/year. The /2Z Chc[!c¡ p estimated annual operating expense for the design with no insulation is about $ 75, 000 less than that summarized in Table 5-l. Since the depreciation costs constitute such a large percentage of the total operating cost, it is clear that the choice of the optimum de­ sign will be a strong function of the rate at which the project is charged for the capital it consumes. Figure 5-7 shows the influence of the depreciation rate on the economic evaluation of the designs sum­ marized in Tables 5-1 and 5-3. When capital must be charged at 8.5 per cent, the two designs are equally attractive from an economic viewpoint. As depreciation rates vary from 8. 5 pel cent, one design might be preferred over the other. Thus, the final design of the sul­ fur pipeline could be altered radically, depending upon the required rate of depreciating the capital invested in the project. As a final step in the financial evaluation, the economics for the sulfur pipeline should be compared with the standard rates for rail and truck shipment as well as with the costs given in reference (2) for conveyor-belt operation. Rail and truck transportation costs for packaged chemicals are given by Tighe [8). Table 5-4 compares these costs with those for the other transportation methods under con­ sideration. � U D ¯ U |200 |JJJ� Deslon Case I 3.9-ln pipe diameter = 8´´�� L ¯ ¯ � ë L U _6´´ 8 On. �umplnQ sialion % L 5 � 4´´�� � ´ � ´ J ´ Deprecooloon rOle. per cenl Figure 5-7. Effect of depreCiation rate on economic evaluation. Sulfur Tnills/)orlalioll TecJmiques 123 Table 5-4. Comparison of Trasprtation Costs Method Rail Truck Conveyor belt Liquid pipeline Cost per 100 lb/mile $0.002 to $0. 003* $0.003 to $0.004* $0.00085 $0.00158 * Approximate 100-mile rates taken from reference (8). Both the conveyor belt and the pipeline appear to show substantial economic benefits over more conventional transportation methods. The use of a conveyor system undoubtedly would result in higher material-handling charges than would the pipeline system. These charges would tend to equalize the economics of the two methods. For convenience, the pipeline would probably be preferred. Further work should be done to ascertain the feasibility of operating a long-diS­ tance conveyor system in the humid climate found on the Gulf Coast. The application cited in reference [3) is located in a comparatively dry region. The mechanical difficulties of operating a conveyor de­ vice in the geographical area contemplated in the present design would probably eliminate this method from consideration. However, in other parts of the world it may well be worthy of further investi­ gation. One additional fact should be pointed out: the possibility that the rail or trucking firms would reduce their rates when faced with the competition from a pipeline. I any event, a preliminary design such as the one illustrated here is quite vluable as a preliminary means of comparing a pipeline system with alternative transportation methods. REFERENCES 1. Eckert, E. R. G., and R. M. Drake, Heat and Mass Transfer, McGraw-Hill Book Company, Inc., New York (1959). ? Economic Section of the :rench Embassy in the U.S.A., French Technical Bulletin No.6, 1, (1964). -- 3. Freeport Sulfur Company, Freeport Sulfur Handbook, Freeport Sulfur Company, Technical Servce Department, New York (1959). 4. McAdams, W. H., Heat Trasmission, 3rd Edition, McGraw-Hill Book Company, Inc., New York (1954). 5. McCabe, W. L., and J. C. Smith, Unit Oerations of Chemical Engineering, McGraw-Hill Book Company, Ic., New York (1956). 121 Clwpler þ 6. Perry, J. H., Chemical Engineers' Handbook, McGraw-Hill Book Company, Inc., New York (1950). Sherwood, T. K. , A Course in Process Design, The M.I.T. Press, Cambridge, Mass. (1963). 8. Tighe, F. C. , Chem. and Eng. News 31,3542 (1953). 9. Tuller, W. N., The Slfur Data Book, McGraw-Hill Book Company, Inc., New York (1954). 6. Vacuum Fractionator Design for the Purification of Styrene Monomer This is tile first of tlCO cases dealing ICi/1 the /JroductiOIl of styrene Iil 0/10111 er from ethylbellzene. This chapter describes tlte design of a fractionating colulIlll for the separation of styrene and ethylbellzelle, wllile C/w/ter 7 lcill deal wi th the dehydrogenatioll reactor for the COil version of etllylbellzene to styrene. In tie present chapter several allenzalive techniques are used ill tlte COlUlIl1l design. Since the distillation must be carried Ollt llnder mcuul/2, special cOllsideration is directed to the mechanical problems engendered by this type of opera/iOIl. / cOIll/mter program l5 pre­ sented to complete the design calculations by Sorel's method. This /Jrogram accollliis for tie s/Jecial equi/)lJ1ent limitation illl/}osed by mClllllll o/Jeratioll alld allon·s tile o/) til/2l1l/2 distillation s)stem to be selected for any specified set of feed conditions. Vandalia Chemical Company South Chicopee, Mississippi To: Wilbur Wol, Chief Design Engineer From: Herman Fox, Vice President Re: Styrene Production from Ethylbenzene A recent market study by the company's Economic Planning group indicates that the demand for styrene monomer will increase at a substantial rate over the next several years. Since the economic fore­ cast looks so promiSing, it is desired that your group prepare a pre­ liminary design for a process to produce styrene via ethylbenzene. Mter completing the design, you are to estimate the capital and oper­ ating expenses for the process in order to assess the feasibility of proceeding with this project. 125 126 Clapter 6 As you know, ethylbenzene is produced by alkylating benzene H the liquid phase over an AICl3 catalyst at 95°C. The ethylbenzene may then be dehydrogented over an alumina catalyst at approximately 600°C to produce styrene monomer. Many dehydrogenation processes require large quantities of steam to be mixed in the feed. However, the catalyst developed in the company laboratories functions most effectively when pure ethylbenzene is used as a feed. It may be neces­ sary to regenerate this catalyst periodically by means of steam. While another design group will be studying the alylation reaction, it is desired that your group concern itself with the dehydrogenation reactor and with designing the fractionatig equipment necessary for producing pure styrene monomer from the dehydrogenation reaction product. The Economic Planning group estimates that the proposed plant should be designed to produce 20 million lb/yr. Some relevant data and notes are herewith furnished. Data ß0 Notes The heterogeneous reaction kinetics for the dehydrogenation of ethylbenzene have been studied by Wenner and Dybdal (10), who pos­ tulated that the following reactions are important: MIO, cal! g mole 527°C 627°C '³uVe 29,715 29,824 24,472 24,282 29,770 (6.1) 24,377 (6.2) C S H5C 2 H5 ¬ H 2 � C S H5CH3 + CH -15,222 -15,537 -15, 380 (6.3) The equilibrium constants for these reactions, shown in Fig. 6-1, indicate that only in the case of Reaction 6. 1 is the reverse reaction important. Some of the kinetic data obtained by Wenner and Dybdal are shown in Table 6-1. Since only Reaction 6. 1 has a signiicant reverse reaction, the authors analyzed their data by assuming the following kinetic expressions for Reactions 6.1,6.2, and 6.3: r 2 = k2PE r3 =ll�EP/ (6.4) (6.5) (6.6) T a b l e Ü ¬ ¹ . C h e m i c a l K i n e t i c D a t f o r t h e D e h y d r o g e n a t i o n o f E t h y l b e n z e n e b y M e a s o f t h e T y e 1 C a t l y s t o f W e n n e r a n d L y D a l ( 1 0 ) C a t a l y s t C o n v e r s i o n B y p r o d u c t s B a s e d o n P e r f e c t E n t r a n c e F e e d R a t e N i t r a t e B e d B a s e d o n R e c o v e r y , l b m o l e s p e r R u n P r e s s u r e ( l b . m o l e / B a t h T e m p . T e m p . P e r f e c t ! b m o l e e t h y b e n z e n e f e d N o . ( a t m ) h r ) ( O C ) ( O C ) R e c o v e r y B e n z e n e T o l u e n e T a d % Y i e l d R - 2 2 8 1 . 0 2 0 . 0 2 0 7 5 5 6 5 5 2 0 . 2 2 5 0 . 0 0 5 4 0 0 . 0 0 6 3 6 0 . 0 0 4 9 2 8 2 . 4 R - 2 2 9 1 . 0 0 0 . 0 1 4 1 5 5 7 5 5 5 0 . 2 2 7 0 . 0 0 9 4 8 0 . 0 0 8 2 5 0 . 0 0 4 7 3 8 0 . 7 R - 2 2 7 1 . 0 2 0 . 0 2 1 9 5 5 7 5 5 5 0 . 2 2 6 0 . 0 0 6 3 0 . 0 0 6 8 9 0 . 0 0 4 5 5 8 2 . 5 R - 2 3 0 1 . 0 0 0 . 0 1 3 1 5 5 7 5 5 6 0 . 2 2 7 0 . 0 0 6 0 4 0 . 0 0 9 3 6 0 . 0 0 4 7 3 8 1 . 9 R - 2 3 7 1 . 0 4 0 . 0 2 4 3 6 0 4 5 9 8 0 . 2 4 6 0 . 0 0 5 8 7 0 . 0 0 8 1 7 0 . 0 0 3 6 2 8 2 . 2 * � R - 2 3 9 Í . 0 0 0 . 0 1 2 8 6 0 4 6 0 0 0 . 2 6 9 0 . 0 0 5 3 4 0 . 0 1 8 9 0 . 0 0 4 5 2 8 1 . 0 i R - 2 5 2 1 . 2 0 0 . 0 2 3 8 6 8 1 6 7 6 * 0 . 3 6 6 0 . 0 3 7 7 0 . 0 4 4 7 0 . 0 1 2 1 1 7 3 . 1 R - 2 5 4 1 . 2 0 0 . 0 2 3 5 6 8 1 6 7 6 * 0 . 3 6 0 0 . 0 3 9 6 0 . 0 4 1 2 0 . 0 1 3 2 8 7 3 . 0 ¯ " � R - 2 4 2 1 . 0 0 0 . 0 0 6 4 0 6 0 4 5 9 8 0 . 2 6 0 0 . 0 1 0 6 0 . 0 1 3 5 0 . 0 0 3 9 6 8 0 . 6 : R - 2 4 0 1 . 2 7 0 . 0 3 2 1 6 5 4 6 5 0 0 . 3 1 0 0 . 0 1 6 7 0 . 0 2 0 4 0 . 0 0 6 0 6 7 9 . 4 º � R - 2 5 1 1 . 2 0 0 . 0 2 2 7 6 7 7 6 7 1 * 0 . 3 5 5 0 . 0 4 3 0 0 . 0 4 5 9 0 . 0 1 1 4 7 2 . 2 0 " R - 2 5 5 1 . 0 0 0 . 0 1 3 1 6 7 4 6 6 8 * 0 . 3 7 2 0 . 0 5 6 1 0 . 0 6 9 6 0 . 0 1 6 8 6 8 . 2 C � v R - 2 3 2 1 . 0 0 0 . 0 0 6 8 9 5 5 7 5 5 5 0 . 1 9 5 0 . 0 0 2 9 8 0 . 0 1 7 7 0 . 0 0 3 6 5 7 9 . 1 7 o ´ z * E s t i m a t e d t A s s u m e d m o l e c u l a r w e i g h t 1 8 0 . - l ¯ 128 Clapter 6 L ¯ N x ! _ ¹ t F + ! _ ª |HêccJion õ |1 ß 2 c o � » L z � x [I _ °_ g /! _ " .,, ., _·. ¸·.. IHêcc¡¡on õ.õ1 _ �_� _ _�_ __ __¨¨ _ _ ¨ ¯0mµ0t01uf£¸¨L Figure 6-1. Equilibrium constants for dehydrogenation. (After Wenner and Dybdal, reference 10.) o ¯ S Maing use of the data of Table 6-1 and rate CQUû!ÎOuS 6.4,6.5, and 6.6 they obtained the following exressions for Ill, Il 2 ' and Il 3 : -11,370 log IO ' . 1 = + 0.883 4.575T -50, 800 log IO k 2 = + 0.883 4.575T -21,800 log IO ' . 3 = 1 9.13 4.575T (6.7) (6.8) (6.9) The data points used in determining Eq. 6. 7 are shown in Fig. 6-2. All of the kinetic data gathered by Wenner and Dybdal were obtain­ ed using an alumina catalyst whose particle size ranged from 4- to 8- mesh standard Tyler screen size. The bulk catalyst density was O1 lb/cu ft. -l M • • • • 8 • • 8 .. • • • • 8 • 1.0 �- ' • • ¯ Z 1.1 1.2 IO/T wtfhT M "K ¯ Vacuum Fractiol1ator Desigll 129 .. 1.3 Figure O-Z. Kinetic constants for the dehydrogenation of ethylbenzene. (After Wenner and Dybdal, ICÎCICnC6 10.) Assumptions for the Distillation Colum Desig 1. The maximum allowable temperature in the column is 90°C, because the styrene will polymerize if this temperature is exceeded (3). In fact, a nonvolatile reaction-retarding agent must be continu- 0usly fed to the top plate of the column in order to make possible an upper limit of 90°C. 2. A vacuum system operating at 40 torr is available. 3. The pressure drop across each tray will be assumed constant at Z in. of water, and the over-all column efficiency will be taken as 70 per cent. Actually, some of the more modern sieve-tray designs allow pressure drops signiicantly below the assumed value (1). Also, special trays of the type licensed by Linde Division of Union Carbide have tray efficiencies far higher than 70 per cent (). The assumed pressure-drop and efficiency values may therefore be thought of as conservative estimates. Once a procedure has been established for the colunm design, it will be of interest to investigate the effects of improving the pressure-drop characteristics and efficiency of the trays to be used. 4. The composition of the distillate and bottoms must be XD = 0. 98 2_ ~ 0. 01 where 2 refers to the mole fraction of ethylbenzene. Common in­ dustrial practice might dictate a limit of 0. 003 for 7 D (1). As in the case of the tray hydraulics, the design computer program may be 1oÜ Chaptel' Ó used to test the effects of bottoms composition on the process econo­ mics. 5. U optimizing the distillation column, the following may be assumed: a. Capital cost for column ~ 12 d 1.2 dollars/tray, where 0 is equal to the column diameter expressed in inches. 0. Assume that the column may be depreciated at 20 per cent per year of 8000 operating hours. L. Steam costs may be taken as $0. 80/1000 lb. d. Cooling water costs $0.02/1000 gallons. The cooling water is avilable at 70°F; in order to minimize scaling problems, this water should not be heated above 125°F. Sggested Nottion D Flow rate of material in the bottoms stream, lb moles/hr C Cost; CD refers to a depreciation cost, L_ the cost for steam, and Ccw to the cost for cooling water, dollars/year 0 Column diameter, it Ï Flow rate of material in the distillate stream, lb moles/hr Î Flow rate of material in the feed stream, lb moles/hr k Kinetic constant for a heterogeneous reaction, lb moles/hr-atm­ lb catalyst for reactions 6. 1 and 6. 2, and lb moles/hr-atm2-lb catalyst for reaction 6. 3 'Î Equilibrium constant for styrene formation, atm Ñ Number of columns W Number of plates L Flow rate of liquid in the rectifying section of a distillation column, lb mole s/hr P Partial pressure, atm o Vapor pressure of a pure liquid, torr Ï Pressure, torr �Ï Pressure drop through the column, equal to Ï B - PD, torr 7 Rate of reaction, lb mOles/hr-lb catalyst Û Universal gas constant, cal/g mole-OK o Number of stages in a distillation column, equal to W ¬ 1 T Temperature, oK O Vapor velocity in a distillation column, ft/ sec V Boil- up rate in a distillation column, lb moles/hr 7 Mole fraction of ethylbenzene in the liquid phase Y Mole fraction of ethylbenzene in the vpor phase VacuulIl Fracliollator Design 131 Ô Relative volatility, equal to P�/ 15 Mr Standard state enthalpy change for a chemical. reaction, cal/g mole �Í Heat of vaporization, cal/g mole ÍL Density of liquid phase, lb/cu ft Í7 Density of vapor phase, lb/ cu ft Subscripts rLJ Refers to the actual number of trays Ö Refers to the bottoms stream; DJ refers to the bottoms stream of column 1, etc L Refers to the critical vapor velocity i a distillation colum as limited by entrainment consideration / Refers to a distillate stream; /] refers to the distillate stream of column 1, etc @ Refers to ethylbenzene Î Refers to the feed stream @ Refers to hydrogen Refers to component l m Refers to the minimum reflu ratio ܧ0IB0IͧÍB • Refers to an equilibrium property DESIGN OF THE REACTOR A FRACTIONATOR FOR ETHYL­ BENZENE PRODUCTION A preliminary flow sheet for the production of monomer grade styrene from ethylbenzene is sketched here. No provision has been made in this sketch for the removal of tars from the reactor product stream nor for that of the hydrogen produced in the reactor. Feed stream Reactor Reboiler To vacuum Ethylbenzene to recycle Styrene product 132 Clwpter Ô In addition, the removal and separate purification of benzene and toluene should be undertaken. Generally, these steps are accom­ plished prior to the ethylbenzene-styrene separation. Finally, the tars are usually removed by use of a finishing tower operating on the styrene product from the ethylbenzene-styrene separation (4). The process shown in the flowsheet makes use of the indirect addition of heat, in contrast to direct heat addition which can be accomplished by injecting steam into the feed mixture. Ohlinger and Stadelmann (5) have described some alternative schemes simi­ lar to that suggested here. A study of their work is most helpful in providing a broader understanding of this particular type of reactor design. In addition, Carra and Forni (1) have provided kinetic data which are useful in interpreting the processes described in refer­ ence (5). The memorandum asks that a design be completed for both the reactor and fractionation units shown in the block flow diagram. Obviously, the designs of these two units cannot be carried out inde­ pendently, since feed rate and composition for the column depend upon the operation of the dehydrogenation reactor. To circumvent this problem and to illustrate the design method used, a feed rate and composition typical of the reactor operation will be assumed, and the distillation column will be designed. A generalized computer program will then be written which will carry out the design calcu­ lations for the fractionator for a wide variety of feed rates and feed compositions. Next, the kinetic data presented by Wenner and Dybdal (10) will be examined in detail. With these data, as modified by the present study, the design of the dehydrogenation reactor will then be com­ pleted. Again, by means of a computer program the reactor design calculations may be carried out for a wide variety of conditions. By combining the computer program for the reactor design with that for the column design, the design of the reactor-column system as a unit may be optimized. DISTILLATION COLUM DESIGN Development of Vapor-Liquid Equilibrium ÏU The vapor pressure data for ethylbenzene and for styrene which are necessary for the column design are tabulated in Perry's Hand­ book (7. These data may be checked for consistency when it is re­ membered that the data for each pure component must be well cor­ related by the Clausius-Clapeyron relationship. Thus, Fig. 6-3 was prepared by plotting the logarithm of the vapor pressure for each component against the reciprocal of absolute temperature. The data fall on a straight line, ad the heats of vaporization as computed from the slopes of these lines agree well with experimental values VuCuuììI Fractiollator Design 133 4 5 ^ -, � _� N ` ` . � - � � `. 4 " � -` � | ` ¿ l0 2.70 2.B0 2.90 3.00 3.I0 3.20 3.30 I000'J wI1D ¯ |D "h Figure 6-3. Vapor pressure data for styrene and ethylbenzene. (Perry's Handbook, reference 7 given in the literature (7). Therefore, the vapor pressure data shown in the figure will be used in the design. Since the molecular structures of ethylbenzene and styrene are very similar and since both materials are reasonably nonpolar, one might anticipate that liquid mixtures of these two components would be ideal. Fortunately, the validity of this supposition can be verified by referring to the paper of Chaiyavech and Van Winkle (2), who per­ formed a very extensive study of styrene-ethylbenzene vapor-liquid equilibria at reduced pressures. For variations in the total pressure of 10 to 200 torr and at temperatures from 26° to 97°C, these investi­ gators have shown that the vapor-liquid system is Ü ideal one. The r\n:~�11 deViR!\On from idealitv. as measured by the activity coeffi­ cients, was less than 2 per cent, and this discrepancy was within the limits of probable experimental error. From the assumption of ideality and the vapor-pressure data of Fig. 6-3, the relative vola­ tility of the styrene-ethylbenzene system may be computed as a function of temperature. This calculation has been carried out for temperatures ranging up to 90°C, the maximum allowable tempera­ ture for liquid styrene in the present process, and is summarized in Table 6-2. 134 Chapter 6 Table Û¬Z, Relative Volatilit of Ethylbnzene-Syrene Miures Computed by Assuig a Idea Liquid Phase T (OC) T (oK 1000iT (oK p o b p o Ë Õ = PEIP' . ,- , . _ _-- -- 40 313 3.19 16.4 22.0 1.34 50 323 3. 10 25.1 34.3 1.365 60 333 3.00 40.8 55.9 1. 37 70 343 2.92 60.0 82.3 1.37 80 353 2.83 92.8 128.0 1.38 90 363 2.75 137.0 190.0 1. 385 Since the variations in relative volatility with temperature are so slight, an average value of Õ may be selected at a temperature level typical of that to be encountered in the process. This value may then be assumed constant for all calculations. In this manner, an average value of 1. 37 is selected for the relative volatility, and the design will be completed on this basis. Cacuation of Minimum Number of Plates Since Õ is assumed constant, the minimum number of plates to complete the desired separation can be calculated using the Fenske equation (8), whereby log ¸ 1 �: ¸¸� ·j| W + 1 .- ------- log Õ N + 1 = log ¸¸ 0 . 9 8 ¸¸ 0. 99 ¸¡ 0.02 0.01 log 1. 37 N + 1 .27 Twenty-seven theoretical stages would therefore be required to carry out the specified separation when operating the column at total reflux. Calculaton of Minimum Reflu Ratio The minimum liquid-vapor ratio in the rectifying section of the column is easily computed from the following equation: where Û(X F ) Y (e -l)X F + 1 and in the present case, (1. 37)(0. 70) Y ~ (0.37)(0.70) + 1 Y = 0.762 Therefore, (a/ V ) . = 0 . 9 8 - 0.762 un 0.9 8 - 0.70 ~ 0.778 VuCuHD JI´uClÍOlI0lOI Design 135 From this value, the minimum reflux ratio, ( O /D)l I lin' can be cal­ culated as follows: (O/ V ) min 0.778 (a/D) i = = -=3 50 m n 1 _ ( O / V )min 0.222 . Cacuation of te Act Nubr of Trays Once the minimum number of trays and the minimum reflux ratio for the desired separation have been established, there are several available methods for computing the number of trays required as a function of reflux ratio. Since these methods vary in their complexity and in the accuracy of the resulting answers, two of them will be illustrated here. In addition, the results of a third one will be pre­ sented. 1. Gilliland Method. Using normalized, dimensionless variables, Gilliland has plotted the number of fractionation stages versus reflux ratio. Using his correlation, we may find the number of stages re­ quired at 1. 3 times the minimum reflux ratio by the following com­ putations: (a/D) = (1 . 3) (3. 50) = 4.55 From Fig. 12-2 of Robinson and Gilliland (8), (a/D) - (O/D) m in 4.55 - 3. 50 = -- = 0.18 9 ( a/D) + Í.M 4.55 ± 1.0 136 Chapter 6 whereby from the chart ~ S m i n Ü·¹ 27. 44 T 0. 44 and Ü= ¬T 9Ü theoretical stages 0. 56 Erbar and Maddox have presented a correlation which for some sys­ tems appears to be more accurate than that of Gilliland. Oliver (6) provides an excellent discussion CÎ this new correlation, which may be used to provide additional insight into the present problem. 2. McCabe-Thiele Method. For a binary system for which the equilibrium data are well known, the most accurate technique for computing the number of trays in a column is the McCabe-Thiele method, which is merely a graphical representation of the Lewis­ Matheson computational technique. With equilibrium data computed using a constant value for Ô of Í. 37, Fig. 6-4 was prepared to illustrate the McCabe-Thiele method for the case of (a/D) = Í. 3 (O/D)mi n . As can be seen, this method indicates that 44 theoretical stages are required for the separation. |.Õ O.Ð O. Ü >- o g Û.7 . O! � Û.D w : Û.A 9 ¯ ± O.Ò a T :; Õ´ Lowet çot¡ioo ot s¡··pp·oq s¢c¡·oo C.C5 C1C O.¡ Û.Z O.Ò Oº O.D O.! O.7 O.Ü O.Ð l.O Mo|e froc!ion o! e!hyIbenzene in |¡quid¡ X Figure 6-4. McCabe-Thiele design of the distillation column. \CCuuD Ïr0CÍlOn0lOT DesiKIl 137 3. Other Techniques. Robinson and Gilliland (8) present several other techiques f or te computation of the number of required stages. For the most part, the calculations required are quite tedious, and it is usually best to rely on the McCabe-Thiele method unless an excep­ tionally large number of trays is needed. One of the methods described in reference (8), that of Lewis, was used in the present study for illustrative purposes. It indicates that 46 stages are required for DID = ¹. 3 (OID)m in; this number com­ pares well with previous computations. 4. Summary of Results. Table 6-3 has been prepared to allow comparison of the various calculational procedures. The number of actual plates required for the separation has been calculated for each case by assuming an over-all tray efficiency of 70 per cent. Tale Û¬ð, Stes Required for the Fractionation of Srene ad Etylbenzene when DID ~ Í. ð (OID >in Number of Àt\DOU Theoretical Stages Gilliland 49 McCabe-Thiele 44 Lewis 46 Nuber Actual Stages 70 63 66 The three methods used are in reasonably close agreement. Gilliland's method is the most convenient to use but also probably the least accurate. If the equilibrium 7-Y diagram is carefully prepared, the McCabe-Thiele method is probably the most accurate; however, when large numbers of plates are involved, as in our case, significant errors may result from using the McCabe-Thiele technique. The Lewis method is a bit cumbersome, but for systems requiring large numbers of trays it is quite accurate. For the present case, it will be assumed that 66 actual stages are required when the reflux ratio is 30 per cent greater than the minimum. Pressure and Temperature Considerations in te Desig Since the design instructions require a 90°C maximum tempera­ ture in the column, it is necessary to determine temperature and pressure profiles for each column design. Because the proposed column is to operate under a vacuum, the pressure drop in the column will be quite important in determining the temperature level on each tray. For example in the 66-stage column just designed, the pressure drop may be computed as follows: N ¯ o-¹ = 65 138 Chapter Ó where it is assumed that MIN T 2 in. of water ¸ 760 ¸ T 2 T 3. 7 torr 34 X 12 and M T 3. 7(65) T 240 torr Since the pressure at the top of the column is 40 torr, that in the reboiler is computed as J 0 T 240 ± 40 = 280 torr However, if the temperature in the reboiler were equal to 90°C, the pressure in the reboiler would be J 0 T � x _ p� T (0. 01) (205) + 0. 99(138) T 139 torr Thus, at the bottom of a tower with 65 trays the temperature would be greater than 90°C, and clearly an alternative design scheme must be proposed if the restriction on the reboiler temperature is to be met. An alternate scheme that might satisfy the temperature limitation would use two towers (Fig. 6-5) . |eed sIreom T0 v0cuum system oI ~~~~ ¬¬~~ 4Ù I0rr 0 vocuum Boltoms streom Io 0!IercooIer ond stor0ge Figre 6-5. Two-column system for the fractiona­ tion of ethylbenzene-styrene feed. To check the feasibility of such a process scheme, the tempera­ ture and pressure in the bottom of the first column must be com­ puted as a function of the number of trays in that column. The \uCuuD JIuClÍOnu|Or LcSl¿lI 139 results of this computation are show in Table 6-4. In these calcu­ lations,X E is read directly from the McCabe-Thiele diagram (Fig. 6-4) , and total pressure at the bottom of the first column is computed on the assumption that T B = 90°C. Table Û¬9, Assumed N l 40 30 35 36 Temperatue 80 CompOSition on Btom Tray of First Colun /_ = PE l = 3. 7 '1 40 ¬ =1 148 torr 188 torr 111 torr 151 torr 130 torr 170 torr 133 torr 173 torr 0. 7 N l 28 21 24. 5 25 PB 2 7_ at 0.7 N l = 205X E (from Fig.6 - 4) ¬ 1óO2 ¿ 0. 4 165 0. 67 182 0. 56 176 Û. 54 174 Hence, a two-tower system with 36 trays in column 1 would satisfy the restriction on the reboiler temperature. Note that the tempera­ ture at the top of the second tower must be low enough so that J__ will be 40 torr. This temperature is calculated by trial and error from vapor pressure data (Fig. 6-3) and the composition of the liquid stream at the 37th tray (Fig. 6-4) . Assumed Temp. oC _o £ ] o ¿ Û.54 p� 0.46 p� P D 2 = � Pi 55 44 33 23. 8 14. 5 38. 3 56 46 34 24. 8 15. 6 40. 4 Therefore, the liquid leaving the first column at point! in Fig. 6-5 must be cooled to 56°C before being fed to the top of the second column. Checking pressure drop through the second column, we find that P B 2 = (30)(3. 7) ¬ 40 = 154 torr Since the X E at the bottom of the second column is 0. 01, P B 2 may be compared with 1_ o ¸which is 1D+ torr at 93. 5°C. Therefore, at a reflux ratio of 1. ó (0/ D) three towers would be required to com ­ plete the separation without exceeding the maximum temperature specification of 90°C. 14Û Chapter Þ RESULTS FOR OTER REFLU RATIOS The results for other reflux ratios are shown in Table 6-5, Table Û¬Ü, Resuts for te Nubr of Trays ad the Nuber of Colus (O/D)/(O/D)m i n (O/D) *ACT Number of Towers 1. 2 4. 20 77 3 1. 3 4. 55 66 3 1. 45 5. 07 63 2 or 3 1. 70 5. 95 60 2 which maes clear that for all (O/D)/(O/D)min > 1. 45 two columns will be required, while for all such ratios < 1. 45 three columns are needed. For the purpose of this design, the number of columns will be arbitrarily limited to a maximum of three, although more than three columns obviously would be necessary at very low OlD ratios. At the other end of the spectrum the minimum number of theoretical trays in the system is 26; this corresponds to 37 actual trays. Thus, it is clear that at least two columns will be required to carry out the desired fractionation, regardless of the reflux ratio. OPTMIZATION OF THE SYSTEM It will be remembered that a feed composition of 70 mole per cent of ethylbenzene has been assumed. The distillation column system will now be optimized while maintaining this assumed feed composition. A computer program will then be developed that will be useful for the entire range of feed compositions as well as for variations in other important design parameters. Computtion of the Colum Diameter In order to ascertain the diameter of the column system, the hydraulics of the liquid and vapor flow within the column must be considered. The limitation on the size of the column is imposed by determining the maximum superficial vapor velocity that can be allowed. In turn, the vapor velocity is limited by the liquid­ handling capacity permitted by the tray design or by the increase in liquid entrainment as the vapor velocity is increased. As men­ tioned previously, a complete consideration of the tray hydraulics is beyond the scope of the present design; however, the computation of the entrainment limitation should serve as a good criterion for this preliminary tye of design. VuCuuD ÍTu0lOnu|OT Desi 141 In the design of a vacuum column where the absolute pressure varies significantly through the column, it is common to specify a larger column diameter in the rectifying section than in the stripping section of the column. This practice is necessary to maintain the vapor velocity within reasonable limits. U the present design were being carried out in detail, the column diameter would undoubtedly be varied through the column. However, to simplify the calculation, a single diameter will be computed at the average column pres- sure of 90 torr. U a tray spacing of 12 in. and Û liquid seal of 0.5 in. are specified, the correlation based on entrainment limitations indi­ cates that (8) O 0 ¸ Í " ¸ ¸¸¸ = 0. 13 ÍL¯ÍV Taing the specific gravity of the liquid mixture to be 0. 8 and com­ puting the vapor density at 90 torr, we have ¸ 49. 9 ¸ ¸ ¸ O 0 = 0. 13 = 5. 5 ft/sec 0. 0279 Using this critical velocity, the column diameter may be computed once the boil-up rate has been specified. More recent correlations have been established for the critical velocity. The most important of these are discussed by Fair and Bolles in Smith's text (9). In pursuing subsequent, more detailed analyses of the tray hydraulics for this design, the reader would be well advised to consult this excellent reference. Heatig ad Cooling Duties To visualize the heat exchange problem for this column, it is useful to construct a "pseudo" pressure - enthalpy diagram for the system, as shown in Fig. 6-6. The numbers on this diagram cor­ respond to those on Fig. 6-5. |74 3 � = ; óÞ ��- [n!h0lpy (¶tu/1bÌ ~ Figre 6-6. Pseudo pressure-enthalpy diagram. Numbers correspond to numbers in Fig. 6-5. 142 Clmpler ó Since the (O/V) m i n ratio in the column may be taen very roughly as unity, the heat exchanger shown in Fig. 6-5 may be used to cool the hot liquid from the first column by heating the condensed vapor from the top of the second column. Clearly, however, this heat ex­ changer can account for only the sensible heat changes of the two streams, and a vaporizer must be supplied to boil the feed to the bottom of the first column. Hence, when two columns are required for the separation, the reboiler and condenser duties are effectively doubled. This is a good assumption, since for liquid ethylbenzene­ styrene mixtures the enthalpy of vaporization is an extremely weak function of temperature and composition. Thus, for (O/D)/(O/D)mi n < ¹. 45, the reboiler and condenser duties will be taen as twice those for a single column. For (O/D)( O/D) m i n < 1. 45these duties will be assumed to be three times those for a single column. Optimization Computtions Restrictions 7g = Û. 70 X D = 0. 98 X B = 0. 01 (1 X B )B ~ 20 ^ 106 lb/year For 8000 hr/year operation (20 Y 106)(0. 99) Ü = = 24. ó lb moles/ hr (8 Y 10 3 )(104. 02) Now to determine V, the boil-up rate, as a function of (O/D) and D. V = L(O/D ± 1) where L = Ï D¸ and ÏX F T D X D ± ÜX B • Hence, in general, and V ¯ Ö ¸ X B - X F¸ (O/D ·1) X F ¯·D Vacuum FracLionalor Design 143 For the present case: ¸0. 01 - 0. 70¸ V = (24. 3) (O/D ± 1) 0. 70 - 0. 98 ~ 60. 0 (O/D ± 1) NOw, the velocity to be used in the specification of a column dia­ meter is to be computed at an average pressure of 90 torr. Thus, ¿760¸¿326¸ (60. O) (O/D ± 1) (359) 90 273 76. 9 (O/D + 1) O = 3600 (1 / 4) Ó^ = ¯ ^ Setting O equal to the maimum allowable velocity of 5. 5 fps, one obtains 0 = 3. 74 (O/D ± 1)1/ ÎI = 44. 9 (O/D + 1)1/ 2 in. and the yearly depreciation of the column is C D = N { 12 [ 44. 9 (O/D ± 1)1/ 2 ] 1 . 2 } (0. 2) = 232N(O/D ± 1) 0 . 6 Note that the capital cost for the column system is taen to be a function of the number of trays only and not of the number of columns. This assumption is obviously a great simplification of the true situation. For styrene, from Fig. 6-3, bH C In p O In 200 ¯ In 20 - = ¯ ¥ ¯ = 47900K Ì C (l/T) (2. 67 - 3. 15) K 10-3 bH = 9500 cal/g mole or 17,100 Btu/lb mole The steam costs for boil-up are (60. O) (O/D ± 1)(17,100) (0. 80) (8000) / C s = - 6780 (0 D ·1) (970) (1000) dollars/year where the heat of vaporization for steam is taken as 970 Btu/lb. It must be remembered that this steam cost is that required for a single column. Costs for condenser cooling water may be estimated as C _ (60.0)( OlD + 1) (17, 100) (0. 02) (8000) LW ¯ (55) (8. 35) (1000) = 358 (O/D ± 1) dollars/year Thus, for a single column, C s + C c = 7140 (O/D ± 1) dollars/year 144 Chapter Ô Now all costs for the distillation system are known in terms of the reflu ratio and the number of trays required for the separation. The computed costs for typical reflux ratios are shown in Table 6-6. These costs may be plotted versus reflux ratio in order to obtain the optimum reflux ratio for this system (Fig. 6-7) . Because of the increased heating and cooling duties required in the three-column system, a discontinuity in the total cost curve fixes the optimal point at (OlD) = 5. 07. In the actual desi n a reflu rS1í^ somewhat higher than this should be used, as slight variations in pro­ cess conditions could lead to temperatures above 90°C if the system were operated exactly at the optimum point. 18 16 140 � � 120 � ñ " ".10 ¬ o ë .� 80 i C �« u % Z Ü 1.0 ' , , ./" , , , b/ a V , , , > , I < , �´ . \ ` ¯ I- e -� 0= 1.2 1.4 1.6 1.8 (0/0)/(0/0) .. 2.0 Figre 6-7. Economic optimization of the distillation column sys ­ tem. DeSign conditions: Legend 7 | ~ 0. 70 ¯ Total annual cost ªD ~ M.Üd A Steam costs 7 0 ~ M.M1 Ø Deprec- iation costs Ï ~ 24. 3 lb £ Cooling- moles/hr water costs , g T a b l e Ü ~ Ü , C o s t s f o r t h e D i s t i l l a t i o n S y s t e m O l D Î = N o . O / D m i n o f T o w e r s ( O l D ) À ( O l D ÷ 1 ) 0 . 6 1 . 2 0 3 4 . 2 0 7 7 2 . 6 9 1 . 4 5 3 5 . 0 7 6 3 2 . 9 5 1 . 4 5 2 5 . 0 7 6 3 2 . 9 5 1 . 7 0 2 5 . 9 5 6 0 3 . 2 0 L D L 3 C C I V $ 4 8 , 2 0 0 $ 1 0 5 , 8 0 0 $ 5 5 8 0 4 3 , 1 0 0 1 2 3 , 7 0 0 6 5 7 0 4 3 , 1 0 0 8 2 , 4 0 0 4 3 5 0 4 4 , 6 0 0 9 4 , 3 0 0 4 9 8 0 L T $ 1 5 9 , 6 0 0 1 7 3 , 4 0 0 1 2 9 , 9 0 0 1 4 3 , 9 0 0 � ¯ ~ � Æ ¯ � � ¯ " o · � 0 � C ¯ � . � - × ~ 1¬Þ Chapter Þ REVIEW OF THE DESIGN TECHNIQUE The two-tower distillation system as discussed in this chapter is a classical design that has been applied to styrene processes for decades. The optimization calculations summarized in Fig. 6-7 are the result of several approximations that were used to simplify the presentation and to emphasize the more important aspects of the design technique. From the results obtained, it is clear that the assumed values for over-all column efficiency and for tray pres­ sure drop are critical in determining the ultimate design economics. For example, the use of a tray design that would provide a higher efficiency at a lower pressure drop would allow a distillation system requiring only one column. Indeed, recent advances in tray design have made this feasible, and the two-tower distillation system has been replaced by single-tower fractionators in virtually every modern styrene installation (4). The column design has been carried through to the development of a rather elaborate computer program, which is here presented so that it may be used to investigate further the economics of the styrene purification process. In particular, the effect of variations in the tray hydraulic characteristics should be studied because of their potential impact upon the process economics. It has been pointed out that the feed concentration to a commercial ethylbenzene-styrene tower is usually 45 to 60 mole per cent ethylben­ zene (4). Many of the newer plants apparently find it advantageous to operate in this range despite the yield losses that must result from the use of higher conversions. Since the present design has assumed 70 mole per cent of ethylbenzene in the feed, the computer program should prove valuable in investigating the economic effects of variations in the feed composition. DEVLOPMENT OF A COMPUTER PROGRM FOR TI DESGN OF THE DISTILLATION COLUM SYSTEM It will be remembered that the distillation system was designed after fixing the feed composition. At this point, a computer program will be written so that computations may be completed for a wide range of feed compositions and reflu ratios. This development will assume that the reader is familiar with the fundamentals of machine programming. In addition, some familiarity with the FORTRAN auto­ matic coding system will be necessary. The reader who is not familiar with the languages and strategy of programming is referred to the comprehensive series of reference manuals published by the International Business Machine Corporation. Figure 6-8 shows the flow diagram for a FORTRAN program for the computation of the number of trays and number of columns re­ quired to produce a styrene monomer product of the desired purity. The program requires as input the flow rate and composition of the feed stream; these quantities will be established only after the reac­ tor design has been completed. For the present, however, the nature Input Material balance Establish operating lines InitialIZe variables compute number of trays by LPwI5·NDThP5OR mPThO0 compute actual number of trays and costs Pr int output \u0|thìII FraclioJlator Design 147 RRMI�, f, Xf, X0 RmN1NI, ANT1NI fT1N1¿CÛT1NI, CMô1N1,ôTCÛô1NI, ÜWô1NI ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯T Figure O¬O. Flow diagram for the FORTRAN computer program. (Circled numbers refer to statement num­ bers in the FORTRAN program.) of the feed stream will be assumed to have been established. Also required are the bottoms (styrene) flow rate and composition. The styrene stream has of course been fixed in the original design specifications at 20 Y 106 lb/year of 99 mole per cent pure product. After reading the input variables, the program then completes a material balance and specifies the distillate flow rate and composi­ tion. The minimum reflux ratio for the required separation is then computed. The method used is conceptually very straightforward; if desired, the program can be shortened substantially if the tray-to-tray calcu­ lations are replaced by the Smoker equations or the Underwood 148 Chapter 6 equations in their binary form (8). Also, since the general shape of the optimization curves (Fig. 6-7) is already known, the computing effort could be reduced to a narrow rage of (O/D) /(O/D) min and the slopes of the cost curves could be tested to determine the opti ­ mum. Either of these approaches would constitute desirable design projects. Next the program enters a "DO-loop" in which the required num­ ber of trays and number of columns are computed for each specified value of the reflux ratio. Actually, the calculation is carried out for a wide range of values for the variable RRCN(I) , which represents the ratio of the operating reflu ratio to the minimum reflux ratio. For each value of RRCN, the equations of the upper and lower operat­ ing lines are first developed. Then, starting from the top of the column, plate-to-plate calculations are made using the method of Lewis and Matheson (8). Since constant molal overflow has been assumed, this method merely involves alternate applications of the equilibrium relationship and the material balance (operating line) expressions. At the conclusion of this calculation, the number of theoretical trays and the feed plate location have been specified. As a final step in the "DO-loop," the column diameter is computed, the required number of columns and the actual number of trays are calculated, and the capital and operating costs are specified. In these calculations the maximum number of trays per column has been set arbitrarily at 33. This of course is an approximation, but it seems suficiently accurate for the purposes of the present work. As the last step in the machine program, a table is printed which shows the number of trays, the feed tray, and the operating and capi­ tal costs as functions of RRCN. The Appendix contains the actual FORTRAN program used as well as the output from this program, which corresponds to a feed stream flow rate of 71 Y 106 lb/year having an ethylbenzene composition of 70 mole per cent. The rela­ tive volatility has been taen as 1. 37 for this computation. The re­ sults shown in the output table compare well with the manually com­ puted results shown in Fig. 6-7. ÏLܯÜP Notation A Slope of upper operating lie when the column is operating at miimum reflux ALPHA Relative volatility AT Actual number of trays required for the desired separation CEPTL Intercept of lower operating line on the Y-ais of a McCabe- COST Thiele diagram Total annual operating cost for a distillation column, equal to the sum of the costs for cooling water, steam, and deprecia­ tion,dollars/year CPCOS Annual depreciation charge for the capital invested in the column, taken as 20 per cent of capital, dollars/year V0CuuD Ï10CÍÍOn0ÍO1 Desi 14Û CWCOS Annual cooling water costs, dollars/year D Distillate rate, lb moles/hr F Feed rate, lb moles/hr FT Feed tray location I Subscript corresponding to plate number N Subscript corresponding to the particular reflu ratio that is being considered NC Number of columns NFT Theoretical number of trays NT Actual number of trays QCEPT Value of Y which corresponds to the itersection of the upper and lower operating lines QN Liquid flow rate in the rectifying section of the column RR Oerating reflux ratio RRCN Ratio of the operating reflux ratio to the minimum reflux ratio RRM Minimum reflux ratio SLOPL Slope of lower operating line STCOS Steam cost, dollars/year TNT Total numbe: of theoretical trays TIDX Internal diameter of column, ft USLOP Slope of upper operating line UCEPT Intercept of upper operating line with the Y axis V Boil-up rate, lb moles/hr XB Mole fraction of ethylbenzene in the bottoms 7 Mole fraction of ethylbenzene in the distillate XF Mole fraction of ethylbenzene in the feed Y(I) Mole fraction of ethylbenzene in the vapor phase YCEPT Equilibrium value of Y corresponding to XF, equal to ¥¨ REFERENCES 1. Carra, S. and L. Forni, Ind. Eng. Cher. , Process DeSign and Development 4, 3, 281 (1965). 2. Chaiyavech, P. , and M. Van Winkle, J. Cher. Eng. Data 4, 1, 53 (1959) lOÜ Clza/ier 0 ð. Faith, W. L.,D. B. Keyes, and R. L. Clark, Industrial Chemicals, John Wiley & Sons, Inc., New York (1950) . 4. Kehde, H., Styrene Technology Center, Midland Division Research and Development, Dow Chemical Company, Midland, Mich. per­ sonal communication, October 1967. 5. Ohlinger, H., and S. Stadelmann, Cher. Ing.-Tech. ðݸ 361 (1965) , 6. Oliver, E. D., Diffusional Separation Processes: Theory, Design, and Evaluation, JohWiley & Sons, Inc�Nork (T 966). 7. Perry, J. H., Chemical Engineers' Handbook, McGraw-Hill Book Company, Inc., New York (1966) . 8. Robinson, C. S., and E. R. Gilliland, Elements of Fractional Dis­ tillation, McGraw-Hill Book Company, Inc., New York (1950). 9. Smith, B.D., Design of Equilibrium Stage Processes, McGraw­ Hill Book Company,lnc.,New York ( 1963) . 10. Wenner, R. R., and E. C. Dybdal, Cher. Eng. Progr. 44, 275 (1948) ¯. ÎlOCBSS LBSÎgD BDU CVB¡UB1lOD ÍOl 1DB ÎlOUUC1ÎOD OÍ Û1¶lBDB þODODBl This case foclises ÓÌÎ the design of a yeact oy for tile catalytic dehydro­ genatioll of ethylbenzelle to /)Yoduce styrene. Initial elllphasis is placed ÓÌÌ tlle analysis of laboratory Idlletic data and on ascertailling Ille iu­ fluence of mass t ransfer effects ÓÎÌ Ihese data. Afler an acce/Iable correlalion of the dala is achieved, a cOlllmercial-sclle dehydrogena­ tion react or is modeled bJ' a set of nonlinear diferential equalions. . com/mler program is IcriltCIl for tie solution of Ilese equations. The effects of mass transfey in the bulll gas and diffusion within calalyst pellets are found lO be particularly significant faciors in tie reactor operalion. The computer program from Chaptey Ô is combined with the reac­ tor design /)Yogram prepared in Chapter 7, so thai a filla/lcial evalua­ tion of Ihe reactoY-fraclionatoy combination call be completed. The optililum process is selected ÓÌÌ the basis of this el'aluation. Vadalia Chemical Compay Suth Chicopee, Mississippi To: Wilbur Wolf, Chief Design Engineer Fyom: Herma Fox, Vice President ÍC´ Styrene reactor design The preliminary design work for the ethylbenzene-styrene frac­ tionating unit which was prepared by your group has been received and is now being reviewed by my staff. Your design appeared to ac­ count for all the important operating variables in the system with the exception of the feed rate and feed composition. Naturally, a de­ tailed consideration of these parameters was not warranted because the reactor design had not yet been completed. 151 1O< Chapter 7 It is now desired that your design group proceed with the reactor design. After completing consideration of the reactor it should be possible to optimize the reactor-fractionator process unit. Most of the information necessary for the reactor design is available in my original memorandum, entitled "Styrene Production from Ethylbenzene. " For the phase of the design involving the reactor, you may find some useful information in the references listed. D addition, some data and notes are given that pertain to the experimental work done in studying the chemical kinetics for the catalytic dehydrogenation of ethyl­ benzene. Data ad Notes The following information describes the bench-scale reactor used by Wenner and Dybdal (12) in obtaining kinetic data for the conver­ sion of ethylbenzene to styrene. Reactor type: Catalytic, fixed bed Reactor diameter: Û. 75 in. Ld. 1. 00 in. o.d. Over-all lengh: 78 in. Preheat section: 1. 5 ft packed with 6-mm porcelain Berl saddles Catalyst section: 4 ft Catalyst volume: 348 cc Temperature was measured in the catalyst bed 1 2 in. from the exit. Because the terms "conversion" and "yield" have been defined in the literature in a number of diferent ways, the following definitions are set forth as those to be used consistently throughout the present discussion: Conversion: Moles of ethylbenzene reacted per mole of ethyl­ benzene which entered the reactor. Yield: Moles of styrene monomer formed per mole of ethyl­ benzene which reacted. NOTATION Ü Specific surface area of catalyst, sq ft/lb catalyst A Cross-sectional area of reactor tube, sq ft, or in Eq. 7. 33 the total surface area in the shell-and-tube reactor, sq ft L Flow rate in bottoms stream of fractionator, lb moles/year CeC l Capital cost for two catalytic reactors, dollars C p Heat capacity, Btu/(lb) (OF) ' n Annual cost for recycling ethylbenzene, dollars/year Cy Annual cost for yield loss, dollars/year Process EmIlio/ion /01' Styrel/c Prodllctio/l 1OJ D Binary diffusivity, sq it/hr d___ Average diameter of reactor tube, ft d_ Pellet diameter, it J 1. 35/z1 P [( 1 * 7 - y - ·) - (P/ll) (xì (x ~ z )] 1 Total ethylbenzcne feed rate to a reactor tube, equal to ( / * 7)/ B000 · number of tubes, lb moles/(hr) (tube) / Ethylbenzene fresh feed rate, ÌD moles/year Õ Mass velocity, lb/(hr) (sq ft) ÇJ Enthalpy change of Reaction 6. 1, Btu/lb mole /o Diffusion j-factor, defined in Eq. 7. 2, dimensionless Í: Boltzmann's constant Í: P Kinetic constant for Reaction 6. 1, g mole/(sec) (g mOle/cm3) (cm3 of pellet volume) k y Gas phase mass-transfer coefficient, lb moles/sq ft (atm) (sec) Í: 1 Kinetic constant for Reaction 6. 1, (lb moles)/(hr) (atm) (lb cata­ lyst) IZ 2 Kinetic constant for Reaction 6. 2, (lb moles)/(hr) (atm) (Ib cata­ lyst) 11 3 Kinetic constant for Reaction 6.3, (lb moles)/(hr) (atm 2 ) (lb cata - lyst) ' j Equilibrium constant for Reaction 6.1, atm l c//ax, see Eq. 7. 2 5 Ç1 Lengh increment În numerical computation, it L Lengh along catalyst tube, ft L Mean free path of a gas molecule, cm à Molecular weight P Mass flux, lb moles/(sq ft) (sec) ¡ Ä Knudsen number, 2y e / L¡ dimensionless ,__ Reynolds number, d_ G/µ,dimensionless [__ Schmidt number, l/pD P Partial pressure, atm P Total pressure, atm J_ Critical pressure, atm Í g Reduced pressure, atm r Reaction rate, ÌD moles/(sec) (lb catalyst) `8 Mean pore radius, cm 1.54 ChuµIcr 7 Ü Universal gas constnt, cal/(g mole) [°K);in computation of effectiveness factor, equal to catalyst pellet radius, cm R Ethylbenzene recycle rate, lb moles/year b y Catalyst surface area, m 2 /g T Temperature, oK in kinetic discussion, ¯1 in reactor -design cal - culations Ü Over-all heat-transfer coefficient, Btu/(hr} (sq ft) (OF) Ü Superficial velocity of reacting gas in tube, ft/sec \ a Specific volume of catalyst bed, cm3/g catalyst ! Critical volume, cm3/g mole ' Specific pore volume, cm3 of pore volume/g catalyst ¹r Specific volume of solid material which comprises the catalyst, cm3/g ¹z Bulk void volume of catalyst bed, taen as Û. 3BV a , cm3/g catalyst Å Degree of conversion of Reaction 6. 1 2 Mole fraction of ethylbenzene in the liquid phase ) Degree of conversion of Reaction 6. 2 I Mole fraction in vapor phase × Degree of conversion of Reaction 6.3 Z Compressibility factor a¿(x) þmæ¡ for flrSt dmerence,egml l0 (X I ¯ ,_)/Q L Ü / /8 /¡ /T Ü ¯ Lennard-Jones force constant, erg Effectiveness factor; ratio of the observed reaction rate to the rate that would be observed in the absence of internal difusion effects, dimensionless Porosity of a catalyst pellet Dynamic viscosity, cp Growth factor in numerical solution 3.1416 Bul gas density Bulk density of catalyst bed, lb m/cu ft Density of catalyst pellet, g/cm3 Intrinsic density of solid material that comprises a catalyst pellet, g/cm3 Lennard-Jones force constant, Å Tortuosity of pores in a catalyst pellet, minimum value equal to 2, dimensionlesss ÍlOccoS ÍIÌt|ulÍO|I (5r $l¸rcnc JìOt/t|cI1O|t JOO T Thiele modulus, Ü VP¸o__¿ dimensionless 1 l+x +. ¦ c Diffusional collision integral, dimensionless Subscripts ave Refers to average value Õ Refers to composition of bottoms stream in fractionation unit 0 Refers to critical property ¿ Refers to ethylbenzene E0 Refers to equilibrium property L2Í Refers to experimental property O1Í Refers to effective diffusivity J Refers to Û log mean property within the film Ñ Refers to condition in bulk gas stream Ü Refers to property of flue gas ÌÍ Refers to property of hydrogen Refers to property at outer surface of catlyst pellet Integer subscript referrig to position within reactor tube Ín1 Refers to an intrinsic chemical kinetic constant ÄD Refers to a Knudsen diffusivity ¿ Refers to a property of styrene FORTRA Nomenclature A Total surface area for heat transfer in shell-and-tube reactor, sq ft ADENt Density of reacting gas at entrance to a tube, lb m/cu ft ADEN2 Density of reacting gas at exit of a tube, lb m/cu ft ADEN (ADENt * ADEN2)/2. 0 AMW Average molecular weight APRESS Absolute pressure at tube entrance, psia AREA Internal cross-sectional area for flow withi a tube, sq ft/tube ATEMP Temperature of ethylbenzene feed, ´1 ATEMPG Exit temperature of flue gas, `1 AVEL Average superficial velocity within a tube, ft/sec ]ÇÓ Clza/>le / BZ Mole fraction of benzene in gas phase CATCST CATDEN CATDIA CATPRC CPEB CPFG DEN EB EBPRCE EK1 EPS ETA FRATE H HYD I J K M MDEL Total capital investment required for catalyst in two reactors Bulk density of catalyst bed, lb m/ cu ft Diameter of catalyst pellet, ft Price of catalyst, dollars/lb Heat capacity of ethylbenzene, Btu/(lb) (OF) Heat capacity of flue gas, Btu/(lb) (OF) Density of reactig gas mixture at any point in the reac­ tor, lb/ cu ft Mole fraction of ethylbenzene in vapor phase Price of ethylbenzene, dollars/lb Equilibrium constant for Reaction 6.1, atm Bulk void fraction of packed bed, dimensionless Effectiveness factor, dimensionless Feed rate of ethylbenzene, lb/(hr) (tube) Over-all heat-transfer coefficient, Btu/(hr) (sq ft) (OF) Mole fraction of hydrogen in vapor Integer subscript controlling the numerical calculations; I advances by 1 for each hal step in distance for which the calculations are completed. Integer variable that controls the value of the temperature, pressure, and composition variables to be used in taing the next distance step. When the value of I is an odd num ­ ber' J is set equal to unity, and the values of temperature, pressure, and composition at the beginning of a distance increment are used to compute the new temperature,pres­ sure, and composition at the midpoint of the distance incre­ ment. Similarly for even I, J equals 2 and the values of the midpoint are used to complete the values at the end of the distance increment (K C 3). Integer variable used in tandem with J. A K value of 2 corresponds to the midpoint of a distance increment where the average values of temperature, pressure, and compOSi­ tion are established. Similarly, a K value of 3 corresponds to the end of a distance increment . Integer equal to 1/2; when M exceeds MM, the temperature, pressure and composition at that point in the calculation are printed. Input integer variable which controls the frequency of printing composition, temperature, and pressure values MM NSLICE PRESS PRESSG PREXG PREXT RATEFG RCCOST RCPRICE RCTCST RK1 RK2 RK3 SLICE STY TDEL TEMP TEMPG TEMPK TID TLEN TOD TOL TOTCST Process El'aluation for Styrene Production 757 as the calculation proceeds. MDEL was set equal to 10 for the example shown in the appendix. Integer used to control printing of output, see definition of M Number of distance increments used for the numerical calculation. A value of 100 was used in the example shown in the appendix. Gauge pressure of reacting gas at any point in the reac­ tor tube, psig Absolute pressure of reacting gas at any point i the reactor tube, pSia Gauge pressure of reacting gas at exit of reactor tube, psig Absolute pressure of reacting gas at exit of reactor tube, psia Flow rate of flue gas, lb/(hr) (tube) Cost of recycling ethylbenzene, dollars/year. Used ID com­ putations for first economic basis Price of recycling ethylbenzene, dollars/lb Capital cost for two shell-and-tube reactors, dollars Kinetic constant for Reaction 6. 1, lb moles/(hr) (atm) (lb catalyst) Kinetic constant for Reaction 6.2, lb moles/(hr) (atm) (lb catalyst) Kinetic constant for Reaction 6. 3, lb moles/(hr) (atm 2 ) (lb catalyst) Equal to NSLICE Mole fraction styrene in vapor Length increment in tube, equal to TLEN/SLICE, ft Temperature of reacting gas mixture at any point in the reactor tube, of Temperature of flue gas at any point in the reactor, `1 Absolute temperature of reacting gas at any point in the reactor tube, oK Internal diameter of reactor tube, in Total tube length, ft Outer diameter of reactor tube, in Mole fraction of toluene in vapor Total operating cost for first economic basis, equal to RCCOST + YLCOST, dollars/year J58 Chapter 7 TUBES VEL VOID X X XMOLE Y Number of tubes required for the reactor Velocity of reacting gas at any position in reactor tube, ft/sec (1. 0 ¯ EPS)/EPS**3 Total convei'sion of ethylbenzene, equal to STY + BZ + TOL The reciprocal of the fraction of TDEL to be used in the numerical calculation. For odd I, XI is set equal to 2. 0, and a "half-step" in distance is taken; for even I, XI is set equal to unity and a complete step in distance is taken. 1. 0 + BZ ' STY Number of distance increments for which calculations have been completed at any stage in the numerical solu­ tion YIELD Per cent styrene yield YLCOST Annual cost for ethylbenzene that is degraded to the undesirable by-products benzene and toluene, computed on the basis of $ Û. 1 2/lb ethylbenzene lost, dollars/year Z Distance along the reactor tube, ft DESGN OF TIlE REACTOR FOR CONVERSON OF ETIIYLBENZENE TO STYENE MONOMER With the fractionator design now complete, it becomes appropriate to consider the design of a chemical reactor for the conversion of ethylbenzene to styrene. Before proceeding with the design calcula­ tions, it is necessary to review the possible influences that mass transfer and diffusion within the catalyst may have upon the per ­ formance of the reactor. With these thoughts in mind, the data of Wenner and Dybdal (12) will be examined to determine their appli­ cability to the present design. Following these necessary preliminary calculations, the actual reactor design will then be completed. As an integral part of the reactor design, it will be necessary to consider various techniques in the numerical solution of differential equations. Proper use of these techniques will allow a computer program to be prepared to carry out design calculations for wide ranges of design parameters. Properties DÎ te Catalyst Used ÎDI the Dehydrogenation DÎ Ethyl­ benzene The data of Wenner and Dybdal are to be used to design a catalytic reactor for the dehydrogenation of ethylbenzene. Before the design can be carried out, it is necessary to determine whether or not mass transfer had any effect on their experimentally determied reaction rate data. Both the effects of mass transfer to the catalyst pellet sur- Process Elyliualioll foy Styrene Production 1OV face and diffusion within the catalyst pellet must be considered. U mass transfer is found to have limited the rate of reaction, then the data must be corrected for these effects before the design can be i mplemented. To ascertain the influence of mass transfer, it is im­ portant that the properties of the catalyst pellets used in their tests be established. The following information is available from the orig­ inal article: Bulk density: 61 lb m/cu ft Pellet size: 4-8 mesh, standard Tyler screen size. From Perry's Handbook (],we find that 4 mesh' 4. 70 mm ' Ü. 185 in. ' 3/1 6 in. 8 mesh' 2. 36 mm ' 0. 093 in. ' 3/ 3 2 in. As an average pellet diameter we may then take 1 _ 3 3 ¸ µ_ C ¯ -+ _¿ in. ¡ Ü. 1 40 in. C 0. 0117 ft 2 16 32 This information constitutes the only speciications given by Wenner and Dybdal for the catalyst used by them. Thus, some "engineering approximations" must be made in order to proceed with the analysis. To carry out a dehydrogenation reaction, one might well turn to a platinum catalyst deposited on a silica-alumina carrier. From Sat­ terfield and Sherwood [9),Table 3 - 1, p. 72, the following data are found for a typical silica-alumina catalyst used in the dehydrogenation of cyclohexane to benzene: Sg 7 240 m 2 /g Ò C 0.59 n, ¡ 1. 33 g/cm3 ºr 7 3 . 2 5 g/cm3 where S is the surface area of the catalyst, Ö the porosity of a catalyst pellet, µ_ the density of a catalyst pellet, and n r the intrinsic density of the solid material that comprises the pellet. For this catalyst, the pore volume per mass of catalyst, _,is given by 1 1 _ C ²/¤, C -¯ ¯ Ü. 59/1. 33 C 0. 443 cm3/g catalyst Þ , n r Now consider a container of volume \ a ,packed full with one gram of catalyst pellets. U the pellets are assumed to be spheres, it is reason- JÞÔ ChaþIæ / able to tae the vid vlume btween pllets, F¿¸as O. 3ßof the ttl vlume of the contier. To find the total vlume 0 the contaier: _ F O. 443 cm3/g catlyst F¿ 4 û.3ßF_ F t F I/g 4 û.3ûß F_ 4 û. 1 5I ± û.3ßFg cm3/g catlyst Hence, F_ 4 1. 21 cm3/g catalyst or the bl density of the catlyst bd is Q F _¸(6.4) F 5I. 5 l/cu Ü Tis numbr is smewht less m the value of 01 l/cu Ü gven in te origi article. However, ü te property vlues Õ " û.5û Pµ " I - 51 P t " ³- I5 are taen, the container volume can be computed in a similar maner to be 1 . 034 cm; /g catalyst . A value of 61. 0 lb/cu ft then follows for µ B . Since only minor modifications were necessary in the listed pro­ perties of a "typical" dehydrogenation catalyst, the last set of proper­ ties in this computation will be taken as those of the catalyst used in reference (1:). General Examination of te Kinetic Dat Before proceeding to analysis relating to the mass transfer and difusion reSistances, it is interesting to examine the kietic data show in Table 6-1 for the possibility that chemical equilibrium may have limited some of the observed conversions. The equilibrium ex­ pression for styrene formation is written as Process Evaluation for Styrene Production 1O1 Values of Í_ are shown in Fig. 6-1. U the side reactions are neglec­ ted for the moment, the conversion of ethylbenzene may be calculated as _2 b ¬ 1 - Ï_ The equilibrium conversion of ethylbenzene, as computed with this equation, is shown in Table 7 = 1e From the comparison of [Y¿) ¿¸ and [Y¿) ¿ _ 1 ¸ it is clear that the measured conversions in runs 227, 228, 229, and 230 correspond almost exactly to those computed using the assumption of chemical equilibrium. Thus, even though the analysis of the data set forth in reference [J3) does take the reverse reaction ¦hydrogenation) into account, there would be no way of analyzing the data from these runs to obtain accurate values of u_+ For example, by doubling the length of the experimental reactor, the same equilib­ rium conversion would be obtained; however, the computed value of u¸ from this hypothetical experiment would be quite different from that obtained from runs 22 7 to 230. Table 1~1. Comparison of Observed Conversions with Those Computed Assumig Chemical Equilibrium Run Number T (OC) Å_ (atm) \²s!sp \¹s¹sxr 227 555 0. 082 0.246 0.226 228 5 52 0. 082 0. 246 0. 22 5 2 29 555 0.082 0.2 50 0. 227 230 556 0. 082 0.2 50 0. 2 27 237 598 0. 2 2 0.3 6 7 0.246 239 600 0. 2 2 0. 3 72 0. 269 2 52 676 0. 95 0. 5 80 0. 366 2 54 676 0. 95 0.580 0. 3 60 242 598 0. 22 0. 3 72 0.260 246 650 0.64 0.500 0. 3 10 2 5 1 671 0. 93 0. 575 0. 3 5 5 255 668 0.93 0. 601 0. 3 72 232 555 0. 082 0. 2 50 0. 1 95 Followig up on the observation that equilibrium was attained in four of the experimental runs, it is interesting to examine the Arrhe ­ nius plot for the kinetic constants obtained by Wenner and Dybdal. The authors did not relate each of the plotted values of /�¸shown in Fig. 6 -2 1OZ Cha/)ter 7 to a specific experimental run summarized in Table O¬1. However, an attempt is made in Fig. 7-1 to associate the P_ values with speciic exerimental runs. This association was accomplished by comparing the temperatures from the data of Table 7-1 with those of the pOints shown in Fig. 7 - 1 . The anticipated discrepancy for runs 227 to 230 i s seen in Fig. 7-1. There is great scatter in the data at a 1 000/T value of approximately 1. 2 1 . It seems clear that the constant conver­ sion obtained when the feed rate was increased from Ü. 1 4 to 0. 21 lb moles/hr led to the computation of P j values that were too high. There­ fore the data from runs 227, 228, 229, and 230 will be discarded i future computations. 3·O²j } . ... Í. tt t t.} K IT wtIh T lf "K Figure 7-1. Kinetic constats for the dehydrogenation of ethylbenzene. [Werer and Dybdal, reference 12.) Identification of experimental runs has been inferred by examination of data tabulation in reference 1Z¿ Table 1. Before proceeding, it should be noted that a rather serious dis­ crepancy remains. A comparison of runs 227 and 232 indicates that when the reactant feed rate was decreased, with all other variables held constant, the conversion was reduced by almost 1 5 per cent. Naturally, by decreaSing the flow rate and increasing the residence time, one would expect an icreased conversion of ethylbenzene to styrene. Other than exerimental error, no reasonable exlanation for this behavior is apparent. Gneral Considerations U the Aalysis of Catalytic Reactions D analyzing a catalytic reaction, seven possible resistances to the progress of the reaction must be considered: 1 . Transfer of reactants from the bul medium to the catalyst pellet surface 2. Difusion of reactants from the pellet surface to the interior Process Em/l/ati ol1 jm' Styrene Productioll 163 of the pellet where most of the catalytically active area is found 3. Adsorption of reactants on the catalyst surface 4 . Reaction upon the catalyst surface 5. Desorption of the products 6. Diffusion of products from within the pellet to the pellet sur­ face 7. Transfer of the products from the pellet surface to the bulk medium A detailed analysis describing the kinetics of adsorption and a consideration of several possible mechanisms for the surface reac­ tion are beyond the scope of the present work. Smith's text (J0) pro­ vides an excellent discussion for the reader interested in this sub­ ject. The kinetics of adsorption and surface reaction will be analyzed by the models originally postulated in reference [J2). However, com­ putations will be made to analyze for possible mass transfer or di­ fusional resistances that may have inluenced the exerimental data of reference (12). Mass-Transfer Rates at the Surace D Catalyst Pellets The system to be analyzed is a packed bed of catalyst pellets through which a reacting gas stream is passed. The rate of mass transfer from the bulk gas to the surface of a pellet in the bed may be expressed as the product of a mass transfer coefficient and a partial pressure driving force: ( 7. 1 ) Mass transfer coefficients have been conveniently correlated i n terms of the Chilton -Colburn )¿ factor. Experimental data have shown that the best exression for )¿ is that given by (9) k A1¡ ] C . NO .66 7 7 0 989 N-O . 41 for ,y¡_ ` 3 50 ¿ Ó cC • ÜO ( 7. 2a) 7 1. B3 �¡�··³¹ for t\¡¸ < 3 50 ( 7. 2b) As the first step in the computation of ] c it is necessary to estimate the Reynolds number for the flow over the catalyst pellets. In this calculation, the lowest mass flow rate obtained will be used (run 242); this is the condition at which mass transfer could have had the great­ est influence on their experiments. The calculation of each of the variables necessary for the estimation of �¸¿ is (a) Mass velocity, Ó For run 242, (0. 0064) ( 106) Ó C 7 0. 061 3 lb m/sec-sq ft (0. 00307) (3 600) 1OJ C|u[Icr 7 (b) Viscosity, þ The viscosity of ethylbenzene vapor is not stated in the literature; therefore, it will be estimated by two different techniques and these estimates will be compared. (i) The viscosity of ethylbenene is probably quite similar to that of toluene, which is listed in Perry's Handbook (7 ) as 0.0202 cp at 598°C. Note that no pressure correction is necessary for this value, since P/PC=PR« 1. (ii) The method of Bromley and Wilke, as described by Reid and Sherwood (8) , is a convenient method of estimating viscosity; by this method (7.3) where from reference (7) 7_ = 346°C and 1_= 38.1 atm. For a Z_ value of 0.27 (equal to that for toluene) , Z_R7, 0.27 (82.05)(619) cc ¹ , = ¯ = =360 P , 38. 1 g mole Therefore, 0.00333 (106 X 619) 1 / 2 (1.137) / = / = 0.0191 cp (360) 2 º which agrees quite well with the value for toluene. (c) Reynolds number and jD 4_G (0.0117)(0.0613) ¹ _ = ��� ~ 56 ¯ - (0.02)(6.72 X 10-4) Hence, from Eq. 7. 2b, jD = 1. 82(56)-0.51 = 0.234 To use this value in calculating the mass transfer coeffi­ cient' it is first necessary to estimate the diffusivity of ethylbenzene in styrene. This will now be carried out using Hirschfelder's equation, as given in reference ¦8): 0.001858 T3 / 2 ( M 1 / 2 D 1 2 = ¬¬¬¬¬¬ � Pa� 2 iD (7.4) Process Evaluation for Styrene Production 1OO The Lennard-Jones force constants are estimated by the conventional empirical method, whereby a 1 2 ¯ 0.833 V¿ / 3 c/u C Ü. 77T c Since no data on the critical constants of styrene are readily available, the critical values for ethylbenzene will be assumed to apply for the mixture. Therefore, the force constants are computed in a straightforward manner: a 1 2 ~ 0.833 (360) 1/ 3 ¯ 5.92 Å c/ u 7 0.77 (619) C 476°K and /:I/c C 871/476 ¬ 1. 83 Thus, from Reid and Sherwood (8) the collision integral is found to be QD C 1. 116 - 0.6 (0.011) 7 1. 109 The diffusion coefficient can now be computed as 0.001858 ( 871) 3 / 2 ¸ 104 + 106 l 1 /2 D ES C 104 K 106 :"-0.168 cm 2 /sec (1. 0)(5. 92)2(1. 109) And the Schmidt number is found as 0.0191 ¹ 8 C J / p D ES C 7 0.772 C 102 (1. 47 K 10-3)(0.168) The mass transfer coefficient can now be calculated: (0.234)(0.0613) lb moles u 7 ~ 1. 73 K 10-4 y (105)(0.9)(772)2/3 sq ft-atm-sec To compute the possible diffusional resistance in the kinetic experiments, the superficial area of the catalyst pellets must be determined. U it assumed that the pellets are uniform spheres of diameter ¿ then the porosity of the bed is 0.38 and the total superficlal area may be computed: (0.62)(7)(0.0117)2 Ü C / ¯ 5.12 sq ft/lb catalyst 1 67(0.0117)361 1ÔÔ Clu[Icr 7 The observed reaction rate in run 242 is 0.00640 (0.26) lb moles EB reacted 7 C C 6.19 K 10-7 3600(0.749) lb catalyst-sec Since at steady state the mass transfer rate must be equal to the observed reaction rate, the partial pressure driving force for mass transfer is found from Eq. 7. 1 to be 6.19 K 10-7 v - p .) = = 7.00 K 10-4 atm Ñ ì (1.73 K 10-4){5. 12) Hence, with an insignificant partial pressure drop due to mass transfer, it is concluded that no important resistance exists for diffusion through the boundary layer at the pellet surface. It may be validly pointed out that a detailed calculation of the dif­ fusion coefficient is unwarranted, since only a rough estimation of the mass transfer rate is required. The details arc presented for illustrative purposes. Diffusion Witin the Catayst Pellet The catalyst used in this work has most of its effective area within the interior of the porous pellets. Thus, limitations due to diffusion within the pores must be considered. The effect of pore diffusion is evaluated in terms of the dimensionless parameter q¸ the effective­ ness factor. The parameter q is equal to the ratio of the actual reac­ tion rate to the reaction rate that would have been observed i all the interior catalyst surface were exposed to a reactant of the same con­ centration and temperature as found at the outer surface of the cata­ lyst pellet. For a first-order irreversible reaction, 7 is found to be (9) 3 ¸ 1 =- -- c tanh c ¢ (7.5) where (7.6) The variable c is conventionally termed the Thiele modulus; it may be thought of as the ratio of the chemical reaction rate to the diffu­ sion rate within the pellet. To facilitate calculations, Eq. 7. 5 has been presented graphically in Fig. 7-2. Process Et:tIuolioit/or Styrene Í1Od/IcÍOH 1&¯ |.0 ` \ 09 0.0 \ 0.4 0.5 0.2 0 2 \ A ` ` " ¯ 4 6 0 Thì8|8 m00u!u5g ç ` ` |0 |2 Figre 7-2. Effectiveness factor as a fuction of Thiele modulus. The effective diffusivity is most frequently computed by assuming that the resistances due to ordinary molecular diffusion and to Knud­ sen diffusion act in series; therefore it may be written that 1 1 1 ~4 ± º-yy lº ¡ »/-yy '²8nÌe1t (7.7) The effective molecular diffusivity is defined as D 12B/T, where ¯g the tortuosity, is the factor that corrects for nonlinearity and nonunifor­ mity of the pores within the catalyst pellet. The effective Knudsen diffusion coefficient is computed from (7.8) where the factor 20/S 0¡ may be thought of as the mean pore radius in the pellet, T. Equa¡ion 7. 8 has been derived from the kinetic theory of gases for cases when 7 is less than the mean free path of the gas under consideration. From Eqs. 7. 5 through 7. 8 the value of q may be computed for each experimental point of Wenner and Dybdal. This trial-and-error computation is illustrated in the following section. !63 Chu[lcr 7 Computaton of Efectiveness Factor for the Exeriment Dat From the definition of (D1 2 ) e f f there follows (0.16�(0. 5� 0.084 (D 1 2 ) eff = = -cm 2 /sec ¯ ¯ And from Eq. 7. 8 we have ( 0.59) 2 1871 0.00610 ¦D ) = 19 400 . = cm 2 /sec hT L11 ² 7(1. 33)(240 K 104) 105 ¯ Since ¦D k ) · __ is much smaller than (D 12)eff' the Knudsen mechanism constitutes the controlling resistance to diffusion within the catalyst pellets. As a check on this conclusion it is interesting to compute the dimensionless Knudsen number. First the mean free path for the reacting gas is found as 1. 881 L= --= 1. 88 (1. 91 X 10-4) .` 0 - % [871 ] 1. 47 K 10- 3 -(8.29 K 107) 105 = Ü, 933 K 10-5 cm = 933 Å From the definition of the mean pore radius, 29 2 (0.59) r e = - = ., -- S_0¡ (240 K 104)(1. 33) C 3.70 K 10-7 cm = 37 Å And the Knudsen number is found to be 2 r e 2 (37) ¿¸ * -= ~= 0.0793 L 933 With Î__ · 0.1, Knudsen diffusion should be the controlling mecha­ nism of diffusion. This calculation checks the previous result. USing 8 as a typical value for the tortuosity, the effective diffusi­ vity becomes 0.0061 Deff ¯ - 8 -= 0.00076 cm 2 /sec With this information, the following general relation for the Thiele modulus may now be developed: � - ¢ = 0.178 = 6.45.k F 0.00076 ( 7.9) Process Evaluation for styYene Pyoduction 169 By combining Eq. 7. 9 with Eq. 7. 5 or Fig. 7-2, a trial-and-error method is made available for the calculation of q. In this calculation the experimental value k l is read from Fig. 7-1; the dimensions of this rate constant must be converted to those of k F g the variable necessary for the computation of the Thiele modulus. The basis for this conversion is g moles (7. 10) The values of l? F computed by this expression represent the experi­ mentally observed rate constants. By first assuming a value for 7, the intrinsic rate constant {l? F ) in _ may be calculated by taking the ratio ( k F ) e x p /7. Then, by using Eq. 7. 9 and Fig. 7 -2, the accuracy of the assumed 7 value is checked. A sample calculation for the deter­ mination of 7 is shown in Table 7 -2. Table 7-2. Caculaton of Q for Üu Zð1 I ¯ 871°K kl 7 1. 10 K 102 ( Fig. 7-1) (kF)e x p 7 0 . 343 sec l (Eq.7.10) Tassumed (k Ant ¢¿ Eq. 7. 9 0.7 0.490 4.52 0. 5 0.687 5. 35 0.44 0. 782 5. 70 7, Fig. 7-2 0. 5 0.45 0. 44 The computed value of q indicates that internal diffusion within the catalyst pellet does indeed provide a major resistance to the rate of the dehydrogenation reaction. In fact , for run 237 the observed reac­ tion rate was only about 44 per cent of the rate that would have been observed if no internal diffusion resistance had existed. It must be remembered that a great many assumptions have been made in com­ puting 7. It would be interesting to determine the effect of variations in these original assumptions ( e.g. , Ü_ or r} on the calculated value of ]. Ater calculating q for each experimental run by these methods, Eg. 7.10 is used to compute corrected values of !hC intrinsic rate constant . These calculations are shown in Table 7 -3 and the cor­ rected intrinsic kinetic constants are plotted in Fig. 7-3. 170 Chapter ¯ ` • � ³F -? z& 4 �` = E H' ¦� r� � � E ` |.0 i.t t. t.} þ7T wt!h T |n "K Figre 7-3. Chemical kinetic constants for Reaction 7.1 after correction for internal difusion resistance. ¯æ10 1¬ó, ÏÜ0C¡1V0DCSS ÏßC¡DIS ad ÎD¡IÎDS1C Üß¡0 LDDS¡ßD\S ÎDI ϶CIÌDCD\ß1 Dat Run I,°k ¯ ( k�i nt ( lzl ) i n t K 102 237 871 0.44 0.780 2.5 239 873 0. 44 0. 782 2.5 252 949 0. 28 2. 19 6.45 254 949 0. 29 2.02 5.94 242 871 0.44 0. 78 2.5 246 923 0.32 1. 70 5.15 251 944 0.33 1. 64 4.86 255 941 0.37 1.11 3. 30 232 828 0. 53 0.402 1. 36 These data are found to be best fitted by the equation ÌD kl 7 19 , 100 _ 7.30 RI [7. 11) The activation energy of 19.1 Kcal is a much more realistic value for a dehydrogenation reaction than the activation energy of 11.37 Kcal computed without correcting the data for diffusion resistance. In fact, the relatively low value of the activation energy derived from the original data would indicate in itself that diffusion might be exert­ ing a controlling influence on the observed reaction rates. The fact Process Elall/ation for Styrene Prodl/ctiol! 171 that Eq. 7.1 1 differs significantly from the rate exression obtained in reference (12) should not be taen as a criticism of this work. It must be remembered that the properties of the catalyst used in reference [!2) are not known and that Eq. 7.11 would be strongly influenced by variations in the assumed properties which have been used in the present calculation. Desig of a Fied-Bed Dehydrogenation Reactor Because the dehydrogenation reaction is endothermic, heat must be supplied to the reacting mixture; therefore, a shell-and-tube reac­ tor of the type shown in Fig. 7 -4 has been selected for the present design in order to provide a large heat-transfer area per unit volume of catalyst. The catalyst pellets will be packed in the vertical tubes, and the heat -transfer fluid will be passed through the shell side countercurrent to the reacting gases. It is anticipated that a stream of hot flue gas will be available to supply heat to the reactor. EIhy¦be¤zeoe- !eed .& . _ ¬1'ue QU5 � . . . . . _ ¯ ReocIìo¤ producI Figre 7 -4. Dehydrogenation Reactor. By referring to Eqs. 6. 1,6.2, and 6.3, the stoichiometry of the reacting gas mixture may be summarized as in Table 7 -4. Here the variables X¸)¡and × represent the degree of conversion of Reactions 6. 1, 6.2, and 6.3, respectively. With the stoichiometry thus established, differential equations will now be derived to determine variations in the composition and temperature of the reacting mixture as it passes through one of the tubes packed with catalyst . 1. Material balances. At any arbitrary position Ï along the cata­ lyst tube, consider a section of tube dL in length. A steady-state 1¯¨ ' !c[lcx¯ Table 1~9. Stoichiometr of the Reacting Mie Basis: 1. 0 lb mole ethylbenzene feed Lb Moles at Lb Moles Position L Compound in Feed Catalyst Tube Ethylbenzene 1.0 J_ ) : Styrene 0 A Hydrogen 0 X·× Benzene 0 y Ethylene 0 ) Toluene 0 × Methane 0 × 1.0 1 ± X ± j material balance written on styrene for this differential element yields the following: or Input - Output 7 Accumulation ¸± d ¸(Fx) JL - ¹ 1 º |dL)0 a ] ¯ 0 dx F - = ^a ¹ 1 dL Substituting from Eq. 6. 4, there results º _ º0 ¡^ ¸ ¸ P¡Pµ ¸ dL Í P ¤ K ¸ (7. 12) (7. 13) By similar consideration of Reactions O.` and 6.3, the following equations are derived: (7.14) (7. 15) Iroccss LIÌIIulÍO|I)¬r S/]rcnc Ir¬uttcl¡oti 173 2. Energy balaces. Considering a differential element of a catalyst tube, the following energy balance may be written: Input - Output ¡ Accumulation FIMC _(T 7 ¿I ' '·" d ave} d L(T · T) r ¡ (AdL) µ_ �Ì -¸I M C peT - To} ' ¸�[F1HC _ ( T - To)] OÏ ¸7 0 If we assume that the quantity F111C p is constant and introduce Eq. 7. 12, it follows that dT 7 ÜõG___ 1 ¯ T ABb/(dX) 0Ï F1 M C_ · çÄC_ dÏ (7. 1 6) It should be noted that the enthalpy changes due to Reactions 6. 2 and 6. 3 have been neglected. Analogously, the energy balance on the countercurrent flue gas stream is written (7. 17) Equations 7.13 through 7. 17 may now be used to determine variations in temperature and composition within any one of the catalyst tubes. The only information still needed for a complete solution to the prob­ lem is a relation that predicts the bulk pressure drop through the catalyst bed. A standard expression for pressure drop through a packed bed will be introduced in a later portion of the analysis (1). Equations 7. 13 through 7. 1 7 constitute a set of first-order, non­ linear differential equations. A curs'JrY inspection reveals that they are not amenable to an analytical solution and that thpy must be approximated by a set of finite difference equations that can be solved by numerical techniques. A trial solution will now be pre­ sented to illustrate the general principles involved. Tria Nuerica Soluton The major disadvantage of solving differential equations numeri­ cally is the fact that specific values of the equations' coefficients must be selected and the numerical solution must be accomplished for each desired set of coefficients. This is a difficulty that must be tolerated when an analytical solution is not possible. The solu­ tion to be presented here is based on the set of design parameters used by Wenner and Dybdal in their original work [12). This set of constants is: Tube dimensions: Feed rate: Feed heat capacity: d_ ¡ 4.03 in; c� ¡ 4. 50 in; Ï ¡ 1 5 ft F ~ 4. 0 lb mole/(hr)(tube) 0. 635 Btu/(lb) (OF) J7¹ Chapt er 7 Feed temperature: Heat of reaction: Feed pressure: Exit pressure: Flue gas flow: Flue gas exit temperature: Flue gas heat capacity: Over-all heat-transfer coefficient: Catalyst pellet diameter: Bulk catalyst density: 550°C 53,600 Btu/lb moles 41 psig 5 psig 6520 lb/(hr)(tube) 1600°F 0.285 Btu/(lbWF) 9.7 Btu/(hr)(sq ftWF) ¡ __ in. 61 lb/cu ft For this sample calculation the total pressure will be assumed to vary linearly through the reactor. This assumption will be abandoned in later calculations; it is used here only to simplify the illustration. With the speCified design parameters and the stoichiometric relations developed in Table 7 -4, Eqs. 7.13 through 7. 17 may be transformed into the following difference equations: �l (x) 7 1. 351P[(1 - x ¯) - z) ¯� (x )(x -z)] �l (y) 7 1.351z2P(1-x ·) ¯ z) �l (z) 7 1. 35k3P (1 - x ¯) ¯ z)(x - z) �l (17 0. 0422 (T G ¯ 7; ¯ 792�1 (x ) �l (TG ) 7 Ü·00615 (Ta - T) (7.18) (7.19) (7.20) (7.21) (7.22) The rate constants used in these equations must be the effective values of these constants. Thus to determine k ¡ an effectiveness factor must be determined for the speCified design conditions. Since the design temperature level is about the same as that used for the laboratory exeriments, it is assumed that the only parameter that Significantly affects q is the pellet radius H. The values of q deter­ mined for the experimental data were about 0.4; the value of ç corresponding to this value of q is about 6.2. Hence it may be written that ad l°/ o , e±ga # 0.44 The vaue m¢ ¡ to b used on the desig is therefore ten to b l ¢¡ /,yy F 0.44 (1.48 X 103 q~1¤.100/k1¡ (7.23) Ircccss EtIttoIicn/cr Styrene IrcJttcI¡cn 175 As an approximation, Eqs. 6. 5 and 6. 6 will be assumed to describe the rate constants for Reactions 6. 2 and 6. 3 accurately. To continue the analysis, the reactor is now divided into a number of sections, as indicated in Figre 7-4 . With the inlet conditions 1=0, the temperature and composition at point Í = 1 are computed. The new values of temperature and composition are then used to calcu­ late the values for Í = 2; computations for subsequent points proceed analogously. This comparatively simple technique, wherein the con­ ditions at the end of the length increment are predicted by using conditions at the beginning of the increment, is conventionally called the "marching" method. Calculations using the marching technique for a reactor subdivided into three length increments are shown in Table 7 -5. Note that the procedure used here is quite simple, since the dependent variables r. re known as Í= 0; in other words, this is an initial value problem. The table shows that a negative value of \ is computed at position Í ¯ 2 in the reactor. Clearly this physical impossibility is the result of some deficiency in the ability of the infinite difference equations to model the differential equations. Genera Considerations i te Solution of Diferentia Equations by Finite Dference Techiques Three basic criteria are conventionally used in evaluating the effectiveness of finite difference techniques for solving differential equations. The first, accuracy, is self-explanatory; the accuracy with which the numerical technique models the differential equation must be evaluated. In most instances, the accuracy of the solution will improve as the increment in the dependent variable is decreased. Obviously, however, there is a lower limit placed on !: L since the number of calculations and the corresponding requirement for com­ puter time increase as the number of increments in the independent variable are increased. The amount of required computer time is the second criterion. The third criterion requires that the stability of the numerical solution be examined. When a differential equation is solved by numerical methods, small round-off errors are generated in the last decimal place of each number used in the solution. In certain instances, these errors can be magnified by the numerical technique being used, and in extreme cases these errors increase until they completely dominate the solution. The accuracy of a finite difference technique is typically checked by examining the solution to a problem similar in mathematical form to the desired problem but analytically solvable. By comparing the analytical and the finite difference solutions, the accuracy of the finite difference solution is easily ascertained. The stability of a numerical solution may be studied approximately by linearizing the nonlinear portions of the original equation and analyzing the resulting linear equation for its stability. Because the results of Table 7-5 indicate gross inaccuracies in the numerical technique, the system of finite difference equations which yielded these results will be examined for its stability. I¯& Chu[Icr¯ Table 1¬Ü. Finite Diference Calculations for the Dehydro­ genation Reactor Using Three Increments in the Lengh Variable Position, Í 0 1 X I 0 0.237 Y I 0 0.0011 ZI 0 0 T I , of 1022 962 (TG)I' of 1600 1618 PI (linear), atm 3.79 2.97 1 -(X+Y+Z)I 1.0 0.752 (x -z) I 0 0.237 i1,Eq.7.23 0.00925 0.00794 k 2 ,Eq.6.5 4.3 K 10-5 1. 5 K 10-5 k 3 , Eq. 6. 6 10- 3 0.6 Y 10- 3 J{l' FÌg. 6-1 8.4 K 10-2 3.8 X 10-2 1. 35 k1P(1 -X-Y -z) I 0.0473 0.0168 1. 35 k1P2xix-Z)I /K1 0 0.097 1. 35 k 2 P (l-x-y ¬×) I 2.2 Y 10-4 1. 35i 3 P2 (l-x-y -z) I (X-Z)I 0 0.0422 (T G -T) I 25.5 792 ^](x) I 37.5 Ü. 00615(TG -T) I 3.55 xI+1, Eq. 7.18 0.237 -0.163 Y I+1, Eq.7.19 0.0011 Z I+ _¸ Eq. 7.20 0 TI+1, Eq.7.21, oF 962 (TG) 1+ __ Eq. 7. 22, of 161 8 A method of analyzing for possible instability in the finite differ­ ence method used in Table 7 -5 may be illustrated by considering Eq. 7. 13 and writing it in the more general form dx - =f(T,x,y, z) JL Process EI:aluatioll 101' Styrene Product ion 1¯¯ Expressing this equation in its finite difference form yields XI+l + XI -- = II = l x I 6L where the preceding equation is written by assuming that the function / ca be expressed as a single-valued, linear function of x. The equation then can be rewritten Using a conventional technique, this equation is solved by assuming that the solution for ^ I 7 A(. Substituting this assumed relation into the difference equation, one obtains � = ( 1 + Ì6L) [7 . 34) It is desirable to maintain the absolute value of the growth factor at a level less than unity, for otherwise a slight perturbation or error in the value of A would cause an unstable magnification of this error with increasing values of Í. To satisfy this stability criterion, values of the product Ï6L must be restricted as follows: 0 > Ì6L > -2 Since the value of Ì is found to be negative, the first portion of the criterion is automatically satisfied. In order to satisfy the second portion, however, it is required that ~3 6L < ­ Í [7 : 35) Equation 7 . 3 5 then provides the basic criterion for the stability of the numerical solution. To implement it, 1 is first calculated as ] ¸ ¸ 7 -1. 3 5 1l 1 P ¸+ � ¦3x ¸ 1 1 The largest value of K would b found when Kmax ¯ -1. 3 5 (9 X 10-3) (3.79) ¸1 ± : 7 ( 1 ,1 8 K 10-2 J And the maximum value of 6L to be used in the numerical calculations is 3 ( 6L) ma x 7 ¯ 1. 7 5 ft 1. 14 1 78 Cho¡lcr7 Since a (Ï value of ft was used in the calculations summarized in Table 7-5, the approximate analysi s j ust carried out would indicate that this value is too high. Smaller values of L will therefore have to be used to mae a stable and accurate solution to the problem possibl e. It was probably intuitively obvious that (Ï was too large in the cal culations shown in Table 7 ¯ ¦ however, the foregoing ana­ lysis provides at least a semiquantitative basi s for selecting an appropriate value of the distance increment. It should be pointed out that there are many other techniques that mi ght have been applied in the numerical solution to this problem; for example the method of lI ilne or that of Runge - Kutta might have been used. Frequently these techniques are available in computation centers in the form of " canned" programs. H applied in the present problem such programs mi ght well reduce the requirements for computation time. Preparaton of a FORTR Program for te Reactor Design A computer program for the reactor design is prepared by solving the finite difference equations, Eqs. 7. 18 to 7. 22. One additional equation, a relation for the pressure drop in the reactor, is requisite for an accurate solution to the problem. The equation to be used in the final design calculations is that given in reference [1) . 0Ï ¡ _ pu z ¸�¸ OÏ u_ 1 - € ( 7. 26) In solving the system of finite difference equations, the " marching" technique used in Table 7 ¯ will be modified so as to insure a numeri ­ cal solution that i s not only stable but also highly accurate. This improved method of solution, sometimes described as the improved Euler technique , consists of the following: 1 . As before, divide the interval of solution into À equal incre ­ ments of length. 2. Since this i s an initial value problem, values of all the inde­ pendent variabl es are known at the inlet. Substituting these values into Eqs. 7. 18 through 7. 22 and Eq. 7 . 26, the varia­ tions in the dependent variables over half the first increment are computed. Using the values of the dependent variabl es computed at the mi dpoint of the first distance increment, Eqs. 7 . 1 8 through 7 . 22 and Eq. 7. 26 are used to compute the changes in the dependent variabl es over the entire first increment. . Steps ( 1) and ( 2) are repeated for all the distance increment s, i . e. , until l ¡ W. This technique may be expressed mathematically as ^r +: ¯^j ) 7 ¹ \ ¹j+i / z • ^ j+: /z ·¨¡+: / z· ª¡+: /z (Ï ( 7. 27) Process EI' (lllalioJ l for Styrene Producli (/ 1¯v Analogous equations may be written for the other dependent variabl es. By use of methods similar t o those previously illustrated, t he growth factor for the numerical solution to Eq. 7 . 27 may be shown to be . ' Ò @ ¸ � = 1 + J l @ 1 + - 2 - ( 7. 28) With a value of -1 . 1 4 for h, the maximum value of (J that will en­ sure stability i s found to be 1 . 75 ft . Thus, the stability criterion has remained unchanged from that for the simpler marching technique; however, use of the improved Euler method should result in a marked improvement in the accuracy of the solution. A FORTRAN program may now be prepared so that design cal cu­ lations can be carried out for wide range s of the parameters th< t characterize the system. The improved Euler method is used for the solution of the finite difference equations. The computer program for carrying out the design calculations is quite straightforward. To facilitate the interpretation of the pro­ gram, a flow diagram for the programming logic i s shown on Fig. 7 - 5 . The program first makes provision for reading the necessary input data, including the flow rate , feed temperature, and exit pres­ sure of t he ethylbenzene feed stream, t he rate and exit temperature of the flue gas stream and the lengh and diameter of the tubes to be used in the reactor. In addition, the program requi res values of the catalyst bulk density and porosity, catalyst pellet diameter, and the effectiveness factor for the dehydrogenation reaction as carried out using catalyst pellets of the specified diameter. Finally, the number of distance increments to be used in the finite difference calculations must be supplied in the input data. As a fi rst step in the calculation, the program estimates the pres­ sure drop through the bed. This value i s computed from Eq. 7 . 26 with use of average values of the gas density and velocity. By adding thi s approximate value of the pressure drop to the specified exit pressure, the ent rance pressure is esti mated. Since the technique of estimating is not exact, an iterativ, procedure is incorporated into the program. By this procedure the initial estimate of the ent rance pres­ sure is used and the enti re problem is solved to yield values of tem­ perature, pressure, and composition at the downstream end of a reac ­ tor tube . If the value of the exit pressure is sufficiently close to the specified exit pressure ( 5 ¯ 2 . 5 psig) , then the finite difference calcu­ lations are assumed complete and the program moves on to the next portion of the calculation. U the indicated agreement on the down­ stream pressure is not aChieved, the entrance pressure is re- estima­ ted and the problem is solved repeatedly until convergence is obtained. The actual finite difference calculations follow directly from the methods previously discussed. In all the computer calculations, 1 00 distance increments were used; even with thi s relatively large num­ ber the program requires only a modest amount of machine time . 180 Chu[Icr7 lnIfìohzø vorIobIe8 IZI KI * IZ I I I + TDEL/Xl o F2 1 � 1 TEMPI KI • TEMP I I I + TDEL /XI . F4I�1 PESSI KI. PESSI I I - TL/XI . 'I I�I WI gW fm0fWMm wìf8 of WK fðflox tdfæs Figre 7 - 5 . Flow diagram for the programming logic of design calculati on. | Circled numbers ref er to statement numbers i n the FORTRN program. ) Multiplying Ï, the ethylbenzene feed rate per tube, with the value of Å found at the reactor exit yields a value for the styrene produc­ tion rate per reactor tube. Then by dividing thi s value into the total required production rate, values for the number of tubes needed in the reactor and the required catalyst volume are e stablished. These quantities are of course necessary in sizing the reactor and in e sti ­ mating the capital requirement s for the process. In order to allow for l osses in the fractionator, a styrene production rate 5 per cent Process Eualualion /0r S/¡rcnc Production 1 81 greater than the required 20 K 106 lb/year has been used to estab­ lish the reactor si ze. This i s an important assumption, and its effect on t he over-all design should be subsequently examined. In order to consider the estimation of costs for the dehydrogena­ tion of ethylbenzene, it is assumed that / lb moles/year of fresh feed must be mixed with ß lb moles/year of a recycle stream and then fed to the reactor. For purposes of illustration, the costs of carrying out the operation were computed on two different bases: First Basis-Optimization of the Reactor Only. On the first baSiS , the costs of operating the reactor were evaluated by taing a fixed price for completing the separation of the reaction mixture; i . e . , the economi cs of the distillation operation was not considered. On this basis the operating cost was assum ed to be composed of the sum of two factors : 1. _ g , the cost of separating ad recycling the unconverted ethylbenzene, taen as $0.01 per lb of unconverted ethyl ­ benzene. 2. ç,the cost of ethylbenzene converted to by-products that were assumed to be valuel ess, taen as $0.12 per lb of ethylbenzene lost. All ethylbenzene was assumed to have been recovered in the separa­ tion step. With the definitions given, it i s easily demonstrated that / � ¸ ' ¸ , (20 X 10')/(104) � � ¸ ¸ ¸¸ (20 K 10')/(104) _ R = ' (106) (0.01) _ _ =q ' :) _ (/ ¬ ')(106)(0. 12) (7. 29) (7.30) (7. 31) (7. 32) In addition to the running costs, the capital cost for the reactor and catalyst also had to be estimated. Here it was assumed that two reactor units would be required and were to be operated in tandem with one uni t on stream while the catalyst in the other is being re­ generated. The capital cost for these units was estimated by fitting an analytical expreSSion to the cost data for stainl ess steel, shell ­ and- tube reactors given by Chilton ¦J) . A correction for the ENR price index was applied to these data to update the costs to Ü ENR index of 980; the result of these operations was L_ __ 7 2340Ao . 57 1 (7.33) where _ _ _ P i s the installed cost of two identical reactors with A sq ft of surface area. The capital required for purchasing the catalyst was also estimated by assuming that silica alumina catalyst of the desired type could be purchased for $3. OO/lb. 1 83 Clapter 7 Second Basis-Optimization of the Reactor - Fractionator System. I n the second cost -estimating procedure the same method of estimat­ ing Cy was used. However, instead of charging for recycle on a fixed price basi s, the distillation program previously presented was applied to each reactor design case. In each case a di stillation column was designed that would separate the ethylbenzene - styrene reaction mix­ ture and produce a product stream containing 99 mole per cent sty­ rene. The reactor design provided a feed stream of known flow rate and composition. Ey specifying the bottoms stream flow rate and compo ­ sition as in the distillation program, the material balance for the column is fixed. Then, as illustrated in the fractionator design, column design calculations were carried out for a wide range of reflux ratios. Thus, for each of 36 selected reactor cases, distilla­ tion columns were designed for each of 60 different reflux ratios, maing a total of 2 1 60 indi vidual reactor- fractionator designs. For each reactor case, the optimum fractionation reflux ratio was selec­ ted. Thus, by adding the cost s f or steam, cooling water, and column depreciation to the sum of Cy and the depreciation charge for the reactor, the total running cost for each reactor -fractionator syst em was computed, as was t he capital requirement for each process sys­ tem. The appendix contains a listing of the FORTRAN program that corresponds to the block flowsheet shown in Fig. 7 - 5. Included in this appendix i s a printout of the results obtained for a typical reac­ tor design calculation. In addition, the design computations are dis­ played for the fractionator required for the reactor being considered. The fractionation program was written as a subroutine of the reactor program, whi ch was called into effect each time the reactor program had iterated to provide an outlet pressure within the prescribed limi t s. From results of t he type shown in t he appendix t he capital and operating costs for each desired reactor design were computed. These costs were estimated both on the first basis where the reactor was considered independently, and on the second basis in which the optimum fractionation uit was selected for each reactor. Selection of the Reactor-Fractionator Desig Cases Using the program in the appendix, it is possible to provide a complete design for the dehydrogenation reactor. From the descrip­ tion of the program, however, i t i s obvious that the large number of design variabl es must be specified before completing the design and that a complete consideration of all these variables would be imprac ­ tical. For example, if 15 different parameters were varied indepen­ dently, the interpretation of the results would become quite complex, even in a situation such as the present where a computer program is available to carry out all the calculations. For this reason, three design parameters whi ch were believed to be t he most critical in determining the economi cs of the reactor design were selected for a detailed investigation. These variabl es, together with the specified values of these variabl es, are shown in Table 7 -6. JIOCCSS L//lt0lÍOl//cr CljICn( JrOdtt Cl lOu 1oJ Table 7-6. Desig Variables Ivestigted U the Present Std Variable Tube l ength Values Studied 1 0, 1 5, 20 ft 1 , 2, 4 in. Tube diam eter Inlet temperature 842, 932, 1 022, 1 1 22°F By taing all combinations of the values specifi ed in thi s tabl e, 36 different cases were made available for the characterization of the dehydrogenation reactor. In order to proceed with the solution, values of the other design parameters had to be selected. Values for these parameters which appeared to be reasonable were determined ad are shown i n Table 7-7. Table 1¬1. Paraeters Fied for All Desig Calcuations Catalyst bul density Catalyst pellet diameter Mass velocity of feed stream to reactor Outlet pressure of reaction mixture Flue-gas exit temperature Over- all heat-transfer coefficient Effectiveness factor Flue- gas feed rate 61 lb/cu ft 1 /_ in. 4 800 lb/( hr) (sq ft) 5. 0 4 2. 5 psig 1 600°F 8 Btu/(hr) ( sq ft) ("F) 0. 44 6520 lb/( hr) (tube) for the 4-in. tube; other flow rates taen as proportional to the square of the outer tube diameter so as to maintain the ratio Ï! Í_ approxi ­ mately constant. With the specified values for the parameters shown in Table 7 -7, the reactor design was completed [or all 36 cases summarized in Table 7 - 6. After the calculations were completed for each case, the costs of carrying out the reaction in each reactor was computed on each of the two cost bases previously described. Results and Discussion of te Economic Evluation The results of the design calculations for each of the 3 6 reactor cases are summarized in Table 7-8. Sufficient results are provded to allow an economic evaluation to be completed on either the first or the second basi s. | ~ ¬ T a b l e T - ö d . R e s u l t s o f U e D e s i g n C a l c u l a t i o n s f o r R e a c t o r s W i t h 1 - m . T b D i a e t e r ¯ < O p e r a t i n g C o s t o n ~ ¯ F i r s t B a s i s - � F l u e - G a s F r a c t i o n R e a c t o r ¨ I n l e t E x i t I n l e t I n l e t E x i t U n c o n v e r t e d F r a c t i o n N u m b e r o f R e c y c l e Y i e l d C o s t , ` L T e m p . T e m p . T e m p . P r e s s . P r e s s . E t h y l - S t y r e n e T u b e s i n C o s t , E q . C o s t , E q . E q . 7 . 3 3 , f t Q Ï Q Ï Q Ï p s i g p s i g b e n z e n e Y i e l d R e a c t o r 7 . 3 1 , $ / y r 7 . 3 2 $ / y r D o l l a r s 1 0 8 4 2 1 3 2 5 1 6 8 2 4 0 . 7 9 6 3 . 9 1 3 0 . 6 0 7 0 . 8 6 3 2 7 4 3 8 3 1 9 7 4 0 8 4 9 4 1 1 6 0 8 9 1 0 9 3 2 1 3 3 5 1 6 7 6 4 2 . 2 8 7 4 . 9 3 6 0 . 5 5 9 0 . 8 4 6 2 4 9 3 2 0 9 9 4 4 6 7 7 0 4 1 0 9 9 6 3 1 0 Ì 0 2 2 1 3 4 6 1 6 7 1 4 3 . 7 3 8 5 . 5 9 0 0 . 5 0 8 0 . 8 2 7 2 2 8 2 6 7 0 3 5 5 3 8 3 9 3 1 0 4 6 1 6 1 0 1 1 1 2 1 3 6 0 1 6 6 5 4 5 . 1 5 3 5 . 8 5 5 0 . 4 5 2 0 . 8 0 4 2 1 0 2 1 9 6 5 3 6 2 4 2 4 3 9 9 9 7 7 1 5 8 4 2 1 4 3 0 1 7 1 1 5 7 . 9 7 3 6 . 7 0 1 0 . 2 6 2 0 . 7 3 2 1 7 2 1 0 4 0 5 0 9 3 9 6 4 2 1 1 2 1 9 3 1 5 9 3 2 1 4 4 0 1 7 0 3 5 8 . 8 4 5 5 . 4 0 5 0 . 2 3 0 0 . 7 1 9 1 6 8 8 9 3 5 9 1 0 0 3 6 2 1 1 1 0 6 7 6 1 5 1 0 2 2 1 4 5 2 1 6 9 6 6 0 . 6 6 4 7 . 0 2 5 0 . 1 8 9 0 . 6 9 9 1 6 4 7 1 4 9 2 1 1 0 8 1 8 7 1 0 9 1 7 6 1 5 1 1 1 2 1 4 6 6 1 6 8 8 6 1 . 4 3 6 4 . 5 3 3 0 . 1 5 7 0 . 6 8 3 1 6 1 5 8 1 8 4 1 1 9 1 1 0 8 1 0 8 1 1 9 2 0 8 4 2 1 5 6 0 1 7 3 0 7 3 . 6 9 4 6 . 5 2 5 0 . 0 3 2 0 . 6 1 3 1 5 6 1 1 6 9 9 1 6 2 3 8 0 3 1 2 5 3 3 4 2 0 9 3 2 1 5 6 7 1 7 2 0 7 4 . 8 8 4 6 . 5 6 5 0 . 0 2 4 0 . 6 0 2 1 5 8 8 6 7 2 1 6 9 7 0 2 5 1 2 5 9 4 1 2 0 1 0 2 2 1 5 7 6 1 7 1 1 7 6 . 0 1 2 5 . 9 8 9 0 . 0 1 7 0 . 5 9 1 1 6 0 6 1 8 4 1 7 7 4 9 4 5 1 2 6 7 2 9 2 0 1 1 1 2 1 5 8 5 1 7 0 1 7 7 . 0 8 1 4 . 7 0 3 0 . 0 1 1 0 . 5 8 0 1 6 2 4 2 4 9 1 8 5 9 7 6 6 1 2 7 7 3 3 T a b l e 7 - 8 a c o n t i u e d O t i m u m C o l u m n C o r r e s p o n d i n g t o E a c h R e a c t o r C a t a l y s t C o l u m n ^ z a ¦ O / / ) D e p r e c i a t i o n H e a t i n g C o o l i n g T o t a l O e r a t i n g L C o s t , F e e d R a t e , ´ S s i n M i n i m u m C o s t , C o s t , C o s t , C o s t f o r C o l u m n , i t D o l l a r s l b m o i e s / y r i n F e e d D i s t i I I a t e R e f l u x ' ' / / / - , - T r a y s $ / y r $ / y I $ / y r º / x r ¯ 1 0 3 0 0 9 5 6 3 4 2 9 0 . 6 4 2 0 . 9 7 4 3 . 8 3 4 ¡ . 3 0 6 6 3 8 0 6 5 6 2 8 4 6 3 3 3 5 1 0 4 2 4 7 ¯ ¯ 1 0 2 7 3 6 5 0 4 7 4 8 0 . 6 0 0 0 . 9 6 9 4 . 0 7 9 1 . 3 0 3 5 3 9 5 9 4 0 2 3 ¯ 6 6 5 5 6 7 2 2 9 5 4 � v 1 0 2 5 0 7 4 5 3 8 4 : 0 . 5 5 5 0 . 9 6 3 4 . 3 8 0 1 . 3 0 6 5 3 2 4 6 3 4 9 4 4 1 2 6 2 4 8 4 5 2 9 v 7 6 5 4 6 P 1 0 2 3 1 5 4 0 9 1 4 3 0 . 5 0 6 0 . 9 5 5 4 . 7 6 2 1 . 3 0 6 5 3 0 2 5 3 4 3 9 5 9 2 3 3 3 � 3 0 0 0 8 3 0 . 3 2 7 0 . 9 0 9 7 . 0 1 2 1 . 2 5 2 3 7 6 5 2 9 4 0 1 1 5 6 0 5 4 7 2 7 r 1 5 2 8 3 4 6 5 ¬ � 1 5 2 7 6 7 2 8 6 2 2 4 0 . 2 9 5 0 . 8 9 5 7 . 6 6 8 1 . 2 5 6 3 2 2 2 2 4 2 7 6 9 8 1 4 7 0 5 1 3 9 3 ~ . - 1 5 2 7 0 2 2 6 9 3 6 8 0 . 2 5 0 0 . 8 7 2 8 . 7 8 0 1 . 2 0 6 6 2 1 7 1 2 2 4 6 5 4 1 3 0 8 4 7 6 7 5 6 1 5 2 6 5 6 2 5 6 8 1 4 0 . 2 1 4 0 . 8 4 6 9 . 9 7 9 1 . 2 0 6 5 2 0 5 5 9 2 3 0 9 1 1 2 2 5 4 4 8 7 6 ¯ 2 0 3 4 4 3 2 1 2 9 6 0 0 . 0 5 2 0 . 4 8 6 2 3 . 3 4 2 1 . 5 0 3 3 9 3 3 4 9 5 8 4 5 0 8 1 9 4 2 7 ~ � 2 0 3 4 7 2 2 1 0 1 0 4 0 . 0 3 9 0 . 3 9 3 2 4 . 9 7 7 1 . 3 5 3 3 8 2 6 7 7 8 2 9 4 1 5 1 6 5 1 3 ¯ � 2 0 3 5 1 0 2 0 7 7 5 7 0 . 0 2 8 0 . 2 8 8 2 5 . 0 1 8 1 . 2 0 3 3 7 0 1 9 5 9 6 0 3 1 6 1 3 2 9 6 C 2 0 3 5 5 9 2 0 5 9 3 2 0 . 0 1 9 0 . 1 7 7 2 1 . 4 4 9 1 . 2 0 4 6 3 7 9 3 1 6 ¯ 2 6 4 4 4 3 2 3 6 ¨ ¯ < ¬ ~ ~ . r ~ ~ ~ ~ ~ ¯ ¯ T a b l e 7 - 8 b . R e s u l t s o f t e D e s i g C a l c u l a t i o n s f o r R e a c t o r s W i t h 2 - i . T b D i a m e t e r ~ ~ ¯ � O e r a t i n g C o s t o n ¯ F i r s t B � s i s ` F l u e - G a s I r a c t ì O n H e a c I O I I n ! e I E X ì I I n l e t I n l e t E X i t U n c O n v e r I e d F r a c t i o n N u m b e r O ! R e c y c l e Y i e l d C o s t , L T e m g . T e m p . T e m g . P r e s s . P r e s s . E t h y I - S I y r e n e T u b e s ¡ n C o s t , E q . C o s t , E g , E q . 7 . 3 3 . f t O F O F - I p s i g g s I g b c n z c n c Y ì e ! d R e a c t o r 7 . 3 1 , $ / y r 7 . 3 2 , $ / y r D o l l a r s 1 0 8 4 2 1 1 4 8 1 6 5 6 3 6 . 9 7 6 4 . 2 7 8 0 . 8 4 0 9 5 . 6 1 8 1 5 6 1 1 7 5 5 4 3 1 1 7 7 0 2 1 1 8 1 3 7 1 0 9 3 2 1 1 7 1 1 6 5 1 3 8 . 2 1 3 4 . 0 7 0 0 . 7 9 4 9 3 . 9 7 6 1 2 3 8 7 6 0 9 8 1 6 4 6 5 0 1 0 3 1 9 6 1 0 I D 2 2 1 1 9 4 1 6 4 7 3 9 . 5 4 4 3 . 8 4 9 0 . 7 4 0 9 1 . 8 4 1 1 0 0 6 6 4 6 3 0 2 2 8 1 7 9 9 1 7 2 3 1 0 1 1 1 2 1 2 1 6 1 6 4 3 4 0 . 9 9 3 3 . 6 3 7 0 . 6 7 9 5 8 9 . 0 9 3 8 4 5 0 9 3 3 8 3 1 4 4 4 9 8 2 7 6 5 1 5 8 4 2 1 2 2 0 1 6 7 9 4 9 . 9 7 3 4 . 6 4 4 0 . 6 8 0 8 9 . 3 1 6 8 4 5 1 0 0 5 7 3 0 7 5 2 0 1 0 4 2 9 4 1 5 9 3 2 1 2 3 6 1 6 7 3 5 1 . 8 4 5 5 . 5 9 4 0 . 6 2 7 8 6 . 6 7 7 7 4 4 1 4 9 4 8 3 9 4 8 0 7 9 7 1 4 5 1 5 1 0 2 2 1 2 5 4 1 6 6 8 5 3 . 6 6 4 6 . 0 2 9 0 . 5 6 7 8 3 . 6 5 6 6 6 3 3 5 6 0 1 5 0 1 7 9 1 9 1 1 1 0 1 5 1 1 1 2 1 2 7 4 1 6 6 3 5 5 . 4 3 6 5 . 8 8 2 0 . 5 0 1 8 0 . 2 9 3 6 0 2 6 7 9 4 6 6 3 0 4 1 3 8 6 0 0 3 2 0 8 4 2 1 2 8 2 1 6 9 9 6 2 . 6 9 4 6 . 4 1 1 0 . 4 9 4 8 0 . 2 4 6 5 9 2 6 0 1 8 9 6 3 2 2 6 8 1 0 0 5 0 4 2 0 9 3 2 1 2 9 8 1 6 9 3 6 3 . 8 8 4 4 . 2 6 2 0 . 4 4 4 7 7 . 8 8 6 5 5 2 1 9 0 8 7 7 2 9 2 5 2 9 6 8 6 4 2 0 1 0 2 2 1 3 1 5 1 6 8 6 6 6 . 0 1 2 5 . 2 3 1 0 . 3 8 2 7 4 . 6 1 9 5 2 1 7 6 6 9 7 8 7 3 6 3 8 9 3 4 2 4 2 0 1 1 1 2 1 3 3 4 1 6 8 0 6 8 . 0 8 1 5 . 3 3 9 0 . 3 1 5 7 1 . 2 4 4 4 9 1 3 8 2 0 9 1 0 3 6 7 1 4 9 0 5 3 0 T a b I O 7 - 8 b c O n t i n u O d C a t a l y s t I C o s t , U D l l a s 1 0 6 6 7 2 1 0 5 2 6 3 1 0 4 2 8 0 1 0 3 5 7 4 1 5 5 3 6 1 1 5 4 7 3 3 1 5 4 2 3 0 1 5 3 8 2 3 2 0 5 0 2 4 2 0 4 7 1 0 2 0 4 4 2 0 2 0 4 1 8 3 C o l u m A • • F e e d R t A i l b m o l e a / y r i F e e d D i s i l l t e 1 3 1 0 9 2 5 0 . 8 4 6 0 . 9 9 1 1 0 2 8 4 3 0 0 . 8 0 0 . 9 8 8 8 2 8 9 3 3 0 . 7 5 6 0 . 9 8 5 6 8 2 4 3 0 0 . 7 0 0 . 9 8 0 6 8 3 1 0 9 0 . 7 0 0 . 9 8 0 5 9 3 3 8 3 0 . 6 6 0 0 . 9 7 6 5 1 8 5 2 7 0 . 6 1 1 0 . 9 7 0 4 5 4 7 0 0 . 5 5 6 0 . 9 6 4 4 7 3 8 5 0 . 5 4 9 0 . 9 6 2 4 0 8 6 0 9 0 . 5 0 6 0 . 9 5 5 3 6 8 6 1 9 0 . 4 5 2 0 . 9 4 5 3 3 2 3 0 9 0 . 3 9 2 0 . 9 3 0 M i i m u m ( P / Þ ) R e f l u ( P / Þ I a ; a 2 . 9 6 0 1 . 4 5 3 . 1 0 7 1 . 4 0 3 . 2 8 9 1 . 4 0 3 . 5 1 6 1 . 3 5 3 . 5 1 5 1 . 3 5 3 . 7 3 6 1 . 3 5 4 . 0 1 3 1 . 3 0 4 . 3 7 4 1 . 3 0 4 . 4 2 7 1 . 3 0 4 . 7 6 7 1 . 3 0 5 . 2 7 4 1 . 2 5 5 . 9 8 4 1 . 2 5 O i m u m C o l u m C o r r e s p n i m E a c h R e a c t � r D p r e c i t i n H e a t i g C o l i g T o t O e r a t i g ¯ C o s t , C o s t , C o s t , C o � f o r C o l u m , ^ T a y s $ / y r $ / y r $ / y r $ / ) ¯ ¯ ¯ 6 6 6 8 7 0 1 1 6 8 1 3 7 8 9 2 4 2 4 5 7 6 2 v v 6 6 5 6 0 4 1 2 6 9 5 8 6 7 8 1 9 1 7 4 2 ¯ ~ 6 5 4 9 8 9 1 1 0 1 1 9 2 5 3 7 0 1 5 8 5 4 < = 6 6 4 3 9 3 7 7 9 8 2 0 4 2 6 1 2 7 9 9 3 - 6 6 4 3 9 6 5 7 9 9 0 5 4 2 4 1 1 2 8 1 1 1 º 6 5 3 9 5 2 1 6 8 6 2 6 3 8 4 2 1 1 1 7 9 0 6 ¯ 6 6 3 6 0 3 4 5 7 3 5 8 3 0 4 4 9 8 4 3 7 � 6 5 3 2 5 0 4 9 5 4 7 2 6 3 0 8 4 6 8 1 ¬ 6 5 3 2 1 5 0 4 8 6 5 0 2 5 8 2 8 3 3 8 3 � � 6 5 3 0 2 2 6 4 3 8 9 4 2 3 3 0 7 8 5 0 ¯ 6 6 2 7 9 9 8 3 7 6 6 6 1 9 9 9 6 7 6 6 4 e � 6 6 2 6 0 7 3 3 3 0 8 1 7 6 8 6 1 0 8 3 � º ~ ~ ` ~ ¯ ~ T a o l e T ¬ & . R e a u l t a o f m e u a Q C a l c u u t i o o a f o r R e a c m r a w i t b 1 - m . T b o a m e t e r ¯ < � ¯ ~ O e r a t i n g C o s t o n ¯ " F i r s t B a s i s ` F l u e - G a s F r a c t i o n R e a c t o r I n l e t E x i t I n l e t I n e t E x i t U n c o n v e r t e d F r a c t i o n N u m b e r o f R e c y c l e Y i e l d C o s t L T e m p . T e m p . T e m p . P r e s s . P r e s s . E t h y l - S t y r e n e T b s m C o s t , E q . C o s t , E q . E q . T . J J f t . O ¡ O ¡ O ¡ p s i g p s i g b n z e n e Y i e l d R e a c t o r T . J ¡ , $ / y r T . J Z , $ / y r D l l a r s ¡ Û 5 1 Z ¡ Û ¡ 5 ¡ ö J J J b . ¡ 5 J 1 . b J T Û . 9 Z ¡ 9 5 . Z ö Z 5 ¡ Z b Z J T 1 1 1 b 1 Z Û ¡ ¡ ö ö 5 Û ¡ Û 9 J Z ¡ Û b ö ¡ ö J Û J b . 1 9 Z 1 . Z 5 5 Û . 5 T 9 ö 9 ö . 9 J J b 1 ¡ ö ¡ J 9 b T 5 ¡ Z b ö 9 Z 5 Û ö ¡ Û ¡ Û Z Z ¡ Û 9 Z ¡ ö Z 5 J T . 5 T 5 J . 9 T J Û . 5 J Û 9 1 . 9 1 Z J 9 ¡ Û 9 9 b ¡ ö ¡ J ö 5 1 ö T T Û 5 9 ¡ Û ¡ ¡ ¡ Z ¡ ¡ Z b ¡ ö Z b J 9 . J ö J J . b ¡ Û Û . T T ¡ 9 Z . ¡ Z Z J Û T 5 ¡ 5 ö Û Z ¡ 9 ö J b ö ö ¡ 9 b ¡ b 5 1 Z ¡ Û T Z ¡ ö 1 T 1 ö . ö ¡ 5 b . 1 ö b Û . 5 1 9 9 b . b 9 1 1 1 ¡ Z ö Z 9 9 ¡ ¡ ¡ 5 J T b ¡ Û J T J ¡ ¡ b 9 J Z ¡ ¡ Û Z ¡ ö 1 1 1 5 . Z 1 b b . ¡ Û J Û . 5 Û Z 9 J . Z J ö J 1 9 Z 5 1 J Z ¡ 5 b J Z J 5 9 9 b 1 ¡ b ¡ Û Z Z ¡ ¡ J ¡ ¡ ö 1 Û 1 9 . 9 9 J 1 . T ö b Û . T 1 ö 9 Û . Û ö 9 Z 5 b 9 ö b Û Z 5 J ¡ 9 Z T 9 b 5 T ¡ b ¡ ¡ ¡ Z ¡ ¡ b Û ¡ ö J T b ¡ . 9 Û J 1 . b Z ¡ Û . ö T 9 5 b . Û 5 ¡ Z J b Z b Û J Û 1 ¡ b J ¡ Û T ¡ b J J Z Û 5 1 Z ¡ ¡ Z Û \ b ö ¡ b ö . T b Z b . J T ¡ Û . T T ¡ 9 ¡ . J Û Z J Û T 5 9 T T T Z 1 1 ö 5 5 9 5 5 Z Û Z Û 9 J Z ¡ ¡ 1 b ¡ ö b 7 b 5 . b 9 ¡ 1 . T 9 1 Û . T ¡ T 5 T . 9 T T Z b b ¡ T T Z b J b ¡ Û Û 9 5 9 b ¡ Z Z Û ¡ Û Z Z ¡ ¡ T Û ¡ ö b Z ö Û . ö Z 1 1 . 1 T Z Û . ö b J 5 J . 9 Û 5 Z Z 1 5 Û 5 1 ö 1 9 Z b 9 ¡ 5 ¡ 5 b ¡ Z Û ¡ ¡ ¡ Z ¡ ¡ 9 b ¡ ö 1 5 ö Z . 9 J Û 1 . b T ö Û . b T T T 9 . Z ¡ J ¡ 9 J ö 9 Û Z 9 b T 1 Û J Z T b b J ö T ¡ 6 T ~ & c o t i u e d C a t a l y s t I C o s t , f t D l l a r s 1 0 1 3 0 ' 1 1 0 8 7 4 7 1 0 6 3 1 7 1 0 4 8 3 5 1 5 1 0 6 3 4 1 5 8 2 8 1 1 5 6 6 8 0 1 5 5 5 4 0 2 0 9 7 6 6 2 0 8 2 1 0 2 0 7 0 1 7 2 0 6 0 9 5 C o l u m F e e d R t e , A ¿ 8 Ä ¿ 8 m I b m o l e s / y r i F e e d D i s t i l l a t e 2 5 8 2 8 1 3 0 . 9 2 2 0 . 9 9 6 1 7 2 4 5 2 4 0 . 8 8 3 0 . 9 9 4 1 2 3 9 2 0 3 0 . 8 3 7 0 . 9 9 1 9 3 9 5 2 6 0 . 7 8 5 0 . 9 8 7 1 3 9 3 4 2 4 0 . 8 5 5 0 . 9 9 2 1 0 7 7 8 0 2 0 . 8 1 3 0 . 9 8 9 8 5 8 9 9 9 0 . 7 6 5 0 . 9 8 6 6 9 8 1 7 8 0 . 7 1 1 0 . 9 8 1 9 4 6 9 9 6 0 . 7 8 7 0 . 9 8 7 7 8 4 6 8 3 0 . 7 4 3 0 . 9 8 4 6 5 5 5 5 1 0 . 6 9 2 0 . 9 7 9 5 5 0 6 3 0 . 6 3 3 0 . 9 7 3 M i i m u m ( P / Þ l R e f l u ( P / Þ l a t a 2 . ' 2 9 1 . 5 5 " 2 . 8 4 3 1 . 5 0 2 . 9 9 0 1 . 4 5 3 . 1 7 6 1 . 4 0 2 . 9 3 1 1 . 4 5 3 . 0 7 5 1 . 4 0 3 . 2 5 4 1 . 4 0 3 . 4 8 6 1 . 3 5 3 . 1 6 9 1 . 4 0 3 . 3 4 6 1 . 3 5 3 . 5 7 4 1 . 3 5 3 . 8 8 2 1 . 3 0 O t i m u m C o l u m n C o r r e s p n d i n g t o E a c h R e a c t o r D p r e c l t l n H e a t i g C o l i g T o t l O r a t i n g C o s t , C o s t , C o s t , C o s t f o r C o l u m , : T r a y s $ / y r $ / y r $ / y r $ / y r C � 6 6 1 0 ' 6 5 4 3 5 5 4 4 ' 1 8 8 6 5 ¯ 4 8 1 9 6 ' v 7 6 6 8 2 7 3 8 2 2 9 2 0 9 1 2 1 6 5 3 2 4 1 1 2 � 6 6 6 6 3 4 0 1 5 8 6 1 9 8 4 1 9 2 3 3 3 7 9 � 6 6 5 4 8 3 6 1 1 5 4 7 7 6 1 2 9 1 7 6 4 2 � - 6 6 7 1 3 5 1 1 7 9 0 8 5 9 5 0 5 2 5 9 9 4 2 ¯ 6 6 5 9 7 7 7 1 3 3 3 3 4 7 0 ' 7 2 0 0 1 8 8 S 6 5 5 1 0 3 1 1 0 5 0 7 6 5 5 7 7 1 6 1 6 8 4 � 6 6 4 4 5 8 7 8 1 7 9 9 4 3 4 2 1 3 0 7 2 8 ` . - 6 6 5 5 1 1 0 1 1 6 4 4 2 6 1 8 0 1 7 7 7 3 2 ¯ ¯ 6 6 4 8 0 5 3 9 2 6 6 6 4 9 1 8 1 4 5 6 3 7 3 6 6 4 2 8 1 2 7 6 4 4 2 4 0 5 7 1 2 3 3 1 1 C 6 6 3 7 4 6 9 � 6 1 2 1 3 3 2 4 9 1 0 1 9 3 1 ~ - - ~ ~ 1 90 Clapter 7 To illustrate the effect of the three critical variables upon the maj or costs associated with the reactor, one typical set of cases was selected for presentation. In this example, a base case of a 1 5-ft ^ 2 ¬in. reactor tube with a feed-gas temperature of l 022°F was selec­ ted; subsequent cases were e stablished by varying the design para­ meters both above and below the values used in the base case . Cost s were computed on the fir st basis where independent consideration i s given t o the reactor; the depreciation charges were found t o be negli­ gible compared to the yield and recycle costs and were not consider­ ed i n the optimization. The results of these calculations are shown in Fig. 7-6, 7-7, and 7-8. U addition, a plot of ethylbenzene conversion ve rsus styrene yield for all 36 design cases i s presented in Fig. 7-9. )O |pOO � � � 000 � � ë Ý � 600 8 �400 6 � C 200 O O � h Î\ � \ % æ % 1eto| epetettog :e._ º ¯ º \ X ^ ^ ¾ ^ N - w * \ ¯¬ \ ¹¥·e|d cest ¸ £y / æ \ X e ¹ '/ ´ ^ ¸�c)cM cest ¡ £p ¯ ¬ ¬ Z ó 4 NOm| nC| tuD¢ di um¢t¢t t i nCh¢5 Figure 7 - 6. Reactor operating costs as a function of tube diameter for a 1 5 -ft tube with a feed temperature of l 022°F. In Fig. 7-6 the effect of tube diameter upon operating cost is illus­ trated. Wile the cost of yield loss decreases with increasing tube diameter, the effect of diameter upon recycle cost i s just the opposite. The explanation of these effects lie s in the fact that for a given tube length and inlet temperature the heat supplied per unit volume of reacting gas decreases with increasing tube diameter. The reaction t emperature i s therefore lower at larger tube diameters. Since the conversion increases with increasing temperature, it can be conclud­ ed that as the tube diameter increases, the conversion is lower and the Prcccss E//i|alictt}cr CI¸Iun0 PrcJitc/ici| 1 º! r ecycle cost is higher. The effect upon the cost of yield loss is the opposite because, as illustrated in Fig. 7- 9, conversion and yield are inversely related. The effect of t he reactor tube length on the operating cost i s plot ­ ted in Fig. 7- 7, indicating that for a given tube diameter and inlet temperature, ethylbenzene conversion increases with tube length. It therefore follows directly that recycle costs decrease with increas­ ing tube length . Si milarly, it i s obvious that yield loss due to side reactions must inc rease as tube lengh increases . C a � ^ � |¸zuu µ00 ² öuu 6 � _ 6uu C C � T 8 o = 4uu � o C zuu 0 ° TOlol optrofln9 cost . ' e # e e » e « - a a 7 ¯ = æ æ " ~ ~a =q= / / ¹ Y' tl d COSt , C y / ` 1 / \ / Z �´ ·` Z �co" , c. º´ ¯t ¬ o |Û l ¿ 4 6 lo zu zz ¯uD0 l 0ngI h , I00I Figure 7- 7. Reactor operating costs as a function of tube length for a 2 -in. -diam tube and feed tempera­ ture of l 022°F. In Fig. 7¬ 8 ) the costs are plotted as functions of inlet temperature. Sice t he conversion increases with temperature, t he effect of in­ creasing temperature is generally similar to that of increasing tube length. Figures 7 -6 to 7 -8 show that each of the selected design param ­ eters causes independent variations in the recycle and yield costs, so that the total operating cost passes through a minimum. However, in selecting an over -all optimum design, all combinations of the de­ sign parameter s must be taen into account, not j ust independent variations in the parameters concerning a selected base case. These conSiderations have been made using t he data from Table 7-8; the Jº 2 Chapter 7 .p _0uu � s � ¬Oa . I 1cro| oøe· onog ::._ _ æO = æ �� � æ~ ^" · · · ·.. __ æ �ëuu � � c C C .4uu : �� - ¯ 8 C C � ¿ zuu ø " æ¯ � 8ec,c| e covt¸Cµ q ~ = ø' �. »¬ 0 öuu ¸ OO | uO j | | uu |ee0 | empër0I ur8 ¸ "| Figre 7- 8. Reactor operating cost s as a function of feed temperature for a 1 5 -ft ^ 2 - in. tube. � C ä |Ou~ ö0~ � ëuÞ � 8 zc~ � � ==� ë � u ¬= ¬� öu �¬ ¸ � u = � O j 5| yr8n8 y| e' 0 ,per cent Figre 7-9. Ethylbenzene conver­ sion as a function of styrene yield. Process Evaluation for Styrene Production J VJ result s are plotted in Fig. 7 - 1 0, which shows the total operating costs for each diameter-length combination versus inlet temperature . The total operating costs were computed by adding the yield-loss cost and the recycle cost, the latter computed on the fir st baSiS, an assum­ ed cost of $ 0. 01/lb of ethylbenzene recycled. On the first baSis for e stimation, the optimum reactor is one having 249 tubes, each ten feet by one inch, and is operated with an inlet feed temperature of approxi ­ mately 900°F. The effect of inlet temperature on operating cost is quite small; this observation should have important ramiications in the control of the reactor. C � � ^ � s < ¯ ,õoo 2, zuuØ _| , 0uu c C S c ¿' , 4uu C C ì C õu�� |00d I0mp0rOI ur0 , " | Figure 7 - 1 0. Total reactor operating costs for 3 6-tube geometries. To illustrate the effects of the fractionator design on the over- all proce ss de sign, Fig. 7- 1 1 was prepared. ÏI is analogous to Fig. 7 - 1 0 in all respects except that here the second economic basis was used; i . e. , the optimum reflu ratio was selected for the reactor-fractiona­ tor combination, and the total running cost for the combination was computed in each case . Figure 7 - 1 1 shows that the combination of 1 0-ft by 2 - in. tubes with a feed temperature of approximately 9aaoF provdes the opt imum process desi gn. For this particular reactor, 7º3 Chapter 7 ¿0` r I ¨ ×* | ,800P- � õ � ¯ U 2 ¸ ·::ø L ¯ � c L ¯ . ::: ¯ ~o � ' ::: - ~� :·= *� ¯ : � : � : �---�� --��--�� ¸ : � : - � |000 ! 0Jµ0| 0 I ur 0 ¡ " | Figure 7 - 1 1 . Total operat ing cost s computed by using the optimum fractionation unit for each dehydrogenation reactor. two 33 -tray distillation columns are required which ar e to be opera­ ted at a reflux ratio of 4. 3 5, or 1 . 4 times the minimum ratio . Table 7-8 reveals that neither that particular reactor nor that particular distillation unit is an individual optimum, whereas the combination of both gives the optimum over-all process unit. Figure 7- 1 1 also shows that the effect of inlet feed temperature on the total conversion cost is quite minimal and in fact can be neglected over the temperature range of 8420 to 1 022°F. This characteristic will allow extremely flexible control and operation. By maintaiing the appropriate reflux ratio in the distillation unit so as to ensure proper product quality, the over- all cost of the conversion of ethylbenzene to styrene will not be strongly influenced by the operating conditions in the reactor. Some interesting conclusions about the economics of the separation process can be drawn by comparing Fig. 7 - 1 1 with Fig. 7- 1 0. Not only does the consideration of the distillation costs lead to the selection of a different reactor, but also the total conversion cost i s significantly lower than that computed by assuming a flat rate of $ O. Ol/lb for separating the styrene. This point s up the danger of using approxi ­ mate rules of thumb in estimating conversion costs. Process E|/ttalion/or Styrene 1roJuc//on J95 Economic Evluation of the Proj ect Table 7-9 provides a rough e stimate of the capital requirement s for this proj ect as based upon the cost e stimates previously present ­ ed. I n preparing this tabulation, the preli minary estimation method recommended by Happel (1) was used. Table 7-9. Equipment Specifications and Cost Total Item Number Unit Cost Istalled Cost Reactor, shell ad tb 2 $ 51, 598 $1 03, 196 160 tbes; 10 ft K 2 i. stinless steel Catalyst 1 754 lb ð 5, 262 Fractiontion colum 2 145, 1 1 2 290, 224 33-tray vcuum colum Colum diameter-S. 75 D Rebiler and condenser 100, 000 Pmps 20, 000 Istruments (10 per cent of 51, 870 abve) $ 570, 552 Item Material Lbor Isulation $47, 000 $ 70, 500 Piping 23, 000 23, 000 Foudations 23, 000 34, 500 Structres 19, 000 3, SOO Fireprofing 4, 700 28, 200 Electrical 28, 000 42, 000 Paitig and cleaup 4, 700 23, 500 Subtotals 149, 400 225, 500 $374, 900 Estimated costs of equipment ad material, istlled 945, 452 (A) Oerhead, 30 per cent of A 283, 636 Total erected cost �, 229, 08S Engineerig Fee, 13 per cent of A 122, 909 Contigencies, 13 per cent of A 1 22, 909 Total capital for process uit $ 1, 474, 906 Mnuacturig bildigs $ðð, 000 1 V0 C/apt er 7 The optimum process, as selected from Fig. 7 - 1 1 , would produce the required amount of styrene at an annual operating cost of about $ 3 60, 000, which corre sponds to $ O. 01 8/lb of product. This figure does not include depreciation of the reactor and catalyst; if these items are computed on a basis of 7 per cent of the capital estimate in Table 7-9, an additional $ 1 00, 000 per year must be included. Thus, a total cost of $0. 023/lb is computed for the conversion of ethylbenzene to styrene . Because of the proprietary nature of the information, no direct comparison with actual commercial costs i s possible; however, this figure does appear reasonable for a continuous proce ss of this type. The capital e stimate summarized i n Table 7-9 is presented as an example of the detailed itemization that must be considered in evaluat ­ ing critically the economics of the proposed proj ect . As subsequent steps in the evaluation, the potential market volume s and estimated selling prices must be forecast for styrene as well as for the import­ ant raw materials and by-products. With such information, a sal es proj ection can be prepared and a return on investment estimated. A great deal of additional work would be required to complete this task, but these considerations are beyond the scope of the present evalua­ tion. The reader is referred to the works of Happel [4) and of Vil ­ brandt and Dryden [JJ) for excellent discussions of the estimating techniques that must be used. One must always be alert to the fact that the accuracy of the available cost and market inormation i s usual ­ l y greatly inferior t o t he reliability of t he process data. Despite the detailed process consideration pre sented here, the viability of the pro­ j ect would hinge upon the availability of reliable market and cost in ­ formation. Even with the development of modern technology, including electronic computers, the most important considerations in evaluating many proj ects must be derived from the semiquantitative estimations of exerienced engineers and busiessmen. General Comments on the Desig It is felt that the design calculations j ust completed provide a good example of the power of digital computation in the completion of com­ plex de sign problems that involve many design var iables. In the ab­ sence of computer facilities the amount of computati on work evi ­ denced in the present design could have been accomplished only by the investment of a great many technical man-hour s . The use of the ma­ chine to ease the computation burden allows the engineer to apply his talent s in the most meaningul way, i. e . , in the interpretation of the result s. The emphasis i n t he pre sent discussion has been upon the technical merits of the process and on the invention and analysiS of a proce ss scheme. As mentioned previously, the market s for the styrene. end product must be given at least the same degree of attention before capital funds are requested. Actually, an economic evaluation of the process as presented here would not in itself have a great deal of meaning, since the economics would undoubtedly dictate that the equip­ ment considered should be a part of an over -all petrochemical com- Process Evaluation for Styrene Production 1V¯ plex, which would utilize a raw petroleum feed stock and would pro­ duce, among other things, a final polystyrene product . It is helpful to compare t he result s of t he present study with the current industrial practices for styrene manufacture (2, &). The com­ petitive economics of the petrochemical industry dictates that styrene be made in very large equipment, and usually in a single train ¦5) . The capital costs for reactor construction can be greatly reduced by using a self-regenerative catalyst that requires steam to be added to the ethylbenzene feed. This type of operation eliminates the need for two parallel reactors; this can be very important in modern, large ­ volume installations. Thus it is in the selection of a catalyst that the present design depart s most significantly from current industrial practice. Also, in the modern, large - scale operations the values of the by-product s from cracking become very significant economic factors. U the present study i t was assumed that benzene , toluene, and hydro­ gen were to be discarded because they were produced only in small quantities. The value of these materials generated from a large - scale proce ss cannot, however, be neglected. Furthermore, it has been point ­ ed out that the assumed value for ethylbenzene of $ O. 12/lb is high [5) and that the effect of a reduction in this cost should be investiga­ ted in subsequent studi es. The suggested change s in these factors would tend to yield an optimum process that operates at higher ethyl­ benzene conversions but lower styrene yields . This trend i s in agree ­ ment with the point made in Chapter 6 that the maj ority of industrial ethylbenzene - styrene fractionator s operate with feed concentrations in the range of 45 to 60 mole per cent ethylbenzene. These values are to be contrasted with the 82 mole per cent feed interpolated from Table 7-8 for the optimum system selected in the present study. As a final i ssue, it has been pointed out that standard commercial practice dictates the use of reactor pressures as low as pOSSible, with values seldom exceeding 20 psig (5) . The late st designs appear to have reduced this even further. This reduction in reactor pressure is probably one of the advatages realized from the development of more active catalysts for the conversion of ethylbenzene to styrene. The optimum process selected in the present study requires pres­ sures as high as 3 8 pSig. Returning to the optimization calculations summarized in Fig. 7- 1 1 , it is clear that a number of critical assumptions have entered into the selection of the " optimum" process unit. Fir st, the assumed temperature and flow rate of the flue gas and the assumed over -all heat -transfer coefficient were critical in obtaining the result s pre ­ sented here. By using the program given in the appendix, variations in these parameters would be investigated readily. The catalyst pel­ let diameter and effectivess factor used were important i n deter ­ mining the results previously pre sented. The effect of varying these parameters should al so be investigated by further use of the pro­ gram provided. For example, the economics of trying t o develop a better catalyst could be studied; this type of investigation would i llust rate the ki nd of work that must be completed by a di rector of research in attempting to place priorities on the different re search proj ects he must evaluate and manage. 1VO Process Evaluation for Styrene Production In addition, it will be remembered that the number of reactor tubes was established by requiring a reactor production 5 per cent greater than the necessary 20 million lbs/year of styrene. This assumption in essence fixes the composit in of the distillate stream in the frac ­ t ionation unit. Since it probably has a substantial effect upon the pro­ cess economics, i t should be the subj ect of further investigation. No consideration has been given to means for removing the by-products from the reaction mixture. The separation of hydrogen, benzene, and toluene should not provide any signiicant problems; however, some thought must be directed toward this matter before the economics of the process can be properly evaluated. Investigation of some of the process variables described may well lead to a result that is superior to the " optimum" case recommended in the pre sent study. Nevertheless it is felt that within the limits of the assumptions made, the result of the present study provide a reali s ­ tic, feasible, and economic process for the production of styr ene mono­ mer. REFERENCES 1 . Bi rd, R. B. , W. E . Stewart, and E . N. Li ghtfoot, Transport Pheno - mena, John Wi ley Ö Sons, Inc . , New York ( 1 960) . - 2 . Carra, S. , and L. Forni, I . and E. C. , Process Design and Develop­ ment 4, 3, 281 ( 1 965) . 3 . Chilton, C. H. , Cost Engineering in the Process Industries, McGraw­ Hill Book Company, Inc . , New York ¦¡9T). 4 . Happel, J. , Chemical Process Economics, John Wiley & Sons, Inc. , New York ( 1 958) . 5. Kehde, H. , Styrene Technology Center, Midland Division Re search and Development, Dow Chemical Company, Midland, Mich . , per ­ sonal communication, October, 1 967. 6. Ohlinger, H. , and S. Stadelmann, Cher. Ing. - Tech. å1, 361 ( 1 965) . 1. Perry, J. H. , Chemical Engineers' Handbook, McGraw-Hill Book Company, Inc. , New York ( 1 950) . 8. Reid, R. C. , and T. K. Sherwood, Properties of Liquids and Gases, 1 st Edition, McGraw- Hill Book Company, Inc. , New York ( 1 958) . 9. Satterfield, C. N. , and T. K. Sherwood, The Role of Diffusion in Catalysis, Addison-Wesley Publi shing Co. , Inc. , Reading, Mass. (1 963) . 10. Smi th, J. M. , Chemical Engineeri ng Kinet i cs, McGraw-Hi ll Book Company, Inc . , New York ( 1956) . 1 1 . Vilbrandt, F. C. , and C. E. Dryden, Chemical Engineerig Plant Desi gn, McGraw-Hill Book Company, Inc. , New York ( 1 959) . 1 2. Wenner, R. R. , and E. C. Dybdal, Cher. Eng. Progr. 44, 27 5 ( 1 948) . Appendix ÏLÜ¯Ü ÏN Program ßO Sample Printout for Chapter D Å C C C C C Û0C1 �ÛÜ? IDC3 PPÛ� PPP� DCf6 D�DT �^P8 DCP9 �01^ (nll PP1? D�1 P"\* 001¶ P^J^ rOI7 0C1P onl9 p^]n P�71 P"Z Þ0} F"?* Þ^75 PD�6 C077 f^ ß /^7Þ P"²^ ÅÅ åÅ DSiG ËW åMWÅ 'IPELlNE 0 - SULfUR 'IPF OIAfTEI IN INHS OS. QTEI OIAETEI OF STEAN 'I'E I . IN"ES 0#Þ QTEI OIANETER OF INSULATION IN IN"ES Ï • T"ICKNE�S OF INSUATIO IN IN"ES , - NNIFI OF PUNPING STATIONS $Õ PÖNÏÅZPÕeZ3 �Ü FONAT'I"I.'�"SULFU 'l'fLINE DESIGN CALCULATIONS/I" II" f 3Ö Foa T"X.2HNIEI Ö PN'IN STATIONS - ,F,.I.I" II q FQI NAT.5X,""INSUATIO T"ICKNSS IN INHf5 - ,F'.l.lH II" II 5O PDNT'X.6'HANUAL COSTS AlE SHW IELOI AS FUNTIONS OF SULFU , II,E OIANETEI,IH fIH J T0 FOMATI, ••I'H'I'E OIA,INH,TX.llHNGlNEIING,9X.9'I'E COST,'X,.H' IUN' CnST ••X.IOHINSUATIO ..... IOHSTfAN COST ••••IOHTOTAL COST' 80 FONATI7FI ••Z' FN-7�CIn.0 90 ÑËD 11" ,T ÏP fY ••••loo.lno IÔ0 PÑ1M ZÖ '1INT 50sP 'liNT "."T "IUNT ÞÜ PR1Nf T0 0 �OO I-I. ZO ÜÞP1ÖÅÏ fJ 05-0+2.6 DI.OZ.O.T DIST-�(."" 'l'E-I'.200.0_015T"10 __ Z•• '+1.10.0_0+30700.0 PUN'-7.700.0/0IST+Z".OOC.O/O"".8 GÏNåÞ31BÖ+Ô••01 __ Z-0S __ ZJ �T.-IO"00O.(/IALOGI2.e.OIDI,+e.0.ALOGI0I/OSI' TOTA-fNG+PI'E+'UN'+CINSU+STN 'RI . T eO.n.fNG."I'P,'UN',CINSU.STN.TOTAL 7Ö0 CDTlI Ü TO Y ••• å¥ØP END ZÜÌ oÜo Appendix � \ ¡ 1 T I 1 P P I P H I ' F D E � T G N C A L C U L A T I O ' S ' U M � F R n F D U M P I N G S T A T l O ' S • Î × V I N 5 U I A T I O . T H 1 I K N E 5 5 î N I ' C H f S • A N N U A L c n S T S ¤ f S H O W � B E l O W A S P I P F D I A ( \ N C H f ' r I N E E R I N G 1 . " ' 7 � " C I . r Q ² + D ^ 7 5 ^ ^ P ¡ ^ º J & P ^ 7 ' O " ( . , r ¬ = " " 7 ' " ( " , n l ¬ = � " 7 5 " � " , ^ \ ¶ . P " 7 - n / , . I ' 7 , D 0 7 " 1 ( ' , ' ' A . n n 7 " " " ' + ¹ ¨ 9 ¬ ¹ P 7 � C N ' . N ' I � = " ' J º ^ ^ P ¿ ^ ^ ¡ À , " " 7 1 C [ C . ( n 1 ' . " " 7 1 " ' '' . ' � I 3 + " l 7 5 D C , C Û J A · P ' J 5 ^ n ^ ¿ ^ ^ ¡ , P ^ n " c c . c " l ^ ¬ ' ' 7 5 P ^ " D Ü 1 7 . " " 7 , n ( n . N � ¡ P × ! " 7 ^ D 0 + P � l R , ^ ^ 7 5 P ¨ D , ^ D ? ^ _ o o 7 6 ^ O ^ ¿ ^ P " + Ü F U N C T I O N S O F S U L f U R P I D F C O 5 ³ 1 ' " 5 ( ! . 0 l 4 8 6 1 9 « 3 ¯ 7 2 1 3 6 . 4 4 1 B ñ R 9 . .+ 4 4 1 5 6 1 2 0 . 1 2 I £ Z T T R + 3 1 I T 4 B P & 4 4 1 1 9 7 1 4 a 1 5 ? D 6 O 9 4 « 5 6 U H I 2 . " C ' 4 1 ( ) 1 . Ï 2 ' " 1 6 1 . 1 2 " " 7 1 1 2 . 1 1 2 9 5 6 . " . ' J l 4 1 8 1 . ' 4 " " " ' 6 . ' 4 ] 5 \ J 4 ' . 1 I " ' ' 8 ' . 4 4 J " I 6 6 4 . 5 D 4 P 7 1 1 7 × 1 º P I P E O I A M E T E R P U P P L O õ J l N 5 U L 4 1 J O N S T U " L Ö ã T T Ü T A L L O ã T 2 4 1 1 5 " ' 6 , 0 " ¬ U + C 2 3 7 5 J . 0 6 2 1 1 " 6 0 . 0 " ( 6 \ 11 . 1 2 . r ¿ ^ 2 5 1 1 " å . 6 Y 1 1 1 1 7 1 ! O O 1 4 J l 1 6 . 7 5 ~ � + ¹ ¿ 0 ð Ñ 9 0 + J ð 7 0 n I 5 . 5 6 4 7 8 ' 6 . 1 ' . n ¡ D 2 7 5 4 J \ . 6 ' 5 6 4 2 2 5 . 0 0 2 6 1 8 9 . 5 5 - � . o Z B 0 1 Z & Õ 0 5 4 4 8 3 1 . 6 2 2 1 5 0 • • P ~ P ¡ ^ 2 ' 6 1 ' 5 . 1 ' 5 5 4 4 1 1 . 2 5 1 8 1 1 7 . 6 2 - � . C 1 0 5 1 1 4 . 6 2 Þ T 3 Ï J Z s Þ Ý 1 7 0 1 7 . 1 5 ¬ Û + P ) 1 4 ' 5 0 . 5 0 5 ' 6 7 5 2 . ) 7 J Þ Þ Ý 1 s 7 0 ¬ Ü « V 3 2 ' ' ' O . J I 6 2 1 4 7 6 ø 6 2 1 6 1 3 1 . ( ' ¬ Ü ¬ U ) ) 2 1 6 . 6 2 6 4 6 ' 9 1 . 6 2 1 6 1 8 ' . 1 5 ¬ V » Ü J 4 0 6 6 0 ø 6 ' 6 7 Z 1 U . I ' I I I ( . 0 Z ¬ ¹ ¬ � $ 4 1 7 6 6 ø 5 7 6 9 " ' 1 8 . 1 1 1 6 0 5 1 . 5 6 ¬ Û + C , ' 6 6 9 1 . 0 0 7 2 5 0 5 4 . 1 1 1 6 0 1 1 . 1 7 * � + D J 6 4 4 5 1 . ) I 7 5 1 1 Ï å e 1 ' 1 5 9 ' 6 . 1 J ¬ Ü + Ü ) 7 2 0 8 4 . 1 7 7 7 1 2 6 2 . " 1 ' ' 8 1 . I I - " . ( 3 7 ' 5 0 ' . 1 1 8 0 n 0 T . 1 1 1 5 9 1 0 . T ¬ Ü + D $ . . . . . . 6 2 1 2 . ' 0 1 . 1 ' 1 5 9 6 " ' 9 - 1 . 0 3 . 4 2 1 7 . 4 4 8 5 5 2 4 0 . 2 5 1 5 ' 5 1 . ' ¬ ' & ' 4 0 1 Þ 0 2 . ' 4 . 1 1 1 2 5 . 4 4 1 ' . 5 4 . 1 1 = D , � 4 0 8 6 4 2 . 6 . ' 0 6 . ' 1 . " FORTRN IV Program and Sample Printout for Chapter 5 203 � U I F U R P I P E L I N E D E S I G N C A L C U L A T l n N S A N N U A L c n S T S A R F S H O W N B E L O W A S F U N C T I O N S U Í S U L F U R P I P E D I A M E T E R º T P F 0 1 A » 1 N C H � � t ' N E f q I N G P I P Ë L O 5 Ä P U M P C O S T 1 , " ( 1 5 t O ( . " � 2 ' 5 ' 5 ( r . ( l ¿ ¬ ß 1 ° 5 3 b + C Ü ² = " " _ ¿ n , ` 4 8 6 B ' . ' 7 º Ü ^ 1 * T ¬ 1 Z ² ¡ ¬ « 7 � Þ n r _ « r 2 2 1 3 6 2 . 4 4 1 4 3 � 7 6 . 7 º = " " 7 " ¹ " Ü + ¹ " 1 b � � 9 � . 4 4 ¬ T 8 9 � + S 9 ¬ . � � 7 < � Þ Þ ¿ � P Ì > 6 0 Z " + Î ¿ 7 � A 8 q . , S 6 . " ' ² ¬ " " P + ¹ P l f 2 7 7 R . l 1 ¿ ! ¬ P � + � P 7 . f � 7 5 ( " ( . ' ' ' 1 7 4 � 2 ( . 4 4 ! Y 1 À 7 + � ? ¤ _ c o 7 K ^ P P , ¨ ' î B 9 T Î å + ³ � ¡ T " ñ T + À ¬ º = � " 7 1 " � r . ( ' 1 � 6 � ? 4 . 5 6 I � S 9 l . 7 6 ! ^ , ^ r f ¬ ! " " = ¨ ¨ ³ 3 I » ¯ Û l A 3 � J . " S 1 1 » ¨ " 7 5 0 ^ � _ » r 2 4 1 1 � 1 . 7 ' 1 ð l ª ô . 7 S l 7 • " " T 5 P ^ n _ » ø 1 " ' 1 6 8 . 1 2 l b 1 0 J + ß Z l J . f ^ T P D C . C P 2 7 7 3 1 2 . ) 1 ! � " 5 1 + � b 1 4 . 1 " 7 1 ( f " . " ' ' Q ' 6 q " . 7 � I h I 1 8 . 1 7 t 5 . � ' 7 ¬ " " 0 . C C 3 1 4 1 8 1 . 9 4 ¡ Ô S S b + 1 ò ¡ = r ¬ 7 1 " n t . " " H 2 7 3 6 . ' 4 l � S 8 1 + 1 8 ! ? , - ¬ 7 � P C P , ^ 0 1 5 1 3 H . � 1 I S 9 7 " . 7 º l � ¡ ^ ^ 7 - ( ( ( . " ' 3 6 ' ' f ' . 4 4 1 5 9 6 3 . 3 9 l S , ^ ^ 7 � C " C = � ¹ 3 8 R 6 6 4 . 5 C I , Q 5 8 . C S 7 " • n o 7 ' 1 ' 1 . ' 1 4 1 7 1 6 2 . 1 ' 1 5 q S 4 . 1 1 I N S U L A T I O N 2 6 1 1 5 . 9 8 H 4 3 5 . 9 q 3 5 Ï V ' . 9 º A � 1 � õ + 9 V � 1 5 1 ' . 9 q � T 8 7 . 0 k b ¬ Z 3 + S Y Ï " õ 9 � + 9 A 1 6 9 5 , . 9 4 R B l S . 9 4 8 q 6 7 S . 9 4 Q 6 ! 3 5 . 9 4 1 0 2 3 9 4 . 6 9 I I R 7 5 S . R I l 1 S 1 1 5 . 8 1 1 2 1 4 7 5 . 8 1 l Z 1 8 � � . S 6 1 3 4 1 9 S . 8 1 1 4 0 5 S S . 8 1 1 4 6 ' H S . 8 1 S T E A M C O S T ! T 0 5 5 1 . C O 1 8 8 6 1 5 . 0 6 2 ( 4 3 1 ' . 7 5 2 1 8 3 2 ' . 6 3 2 1 1 1 0 5 . 6 1 2 4 2 ' 2 2 . 4 4 2 5 3 ' 7 8 . ' 4 2 6 4 4 1 8 . 3 1 2 7 4 3 4 ' . ' 4 2 8 3 . 5 2 . 6 ' 2 9 2 ' ' 4 . 8 7 3 0 1 8 2 7 . 0 6 3 1 0 3 9 2 . 0 0 3 1 8 7 2 2 . 3 1 3 2 6 8 . 8 . 8 1 1 3 4 7 ' 5 . 3 7 3 4 2 5 ' 3 . 5 6 3 5 0 2 2 ' . 6 9 3 5 7 7 " ' . 5 0 3 6 5 1 5 7 . 4 4 T O U L C O S T 2 8 0 " 7 0 . 0 . 0 I 6 B B 3 T Û « Û 0 0 B Z 5 9 ø 8 7 5 5 2 2 7 8 . 8 7 5 " 1 3 3 1 . 1 9 5 5 9 0 8 0 . 5 0 5 8 6 1 5 Z . ' 6 1 6 . 1 6 . 1 2 6 U ' 9 1 . 1 ' 6 8 1 . 1 3 . 6 2 T 1 9 Ñ 1 & 3 I 1 4 8 0 3 " . ' " 7 8 1 1 5 0 . 5 6 8 1 4 Î º + Û Û 8 4 7 1 4 . 6 9 8 7 ' ' 8 ' . 2 5 9 1 2 7 3 4 . 6 9 9 4 5 3 7 8 . 3 1 ' 7 7 ' 2 7 . 1 1 1 0 1 0 3 8 ' . 5 0 oÜ 7 Appendix � I 1 J F l i P P I P f 1 . I N F D F � T 1 N C A I . C U L A T l n N � N U � � E � n F D I I M O J N � S T ' T r n � � =  & ¹ I N � U l ' T ' O N ' W I C K N F S � î N ! N L H F � • I . � ¤ N N A L L Û 5 T S 4 R E S H O W N B e l O W � S F U N C T I O N S O F S U L F U R P I P E O J A M F H R P I P E f U . I N C W F ' ( ' ' H R I N r P I P E C I � T P U M P C O S T I N S U L A T I O N S T E A M C O S T T Ü T m L Ü 5 T  & Ü ¯ 7 C " Ü + � " Ý Ñ � Ñ " ' Û & ^ Í Ý 9 E 1 � Ñ Û � & Ô ¯ Ñ 1 Û Û ¯ & Ý Û 1 2 0 ' 1 0 . 0 6 2 1 0 6 1 3 0 4 . 0 ? & ¯ ' } q ( r n _ » r 9 B 6 \ ¶ � & § ¯ V Û ^ B Å & Å Ý Â 1 b Õ B ¯ & Ñ 9 U 5 9 2 0 . 2 5 1 , , 9 6 2 7 . 0 0 Û & � L ¯ Õ Û � \ & Ü ¯ ¿ Ý ³ Û b ¯ 9 9 Å 9 ¯ Ü ¯ Þ & ¯ Õ Â Õ Õ º Þ ¯ & Ñ 9 1 4 9 7 1 7 . 6 2 7 2 4 6 . . . 7 5 4 . � ' ¯ < ^ r � & * r 1 � 5 � 9 � . 4 4 9 ¯ ^ Ñ b & Ý Ñ Â ° 9 Õ A B & Õ Ô 1 6 2 5 1 1 . 9 4 6 0 5 l n . 2 5 5 + " º 7 5 P � Ü + P P  � ^ B Z \ & 1 Ý ¿ ^ � E H & � Õ Ï Î b Z Û & ¯ Û 1 7 4 1 8 7 . 0 0 6 0 6 7 2 4 . 6 2 ñ & Þ r · ¯ ¬ ¹ ¯ Í & ¹ Ü À Þ Ý ¯ ¯ Þ & Õ Â ¿ ! � Û Õ & B Û Å Ñ ¿ ¯ Û ñ & Û Û 1 1 5 5 1 1 . 9 4 6 3 6 5 0 9 . 0 0 t . e n 7 ¬ � ^ Ü + P C \ ¯ 9 * Z � & º 9 I � Å Â ¯ & Þ Ý Ý Å Å ¯ B ¯ & Ñ 9 1 9 6 0 5 1 . 3 7 6 7 5 7 7 7 . 3 1 � + ^ ^ 7 5 ^ D ^ ¸ ^ Þ Å Þ Ý ¯ 1 9 & ¯ Õ Å ¯ Û � ¯ & ¹ Ô 2 3 " � 6 7 . 9 4 2 0 6 0 7 1 . 1 1 7 1 1 7 4 1 . 6 2 V « " ¯ Õ Í ! Ü & ¹ r Ü Þ Û Ñ º & � Þ Ì b ^ Ñ Å & ¯ Þ ¿ Ñ Ñ 9 ¯ & Ñ 9 2 1 5 6 1 5 . 1 3 T 6 n 0 9 . ' 1 ! ^ ¿ ^ r ? ¬ ! " " & P P ¿ 3 1 + ^ " Å ^ ¯ 3 & ¯ � ¿ b Ñ ! Ý ¯ & Ñ 9 2 2 4 9 0 0 . 0 6 l o n n . o o ! 1 ¬ " l T " " " ¹ = ¨ " Ý º  � ¯ Å & ¯ � Ì ^ À B ^ & ¯ Õ Ý Ý B À Ü b & O Ñ U l I O I . 1 7 1 5 4 1 2 9 . 0 6 î Z = ¨ " 7 - " 0 " . " ' ' � 9 � 6 R . 1 2 Î � Å ¹ Õ & ß Z Õ ! ¯ 1 F & Õ Þ 2 4 2 4 2 0 . 0 0 1 9 9 7 7 1 . 5 0 Å � & ^ ^ y r ^ Þ , P Ü ² ¯ ¯ ¯ Å ¿ & ¯ Å Â h Û Õ 1 & � Þ Õ Z b Ý b b ¬ Õ 1 2 5 0 " 1 . 7 5 9 4 5 4 1 9 . 0 0 ! º & ¯ ¯ ¯ ¬ ¹ " Ü & D P ¿ Ý Õ Þ Ý ¯ & ¯ � Î b ¹ 1 ^ &  ¯ 1 º Õ Õ º ¯ & Õ Ü 2 ' ' 9 ) 5 . 6 2 9 9 0 9 9 9 . 0 0 l ' . " 1 7 5 ^ " C = � C 3 Å 9 1 Û Â & Ñ 9 Â Õ Ñ Ñ b & Â Û 3 6 4 4 2 8 . 2 5 2 6 6 8 1 5 . 5 0 I n 6 4 9 l . 1 1 ! ^ = � " ² ¬ ' " " ¬ ! " ð Ý ¯ b & Ñ ª Â Õ Ý F Å & Å ^ Õ Ñ ¯ � ¹ B & Ý Õ 2 7 4 6 5 1 . ' " 1 0 1 1 1 . 4 . 0 0 ¡ 7 , C " ¯ " ' ¹ Ü & Ü Ü Õ Õ Å Õ 9 ¯ & Ý ¡ Å ° Ñ ¯ Û & T º Û Ý ^ Û Û & Ý Õ 2 I Z Z 7 ) . _ 4 1 1 2 7 1 7 6 . 0 0 1 A _ « e ¯ ¯ ¯ ¯ Õ + F O ² ^ 9 9 8 9 , 4 A 1 ^ Ñ b � & Õ Ñ º Z À b b ¯ & Ö Û Z 9 7 4 ' . M 1 1 7 2 ) 6 5 . 0 0 À 9 , Þ D T ¬ � � C = � � Õ B h Þ ^ 9 & ^ 1  ^ Ñ Õ * & Ü � 9 9 Ü ¯ ¬ & Ô Û 2 9 7 0 . . . 9 4 l Z I 7 4 " . 0 0 ¯ " , ^ r T 5 P " , P 0 9 I ¯ ¯ ^ ¿ & Å H  " Ñ � 9 &   9 � Ñ � 7 & Õ Ü 3 1 4 J l ' . 6 1 1 2 6 2 4 5 9 . 0 0 � U L f U R P I P f L I N f D E S I G N C A C U L A T I O N S N U M B E R U F P B P T N G S T A T I O N S . Z + O I N S U L A T I O N T H I C K N E S S I N I N C H E S • 0 . 0 A N N U A L C O S T S A R E S H O W N B E L O W A S F U N C T I O N S O F S U L F U R P I P E D I A M E T E R P I P E D I A . l N r H E N G I N f E R I N G P I P E C n S T P U M P C O S T I & Û U 7 5 � 0 Û » " 0 1 5 ( � 5 0 0 . ( O 2 1 8 3 1 8 7 2 . " 0 2 . ( ' 7 � P Ü Ü + Ü Ü 2 7 7 2 1 9 . 6 9 Y Z Z 1 Z 1 » 1 Z 3 ¡ D 0 7 5 0 0 0 . 0 0 1 5 4 2 3 1 . 1 9 1 5 9 0 1 6 . 7 5 � . ( n 7 5 n f ( . " ( ¡ � � ñ H ô + 1 H 6 3 8 3 6 . 8 9 5 & D D 7 5 0 0 0 . 0 ( 1 4 0 7 6 0 . 0 6 4 2 8 2 ' . � 5 6 . n " 7 5 0 ( 0 . ( 0 1 � 3 1 3 ' . 1 2 3 6 " � 3 » 8 0 3 ¡ 0 O 7 5 0 0 0 . 0 0 1 6 8 5 6 1 » I 9 3 4 0 5 7 . 6 2 ß = D O 7 � ( ( ( . ( ( U 5 4 � 7 . 3 1 � 3 0 2 7 . 1 5 9 . 0 n 7 5 0 0 0 . 0 0 2 0 2 H 9 7 . 2 5 3 2 5 3 1 . 7 6 I n . n t 7 5 0 " O . / ( 2 2 1 0 0 6 . ( 3 2 2 1 3 . 0 5 I I . n n 7 ¬ 0 M . o n 2 3 9 2 6 � . 8 7 3 2 1 2 8 . 7 5 1 2 . " " 7 ¬ D O + P O 2 5 7 M " . " 6 3 ? 0 � 3 . 8 2 I « " " 3 ¬ U P Ü = Ô 0 2 7 6 2 M . 1 2 3 H H 9 1 . 5 6 I � . n " 1 ' ( ( 0 . C ' 2 9 4 7 9 8 . 8 7 3 1 9 5 ñ . 1 7 j � ¿ D D 7 5 0 1 0 . 0 1 � 1 3 4 4 0 . 9 " 1 1 9 3 6 . 1 3 Ì ^ + " Û 7 5 " n ( . M I 3 Z 1 1 ß + ^ ¬ 3 1 9 2 1 . 1 8 ( 3 ¡ 0 D 7 � n 0 0 . n n ¹ 5 0 S 2 . S 3 3 1 9 1 0 . 7 8 l f . " n T õ Ü Ü Ü + ¹ D ) 6 9 5 " 4 . 6 ' 3 1 9 C ' . 3 9 1 9 . 0 n 7 5 1 0 0 . 0 ( 3 8 8 2 8 2 . ' 5 3 1 8 9 8 . 0 5 ¿ P » ! ¯ ? 5 P " U = D C 4 ( 7 " 3 I . n 6 3 1 8 H � . 1 1 I N S U L A T I O N S T E A M C O S T - 0 . 0 2 3 1 3 3 3 . 0 6 ¬ D « V 2 5 1 3 9 5 . 6 9 - 0 . 0 2 6 3 9 1 6 . 3 8 - 0 . 0 2 7 5 H I . 6 9 - 0 . 0 2 8 6 1 2 2 . 0 0 - 0 . 0 2 9 6 1 9 5 . 1 9 - ( . 0 3 0 5 7 H . 6 2 - 0 . 0 3 1 " ' 5 0 . 5 0 - 0 . 0 3 2 3 1 9 0 . 3 1 - 0 . 0 3 3 Z 3 h 6 . 6 2 ~ Ü & Ü H 0 6 6 0 . 6 9 - 0 . 0 H 8 1 6 6 . 3 1 - 0 . 0 3 5 6 6 9 1 . 0 0 - D . 0 3 6 4 " 5 7 . 3 1 - 0 . 0 3 7 2 0 8 4 . 8 7 - 0 . ( 3 7 H 5 8 9 . 8 1 - 0 . 0 3 8 6 9 8 6 . 6 2 - 0 . ( 3 9 " 2 8 7 . � " ¬ Ü » C � 0 1 5 0 2 . 9 1 - 0 . 0 4 0 8 6 � 2 . 6 9 Ï Ü Ï L Ü Ü å Î 2 6 6 . . . . . 0 1 ' 2 5 " " . 0 0 0 Þ Z Ñ a  Π" 0 1 6 6 . 1 5 , , " 1 1 1 . 5 6 5 6 0 " 1 . 0 6 Þ 0 1 Ý 2 . . . 0 0 1 3 0 . 0 . , . , 1 9 . 3 1 6 6 0 6 2 ' . 6 2 6 1 7 0 5 5 . 1 1 7 1 , . , , . 2 5 T . . . . . 0 Ý 7 6 6 2 1 " . 1 1 7 9 2 " 6 1 . M 1 1 1 6 2 ' . ) 7 1 9 9 U Ý . 2 Þ 0 T Ü T Þ + % B Y 0 0 B S s 1 Y ' 1 2 5 6 7 . 1 . g ; � � ~ � 4 � � � � Þ Ð � � � 4 . . Þ - ¯ Ñ - � � g 1 � u � 5 U L F U P F J F f L 1 � E D E S I G N C A L C U L A T I O N S N U � ß 1 P D F F J P P T � G S T A T I O N S = z . r I N S l I l A T l O " T H l f K " F S S î � l N C H F S • 1 . 5 A N N U A L C O S T S A R E S H O W N B E L O W A S F U N C T I O N S O F S U L F U R P I P E D I A M E T E R º î º F P Ï A • î N C ' F N 0 T N b º T N G F 1 F 1 C O S T F U º F C O S T 1 . � ' 7 5 " � " . � r 1 5 0 4 � o � . n r 2 4 8 3 1 6 H . O O ² = ¹ " 7 s n n , ., o � 2 7 7 Z I 9 . 6 9 ' 7 2 1 Z I . 1 2 3 , P P 7 S ( " ( . O ( 1 5 4 2 3 1 . 1 9 1 5 9 C 1 6 . 7 5 4 . ( ' 7 1 " ( ( . ( " n � a q " . l q � , " 3 6 . 8 9 ¬ = � " 7 5 ¹ " " = ¹ U 1 4 0 1 6 0 . 1 6 4 2 8 2 9 . 5 5 6 . " " 1 ¶ « ^ n ¸ ¤ ^ 1 5 1 0 ' . 1 2 3 6 4 4 3 . 8 " 7 . " ( 7 5 0 ( ( . ' ' ' 1 6 " 5 6 " . 1 9 3 4 C 5 7 . 6 2 � ¸ n c ) 6 ^ ^ ^ , P " ) B õ ¬ " T + 3 ? 3 1 ( 2 1 . 1 5 q . " ! 7 5 0 0 D . O ( 2 0 2 9 9 7 . 2 5 3 2 5 3 1 . 7 6 Î ^ ¸ ' " 1 6 ^ Þ Þ ¸ ¤ ^ 1 7 1 " n 6 . " � ' 2 2 7 1 . n � 1 1 . ( 0 7 5 ( ' C . ( 0 2 3 q z 6 � . 8 7 3 2 1 2 8 . 7 5 1 , . " , 7 " " ' ' ', ( 1 2 5 7 1 8 4 . 0 6 3 Z t 4 3 . a 2 l 3 = " " 7 5 0 0 ( . 1 � 2 7 6 2 0 6 . 1 2 3 1 9 9 1 . 5 6 1 4 . 1 t 7 s n n n . ( n 7 Q 4 7 ' � . R 7 3 1 9 5 8 . 1 7 ¡ ñ o � � 7 5 � C C . l n 3 1 3 4 4 0 . 9 4 3 1 9 3 6 . 1 3 l l . " I 1 5 n n c . � � � 3 1 I l R . 4 4 3 1 ' 2 1 . 1 8 1 7 . 0 ( 7 5 D � t . P Ü 3 5 0 8 1 1 . 8 7 3 1 H O . 7 8 l R . " f 1 1 ' P " - " 1 6 ' 5 4 4 . 6 ' 3 1 9 ( 3 . 1 ' l C . I ' ' 7 5 0 D ( . o r 3 R R 2 8 2 . 7 5 3 1 8 ' 8 . 1 5 ? " » " " 7 $ ^ ^ n _ o Þ 4 r 7 0 J I . " 6 3 1 " 9 4 . 1 1 I N S U L A T I O N S f E A M C O S T 9 7 3 0 7 . B 8 1 2 0 5 8 0 . 0 6 1 1 6 3 8 1 . 9 4 1 3 5 ' Z O . 2 5 1 3 5 4 6 7 . 9 4 H 9 7 I T . 6 2 1 5 4 5 4 8 . 0 0 1 6 2 5 3 1 . 9 . 1 7 3 6 2 8 . 0 0 1 7 . , 8 7 . 0 0 1 9 2 7 0 � . ( ( 1 8 5 5 U . 9 � 2 1 1 7 8 7 . 9 4 1 ' 6 0 5 1 . 3 1 2 3 n 8 6 7 . 9 4 2 0 6 0 7 8 . 8 1 2 4 9 9 4 7 . 9 4 2 1 5 6 1 5 . 1 3 2 6 9 0 2 7 . 9 4 2 2 . 9 0 . 1 6 2 8 8 1 0 6 . 1 9 2 1 3 8 0 1 . 8 7 3 C 7 1 8 6 . 5 6 Z U . Z O . O O 3 2 6 2 6 6 . 3 7 2 5 0 7 8 8 . 7 5 3 4 5 3 4 7 . 5 0 2 5 8 9 3 5 . 6 Z 3 6 4 4 2 8 . 2 5 2 6 6 8 8 5 . 5 0 3 8 3 5 n R . 2 5 2 7 . 6 5 8 . " 4 C 2 5 8 8 . 2 5 2 8 2 2 U • • • 4 Z 1 6 6 7 . 5 0 2 8 9 7 . 5 . 5 0 4 � O H 7 . 5 0 2 9 7 0 " . 9 4 5 ' 8 2 7 . 5 0 3 0 4 3 1 5 . 6 2 Ï Ü T L L Ü ã T 2 6 6 2 ' 2 3 2 . 0 0 1 5 2 6 6 . 1 . 0 0 6 U 5 0 3 . 5 0 5 ' 1 8 1 5 . 0 6 0 6 6 0 • • 5 6 6 U 8 ' . 1 I 6 " . 5 1 . 1 2 U 0 3 1 1 . 2 5 1 1 6 1 5 2 . 0 6 8 2 2 2 0 1 . 0 8 6 8 3 0 3 . 1 . . " ' 3 3 • « • • 9 6 0 Z 5 2 . 8 1 1 0 0 6 0 . 0 . 1 2 1 0 5 1 6 9 0 . 0 0 1 0 ' 7 2 0 6 . 0 1 1 4 2 5 ' • • W 1 1 8 7 8 6 1 . 0 1 2 3 3 0 1 6 . 0 0 1 2 7 8 0 6 1 . 0 0 � ¯ ¯ � : ¤ � � � . FORTRAN IV Program and Sample Printout for Chapter Ó oܯ � U L F L J R P I P F L I N F n F S l r � C A L C U L A T I O N S N L J � A F R P � J � P T N 6 S T A T [ " N S • ¿ + � 1 N S U ¡ A T J O N T � 1 L X N F õ 5 I N I N C H F S • � . r A N N U A L C O S T S A R E S � O W N B E L O W A S F U N C T I O N S U f S U L F U � P I P E Û 1 A � E T E R P I P F n I A . r N C � F N C N F � � 1 � C P T P � L O � à P U " P L U b 1 I N S U A T I O N S T E A I C O S T T O T A L C O S T I . � n 7 5 D " " . ^ P 1 5 ( . 5 0 � . O ( ¿ ¬ � ò 1 ß J ? ¬ C Û 2 5 U 5 5 . 9 . 9 2 . 6 2 . 2 5 2 6 7 5 5 6 4 8 . 0 , . n n 7 ¹ ^ ^ ¡ ^ ( H 1 ? 1 9 . ( 9 " n I 2 1 . 1 ? 2 9 0 ( 1 5 . 9 . I O U 0 1 . 3 1 1 6 6 8 5 5 8 . 0 0 3 & � " 7 ¬ " P " . � � 1 5 4 Z l I . 1 9 ¡ � S U ! ^ & ² Ô 3 2 8 1 7 ' . 9 4 1 1 ' 0 7 1 . 4 4 U l 4 n . i l k , P ^ 7 5 ^ O t , [ ( 1 1 5 8 9 8 . 1 9 6 1 R � � . A 9 3 6 6 3 1 5 . 9 4 1 2 5 2 6 . 8 l 1 6 6 3 n . 8 l ? & * ¿ 7 5 " � Ð . ¨ " 1 4 " 1 ( 1 . 1 6 ¬ ¿ ð ¿ 9 ¬ Ô > 4 0 . 4 9 5 . 9 4 1 3 . 9 1 0 . 1 2 1 9 8 0 0 5 . 6 2 ô ¡ ^ n 7 º ^ ^ { ¸ ^ r 1 ' 1 U 9 . 1 1 3 � k k 3 , F D 4 . 2 6 ' � . 9 4 1 • • 1 2 3 . 9 . 8 5 1 3 6 2 . 1 5 7 « Û ¯ 7 5 P " � . ¨ C 1 6 B 5 6 P . 1 9 ð 4 � ¬ T - ^ Z U / 8 l ' . 9 . 1 5 2 9 4 6 . 1 5 9 1 1 3 8 0 . 5 0 P , ^ o ² ¬ ' " " . P " I M . " 1 . H ª Û 7 + À " 5 1 8 9 1 4 . 6 2 1 6 1 4 4 2 . 0 6 9 1 ) 8 5 1 . 1 9 9 & 0 0 ! ¬ Û " Û + ¨ P 2 C Z ' 9 1 . 2 5 ò ¿ > 3 1 e 7 ^ 5 5 1 U • • Þ P 1 6 9 6 5 1 . 6 . 1 0 3 7 3 1 5 . 1 9 I P ¬ " " ) 6 ^ r ^ _ ^ r 7 2 1 " " 6 . ( " J ? T + � > 5 9 5 2 < 4 . 3 1 1 1 7 6 1 0 . " 1 1 0 1 1 8 3 . 0 0 1 1 & " " 7 5 ^ ^ P . C 0 2 3 9 2 6 ' . 8 1 J Z ! 2 ð + ² Ô 6 3 3 . 5 4 . 1 9 1 8 n . 6 . ? 5 1 1 6 5 1 . 5 . 0 0 Î Z + " " 7 6 ^ O ^ ¸ ^ r Z � 7 M 4 . 1 6 ð Z P 4 ð , * Z 6 7 1 6 1 • • 8 1 1 9 2 8 8 • • 6 9 1 2 2 9 2 2 7 . 0 0 1 ? . D P 7 ¬ ! O , C ^ 1 1 6 2 1 6 . 1 2 3 1 S 9 1 + õ ó 7 ( 9 1 7 4 . 6 9 2 0 0 2 4 4 • • 9 1 2 . 3 2 1 6 . 0 0 I ¬ + P " 7 ¬ ^ ^ O _ + r 7 ' 4 7 9 � . 8 1 ª I " Ô ß . 1 7 1 4 7 9 H . 8 1 2 0 7 . 4 4 . 6 2 1 3 5 7 1 ] 6 . 0 0 I * ¡ ^ ^ T ¬ P " Û + P P 3 1 1 . 4 1 . ' 4 J ¡ 9 3 ó + 1 ð 7 8 6 0 9 5 . 8 l 2 1 H 9 ' . 5 6 1 4 2 0 . 7 1 . 0 0 I A _ « ¬ ) < ^ r n _ ^ r 1 3 1 I 1 A . 4 4 ò 1 S 1 ¬ ! B ! 2 4 1 5 5 . 8 l 2 2 1 U 3 . 0 6 I U . 7 1 8 . o Ì 7 , C ^ 7 ¬ " " , P P 3 5 0 1 1 1 . 8 7 ò 1 9 1 � = ² ß 8 U 4 1 5 . 8 1 2 2 8 2 2 7 . 0 0 1 5 4 u n . O O î F + P ¹ 7 S ^ ^ C . " " 1 6 Q ' 4 4 . 6 9 5 ! R U 3 + ¹ 9 0 0 5 7 5 . 0 6 2 3 4 9 2 1 . 6 . 1 6 1 1 9 4 4 . 0 0 î R = " P 7 5 Ð ^ ^ ¸ ^ ^ 3 � 8 2 1 2 . 2 5 3 1 8 9 6 . 0 5 9 3 8 7 ] 5 . 1 6 2 U 5 1 6 . 5 0 1 6 1 5 . 1 1 . 0 7 n . " " 7 5 ^ ^ ^ _ ^ r 4 n 7 1 3 1 . ! 6 ð ! ß ¬ . 1 1 ' 7 6 8 9 5 . 8 1 2 4 8 0 2 0 . 1 . 1 7 3 8 8 4 0 . 0 0 � U 1 T U P P 1 P E t à � F n r S I G N C A L C U L A T I O N S � U N R T P D F º J H P 1 N C S T A T à O N � • � . " 1 " � U l A T l n ' T H 1 L K N F S 5 1 N 1 N C H F S • I , ^ A N � U A ) C O 5 T 5 A R E 5 H D V N B E l O W A 5 F U N C T Î U N 5 U F S U L T U K P J P E D 1 A H E T E R º 1 t 0 1 « T N H F N õ T N ? Ë R T N 6 º 1 º L C � 5 P U * P L O 5 1 l . f r 7 � 1 0 ( . o r 1 � l q 4 9 � , H 2 4 8 4 7 9 C 9 . 0 " Z & � ^ Ï 5 ª P P & ª � 2 n 7 5 7 9 . 6 9 9 l A n 6 1 . t 2 3 & P " ' 5 ( 4 t . � � 1 3 1 8 5 4 . 1 2 1 7 4 9 5 6 . 7 5 4 . " " 7 � I " O . ( " l 2 � b 9 � , R ) 7 9 7 7 6 . 8 7 ¬ o " " " O " O . ( � I ³ ¬ ¬ " ò + t S 5 e 7 6 9 . � 7 ô . " T � 0 M . 0 P I A 9 9 ? f . ^ 6 � 2 1 8 3 . � Z 1 . � t 1 5 , ( 0 . ( ' l b ¬ T = ¬ ¬ 4 9 9 9 1 . � � 8 ¡ Þ n T 5 P 0 P ¿ R P I ? ² 7 1 . ^ k b º ó 7 = 1 � 9 & D ^ 1 0 o c . r f Z C 1 9 6 4 + ß I 4 8 4 7 1 . 7 9 Î ^ ¡ Þ n Î " � ^ " + ¯ " ? 2 " ? 3 + ¹ 1 ¬ B ? 1 ³ + ^ º I I . " " 7 � f l " . " t 7 H � 7 7 . ] � 4 A O A A . 1 8 Î 7 » � Î T � " Ü f » ^ P ¿ ¬ J ? 7 � S 4 7 9 º l e 9 � ¡ & P 7 ' 1 ' ( . l n 2 7 , A U . 4 4 4 7 9 1 1 . 5 9 1 4 . - " T � P ^ P ¡ � P 7 � 4 4 Þ Þ , ? * 4 7 R 9 8 . 2 . . f * ¡ P P T � U D D & O 0 3 1 3 1 H 3 « H ¬ ¬ 7 8 7 b o 1 6 Î B + ^ Ü T Y ^ Ç ¡ ^ Þ 3 3 1 9 1 2 . 1 1 ¬ J 6 6 1 + 2 0 1 7 . n t l � I ' O . ( 1 l � n ò 4 7 . 9 4 4 7 8 5 0 . 8 1 Î 8 , 0 Þ T 5 O O O ¿ P P 3 6 9 3 9 6 . 4 4 ¬ J 6 ¬ 3 + ¬ ? 1 9 . " 1 n l l O . l n ² 8 F 1 ^ 4 + B \ 4 1 8 3 A . r 7 ¿ " « � " T � " ( ' . " ( º ! ^ S ? V ¬ b S ¬ T � 3 ^ ¬ 1 ¬ 1 N S U L A T 1 O N S T U N C O S T 5 8 5 1 1 . 9 3 1 3 9 1 3 3 . 1 2 7 l 2 3 1 . 9 � 1 5 6 0 6 2 . 5 6 6 ) 9 5 1 . 9 4 1 7 1 1 1 2 . 1 5 9 b 6 7 1 . 9 4 1 8 � 7 6 6 . 1 2 1 1 9 3 9 2 . ( 0 1 9 1 ) 3 9 . 1 2 1 2 l 1 1 2 . 0 0 2 0 9 0 5 2 . 1 9 1 3 4 8 3 1 . 9 4 2 2 0 0 6 � . � � 1 4 7 � 5 1 . 9 4 2 3 0 4 9 6 . 3 8 1 6 0 2 7 1 . 9 4 2 4 0 4 4 0 . 0 6 1 7 2 9 9 1 . 9 4 2 � 9 9 6 8 . 0 6 1 8 5 7 1 1 . 9 4 2 5 9 1 3 8 . 6 9 I 9 8 4 3 � , 6 9 2 6 8 0 0 0 . 0 6 2 1 1 1 5 C . 5 6 2 1 6 5 8 9 . 8 1 2 2 3 8 7 1 . 6 9 2 8 4 9 4 1 . 8 1 Z 3 b õ 9 1 + t 9 2 9 3 0 8 3 . 7 5 2 � H I 2 . � 4 1 0 1 0 3 8 . 1 5 2 6 2 0 3 2 . 4 4 3 0 8 8 2 7 . 1 5 2 7 4 1 5 1 + 1 9 3 1 6 4 6 1 . 5 0 Z b J ¬ J À + b 9 3 2 3 9 1 3 . 6 2 3 1 0 1 9 1 . 6 9 3 3 L l 5 9 . W T O T A L C O S T 2 6 1 3 9 9 2 0 . 0 0 1 � � 7 9 n , o o Þ Ö Þ B T Þ + Þ Þ 5 6 2 1 1 3 . 1 5 5 1 5 9 0 1 . 3 1 6 0 M l � , 0 6 6 � U 6 1 . " 6 8 5 9 1 1 . 0 0 7 2 6 1 4 8 . Þ 6 7 6 M I O . 3 1 8 0 6 5 9 6 . 6 2 8 4 6 6 ' 7 . 2 5 8 8 6 5 0 9 . " 9 2 6 2 L L . 0 0 9 6 5 1 U . 5 0 1 0 0 5 1 2 4 . 6 9 1 0 4 4 3 5 8 . 1 1 1 0 8 3 4 5 9 . 0 0 l L 2 2 4 3 8 , O O 1 1 6 1 3 0 6 . 0 0 | � � � � ; : P � . 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" " � " � � . 6 ' 1 1 9 5 ' � . 1 9 5 8 1 3 . 5 9 1 5 8 8 9 3 . 3 7 1 . � " ô A _ Þ n ³ • • P ¯ � 2 � 5 9 . 1 0 1 1 1 ( 9 1 . 1 1 6 0 0 2 . 5 2 1 6 1 5 5 5 . 6 2 I s 3 5 ô 3 ( ^ ^ Z B n Ô " � U Ý . " Z 1 1 1 6 9 . 0 � 1 2 7 . 6 3 1 2 3 1 8 6 . 6 2 t + 4 " � < + ^ ^ Ï 6 ¡ Þ Þ � 1 1 1 � . " " I O l U . ( 6 4 ' 5 3 . 5 9 1 2 5 7 6 9 . 6 9 I + � 5 � 1 + � " Z ^ + P " � 1 4 2 • • ' 6 1 2 5 1 " . 1 9 4 3 7 9 . 5 4 1 2 8 3 2 0 . 5 6 f ¡ 5 ^ � • • f P Z ^ « 0 P � 1 1 5 " . " 1 1 4 1 1 1 . 2 5 4 5 0 5 . 4 9 1 3 0 1 4 8 . 8 \ 1 . 5 . 9 � u � � ^ ? « ^ � � o n 2 . " 8 1 2 6 1 . 3 1 4 6 1 1 . 4 5 1 3 2 6 2 5 . 3 1 I & ñ ^ ª 0 & P P ³ . " ¯ ' ' 9 6 6 . 1 1 1 9 6 1 � . 5 0 4 7 5 7 . 4 0 1 3 � 3 5 8 . 1 2 I + Þ ^ � 0 & Ô ] 3 u Û f � � 9 1 . l l n O O T . 5 6 � 8 8 3 . 3 6 1 3 H 8 8 . 6 9 Ì + ¯ Þ 9 � & Î ] / s ¯ Þ � " � ' 6 . ' 9 � " 1 " . 1 ' 5 0 n 9 . � 1 1 3 9 8 7 6 . 8 7 1 . 1 " 5 3 e T P 2 ' . 1 0 ' 9 0 0 . I T 9 6 1 5 ' . 1 1 5 1 3 5 . 2 7 1 � 1 4 8 9 . 3 1 Î , A n � 3 = � � Z ? + ^ C 4 ( 1 8 � . 1 7 9 9 1 2 h s S 4 5 2 6 1 . 2 2 1 4 4 5 6 8 . 2 5 " I . A � ¬ 3 & ¨ " Z = D C 4 1 7 5 4 . � ? I C 1 5 0 0 . 0 1 5 3 8 7 . 1 7 1 4 7 6 H . 6 9 g ' � , Þ n C ? t I ? 1 ¬ � � 4 1 � 4 3 . 9 1 1 1 3 8 7 3 . 1 2 5 5 1 3 . 1 2 1 4 9 9 J O . 1 2 s ! 1 ¬ 9 5 ¬ � » ¹ " ? \ , ^ � 4 1 � 9 7 . 1 � 1 0 6 2 4 6 . 1 9 5 6 3 9 . 0 8 1 5 2 9 8 2 . 3 7 º " : ² + " " ¬ \ _ « ¬ ¿ 1 ¸ ^ n 4 " 8 4 4 . ' C I I R 6 1 9 . 3 1 5 7 6 � . 0 4 1 5 5 2 2 8 . 8 7 " � ? ¡ " * ¬ \ & " ^ 2 1 . n r 4 1 1 7 7 . 7 ( 1 1 0 9 9 2 . 4 4 5 8 9 0 . 9 9 1 5 8 2 6 1 . 1 2 � í � Z « 1 ¯ � 1 . " " ' l . n l 4 1 o n " . � n Î 1 3 3 6 5 . 5 6 6 � 1 6 . 9 4 1 6 1 2 8 8 . 7 5 í Æ I . ? 1 � ¬ 9 , ^ ^ ! R + P ! 4 C T 6 6 , � ^ 1 1 5 7 3 8 . 6 9 6 1 4 2 . 8 9 1 6 2 6 4 8 . 0 6 ~ í ? ¡ ¬ n ¬ º + P " ! R = ^ P 4 1 2 f 5 . 9 9 I I R I I I . 7 � 6 2 6 8 . 8 5 1 6 5 6 4 6 . 5 6 � ¯ ~ W 2 . ? � 4 c . ( f 1 9 . " 1 4 1 7 6 1 . 4 � 1 2 0 4 8 4 . 8 7 6 3 9 4 . 8 0 1 6 8 6 4 1 . 1 2 " � ~ . Æ ² = " " ¬ 9 ¡ ^ P ! P , Q P 4 1 2 5 3 . 1 3 1 1 2 8 5 8 . C r 6 � ? 1 . 7 6 1 7 1 6 3 1 . 8 7 ~ ¯ � + � . � � k R ¡ � P Î R + ^ P " 1 8 6 8 . 6 9 1 2 5 2 3 1 . C 6 6 6 4 6 . 7 1 1 7 3 H 6 . 4 4 � � ¯ + ¬ ^ ¬ � , ^ n I q . t I 9 ? 3 ª � & S 6 1 2 7 h 0 4 . 1 9 6 7 7 2 . 6 7 1 7 6 7 1 9 . 8 1 ( Æ ~ ² + 4 5 ¬ R . P ^ ¡ R , � P 4 ? � I + t T 1 2 9 9 7 7 . 2 5 6 8 9 8 . 6 2 1 7 9 6 8 9 . 5 0 ¯ ~ W � ² = " " k R ¸ ^ r ¡ R ¡ ^ 4 � ' ' I '. Q 1 1 � Z 3 ¬ � + 3 7 7 0 2 4 . 5 7 1 8 2 6 5 5 . 8 7 ¯ Z + � � ¬ ß , ^ ! P , D ^ 4 1 7 4 4 . ' 1 1 3 4 7 2 3 . 5 0 7 1 5 0 . 5 3 1 8 5 6 1 8 . 9 4 t | | t ~ t Z , ¹ ^ 4 A . " " I q . " r 4 4 7 � � . � � l 3 7 r 9 6 . 6 2 7 2 7 6 . 4 8 1 8 8 5 7 8 . 7 5 : . � � � + � � 9 6 + � " l ñ , P � 4 2 � � � . 1 9 1 3 9 4 6 V . 6 9 7 4 n . 4 3 1 B Y ô T h & 3 1 � $ . � . Z + T " 4 1 . " ' ! P ¡ ^ n 4 1 7 3 7 . 1 ' 1 ¬ 1 ¥ ¬ Z + ß 1 7 � 2 8 » 3 9 1 9 2 6 0 8 . 8 7 ? 7 � 1 , 6 . ( 1 1 " . " " 4 ' � 7 n . l � 1 4 4 Z 1 J a ß T 7 6 5 4 . 3 4 1 9 5 Þ 4 Û . 5 6 ² + * " 4 , . . " " | º , ^ P 4 4 1 1 ( . " 7 14 6 � 8 9 . ( O 7 7 8 ( . 3 0 1 9 8 " 6 Y . 3 1 4 6 . � 1 ! � _ r n 4 4 5 2 7 . � � t ¬ ß V b Z + 1 Z 7 9 0 6 . Z b Z Ü 1 3 Y b « 3 T ª ^ , ! " 1 º , M " 4 9 5 1 . 1 1 15 1 3 1 � . 2 5 8 0 3 2 . 2 1 2 0 4 3 1 8 . 6 9 ° ^ , ^ r 1 " . " " 4 5 H 2 . 9 � î Ô 3 T D ß + 3 T � I b 8 . 1 ô 2 0 7 2 3 9 . 3 7 4 , . " " ! � ¡ ^ ^ 4 4 7 ' ' . 4 1 1 � 6 r 8 1 . 4 4 ß Z ß ¬ ¬ 1 1 2 0 9 1 6 2 . 0 0 1 . 5 . ( ( l R , � ^ 4 � 7 � 3 . 9 1 1 5 8 4 5 4 . 5 0 ô 4 I Ü . 0 6 2 1 2 0 ó 8 . 4 h ª ¬ + " ! I A . " " 4 5 � n � . A 9 1 6 0 8 2 7 . 6 2 � 5 3 6 . 0 2 2 1 4 9 7 Z . b 0 4 1 . t ' ' I q . � o 4 M I I. � 4 1 6 3 Z � " . 7 5 ß 6 ó 1 . 9 7 ¿ 1 Ï 8 Ï h . 2 Þ ª ¬ + " " ! � + " " 4 M l I . Q r 1 b � º T + ß 1 8 Ï ñ 7 . 9 J 2 2 0 7 7 3 . 5 0 ¹ s ¶ _ D n I � . � o 4 , � ( q . 7 3 16 7 9 4 6 . 9 4 8 9 1 3 . 8 8 2 2 J 6 7 Û . 5 0 ^ = ^ ' 4 - . " 1 ) A , n o 4 3 Z ^ ° + A 5 1 7 0 J 0 . C 6 ' 0 3 ' . ð 2 2 6 � 6 5 . 3 7 � ³ & ¹ " 4 t . � , î R + � P 4 7 ' q q . � 1 1 7 2 6 9 3 . 1 ' 9 1 6 5 . 1 9 2 2 ' H 1 . 9 � g ' . ' . " 4 1 . ' 1 ¡ P , ^ P 4 7 º 9 � . 4 � 1 7 � C 6 6 . 3 1 n 9 1 . 7 5 2 1 2 3 4 8 . 5 0 ; 4 � 3 . 4 � 4 � + � " l P , ¹ " 4 . 3 7 9 . 1 6 1 7 7 4 3 ' . 3 7 9 ' 1 + 7 0 2 3 5 2 3 6 . 6 9 . .. � ² ¸ º ^ 4 ' . " " ¡ F + ¨ " 4 6 � 9 q . � " 1 7 9 8 1 2 . 5 0 9 � 4 3 . 6 5 2 3 5 9 5 5 . 6 2 � ² ¡ A < ¬ ^ » ' " ¡ R , " 4 6 9 6 1 . � n 1 8 2 1 8 5 . 5 6 9 6 6 ' . 6 1 2 H 8 2 2 . 6 2 � Î ; ² , ¹ ^ 9 * & ^ " 1 , . 1 ' 4 7 3 n . 6 b 1 8 4 5 5 R . 6 9 9 1 ' 5 . 5 6 2 4 1 6 8 7 . 8 7 Î Æ � ^ + � ¬ 4 3 , P P ! A + ^ " 4 7 6 ' 7 . º 8 1 8 6 9 3 1 . 8 1 9 9 2 1 . 5 1 2 H 5 5 1 . 1 9 « Î ; ² + ² " º ^ + P " ¡ 1 , ¹ P 4 8 1 6 � . 3 n I R 9 3 � 4 . 9 4 1 0 1 4 7 . 4 7 H 1 U 2 . 6 9 � - W × ¿ ? º 4 , . r l l 1 1 . 1 1 4 A 4 2 0 . ß 9 1 9 1 6 7 8 . C O 1 0 I n . � 2 2 5 0 2 1 2 . 3 1 � . .. Æ ^ + � " 4 ^ + ^ P Î ^ + " " 4 . 1 7 ³ = � ? 1 ' 4 1 5 1 . 1 2 1 0 2 9 9 + 3 7 ¿ Þ > 1 > U » 1 Z . . ¯ Ñ . . 3 « ° ¬ 4 ' . " 1 l ^ = ¹ " 4 9 1 3 6 . 7 1 1 9 6 4 2 4 . 2 5 1 0 4 2 5 . 3 3 2 5 5 9 B 6 . 2 5 ' � ! . ? ^ 4 " . " ' 1 " . l f 4 ' 4 ' 2 . 0 7 I 9 B 7 º ? 3 \ 1 0 5 5 1 . 2 8 2 5 8 8 4 0 . 6 2 ¯ ; 3 . q � 4 ° ¬ * ¬ l A + C ^ 4 9 R 4 5 . 7 I 2 0 1 l 7 t . 4 4 1 0 6 7 1 + 2 4 � 2 6 1 6 9 3 . 3 7 . . W � 4 , " ' ' l ^ + ^ " 5 P 1 9 7 . 6 4 ? ( 3 � 4 1 . 5 n 1 1 8 1 3 + 1 9 2 6 4 5 � � . 3 1 ¯ � ~ Z1÷ Appendix ÏLܯ Ï ÏIDgIæ æQ Spe ÏIUÍDuÍ ÍDI LDßQÍ0I Ý 000 1 o�oz 0013 uOO� OOO� OOOb 0007 OOOH 0;09 00 1 � (011 OOIZ CU13 00 1 � 0,1 ' COlb 001 7 OOh 0019 OJlO OOZI OOZZ OOZJ ( ..2� OOZ, COlb C027 002A OOl9 t030 0 031 OOJl �033 C03� 003� 0�3b 0037 003H C039 CO�O C041 UC¬Z 00�3 OOH (0�' 10�b 0047 OO�H (049 005� !C�1 UO�Z 0053 Oi'� u05� OO,b 00$1 CO,d li�9 OOb' OObl OOol 00b3 00b4 Oub� "Obb 00b7 L P<UCESS OESIC� FU� STV�fNE PROOUCTIUN UIMfNSIU� E813I,�TVI3I,BlI3I,TOLI3I,HVDI)I,TEMPI3I,TEMPGI)I,PRESSI ló I LUÞ�U� TlE�,rIO,rOu,FRATE,rEMP,TE�PG,CArOIA,CATOEN,ETA,fPS,H,ePEB, ILP.G,<ATEFG,PR(XC,�SLICe,SrV,TOL,dl,ES,PRESS,HVD,X�OLe,PRESSG,V,M, LI,�,XI,K,J,VleLO,rUeL,RKI,RKZ,RK3,EKI,eONSTI,CONSr2,CONST3,eONsr4, 3VJli,AR�A,AT(MP,Are�PG RtAD 13,CATO��,p"Exlr,FGRATE,CPEB.CPFG,H,EPS "fAD 13,CATDIA,�TA "tAi 1�.�SLICE,�OeL "tAu 13,�CPRCf,tdP"CE,eArp"C L f�kMAT STATFMtNTS Il .�kMATIIH,ZX,fI0 . 3,5FI�. �,fI 0 .Z,FIO. Z,Zf10. 31 ]± FJKMArI8FIC. 51 14 fJR�AT181101 PRExG=PREXIT-14 . 7 Zû READ IJ,TIO,TOO,REI L CONTkOL tARO FU. STUPPING PkOGRAM IF Irl01999,99 9,ZI ZI R�AU 13.ATEMP,ATfMPG A.EA=3. 141�9.Tlu**Z/57�. V�10=11. -EPSI/EPS·*3 SLIt E=NSLI CE lu<L=TLE�/SLltE F{ATE-�Z' . *lrID/4 . 031**Z. RATEF�=FCRATE·ITOO/�.�O'·*l. JO tALL PRTLAT tO�sr l=tArO�N*A��A*IOb. I.RATf CuNSTl-H*TUO/1 2.*3. l�I;9/ItPES*FRATEI CuNSTJ=;3bOu./ICPEB*IOb. 1 CJ�Sr4=H.rOO/IZ. *3. 141;9/ICPFC*RATEFG' LALtULATE ENrRANCE PRESSURE AOlNZ·PREXlr / l�. 7*8;. *.CbZ4/IC.99*0. 08Z0b*1 ATEMP +bOO.'*0.;;561 A�.ESS·3 l . *L. Olb7/CATOIA*F<ATf**Z/4Z;. **Z*0 . 0 8 8;**Z/AREA**Z*TLENI 1 1�.'19 . 7 APkESS=I. lOAPPESS Uû 100 l-l,ZC AOtNI=APkESS/14 . 7*10o.*0 . ObZ4/10 . 9 9*O. 0 820b*1 ArE�p +4bG. I*O . �;;bl AvEN·IAOtNI+AD(�ZIIZ. AVtL=FkATE/IAD��*3bOO. *A�fAI ID� A�kfSS-PRExlr'TLEN*0 . OOOZI�84.1.7'/CATDIA.ADEN.AVEL**2*VOID APRESS- l . I*APRESS ¾U TEMPI31=ATEMP rtMPGI3'-ATEMPG PrtSSI31 =APRESS SrV( 3' =0. ruLI3I=O. bLI3I-0. MM-O N=Z*tSLltE+ l UU so. I=I,� 19� (FII-Z*(I/ZII 100,ZOO,jOO �OO t�IZI=1. -(STVIZI+�LI21+rLLIZI' hVOIZI-STVIZI-TJLIZI XI=l. J·Z K=3 XMOLE- l • • B1IZI'STVIZI b� TO 4CC 3CO CALL RE INIT IF IM-MMI j02,30 l,30 1 301 M= M"+MOLL P<I NT 1 Z ,M, X, �BI 11 ,S TV III ,811 I" hILI II ,HVDII' ,TEMP III ,Tf OPG I 11 , ¡ PRESSG,VIELI JbZ XI=Z. J=I K-Z �CO rEMPK=ITEMPIJI+400 . I*C.;5;o K(I=�XP l- l90�4. /ll . 987*rE�PKI+ 7 .Z9I' kKl=ETAORKl kKZ=�XP 1-'0800. /11. 9 81.Tf�PKI+ZO. 9991 <K3=EXP I-ZI800 . /11. 98 7*TEMPKI+b. 3941 f�l=�XP 1-3.�7377+(3. H1 0Z4/3bO.'*lrEMPIJI-q3Z. 11 40 1 tALL tHE M I+ IP<tSSIKI-p"cXlr+2.51�0'.;00,�lO ¬CU tJ�rl"UE ;40 lFIPRE�SIKJ-7 . ;-I". 71��l,50 l,��0 CObb OObQ COlO 0011 0012 0013 OJ14 COH 001b 0011 001. 0019 COSO OiOI 0002 000) 0004 OOO� ODOb 0001 0008 C009 0010 0011 0012 0013 0014 �Ol� uOlb C017 Ool8 0019 C020 0021 �022 "OZJ u024 C02� 002b COZ1 OOlb OJ29 �03C OOH COll 0033 '034 003� 013b C037 C03S 0039 (040 (041 C042 ,043 0001 0002 0003 C004 CJO� CUub 0001 ûûUo (oeq OOIC COli 0012 FORTRAN IV Program and Sample Printout for Clzapter ¯ Z1J L I_ITIAL P�t��URE TOO HIGH ��U AP¤E��=APkt ��~0.ª IPKES�IK| -14. Ϭ5 . 0 l Gj TO 40 ;01 CAl� REACT<IKCP" C¢ .EdPRCE.CATPHC.TUSESI 70U CALL II�TILIFRATE.TUBES.EB.STYI GJ TO 20 >ûb l� I TlE N¬X¬TL L �/IO. 1 �Jl.�Ol.;Ob >b AP Rt SS=APRE�SH. GJ TQ bC8 ;(1 "Pkt��=APRt��+I. �ûd P·U�T ll,M,X.fBtll,STYClJ,tH(1).rOlCl),rYOtl),TE"P(1),TE"PG(1), I PKES�G.YIELD GU T O 40 V�H �luP END �UoRUUIINE PRIDAT o I ME NS IllN LbI 3 I • STY l jI • Sll 3 1• TOLl \I. H YD I 3 I • 1E�P 13 I • TE �PG l3 l • PR ES 5l 131 tuMMUN TL� N, 1 1U,TJu,f RAT E ,TEMP,TtMPG,CATDIA.CATDEN,ETA,EPS,H,CPEB. lCP�G,�ATlfG.P�Exu,NSLICE,Sry,TOl,dl,Ed,P�ESStHYO,X"OLE,P�ESSG,y,,, , �1,x,Xl,K,J,YlfLu,TO[L.��1,�Kl,�K3,EKl,CONSTltCONSTZtCO�ST�,CONST4, 3VJI�,ARtA.AT�MP,ATE�PG P"INT 4.TLEN P"I'T 2.TUD PHINT ),TID P<tNT I.FRATE PtINT 7,ATtMP P41 NT /J¬A1VPG P×1�1 17.CATDIA ""INT Ib.CATUEN PRINT 14.EU PRINT 13.EPS P{ I �1 19.H PKI�T 18.CHO P�INT 22.CP�G PRINT 20.�ATEfG P"INT �. PREXG P{INT 8."SLICE "" INT 9 PRINT 10 PKI NT II KE 'UR� fJKMATlbX.IIHf(EO RATE =.FI0.3.3x.25HLB ETHYL 8E NIE NE/HR/rU8E fJKMATlbX.23hOUTSIDE TUBE DIAMETER =;11D+Ô;3X+O¬1N l FJ×MATlbX.22HINSIJE 1U�E OI A�ETER =.FID.5.3x.3HIN I ¬ íUP*AT11H1+ÔX+13HTU8¢ lE�GTH =,F10.5,)X,)HFT ) > f�kMATlbX.23HASSU"E� EXIT PRESSUKE -+F¡D•••3X.5HPSIG I 1 f 3 k�ATlbX.2b�I NI TIAL FEED TE�PERATURE =.fIC.2.3X.IOHUEGREES f I d rJKMATlbX.22H�U�BEK Of I NC�EMENTS =.15.IH IIH IIH IIH IIH I 9 F,×HAT I 3X,9H l NC� E��NT,/X,b¬lENuTH,4X.5HLTHYL,4X,ÏHSTYRENE.3XçTHBEN Ilt�E.3X.7HTULUENE.2X.bHHYD�UGEN.2X.SHKEACTION 2x.8HfLUE GAS.2X.SHP 2RESSU�E.�X.bHYIElD I l� �)KMAT(5X.bHNU�dER.5X,lHFT.5X.7HBENlENE.l'3x,8HETHYLENE,2X.7H�£TH4N lE,14X,4HTEMP,2x,4X.4HTEMP.6X.4H�S[ G,4X.14HlB MOLES STY IIH , II FJKMATI23X.��H lB MOlE� fOR"E� PER L8 MOLE Of ETHYlBENIENE FED DE I� f. �X.5HDE G F.IJx.I�HlB MJLE EB RtACTED IIH IIH I lb fJRMATlb ••23HCATAlYST �UlK DE NSITY= fIO.5.3X.9HlB/CU fT I 17 r JKMAT l b X.2bHCATALYS T PELLET DIAMETER =.fIOe 5.3X.3 rfT l ¡B � JKMAT l bX.J2HHEAT CAPACITY Of ETHYL BENIENE =.fIO.5.3X.RHBTU/LB/fl 1 V �JKMATlb'.3bHOVER-ALL �EAI T�A�SFER COEffiCIENT =.fIO.�. )X.1 5HBTUI lH×7SU FT/f I 20 fJKMATlbX2CHfLUt GAS FLO" RATE =.fI0.3.)X.20HLR fLUE GAS/HR/TUBE I 21 f""MATlbXdIHA�SUIEJ EXIT TEMP iJF F LUE GAS =.FIO.3.3X.9HDEGREES FI l2 � JRMATlbX.21HHEAT CAPACITY uF f lUE GAS " .FIO . 5 s 3X.QHBTU/lB/f I 23 fUKMATlbX.29HVOIO fRACTIO� Uf PACKED dED = .FID.5 .IH l 24 fjKMAT(bX.2JHEffECTIVENE�S �ACTOR = fIO.2.IH I ci+U Su�ROUTI"E KtlNIT U I ME NS I O� LBI3 I • 5TV I Jl.8111 1•TUL I JJ •H YO I 3 I • 1L"PI 31 • T EM PG 131 • PR E S5 I 1; • CJMMUN TlE�,T[U,TOO.fRAT[,TEMP,rEMPG,CATDJA,CATOEN,ETA.EPS.H,ePE6, lCPfG,�ATtFv,PRtXu,NSlICE,�TV,TUL.Bl.E�.PRESS.HYO.X�OLE.PRESSG.Y.�. 21.x.xt ,K.J.YIEL0.TOEL,RK 1 .�K2.kK3,�Kl.CO�STl.CONST2.CONST3.CONST4, 3VJIO.AREA STYlll=�TYI3I lJLllI=W1I31 Bllll=BlIJl T<MPIII=TEMPI)) TtMPGl1 I=TEMPGI 11 �×t�o111?FKL´S1¹1 Ed I I I = I . -I STY I II +òI I I + T OLlII I HY(III=�IYIII-TJLllI XMLlt·I.+SlIII+STYIII Z1Ô Appendix �Ol) 0014 001� �Olb 0017 0018 0019 OOZO OOZI 0022 vOZ J 00Z4 OOZ� 002b 0001 OOOl 0003 OJ04 OvO� OOOb 0007 COO� 0009 0110 Gull OOIZ 0013 COl4 0001 OOOZ OOu) 0\04 COOS COlb 0007 0008 0009 DOLO DOLI (OIZ DOL) OOH OOI� OOlb (017 0018 COl9 0021 COZI 0022 C023 (OZ4 VOZS OOZb 0017 P�tSSG=PRESSIII-14.7 X= S TYI 11 +BII l) +TOUl) IfIX)j�3.3�1.)52 3�1 YI�LO=O.O Gu Tl 3S4 "�l P�INT 101 CALL bXIT 101 fJkMATI�HNEG. SUMI 3�2 YIELD=STY(1)OIOO./X 3�4 Y=IIZ M=I/Z x=YOTOH KdURN ��U SUoROUT I /E CHEM 01nN5 ION F�I J1. SIYI ì I .B?I J1• lUll 31 • H YO, 31 • TE�P I 31 • r EMPG (31 • PR ES S l 131 COMMUN llEN.TID,TUO.fRATE,TE�P.T��PG.CArOIA.CATOEN,fTA,EPS,H,ePEB, l�P�G,KATEFG,P��XG.NSlICE,STY.rO,dl.EB,PQESSfHYD,XMULE,PRESSG,y,M, Ll,x,XJ,K.J,YIELU,TDEL,KK1,KK2,RK3,EK1,CONST1,cnNST2,CONST3.CONST4, 3VuIO.ARH SIYIKI=SIYIII.rO(L/xl*cnNSTI'"KIOPIESS(J I /I14.70X�OLE I oIEBIJI-STYI ¡J1 +HYO, J 10PI � S S' J 1/1 E K 1* 14.70 'MO LE I I blIKI=dllll+rOtL/IIOCU�STI'RKZ"P�ESSIJI/I14.70XMOLEloEBIJ I 1O11K 10 lull II +1tL7X l*CLJNST1"HK+1 PRE SS I J 1/ l 14. 70 X�OLE I l""ZOEBI J 10 IHY! l J 1 TEMP I81 = TEMP l 11+ reEL! x I "CO�S TZ* I TEMPGI J I-TEM PI JI I -CONSH"I STY, K I -S I TY I I I I T.MPGIKI=TEHPGII I +TOEL/XI"CONST40ITEMPGIJI-TtMPIJ I I A�.=IEBIJ I '106.+STYIJ I 'IO�.+HYOIJloZ.+TOLIJ I 0108.+BlIJ10106. I /XHOL IE Ot�oPRtSSIJI/14.1'AMWO.ObZ4/10.99"0.OB20b'ITEMPIJI+460.100.55561 VcLoF�AIE/IOEN03000.0A�EAI P�ESSIK I =P�ESSII I -TOEl/XI'0.000215S401.7S/CATOIAoDENOVELOOZ_VOID KEIU"N cNL S���OUTINE REACT�IRCPRCE.tdPR CE.CATPR C.TUBESI UIMENSION E8131.STYI31.8LI31.TOLI31.HYO I31.TE�PI31.TEMPGC)I.PRESSI 131 CJ�HO� TlE�.TIO.TOO.FR.TE.T�M�.TE�PG.CATOIA.CATOEN.ETA.EPS.H.CPEa. lCPfG.RATtfG.PREXG.�Sl ICE.STY.TU.dl.E8.PRESS.HYO.X�l E.PRESSG.Y.�. ll.X.XI.K.J.YIEl�.TO�l.�KI.RK2.�K).EKI.CO�S'I.CONS'2.CO�ST3.CONS'�. 3VûI O. AREA TUDES-l.0S*20000000.*IJb./lfRATE*STYlll*IO�.*dOOO.1 P�I�T IS.TUBES Kccosr-RCPKCE*20UOOOUO.*I.OS*I06./II 04.*YIElDI*EBIII/CI.-ERIIII RCtOST-R CCOST*I�O. 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RRCNCNI.ANT1NI.FTI NI.CPCOS1N).STCUSCNI.CwCOSCNI.COSTCNI IO� FJ�HATC7FI8.2/11 G" 1U 5ec 999 STuP SUO "E TURN ENO Z1¯ T U B E L E N G T H = 1 0 . 0 0 0 U O F T O U T S I D E T U S f 1 1 A H c n R = 1 . 3 1 5 0 0 I � I � S I I E T U d E u I A H L T � K = 1 . 0 4 9 0 0 I N f � E U R A T ¢ = 2 8 . 7 9 b L B E T H Y L B E N l E � E / H � / T U S E I N I T I A L f E t � n M P L k A T U R E = 9 3 2 . 0 0 O � G � F E S F A S S U M E D b 4 l T E M P O F f L U L G A S = 1 6 0 0 . 0 0 0 D E G R E E S F C A T A L Y S T P t L L E T D I A M e T e R = 0 . 0 1 0 4 0 F T C A T A L Y S I d U L K D E N S I T Y ' 6 1 . 0 0 0 � 0 L B / C U F T E f F E C T I V E N E S ) F A C T O R = 0 . 4 4 V U I D � K A C T I U N U F P A C K e D B E D = 0 . 3 8 0 0 0 O V t � - A L l H E A T I R A � S F E R L U E I F I C l E � T = 8 . 0 0 0 0 0 B I U / H K / S Q F T / F H E A T C A P A C I T Y U I E T H Y L B t N Ï E � E = O . 6 3 5 0 C B T U / L 8 / F H E A l C A P A C I T Y U í F L U E G A S = 0 . 3 0 0 0 0 B T U / L � / F F L U E G A S F L � � R A T E ' 5 5 6 . 7 b 7 L 8 F L U E G A S / H R / T U 8 E A S S U M t U t X 1 1 P � t S S J K E = 5 . C O O O O P S I G N U H ó c K U f l N C K E M L N f S - 1 0 0 I N C R c M E N T L E N u T H L T H Y L N U M d E o F T b L N î L N L S T Y R c N E b c N ¿ í � c E T H Y l E N E T O L U E N E M L T H A l E H Y U � O G E N L 8 M U L E S r U × P L J P E R L B " U L E O f E T H Y L 8 E N l E � E F E D 0 0 . 0 I . O O O O C C . O 0 . 0 0 . 0 0 . 0 1 0 1 . J v l u . 9 8 0 7 C C . O I ' l l 0 . 0 0 0 0 6 0 . 0 0 0 1 l 0 . 0 1 � 0 0 2 0 l . � O O 0 . 9 � O 0 7 0 . 0 4 d 7 1 0 . 0 0 0 4 1 0 . 0 0 0 1 5 0 . 0 4 8 0 ? 3 0 3 . 0 0 � 0 . 9 0 � d 3 0 . 0 8 & 5 2 0 . 0 0 1 2 5 0 . 0 0 2 4 0 0 . 0 � 4 1 3 4 0 4 . 1 0 0 u . b o ¿ 6 Î 0 . 1 2 8 " 4 0 . 0 0 2 8 8 0 . 0 0 5 1 1 0 . 1 2 1 6 3 5 0 5 . 0 ( ( 0 . 8 1 1 9 0 0 . 1 7 3 2 0 0 . 0 0 5 � 1 0 . 0 0 9 4 0 0 . 1 6 3 8 0 6 0 & . ( 0 0 O . 7 � 9 0 5 0 . 2 1 7 4 1 0 . 0 0 9 2 5 0 . 0 1 4 2 9 0 . 2 0 H 2 7 0 7 . U O O 0 . 7 0 & 1 5 0 . 2 & . 2 5 0 . 0 1 4 1 3 0 . 0 1 9 4 6 0 . 2 4 0 7 9 8 0 8 . � v O ; . 6 5 � 0 0 0 . 3 0 0 � 9 0 . 0 2 0 0 6 0 . J 2 4 3 5 0 . 2 7 6 2 4 9 0 9 e 0 0 û � . 6 U 7 b 2 0 . 3 3 7 0 6 O . C 2 6 1 � o . n a � 8 0 . J O d 6 8 9 � � . 9 0 0 J . ¬ 1 8 1 0 . 3 6 4 , 2 0 . 0 3 2 8 7 0 . 0 3 0 d O 0 . 3 H l l 0 0 . " 1 . 0 0 . 0 0 0 . 0 0 . 0 0 . 0 0 . 0 1 0 1 . 0 0 C w . 9 d U 3 1 0 . ( 1 9 4 3 0 . 0 0 0 0 8 0 . 0 0 0 1 2 0 . 0 1 9 3 1 2 0 2 . 0 0 1 0 . � 4 9 3 1 0 . 0 4 9 4 ' 0 . 0 0 0 4 2 0 . 0 0 0 7 9 0 . 0 4 H O 3 ( ) . U I O 0 . 9 0 8 5 9 0 . 0 8 7 b 3 0 . 0 0 1 2 6 0 . 0 0 2 5 2 0 . 0 8 5 1 1 4 0 4 . u J O J . 6 b 1 1 b 0 . 1 3 0 3 6 o . O C 2 � O 0 . 0 0 5 5 1 0 . 1 2 4 7 9 5 0 Þ e 0 0 u J . 8 0 9 6 8 0 . 1 7 � 9 0 0 . 0 0 5 5 5 0 . 0 0 9 8 1 0 . 1 6 � 0 3 1 0 o . O v O 0 . 7 5 o 2 2 0 . 2 l � � 1 0 . 0 0 ' 3 3 0 . 0 1 5 0 4 0 . 2 0 4 3 7 7 0 1 . 0 u O v . 7 0 2 5 2 0 . 2 6 2 b 4 0 . 0 1 4 2 8 0 . 0 2 0 5 6 0 . 2 4 2 0 8 8 0 8 . t O ( u . 6 � 0 2 8 0 . 3 0 3 5 5 0 . 0 2 0 3 2 0 . 0 2 5 8 5 0 . 2 7 1 1 0 9 0 � . � 0 u 0 . 6 0 1 4 9 0 . 3 4 0 9 5 0 . 0 2 7 2 1 0 . 0 3 0 3 4 0 . 3 1 0 6 1 1 0 0 1 0 . O L O 0 . 5 5 ' 2 4 0 . H l d 1 0 . 0 3 4 4 0 0 . 0 3 3 5 0 0 . \ 3 9 3 7 R E A C T I O N f l U E G A S T E � P T E M P D E G f D E G F 9 3 2 . 0 0 1 6 0 0 . 0 0 1 0 1 1 . 9 3 1 6 1 0 . 4 2 1 0 1 4 . 2 8 1 6 1 9 . 8 2 1 1 2 1 . 2 1 1 6 2 8 . 4 7 1 1 6 3 . 0 5 1 6 3 6 . 5 3 1 1 9 1 . 0 8 1 6 4 4 . 1 1 1 2 2 7 . H 1 6 5 1 . 7 9 1 2 5 5 . 5 3 1 6 5 8 . 1 0 1 2 8 2 . 4 9 1 6 6 4 . 5 7 1 3 0 9 . 4 4 1 6 7 0 . 1 9 1 3 3 5 0 1 8 1 6 7 5 . 9 1 9 3 2 . 0 0 1 1 0 0 . 0 0 1 0 1 1 . 1 9 1 6 1 0 . 4 2 1 0 7 3 . 1 8 1 6 1 9 . 8 3 1 1 2 2 . 5 0 1 6 2 8 . 4 9 1 1 6 2 . 2 1 1 1 3 6 . 5 1 1 1 9 6 . 1 5 1 1 4 4 . 1 6 1 2 2 b . 4 2 1 6 5 1 . 3 5 1 2 5 4 . 3 9 1 6 5 8 . 1 8 1 2 8 1 . 1 0 1 6 1 4 . 6 7 1 3 0 7 . 5 1 1 6 7 0 . 8 3 1 3 3 5 . 2 5 1 6 7 1 . 6 4 P R E S S J R E P S [ G 4 1 . 2 8 7 3 9 . 3 6 5 3 7 . 2 2 0 3 4 . 8 1 9 3 2 . 1 1 7 2 9 . 0 5 8 2 5 . 5 5 6 2 1 . 4 8 5 1 6 . 6 2 5 1 0 . 5 2 9 2 . 9 8 3 4 2 . 2 8 1 4 0 . 4 0 0 3 8 . 2 9 6 3 5 . 9 4 5 3 3 . 3 0 5 3 0 . 3 2 3 2 1 . 9 2 5 2 2 . 9 9 7 1 8 . 3 5 2 1 2 . 6 3 3 4 . 9 3 5 ¥ Ï Ë L 0 L ð R Ü L t å å T Y f L I R Ü L Ë E I R E A T E D 0 . 0 9 8 . 9 8 9 9 7 . 6 1 4 9 5 . 9 5 3 9 4 . 0 2 7 9 2 . 0 7 7 9 0 . 2 3 1 8 8 . 5 6 7 8 7 . 1 2 8 8 5 . 9 H 8 5 . 1 3 0 0 . 0 9 8 . 9 7 0 9 7 . 1 1 3 9 5 . 8 6 4 9 3 . 8 9 5 9 1 . 8 9 8 9 0 . 0 0 3 8 8 . 2 8 8 8 6 . 7 9 1 8 5 . 5 5 1 8 4 . 5 9 6 � ~ � � ¯ × � � . N U K b � � U I T U b L � = 2 4 9 . 1 8 1 A � N U A L L U � ¡ U r � L L Y L L l � õ L 1 H ¥ L b L N ¿ b N c A T 0 . 0 l 0 f f L � = 3 2 1 0 1 8 . $ ¥ R A N N U A L C U > ¡ U F c H Y L b � N ¿ L N L C O N V E R T E D T e b ¥ ¬ F R U 0 U C T $ A T 0 . l ¿ 0 $ L ß = 4 6 7 6 7 3 . H Y R I U ¡ A L A N N U A L u P � R A T I N G C U $ î = 7 8 d 6 Q 2 . $ ¥ R S U � f A C E A R � A U F × c A C T U R = 8 5 1 . 0 4 4 S O F T ² C U > ¡ U F 1 W U K L 4 û ¡ U K S U F A b U V c S I l E = 1 0 9 9 6 0 . 0 0 C U S ¡ U F L A T A L V , ' A T 3 . 0 0 $ / L B ? 2 7 3 0 . 7 9 8 $ ¯ � D I S J I L L A J I O N t A L t U L A J I O N S f O R R E A t J D R D E S C R I B E D A 8 0 V E ; � f E E D Ñ Å Ë P 5 4 7 1 . E _ F R A t J I O N I N F E E D 0 • • 0 0 E B F R A t J I D N I N 0 I S J I L L A f E - 0 . 9 . 9 � I N I " U " R - " . 0 7 9 � ª * R R f A C l L i T R A Y S F E E D f R A Y D E P R C O S T H U T L U ã L U J L L U 5 1 T t ¤ K L Ü 5 I � � 1 . 0 5 9 • • 0 0 • • • 0 0 • • 1 1 2 • • • 7 0 0 0 1 . 1 9 3 7 1 5 . 3 5 1 2 0 0 2 9 . 1 9 � Þ � 1 . 1 0 8 5 . 0 0 3 9 . 0 0 • 1 � 8 . 6 2 7 2 7 0 3 . 4 • 3 8 5 8 . 7 8 1 1 8 5 1 0 . 8 1 Þ < L ø L Þ 7 8 . 0 0 3 5 . 0 0 3 9 3 . 6 . 2 . � 7 S . 0 S . U 4 0 0 2 . 2 1 1 t 8 7 5 4 . 2 5 Þ Þ 1 . 2 . Ï 2 . 0 0 3 Z . 0 0 3 7 0 5 . 0 5 7 8 1 0 8 . 1 2 4 1 4 5 . 6 3 1 1 9 3 4 8 . 7 5 � � 1 . 2 5 . 9 . C O $ 1 . 0 0 3 U 8 Z . 3 2 8 0 8 1 0 . 5 0 4 2 8 9 . 0 6 1 2 1 3 8 1 . M � � ~ . 1 . 3 0 • • • W 2 9 . 0 0 3 5 1 9 6 . 5 7 8 3 5 1 2 . 1 1 4 " 3 2 . 4 9 1 2 3 3 H . 8 7 Æ C � I . J 5 u . O O 2 B . 0 0 3 4 U 9 . U 5 7 . 7 6 . 7 7 3 0 5 0 . 6 1 9 4 9 6 6 . 8 1 ' � 1 . 4 0 . 2 . 1 0 2 6 . 0 0 3 U U . 2 6 5 9 2 7 8 . 2 9 3 1 4 b . 2 J 9 6 9 5 0 . 7 5 ¯ � 1 • • Þ 6 1 . 0 0 2 6 . 0 0 3 . å 8 å . 1 1 . 1 0 7 9 . 1 3 2 4 1 . 8 5 9 8 9 0 6 . 8 1 { � � L ø Þ Ú 5 9 . 0 C 2 5 . 0 0 3 4 0 3 9 . Ï 6 2 8 8 1 . 3 8 3 3 3 7 . 4 1 1 0 0 Z 5 8 . 5 6 ¨ 1 . 5 5 S 8 . C O 2 5 . 0 0 3 4 0 ' • • 7 . . . 6 B 2 . 9 6 3 4 3 3 . 0 9 1 0 2 1 5 0 . 7 5 Þ ~ � l . b J 5 < . C O 2 3 . 0 0 l . b 5 5 5 . C O 2 3 . 0 0 1 . 1 � 5 5 . C O 2 3 . 0 0 1 . 1 > 5 3 . V O 2 2 . 0 0 1 . 8 0 5 3 . 0 0 2 2 . 0 0 1 . 8 5 5 2 . C O 2 2 . 0 0 1 . 9 J 5 2 . J 0 2 2 . 0 0 ¡ = � 7 ) 1 . C O 2 2 . 0 0 ¿ - v J 5 ¡ . C O 2 1 . 0 0 2 . 0 ) 5 1 . 0 0 2 1 . 0 0 T U B I L E N � T H = ¡ b . 0 0 0 û 0 F T O U T , I U E T U � E U I A M I T E R . 4 . 5 0 0 0 0 Î N I N , I U E T U d e U I A M E T E R ' 4 . 0 2 6 0 0 I N f L 0 � A I E ' 4 2 4 . 1 5 . L a t T H Y L B E N l E " E I H o I T U B E l N l 1 I A L F E b ) T O W l iU T U R E . 1 0 2 2 . 0 0 D E G R E E S F A > S U M I D E X I T ¡ c H P U F F L U E G A S ' L m 0 o 0 0 0 D E G R E E S F C A T A L Y S T P I L l t r U l l M E T E R . 0 . 0 1 0 4 0 f f C ¤ ¡ 4 L Y S ¡ ö U L � U I N , I T Y . . 1 . 0 0 0 G O L d / C U f T E F F E C T I � E N I 5 . F A C T O K • 0 . 4 4 V O l o F R A C T l O " O F P l C K E D B E D . 0 . ) 8 0 0 0 3 3 4 0 1 . 2 4 3 H 4 1 . 2 1 3 3 8 6 6 . 3 3 H I 3 5 . 5 8 3 3 6 3 1 . 3 1 3 3 ' Î 8 . 4 4 3 3 9 5 5 . 5 5 3 3 7 6 6 . 1 3 3 4 2 2 5 . 4 6 3 4 6 8 0 . 1 8 O V E � - A L L t l A T T k A � S f E R C O E F F I C I E N T ' 8 . 0 0 0 0 0 B T U l l / S O f T l f H l A T C A P A C I T Y O F " T H Y l B E N Z E N E ' 0 • • 3 5 0 0 B T U I L B l f H I A T C A P A C I T Y U l F L U k G A S . 0 . 3 0 0 0 0 B T U I L B I F F L U E G A S F L U W t A l t . 1 5 2 0 . 0 0 0 L I f l U E G U / H R I T U I E A > S U M I U e X I T P R t S � U R E ' 5 . 0 0 0 0 P S I G N U M B E k � F l N L � c H c N Ï ã º 1 0 0 6 6 4 8 4 . 5 0 3 5 2 8 . 7 0 1 0 J 4 2 0 . 4 4 � ¯ 6 8 2 8 6 . 0 6 3 6 2 4 . 3 2 1 0 5 2 5 1 . 6 3 7 0 0 8 7 . 5 6 3 7 1 9 . 9 4 1 0 7 6 B . 8 1 1 1 8 8 9 . 1 9 3 8 1 5 . 5 6 1 0 8 8 h 0 . 3 l � ¯ ¯ R 7 3 6 9 0 . 6 9 3 9 1 1 . 1 8 1 1 1 2 3 3 . 1 9 � � ) . 7 5 4 9 2 . 2 5 4 0 0 6 . B O 1 1 2 9 7 7 . 4 4 7 7 2 9 3 . 8 1 U 0 2 . 4 1 1 1 5 3 5 1 . 7 5 7 9 0 9 5 . 3 1 4 1 9 B . 0 3 1 1 1 0 5 9 . 5 0 8 0 8 9 6 . 9 4 4 2 9 3 . 6 5 1 1 9 4 1 6 . 0 0 8 2 6 9 8 . 5 0 4 3 8 9 . 2 1 1 2 1 7 6 8 . 5 ) I N C R E I E N T l E N v T H t T H Y L ' T Y R E N E 8 E N Z E N E T O L U N E H Y D R O E N R U C T I O F L U E G A ã P R E S S U R E Y l E L ' N M 8 E R F T 8 b N ¿ E N � E T H Y L E N E O U H A N E T E I T E M P P S I G L B K 0 L L 5 5 T Y f L 8 M L c â F O R M E D P b K L 0 M O E D E T H Y L B N I E N E F E D D E G ? D E G F L B P D L E L õ R E A C T E D � 0 Û ø 0 1 . 0 0 0 0 0 0 . 0 0 . 0 0 . 0 0 . 0 1 0 2 2 . 0 0 1 6 0 0 . 0 C 5 3 . 6 6 4 J - 0 @ 1 0 1 . 5 0 C : . U U O 0 . 0 6 3 0 O . O O O ) ! 0 . 0 0 0 8 5 0 . 0 . s 4 5 1 0 1 5 . 7 9 1 6 0 4 . 2 2 5 1 . 1 9 0 9 7 . 4 6 9 2 0 â e Û m 0 . 9 1 7 4 ) 0 . 0 7 9 2 0 0 . 0 0 0 6 5 0 . 0 0 2 7 1 0 . 0 7 6 4 9 1 0 2 0 . 5 1 1 6 0 8 . 4 1 4 8 . 5 1 9 V b . 9 2 1 � 3 0 4 . : O U 0 . 8 9 0 4 6 0 ø Î Ü å 9 9 0 . 0 0 0 9 8 0 . 0 0 5 1 2 0 . 0 9 8 3 3 1 0 3 1 . 8 9 1 6 1 2 . 7 0 4 5 . b 3 6 9 4 . 4 3 2 4 0 6 . , r : . 8 6 7 ) 2 0 . 1 2 3 4 1 O . O O l U 0 . C 0 7 9 0 0 . 1 1 5 5 1 1 0 4 6 . 2 2 1 6 1 6 . 1 6 4 2 . 5 1 8 V J e 0 ¡ ¿ 5 0 7 . 5 0 0 , . 8 4 n 4 0 . 1 4 1 6 5 0 . 0 0 1 1 5 0 . 0 1 0 9 6 0 . 1 ) 0 6 9 1 0 6 1 . 3 1 6 2 0 . 9 5 1 9 . 1 2 6 V l e Ï 0 Ï � 6 0 9 . 0 U U 0 . 8 2 3 9 9 0 . 1 5 9 4 0 0 . 0 0 2 4 3 0 . 0 1 4 1 8 0 . 1 4 5 2 2 1 0 7 6 . 3 0 1 6 2 6 . 9 5 J b e 9 0 ¯ 9 0 . 5 6 3 7 0 1 , . 5 0 ( 1 . 8 0 2 2 7 0 . 1 7 7 1 9 0 . 0 0 3 1 1 Ü ø Ü Î 4 0 . 1 5 9 7 6 1 0 9 0 . 6 5 1 6 2 8 . 8 8 3 1 . 2 8 1 8 9 . b 1 1 º 8 0 1 2 . 0 0 0 a f 0 å ð 0 . 1 9 5 1 9 0 . 0 0 3 8 9 0 . 0 2 0 5 4 0 . 1 7 4 6 5 1 1 0 6 . 3 1 6 3 2 . 7 3 2 6 . 6 2 5 8 8 . 8 1 6 � 9 0 U . : U 0 . n U 8 Û . 2 L J 6 0 . 0 0 7 4 0 . 0 2 3 ) ) 0 . 1 9 0 0 1 1 1 1 7 . 3 4 l 0 6 . 5 1 2 1 . 2 3 b 8 8 . 3 1 2 � 1 0 0 L ø Ü V Ü 0 . 7 ) 7 4 4 O . 2 J Î " 0 . 0 0 5 6 1 0 . 0 2 5 6 0 0 . 2 0 5 7 4 l U O . 0 2 1 6 6 0 . Z 1 4 . 7 0 9 8 8 . 1 1 2 0 " . 0 1 . 0 0 0 0 0 . 0 0 . 0 0 . 0 0 . 0 1 0 2 2 . 0 0 1 6 0 0 . 0 0 4 8 . 9 9 1 0 e 0 � 1 0 1 . 5 0 0 0 . 9 : : 0 8 0 . O U 8 8 Ü o Ü Ü Ü J 0 . 0 0 0 7 1 0 . 0 9 J Î 8 1 0 1 Ï . 6 6 1 6 0 4 . 2 1 4 6 - J 3 2 V 1 e ô ô ô � J o Ü Ü 0 0 . 9 2 0 . 1 C . 0 7 6 4 9 0 . 0 0 0 6 3 0 . 0 0 2 2 7 0 . 0 7 4 2 2 1 0 2 2 . 5 0 1 6 0 8 . 4 5 4 3 . 4 4 1 9 6 . 3 4 9 K 4 . 5 0 0 0 . 8 9 U 9 0 . 1 0 U ' 0 . 0 0 0 9 4 0 . C 0 4 2 9 0 . 0 9 7 0 9 1 0 ) ) . 2 8 1 6 1 2 . 6 7 4 0 . 2 9 Ï V > e 0 V 9 ; 6 0 6 . 0 0 0 0 . 8 6 9 9 7 0 . 1 2 2 U O . O O l n 0 . 0 0 6 6 0 0 . 1 1 5 ! 3 1 0 6 6 . 9 3 1 6 1 6 . 1 l 3 6 . 8 6 0 9 3 . 9 2 1 5 0 7 . 5 0 0 0 . 8 4 8 2 1 0 . 1 4 0 9 8 0 . 0 0 1 7 4 0 . 0 0 9 0 8 0 . 1 ) 1 9 0 1 0 6 1 . 5 5 1 6 2 0 . 9 0 J - J Î 0 9 2 . 8 1 4 K 6 0 9 . L O O 0 . 8 2 1 0 3 0 . 1 5 9 1 2 0 . 0 0 2 2 5 0 . 0 1 1 6 1 0 . 1 4 7 5 1 1 0 7 6 . 1 8 1 6 2 4 . 9 0 2 8 . 8 3 9 9 1 . 9 8 8 Æ 7 0 1 0 . S O l 0 . 8 0 0 7 0 . 1 7 1 0 6 0 . 0 0 2 1 4 0 . 0 1 6 0 4 0 . 1 6 3 0 1 1 0 9 0 . 6 2 1 6 2 ' . 1 3 2 4 . 0 2 1 9 1 . 2 9 7 R 8 0 1 2 . 0 0 0 0 . 7 1 5 4 4 0 . 1 9 4 . 8 0 . 0 0 3 4 8 0 . 0 1 6 2 1 0 . 1 7 1 " 1 1 0 6 . 2 3 1 6 3 2 . 6 8 1 8 . 3 6 2 9 0 . 8 2 6 � 9 0 L e Þ Û Û 1 . 7 0 5 7 3 0 . 2 1 2 2 2 Ü ø Û Ü 9 Î å 0 . 0 1 7 9 1 0 . 1 9 4 ) 1 1 1 1 7 . 8 9 1 6 3 6 . 6 7 1 1 . ] 2 0 9 0 e b V ¡ 9 8 1 4 . 7 0 0 " . 7 : 1 7 0 0 . 2 2 4 9 0 0 . 0 0 4 6 1 0 . 0 1 8 7 9 0 . l 0 6 1 1 1 1 2 9 . 6 1 6 3 9 . 6 6 ] . � 6 6 9 l . 5 1 3 ; 0 0 . 0 1 . 0 0 0 0 0 0 . 0 0 . 0 0 . 0 0 . 0 1 0 2 2 . 0 0 1 6 0 0 . 0 0 4 ' . 9 9 ] J e 0 � r 1 0 1 . s t l 0 . 9 l U l 0 . 0 9 4 9 1 0 . 0 0 0 3 6 0 . 0 0 0 7 . 0 . 0 . 3 6 8 1 0 1 7 . 2 5 1 6 0 6 . 2 1 4 1 . 3 7 4 9 7 . 6 4 2 � 2 0 3 . 0 1 0 1 . 9 1 9 9 0 0 . 0 7 7 1 1 0 . 0 0 0 1 3 0 . 0 0 2 1 6 0 . 0 7 . 7 5 1 0 2 2 . 0 . 1 6 0 8 . 6 6 4 4 . 5 1 4 9 6 . 2 b O ¯ 1 0 4 . 5 1 0 0 . 8 9 2 7 1 0 . 1 0 1 8 8 0 . 0 0 0 9 5 0 . 0 0 . . 6 0 . 0 9 7 6 2 1 0 3 2 . 9 " 1 6 1 2 . 6 7 ¬ l e 9 b 0 9 4 . 9 5 6 6 0 • • 1 0 0 Û ø ð b Y J 9 0 . 1 2 2 " 7 0 . 0 0 U 2 0 . 0 0 8 7 0 . 1 1 5 6 1 0 • • 7 2 1 6 1 6 . 8 3 3 8 . 0 8 7 V 3 . 7 3 3 � ~ . 5 0 7 . : 0 0 0 . ' . " 7 0 . 1 " 1 2 0 0 . Ü 0 l I 6 0 . 0 0 9 6 7 0 . 1 ) 1 7 2 1 0 6 1 . 6 1 6 2 0 . 9 1 3 4 . 3 9 2 9 2 . b 3 0 Æ 6 0 9 . 1 1 0 I . U U O 0 . 1 5 9 2 6 0 . 0 0 2 2 9 0 . 0 1 2 1 5 0 . 1 . 7 1 1 1 0 7 6 . 1 5 1 6 2 6 . 9 1 3 0 . 2 8 4 9 1 . 6 8 9 ~ ¯ 7 0 1 , . Þ Ü L 0 . 8 0 ! 1 6 0 . 1 7 7 1 9 0 . 0 0 2 8 9 0 . 0 1 6 7 5 0 . 1 6 2 . . 1 0 9 0 . 6 0 1 6 2 8 . 8 6 2 5 . � 3 9 9 0 . 9 4 2 Ñ 8 0 1 2 . . 0 0 0 . 7 1 4 2 2 0 . 1 9 l 1 0 0 . 0 0 J S 7 0 . 0 1 7 1 2 0 . 1 7 7 9 . 1 1 0 . . 1 . 1 6 3 2 . 7 0 2 0 . 2 4 2 ' 0 . 4 1 4 ~ 9 0 U . : O 0 . 7 . 3 ' ! 1 . 2 1 2 7 J 6 . 0 0 . 2 . 0 . 0 1 9 0 S 0 . 1 9 3 6 8 1 1 1 7 . 5 9 1 6 3 6 . . . 1 3 . 6 6 8 V 0 e ¡ ¿ ¿ � 1 0 0 U . O O l U e Ï 9 l . 2 0 . 1 2 9 1 2 0 . 0 0 . 9 2 0 . 0 2 0 ] 6 0 . 2 0 8 7 8 1 1 3 1 . 5 1 1 6 6 0 . 1 9 4 . 1 6 5 V 0 e 0 1 0 � N U N 8 E M � f T U t t i • 2 7 . 5 ] 1 ¯ A N N U A L c u S T O F K L L Y C L I N G E T H Y L . E N l t . 1 E A T 0 . 0 1 0 " L 8 • . 9 . 5 5 ) . å f T P ~ A N N A L C O S T U f c f H T L ' � N Z t N t C O V E M T E D T O B Y - P R O D U C T � A T O . I Z O . / L ' • 2 8 ] 1 Ï 9 . $ f Y 8 . f U I A L A h N U A l I t M A T I N G C O � T • 9 7 9 7 3 2 . i l Y R ~ S U R F A t t A I E A a K E A t T O R • 4 8 6 . 5 0 9 S Q F r � � C U � T W f � U 4 t A L f Ü K â U f A 8 V � i Î ¿ E • 7 9 5 8 9 . 6 9 • C O S T U f C A T A L Y S T A T ] . O O . / L I • 6 6 8 0 . 8 9 8 • � D I S T 1 L L A T I � N C A l C � l A T I U N S F O R R E A C T O R D E S C R I B E D A 8 0 V E � � F E E D R A T E - d , 9 J 4 8 . L b F R A C T I O N I N F E E O - 0 . 7 6 b L ô f M A C I l U N l N D I S T I L l A T E = O . 9 8 6 P l N l R U R K * 3 . 2 5 4 K � f k L I U M I 8 k ¥ 5 0 L P M L U S f H t k f L U 5 1 L U J L L U 5 r Y b Å K L U 5 Ï � | l . ¦ ã 1 0 5 . e o 1 1 8 3 6 . 7 5 1 6 7 0 8 0 . 3 7 8 8 6 7 . 8 9 2 4 7 7 8 5 . 0 0 1 . l � 9 1 . 0 0 6 3 6 2 4 . 1 1 l Z 9 9 Z 6 . 4 4 6 8 9 5 . q z 2 0 0 4 4 7 . 0 6 4 ¯ ¯ 1 . 1 5 8 Z . 0 0 5 8 5 4 5 . 1 1 1 3 4 5 4 Z . 5 0 7 1 4 0 . 9 2 2 0 0 2 2 9 . 1 2 º Æ ~ 1 . 2 1 7 8 . 0 0 5 6 d 2 8 . 5 2 1 3 9 1 5 8 . 6 2 7 3 8 5 . 9 3 2 0 3 3 7 3 . 0 6 � . 1 . 2 � 7 3 . 0 0 5 4 2 H . 3 0 1 4 3 7 7 4 . 7 5 7 6 3 0 . 9 3 Z 0 5 6 � 2 . 9 4 1 . 3 0 1 1 . 0 0 5 3 1 6 1 . 1 4 1 4 8 3 9 0 . 8 7 7 8 7 5 . 9 3 2 1 0 0 2 7 . 9 4 1 . 3 , 6 8 . 0 0 5 2 4 H . 6 8 1 5 3 0 0 7 . 0 0 8 1 2 0 . 9 3 Z 1 3 5 7 2 . 5 6 1 . 4 0 6 5 . e o 5 1 0 3 3 . 0 1 1 0 5 0 8 Z . 0 6 5 5 7 7 . 2 9 1 6 1 6 9 Z . 3 1 1 . 1 5 6 3 . e o 5 0 3 2 6 . 8 5 1 0 8 1 5 9 . 5 0 5 7 4 0 . 6 3 1 6 4 2 2 6 . 9 4 1 . ! I 6 2 . 0 0 5 0 3 6 8 . 7 8 1 1 1 2 3 6 . 8 7 5 9 0 3 . 9 6 1 6 7 5 0 ' . 5 6 1 . 5 ; 6 1 . e o 5 0 3 7 4 . 5 1 1 1 4 3 1 4 . 3 1 6 0 6 7 . 3 0 1 7 0 7 5 6 . 1 2 ¡ = ò û 5 9 . C C 4 9 5 0 5 . 6 4 1 1 7 3 9 1 . 7 5 6 2 3 0 . 6 4 1 7 3 1 2 8 . 0 0 1 . 6 ! 5 9 . 0 0 5 0 2 8 0 . 3 6 1 2 0 4 6 ' . 1 9 6 B 3 . 9 7 1 7 7 1 � 3 . 5 a 1 . 7 0 5 8 . 0 0 5 0 1 8 1 . 9 2 1 2 3 5 4 6 . 6 2 6 5 5 7 . 3 1 1 8 0 2 8 5 . 8 1 1 . 7 ) 5 8 . C O 5 0 q z 8 . 2 2 1 2 6 6 2 4 . 0 0 6 7 2 0 . 6 4 1 8 4 2 7 2 . 8 1 l . d J 5 6 . 0 0 4 9 8 8 5 . 6 8 1 2 9 7 0 1 . 4 4 6 8 8 3 . 9 8 1 8 6 4 7 1 . 0 6 1 . 8 5 5 6 . 0 0 5 0 5 9 2 . 5 7 1 3 2 7 7 8 . 8 7 7 0 4 7 . 3 2 1 9 0 4 1 8 . 7 5 1 . 9 0 5 5 . C O 2 3 . 0 0 5 0 3 7 6 . 8 7 1 3 5 8 5 6 . 2 5 7 2 1 0 . 6 5 Î Y 5 ª ª 5 ø Ï ¬ t . v ã 5 5 . 0 0 2 ) . 0 0 5 1 0 5 8 . 4 6 1 3 8 9 3 3 . 6 ' 7 3 7 3 . 9 8 1 9 7 3 6 6 . 1 2 ² 2 . G O 5 3 . 0 0 2 2 . 0 0 1 9 8 5 2 . 8 1 1 4 2 0 1 1 . 1 2 7 5 3 7 . 3 2 1 9 9 1 0 1 . 2 5 g 2 . J 5 5 3 . C C 2 2 . 0 0 5 0 4 1 8 . 2 3 1 4 5 0 8 8 . 5 6 7 7 0 0 . 6 6 Z 0 J ¿ d I o 9 9 ; � < ¿ . I J 5 3 . 0 0 2 2 . 0 0 5 1 1 3 8 . 2 0 1 4 8 1 6 5 . ' 4 7 8 6 3 . 9 ' 2 0 7 1 6 8 . 1 2 ¬ � ¿ - ¡ > 5 2 . 0 0 2 2 . 0 0 5 0 7 ' 5 . ' ' 1 5 1 2 4 3 . 3 8 8 0 2 7 . 3 3 ¿ ¡ 0 0 ò ò o ò 9 ¯ ¯ � 2 . 2 0 5 2 . C C 2 2 . 0 0 5 1 4 1 3 . 6 3 1 5 4 3 2 0 . 8 1 8 1 9 0 . 6 6 2 1 3 9 2 5 . 0 6 � ; 2 . 2 5 5 2 . V O 2 1 . 0 C 5 2 0 2 6 . 3 8 1 5 7 3 9 8 . 1 9 8 3 5 4 . 0 0 2 1 7 7 7 8 . 5 6 � Æ � 2 . 3 J 5 2 . 0 0 2 1 . 0 0 5 2 6 3 4 . 3 8 1 6 0 4 7 5 . 6 2 8 5 1 7 . 3 4 2 2 1 6 2 7 . 3 1 Í � ; 2 . 3 5 5 1 . 0 0 2 1 . 0 0 5 2 2 1 3 . 8 6 1 6 3 5 5 3 . 0 6 8 6 8 0 . 6 7 2 H 4 I 7 . 5 6 ¯ � 2 o ¬ 0 5 1 . � 0 2 1 . 0 0 5 2 8 0 1 . 1 8 1 6 6 6 3 0 . 5 0 8 8 4 4 . 0 1 2 2 8 2 7 5 . 6 ' ¯ ^ ~ . Æ ¿ = ¬ 7 b l . 0 C 2 1 . 0 0 5 3 3 8 1 . 1 0 1 6 ' 7 0 7 . ' 4 V 0 Û 7 o 3 9 Z J 2 0 ' 9 . 3 I 0 ~ ~ ¿ - � 0 ã t . c 0 2 1 . 0 0 5 3 9 6 2 . 8 2 1 7 2 7 8 5 . 3 1 9 1 7 0 . 6 8 2 3 5 9 1 8 . 7 5 ' ¯ 2 . � � 5 1 . 0 0 2 1 . 0 0 5 1 5 3 7 . 5 3 1 7 5 8 6 2 . 7 5 9 3 3 1 . 0 2 2 3 9 7 3 4 . 2 5 ¯ ~ � ¯ 2 . b J 4 9 . C O 2 1 . 0 0 5 2 9 1 6 . 9 7 1 7 8 9 4 0 . 1 9 9 4 9 1 . 3 5 2 º 1 3 ô . 5 0 � ¯ Z o b � 4 9 . V O 2 1 . 0 0 5 3 4 9 1 . 4 4 1 8 2 0 1 1 . 5 6 9 6 6 J . 6 9 2 4 5 1 6 9 . 6 9 ¯ 2 . 7 0 4 9 . C O 1 ' . 0 0 5 4 J 3 2 . 3 1 1 8 5 0 9 5 . 0 0 9 8 2 4 . J 2 2 4 8 9 5 1 . 3 1 | | 2 . 7 5 4 9 . 0 0 l V . 0 0 5 4 5 6 9 . 5 4 1 8 8 1 7 2 . 4 4 9 9 8 7 . 3 6 2 5 7 7 2 9 . 3 1 ~ 2 . 8 0 4 9 . C O 2 . 8 5 4 9 . 0 0 2 . 9 0 4 8 . 0 0 2 . 9 5 4 8 . 0 0 3 . C O 4 8 . 0 0 T U 8 E L E � 6 T H · 2 0 . 0 0 0 0 0 F T O U T S I D E T U B � D I A M T E � P 2 . 3 7 5 0 0 I N I N S I D E T U ' . D I A M E T E R · 2 . 0 6 7 0 0 I � 1 9 . 0 0 1 9 . 0 0 1 9 . 0 0 1 9 . 0 0 1 9 . 0 0 F E e D R A r E . L L L • • 0 � L B E T H Y L 8 E N Z E � E / H R / T U B E I N I T I A L F E E D T E M P E R A T U R E . 8 4 2 . 0 0 D E G R E E S F A S S U M E D � X I T T E M P U F F L U E G A S . 1 6 o . 0 0 D Q E G R E E S F C A T A L Y S T P E L L E T D I A M E T E R . 0 . 0 1 0 4 0 F T C A T A L Y S T B U L K D � N $ I T Y . 6 1 . 0 0 0 0 0 L B / C u F T E F F E C T I Y E � E S S F A C T D R • 0 . 4 4 Y O I D F R A C T I O N U t P A C K E D B E D · 0 . 3 8 0 0 0 5 5 1 0 ) . 1 9 5 5 6 3 3 . 5 2 5 5 0 1 4 . 3 7 5 5 5 2 7 . 4 6 5 b 0 3 7 . l q O Y E R - A L L H E A T T M A � $ F E R C O E F F I C I E N T . 8 . 0 0 0 0 0 B T U / H R I S Q F T / F H E A T C A P A C I T Y O F E T H Y L 8 E N Z E N E · 0 . 6 3 5 0 0 8 T U / L B / F H E A T C A P A C I T Y U � F L U E G A S · U . 3 D � 0 0 B T U / L 8 / F F L U E G A S F L O . R A T E . 1 8 1 6 . 1 4 3 L 8 F L U G 4 S / H K / T U 8 E A S S U M E D E X l r P R E S S U R E · 5 . 0 0 0 � O P S I G � U M 8 E R U F I � C R E M E � T S · 1 0 0 I N C R E M E N T L t N � I H E T H Y L S T Y R E N E B e N l E N E T U L U E N E H Y O R O G E � R E A C T 1 O N N U M � E R F r 8 E N l E N E E T H Y l E N E M H H A � E T E M P L a M O L E S f O R H � v P E R L B M O L E O F E T H Y L B E N l E N E F E D D E G F 0 J e Û 1 . 0 0 0 0 0 U - U 0 . 0 0 . 0 0 . 0 8 4 2 . 0 0 1 0 2 . 0 0 U U - 9 ! ! > 9 0 . 0 2 2 2 0 0 . 0 U 0 0 3 O . O O O l d 0 . J Z 2 0 2 9 > o 3 8 2 0 4 . 0 U U J . 9 4 ¿ H 2 0 . 0 ¬ 5 7 1 0 . 0 0 0 1 7 O . O O I H 0 . 0 5 4 4 0 9 9 1 . 1 5 3 0 b . O O O ; . 8 q � S 8 U = U 9 > ¿ 0 0 . 0 0 0 6 0 0 . 0 0 4 ) 1 0 . 0 9 0 8 9 1 0 4 5 . 4 3 4 0 d « 0 Þ û u + d > U I > 0 . 1 3 7 8 7 0 . O C I � 2 0 . 0 U 9 6 0 . 1 2 8 1 1 1 0 Y . 6 8 5 0 1 0 . 0 0 0 0 . I 9 6 1 5 U - l b ¿ > 0 . 0 0 3 5 6 0 . 0 1 7 5 4 0 . 1 6 5 2 ¿ l l 3 l . 5 6 6 0 ¡ ¿ e 0 Þ 0 0 . 7 3 1 4 5 0 . 2 2 ' 0 5 0 . C 0 6 6 6 0 . 0 2 6 8 4 0 . 2 0 ¿ ¿ 0 1 1 6 6 . 4 4 Ï U 1 4 . J C O 0 . 6 1 6 9 6 0 . 2 1 > 6 6 0 . 0 1 0 9 6 0 . 0 3 6 4 2 0 . 2 3 9 2 > 1 1 9 1 . 7 3 8 0 1 6 . 0 0 0 0 . 6 1 1 8 2 0 . 3 2 l l 5 0 . 0 1 6 2 4 0 . 0 4 4 8 0 0 e 2 7 6 3 5 1 2 2 6 . 9 1 9 0 1 8 . 0 0 ( 0 . > 6 4 9 8 0 . 3 6 2 6 7 0 . 0 ¿ l 8 3 0 . 0 5 0 5 1 0 . 3 1 Z 1 5 1 2 5 6 . ) Î 9 ) 1 8 . b O � 0 . 5 , 1 9 0 0 . 3 7 ) 2 5 0 . O Z 3 3 6 0 . 0 5 1 4 9 0 . ) 2 1 7 6 1 2 6 6 . 0 8 1 9 1 2 4 9 . 8 7 1 0 1 5 0 . 7 0 2 5 6 5 0 3 . 7 5 f � 1 9 4 3 2 7 . 2 5 I O H 4 . � 3 2 6 0 2 7 4 . 1 5 1 9 1 4 0 4 . 6 9 1 0 4 7 7 . 3 7 2 6 2 8 9 6 . 3 8 � � 2 0 0 4 8 2 . 1 � 1 0 6 4 0 . 7 0 2 6 6 6 5 0 . 2 5 G Æ ~ ~ . 2 0 3 5 5 9 . 5 0 1 0 8 0 4 . 0 4 2 7 0 4 0 0 . 6 9 � f l U E G A S P R E S S U R E Y I E L D T E M P P S I G L B ª U L E 5 5 T Y f O E G F L B K U L L L b 8 F k L 1 t Û 1 6 0 0 . 0 0 5 8 . 6 ' 4 0 . 0 1 6 1 3 . 1 7 5 5 . ' 3 5 Y Y . 0 0 ¿ I b 2 5 . 2 1 5 2 . 8 1 4 9 7 . 4 ¿ 0 1 6 3 6 . 3 8 4 9 . 2 1 5 9 ¬ . 0 8 º 1 6 4 6 . 8 4 4 5 . 2 4 2 Y ¿ e J 1 ¿ 1 6 5 6 . 6 9 4 0 . 6 0 3 8 9 . 6 5 1 ¡ 6 6 6 . 0 4 3 5 . 1 8 4 8 7 . 2 3 º 1 6 1 4 . 9 5 2 � . 6 9 0 8 5 . 3 3 3 1 6 8 3 . 4 7 2 0 . 5 2 6 8 4 . 0 3 0 1 6 9 1 . 6 2 9 . 0 4 1 8 3 . 3 6 9 1 6 9 3 . 9 8 4 . 1 1 3 ß J . ¿ 9 0 û J + 0 1 . 0 0 0 0 0 0 . 0 0 . 0 0 . 0 0 . 0 8 4 2 . 0 0 1 6 0 0 . 0 0 5 9 . 6 9 4 0 e u 1 0 2 . 0 0 0 0 . 9 1 7 3 3 0 . 0 2 2 4 b 0 . 0 0 0 0 3 0 . 0 0 0 1 9 0 . 0 2 2 2 7 9 2 5 . 1 9 1 6 l l . 1 7 5 6 . 9 7 3 Q q . 0 4 0 2 0 4 . 1 0 0 0 . 9 4 2 3 5 0 . 0 5 b 1 3 0 . 0 0 0 1 7 0 . 0 0 l l 6 0 . 0 5 4 7 7 9 9 0 . 8 7 1 6 2 5 . 2 1 5 3 . 8 9 9 9 7 . J 5 5 3 0 b . O O O 0 . 8 9 9 3 1 0 . 0 9 5 b l O . O O O b l 0 . 0 0 4 4 7 0 . 0 9 1 1 4 1 0 4 5 . 1 9 1 6 3 6 . 4 0 5 0 . U 8 9 4 . 9 5 8 ' 0 d . O u O 0 . 8 5 0 0 5 0 . 1 3 S I 9 0 . 0 0 1 b 5 0 . 0 1 0 1 1 0 . 1 2 8 0 8 1 0 9 1 . 5 3 1 6 4 6 . 8 5 4 6 . 4 6 0 9 2 . 1 5 8 ¯ 5 0 1 0 . 0 V O 0 . 7 9 ! 1 5 ( . 1 8 3 0 3 0 . 0 0 3 b 2 0 . 0 1 8 2 0 0 . 1 6 4 8 2 1 1 3 1 . 4 7 1 6 5 6 . 7 1 4 1 . 9 1 9 8 � . 3 4 7 � b O l ¿ . J u O Û e 7 3 5 9 � 0 . 2 2 9 3 2 0 . 0 0 b 7 9 0 . 0 2 7 9 5 0 . 2 0 1 3 7 1 1 6 6 . J 1 1 6 6 6 . 0 6 3 6 . 6 3 9 8 6 . 8 4 5 7 0 L o U 0 0 : . 6 7 4 6 9 0 . 2 7 b 0 2 0 . 0 t l 2 2 0 . 0 3 8 0 8 0 . 2 ) 7 9 4 1 1 9 7 . 6 1 6 7 4 . 9 7 3 0 . 3 5 2 8 4 . 8 4 7 � 8 0 I b . O O ( 0 . b 1 " 3 8 0 . 3 2 1 8 0 0 . 0 1 b 6 9 0 . 0 4 7 1 3 0 . 2 7 4 6 / 1 2 2 6 . 5 9 1 6 8 1 . 5 0 2 2 . 5 5 0 8 3 . 4 4 9 ' 0 I d . L O O 0 . 5 5 9 3 8 0 . 3 b 4 3 3 0 . 0 2 2 b 3 0 . 0 5 3 6 6 0 . 3 1 0 6 7 1 2 5 5 . 3 2 1 6 9 1 . 6 5 1 1 . 9 3 9 8 2 . b 8 6 9 5 B . O O O a . B 6 S 7 0 . 3 8 l 5 3 0 . C 2 5 H 0 . 0 5 5 5 3 0 . 3 2 7 0 0 1 2 7 1 . 0 0 1 6 9 5 . 5 9 4 . 2 1 7 8 2 . 5 ê � 0 0 . 0 1 . 0 0 0 0 0 0 . 0 0 . 0 0 . 0 0 . 0 8 4 2 . 0 0 1 6 0 0 . 0 0 6 0 . 6 9 4 0 . 0 1 0 2 . 0 0 0 0 . 9 7 7 0 6 0 . 0 2 2 7 1 0 . 0 0 0 0 3 0 . 0 0 0 2 0 0 . 0 2 2 5 1 9 2 5 . 0 0 1 6 1 3 . 1 7 5 8 . 0 1 0 9 9 . 0 1 Ï ~ 2 0 ' 0 . 0 0 0 0 . 9 4 1 8 8 0 . 0 5 b 5 4 0 . 0 0 0 1 7 0 . 0 0 1 4 1 0 . 0 5 5 1 3 9 9 0 . 5 9 1 6 2 5 . 2 3 5 4 . 9 8 1 9 7 . 2 8 9 ° 3 0 b . o o e 0 . 8 9 8 7 7 0 . 0 9 5 9 9 O . O O O b l 0 . 0 0 4 6 2 0 . 0 9 1 3 7 1 0 4 4 . 9 7 1 6 3 6 . 4 1 5 1 . 5 5 7 9 9 . 8 2 6 ¯ ' 0 8 . 0 1 0 0 . 8 4 9 3 7 0 . I H 4 9 0 . 0 0 1 b 7 0 . 0 1 0 4 7 0 . 1 2 8 0 2 1 0 9 1 . 4 1 1 6 4 6 . 8 7 4 7 . 6 7 0 9 1 . 9 4 2 � 5 0 1 0 . J O G 0 . 7 9 " 1 9 O . 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I O O 0 . 6 1 1 0 9 � . 3 2 2 2 9 0 . 0 1 7 1 4 0 . 0 4 9 ' " 0 . 2 1 2 8 2 1 2 2 6 . 3 6 1 6 8 3 . 5 2 2 4 . 4 9 6 8 2 . 8 7 2 � 9 0 1 8 . 0 0 0 : . 5 5 " 2 2 0 . 3 b � 5 8 0 . 0 2 3 4 1 0 . 0 5 / 7 9 0 . 3 0 8 8 0 1 2 5 4 . 5 6 1 6 9 1 . 6 9 1 4 . 5 8 9 8 2 . 0 t t 9 7 1 9 , " 0 0 0 . 5 2 1 0 8 0 . 3 9 1 b 7 0 . e 2 7 5 1 0 . 0 5 9 7 4 0 . 3 3 1 9 3 1 2 7 5 . 9 1 1 6 ' 7 . 1 7 4 . 3 3 3 8 1 . 7 8 ? í 0 0 . 0 1 . 0 0 0 C O 0 . 0 0 . 0 0 . 0 0 . 0 8 4 2 . 0 0 1 6 0 0 . 0 0 6 1 . 6 ' 0 . 0 � 1 0 2 . 0 0 0 0 . 9 7 6 8 1 0 . 0 2 2 9 b 0 . 0 0 0 0 3 0 . 0 0 0 2 0 0 . 0 2 2 7 6 9 2 4 . 8 2 1 6 1 3 . 1 7 5 9 . 0 4 6 9 9 . 9 9 5 � 2 0 4 . 0 0 0 0 . 9 " 1 " 3 0 . 0 5 b Q " 0 . 0 0 0 1 7 0 . 0 0 1 4 6 0 . 0 5 5 4 8 9 9 0 . 3 2 1 6 2 5 . 2 3 5 6 . 0 6 1 9 7 . Z 2 2 � ) 0 b . J O O 0 . 8 9 8 2 " 0 . 0 9 b 3 5 0 . 0 0 0 b 2 0 . 0 0 4 7 8 0 . 0 9 1 5 7 1 0 4 4 . 7 7 1 6 3 6 . 4 2 5 2 . 6 9 1 Q " . b 9 2 ¬ U d - L L 0 a . 8 " 8 7 3 0 e l ô 1 5 0 . 0 0 1 b 9 0 . 0 1 0 8 3 0 . 1 2 7 9 2 1 0 9 1 . 3 0 1 6 4 6 . 8 8 4 8 . 8 7 3 9 1 . 1 2 4 � 5 0 1 0 . t t O 0 . 7 9 3 2 5 0 . 1 8 3 4 b 0 . 0 0 3 1 4 0 . 0 1 9 5 6 0 . 1 6 3 9 0 1 1 3 1 . 3 7 1 6 5 6 . 7 4 4 " . 5 1 6 8 8 . 7 1 4 " ~ 6 0 1 2 . 0 0 0 0 . 7 3 3 0 6 0 . 2 2 n l 0 . 0 0 1 0 5 0 . 0 3 0 1 8 0 . 1 9 9 5 3 1 1 6 6 . 3 1 1 6 6 6 . 0 9 3 ' . 4 8 7 8 b . 0 5 1 w 7 0 I " . O L O 0 . 6 7 0 3 5 0 . 2 1 6 5 1 0 . 0 1 1 7 2 0 . 0 4 1 4 2 0 . 2 3 5 0 9 1 1 9 7 . 4 9 1 6 1 5 . 0 1 n . 5 6 9 8 3 . 8 7 9 � S O I b . I " O 0 . / 0 7 9 4 0 . 3 2 2 b b 0 . 0 1 7 5 9 0 . 0 5 1 8 1 0 . 2 7 0 8 6 1 2 2 6 . 2 1 1 6 1 3 . 5 4 2 6 . ) 7 5 8 2 . 3 0 0 9 0 l d . O O u 0 . 5 4 9 4 2 0 . 3 6 6 5 2 0 . 0 2 4 1 6 0 . 0 5 9 9 0 0 . 3 0 6 6 1 1 2 5 4 . 0 0 1 6 9 1 . 7 1 1 7 . 0 5 1 8 1 . 1 4 3 N . 9 9 1 9 . d O û ( . 5 0 5 � � 0 . 4 0 0 b 5 0 . 0 2 9 7 7 0 . 0 6 4 1 3 0 . 3 J 6 5 2 1 2 8 0 . 8 2 1 6 9 8 . 7 4 4 . � 5 9 8 1 . 0 1 2 � Û 0 . 0 1 . 0 0 0 0 0 0 . 0 0 . 0 0 . 0 0 . 0 8 4 2 . 0 0 1 6 0 0 . 0 0 6 2 . 6 ' 0 . 0 0 1 0 2 . V O O 0 . 9 7 6 5 5 0 . 0 2 3 2 1 0 . 0 0 0 0 3 0 . 0 0 0 2 1 0 . 0 2 3 C O 9 2 " . 6 3 1 6 1 3 . 1 8 6 0 . 0 8 2 9 8 . 9 1 2 K 2 0 4 . 0 0 v 0 . 9 " 1 0 0 0 . 0 5 7 3 3 o . O O O l 7 0 . 0 0 1 5 1 0 . 0 5 5 8 2 9 9 0 . 0 6 1 6 2 5 . 2 4 5 7 . 1 ) 9 9 7 . 1 5 5 ~ 3 0 b . G O O 0 . 8 9 7 7 4 0 . 0 9 6 6 9 0 . 0 0 0 0 3 0 . 0 0 4 9 4 0 . 0 9 1 7 5 1 0 4 4 . 5 8 1 6 3 6 . 4 3 " . 8 2 2 9 4 . 5 5 6 � " 0 d . 0 0 0 0 . 8 4 � 1 0 0 . 1 3 8 9 9 0 . 0 0 1 1 1 0 . 0 1 1 2 0 0 . 1 l 7 8 0 1 0 9 1 . 2 2 1 6 4 6 . 8 ' 5 0 . 0 6 9 9 1 . 5 0 4 � S O 1 0 . 0 U 0 0 . 7 9 2 3 � 0 . 1 8 3 6 3 0 . 0 0 3 7 9 0 . 0 2 0 2 4 0 . 1 6 3 3 8 1 1 3 1 . 3 5 1 6 5 6 . 7 5 4 5 . 1 9 8 ß � o ¬ Z ¬ ¯ 6 0 L ¿ . 0 0 û 0 . 7 3 1 6 6 0 . 2 2 9 8 5 0 . 0 0 7 1 8 0 . 0 3 1 ) 1 0 . 1 9 8 5 " 1 1 6 6 . 3 2 1 6 6 6 . 1 1 4 0 . 8 8 1 8 5 . ò 7 � 7 0 1 " . V O O 0 . 1 6 8 2 6 0 . 2 7 b 6 0 0 . 0 I I 9 8 0 . 0 4 3 1 0 0 . 2 ) ) 5 6 1 1 9 7 . 4 8 1 6 7 5 . 0 2 ) 5 . 1 ) 0 8 3 . 3 ' " Æ í 8 e 1 6 . 0 0 e . 0 . 6 0 " 8 9 0 . 3 2 2 9 3 C . 0 1 8 0 3 0 . 0 5 4 1 4 0 . 2 6 8 7 9 1 2 2 6 . 1 2 1 6 8 1 . 5 6 2 8 . 1 9 6 8 1 . 7 3 2 " 9 0 I S . J u O 0 . 5 4 " 8 9 C . 3 6 7 2 0 0 . 0 2 " 9 0 0 . 0 1 3 0 1 0 . 3 0 � 1 9 1 2 5 3 . 6 2 1 6 9 1 . 7 3 1 9 . 3 6 8 8 0 . 6 8 � ~ 1 0 v 2 0 . 0 0 0 0 . 4 9 3 8 2 0 . 4 0 6 2 0 0 . 0 3 1 6 0 0 . 0 6 8 1 9 0 . H 7 8 1 1 2 8 2 . 5 2 1 6 9 9 . 5 4 6 . 4 1 0 8 0 . 2 4 7 ( � N U K b L K Û í ¡ U b L > • 5 8 . 9 1 3 ¯ A N N U A L C O S T O f R E C Y C L I N G E T H Y L 8 E N Z E � E A T O . O I O S / L B • 2 6 0 2 1 1 . S / Y R A N N U A L C O S T Û F E T H Y L B E N Z E N E C O N V E R T E D T O B Y - P R O D U C T S A T 0 . 1 2 0 S / L B • b 3 2 2 3 1 . S / Y 8 T O T A L A N N U A L U P E R A T I N G C O S T · s n 4 4 2 . S f Y R S U R f A c e Å K E A U r � E A C T O R • 7 3 2 . 6 0 4 S O f T � C O S T O f T w a K E A C T O R S O f A 8 U V E S I Z E ' 1 0 0 5 0 5 . 7 5 C O S T U r C A T A L Y S T A T 3 . 0 0 S / L 8 • 5 0 2 4 . 5 3 5 W D I S T I L L A T I U � C A L C U L A T I O N S f O R R E A C T O R D E S C � I S E O A 8 0 V E F E E D � A T f ' � � 7 4 0 � . � b F R A C T I O N I N F L L D × 0 . 5 � 9 E 8 F R A C T I O N I � D I S T I L L A T E = 0 . 9 6 2 � Ï N l K U H K × R R F A C r O � ¡ - � Þ 1 . 1 0 I . I � 1 . 2 0 ¡ - ¿ Þ ¡ . 3 0 l o J 5 1 . " 0 1 . " ; t » Þ U ¡ + Þ Þ l . b O 1 . 6 5 1 . 7 0 1 . 7 5 T � A Y S 9 5 . 0 0 8 3 . C O 7 1 . . 0 0 ? l . 0 0 6 8 . 0 0 6 � . 0 0 6 3 . 0 0 6 1 . C O 5 ' . 0 0 5 8 . 0 0 5 6 . 0 U 5 5 . 0 0 5 � . O O 5 3 . 0 0 5 3 . 0 0 F E E D T R A Y " 3 . 0 0 3 8 . 0 0 3 3 . 0 0 3 1 . 0 0 2 9 . 0 0 2 8 . 0 0 2 6 . 0 0 2 6 . 0 0 2 Þ . 0 Û 2 5 . 0 0 2 3 . 0 0 2 3 . 0 0 2 3 . 0 0 2 l . 0 0 2 2 . 0 0 O E P R C O S T H E A T C O S T 4 2 2 0 6 . 7 9 6 1 0 2 2 . 2 7 3 1 1 3 5 . 7 8 6 3 4 1 3 . 6 2 3 5 3 2 9 . 2 2 6 5 8 0 4 . 9 4 3 ' 1 9 4 . 3 6 6 8 1 9 6 . 2 5 3 2 9 6 9 . 4 6 7 0 5 8 7 . 6 3 3 2 1 5 1 . 2 " " 8 6 5 2 . 6 6 3 1 7 7 0 . 6 6 5 0 2 ' 6 . 8 9 3 1 3 " " . 0 " H 8 1 • • 1 2 3 0 8 7 2 . H 5 3 4 3 5 . 3 3 0 8 8 9 . 1 6 5 5 0 2 9 . 6 0 3 0 3 3 9 . " 8 5 6 6 2 3 . 8 J 3 0 2 9 8 . 2 ' 5 8 2 1 8 . 0 3 3 0 7 9 3 . 3 5 5 9 8 1 2 . 2 3 3 0 1 " 5 . 7 0 6 1 ' 0 6 . 4 8 3 0 b 1 2 . 8 4 6 1 0 0 0 . H � ¯ � . � 2 7 C O O L L J 5 f Y E A R C O S T 4 � 3 2 3 8 . 7 Y 1 0 6 4 6 7 . 8 1 � < � ~ . 3 3 6 5 . 7 1 1 0 4 5 ' 5 . 0 6 � 3 º 9 2 = 6 " 1 0 4 6 2 6 . 7 5 3 & 1 9 . 5 6 1 0 6 0 1 0 . 1 2 3 7 9 6 . " 8 1 0 7 3 0 3 . 5 6 2 5 8 2 . 2 7 8 3 3 8 6 . 1 2 2 6 6 6 . 8 8 8 4 6 8 ' . 3 1 2 7 Þ 1 . Þ 0 8 Ô 9 3 6 e 6 2 2 8 3 6 . 1 ¡ 8 7 H 3 . 7 5 2 9 2 0 . 1 3 8 8 8 3 9 . 4 4 3 0 0 5 . 3 9 8 9 9 6 8 . 6 2 3 0 8 9 . 9 6 9 1 6 0 ó . ¡ 9 3 1 Ï . 5 Ï ' 3 7 8 0 . 1 2 3 2 5 9 . 1 8 9 4 8 l ¡ e 3 1 3 3 4 3 . 8 0 9 6 9 5 7 . 3 T ¡ o d J 5 2 . C O 2 2 . 0 0 3 0 4 i 8 . 9 7 6 4 5 9 4 . 9 4 H 2 8 . H 9 8 5 1 2 . 3 1 1 . 8 , 5 2 . 0 0 2 Z . 0 0 3 0 9 3 8 . 2 6 6 6 1 8 9 . 1 9 3 5 1 3 . 0 3 1 0 0 6 4 0 . 4 4 ¯ 1 . 9 0 5 1 . G O 2 2 . 0 0 3 0 7 7 9 . 6 8 6 7 7 8 3 . 3 7 3 5 9 7 . 6 4 1 0 Z 1 6 0 . 6 9 @ 1 . 9 > 5 1 . C O 2 1 . 0 0 3 1 2 1 Z . 0 5 6 9 3 7 7 . 6 3 3 6 8 2 . 2 6 1 0 4 2 7 1 . 8 7 � � 2 . � 0 4 9 . 0 0 2 1 . 0 0 3 0 3 9 9 . 6 2 7 0 9 7 1 . 8 1 3 7 6 6 . 8 7 1 0 5 1 3 8 . 2 5 ª * ¯ ¿ = b > 4 9 . 0 0 2 1 . 0 0 3 0 8 0 7 . 5 4 7 2 5 6 6 . 0 6 3 8 5 1 . 4 9 1 0 7 2 2 5 . 0 6 " � ¯ 2 . 1 0 4 9 . 0 0 Z I . 0 0 3 1 Z 1 1 . 8 7 7 4 1 6 0 . 2 5 3 9 3 6 . 1 0 1 0 9 3 0 8 . 1 9 í � 2 . 1 5 4 8 . 0 0 Z I . 0 0 3 0 9 6 7 . 5 6 7 5 7 5 4 . 5 6 4 0 2 0 . 7 2 1 1 0 7 4 2 . 8 1 Þ = � l . 2 0 4 8 . C O 2 1 . 0 0 3 1 3 5 7 . 0 0 7 7 3 4 8 . 8 1 4 1 0 5 . 3 3 1 1 1 8 1 1 . 1 2 � � 2 . l 5 4 R . 0 0 2 1 . 0 0 3 1 7 4 3 . 1 5 7 8 9 4 3 . 0 0 4 1 8 9 . 9 5 1 1 4 8 7 6 . 0 6 � � 2 . 3 0 4 8 . 0 0 1 9 . 0 0 3 2 1 2 6 . 2 5 8 0 5 3 7 . 2 5 4 2 7 4 . 5 6 1 1 6 9 3 8 . 0 ) ¯ ^ � . 2 . 3 5 4 6 . 0 0 1 9 . 0 0 3 1 1 5 1 . 8 9 8 2 1 3 1 . 4 4 4 3 5 9 . 1 7 1 1 7 6 4 1 . 5 0 0 ~ + 2 . 4 0 4 6 . 0 0 1 9 . 0 0 3 1 5 1 3 . 2 5 8 3 7 2 5 . 6 2 4 , . 3 . 7 9 1 1 9 6 8 2 . 6 2 ' ^ 2 . 4 : 4 6 . 0 0 1 9 . 0 0 3 1 8 7 1 . 9 2 8 5 3 1 9 . 8 7 4 5 2 8 . 4 0 1 2 1 7 2 0 . 1 9 ¯ ~ × � 2 . 5 U 4 0 . C O 1 9 . 0 0 3 2 2 2 7 . 9 2 8 6 9 1 4 . 1 3 4 6 1 3 . 0 2 1 2 3 7 5 5 . 0 6 ~ � ¯ 2 . 5 5 4 6 . 0 0 1 9 . 0 0 3 2 5 8 1 . 3 3 8 8 5 0 8 . 3 1 4 6 9 7 . � 3 1 2 5 7 8 7 . 3 1 ¯ 2 . 6 0 4 > . 0 0 1 9 . 0 0 3 2 2 1 6 . 2 9 9 0 1 0 2 . 6 2 4 7 8 2 . 2 5 1 2 7 1 0 1 . 1 2 � ¨ Appendix FORTRAN listings and TY/Jical Results for the Com/JII/er Programs Used in Chapters 5, 6, and 7 Index Absorption, 9 Activation energy, 170 Activity coefficient, 61 Adsorption,kinetics of, 163 Analysis, economic, see Economic evaluation - Approximations, 86 Arrhenius correlation, 9, 41, 161 Batch reaction, 35 Bench-scale experimentation, 4, 19. 76 Bleed strea, 87, 89 Boiler design, 88 Caculations, iterative, 66 Calculations, tabulation of reactor- design, 80, 172 Calculus of variations, 11 Capital cost estimation, 131 Catalyst, activity of, 97 kinetics on, 9 porosity of, 159 properties of, 158-160 surface area of, 159 Catalyst pellets, 9, 98, 162, 166 Censorship, 7 Chemical equilibrium, effect of temperature on, 85 Chemical reaction, see Reaction Chilton-Colburn equations, 9, 163 Chlorination, chemical kinetics of, 22 Chorobenzenes, production of, 22 Clausius-Clapeyron equation, 9, 132, 143 Computer, classroom use of,2 229 Computer program flow sheet, 147, 180 Computer programming, 146, 178 Consecutive reactions, 22 Control, production, 8 quality, 8 Conversion of a chemica reaction, 85,97,152,192 Conveyor belt, 103, 194 Continuous stirred-tank reactor (CSTR), 11, 24 Cooling water, cost of, 58 temperature rise of,43 CorrOSion, 106 Cost, capital, 38, 57, 58, 181, 195 conversion, 73 operating, 73 optimization of, 28, 39, 70, 116, 142,183 raw-material, 38, 178 Cost accounting, 12, 13 Cost correlations, 57 Counter-current staged process, 69 Crystallization, 9 Cyclohexane production, 97 Data, consistency of, 6 correlation of, 9, 60 extrapolation of, 9, 60 Data analysis, 8, 22 Data processing, 3 Data reduction, 8 Depreciation, 122 DeSign, industrial practice of, 1-17 DeSign parameters, 8 Design results, extrapolation of, 95 Design strategy, 10, 11 Desorption, 162 230 The Industrial Practice of Clemical Process Engineering Difference equations, 174 Differential equations, derivation of, 81,172 numerical integration of, 173 Diffusion within catalyst pellets, 9, 98, 162, 166 Diffusivity, binary, 164 effective, 166 Knudsen, 167 Distillation, see Fractionation Distribution cfficient, 9, 61 Dynamic programming, 11 Economic evaluation, 2, 38, 71, 72, 96,98,115, 181 terminology of, 12 Efectiveness factor, 9, 166, 169, 174 Efficiency, tray, 9 mixer-settler, 69 Enthapy of formation, 42, 77 Enthalpy of reaction, 42, 80, 82 Equilibrium, chemical, 77, 85, 86, 169 liquid-liquid, 9, 54,60 vapor-liquid, 9, 57, 132 Erbar and Maddox correlation, 134 Error, experimental, 162 probable, 8 Error analysis, 8 Experimental variables, selection of, 60 Experiments, in-plant, 8 statistically designed, 8, 54, 59 Extraction, liquid-liquid, 9 Extrapolation of design results, 95 Factorial experimental design, 54 Fanning equation, 9, 109 Fenske equation, 134 Financial evaluation, see Economic evaluation - Financial incentive, 10 Finite difference techniques, 173 First law of thermodynamics, 82 Flooding velocity, 141 Flow sheet, process, 63, 69, 97, 131, 138, 147 Fluid mechanics, 110 FORTRAN, 146, 180 Fractionator, design of, 9, 67, 132, 140 optimization of, 142 tray design for, 146 vacuum, 138 Fractionator column, diameter of, 140 Fugacity, 61 Gibbs-Duhem equation, 7, 9 Gilliland correlation, 135 Heat exchanger, 141 Heat of solution, 7 Heat transfer, boiling, 9 fluids of, 88 indirect, 132 Heat transfer to buried pipes, 111 Heat transfer coefficients, 43 Heat transfer of condensation, 9 Heat transfer in reactors, 171 Henry's law, 9 Hoop stress, 110 Hydraulics, distillation-tray, 140 Hydrogen, industrial sources of, 87 Hydrogenation, catalyic, 77 Incentive, financia, 10 Integration, numerical, 84 Investment, return on, 13, 196 Isothermal reaction, 39 Iterative calculation, 66 Kinetic data, analysis of, 22, 80, 161 Kinetic data, correction for diffusion effects on, 170 Lennard-Jones force constants, 165 Lewis-Matheson method, 136, 148 Limiting case analysis, 4, 95 Linearization, 93, 177 Liquid -liquid extraction, 9 equilibrium data for, 9, 54, 60 process-design for, 64 Literature, methods for searching, 6 Market demand, 13 Market information, 5 Market price, 13 Market research, 5 Mass transfer to catalyst pellets, 9, 98, 163 Mass transfer to gas bubbles, 9 Mass transfer in packed beds, 162, 165 Mass transfer in slurry reactors, 9 Mass transfer in sparged reactors, 9 McCabe-Thiele diagram, 136 Mean free path, 168 Mixer-settler design, 58, 64 Murphree efficiency, 9 Nernst's law, 9, 61 Optimization, 3, 70, 80, 113, 116, 140, 182,193,194 Oral presentations, 14 Partition coefficient, 9, 61, 62 Parallel reactors, 35, 197 Petrochemical industry, 196 Phase diagram, 62 Pipeline, pressure drop in, 109 thermal expansion in, 105 transportation by, 102 Plug-flow reactor, 38 Pneumatic conveyance, 102 Pore radius, 167 Pressure drop in fractionators, 137-139 Pressure drop in packed bed reactors, 98 Pressure drop in pipelines, 109 Pressure-enthalpy diagram, 141 Process economics, 11 Process engineering fundamentals 1-17 Process flow sheet, see Flow sheet, process Production control, 8 Programming, discussion of, 146 dynamic, 11 FORTRAN, 146 linear, 10 Quality control, 8 Raoult's law, 7, 9 Raw material costs, 39 Reaction, adiabatic, 87 catalytic, 162 equilibrium, 9 isotherma. 39, 87 kinetics of, 9 temperature of, 39 yield of, 40,152,192 Reaction conversion, 80, 85, 97, 152, 192 Reactor, bench-scale, 152 cataytic fixed-bed, 9, 38, 80, 171 continuous stirred-tank, 11, 24 parallel, 35, 197 pressure drop in, 98 shell-ad-tube,l71 slurry, 9 sparged,9 Reactor control, 42-48 Index 23] Reactor design, 24,41, 81, 86, 171 Reactor flow sheet, 25, 89, 171 Reactor stability, 42-48 Recycle, 38, 87, 97 Reflux ratio, 134 Residence times, 38, 58 Resistances to catalytic reactions, 162 Results, presentation of, 14 Return on investment, 13, 196 Risk analysis, 13 Safety, 43 Sales forecast, 5 Scale-up, 87, 95 Selling price, 13 Simpson's rule, 84 Simulation, 3, 8 Slurry, pumping of, 102 Slurry reactor, 9 Smoker equations, 147 Solubility, gas in liquid, 9 liquid in liquid, 9, 54 solid in liquid, 9 Solubility data, 7, 9 Solution, heat of, 7 Sparged reactor, 9 Stability, reactor, 42-48 Stability of finite difference equa­ tions, 175 Staged process, economic evaluation of,72 Statistically designed experiments, 8,60 Steam costs, 58 Steepest ascent, method of, 11 Stoichiometry, 80, 172 Stripper design, 67 Syrene, industrial manufacture of, 126,129,146,197 Suboptimization, 69 Sulfur, mining and production of, 101 properties of, 106 Supersolubility, 9 Surfactant, 73 Temperature of reaction, 39-41 Thermal expansion, 105 Thermodynamics, first-law balance of,82 Thiele modulus, 9,166-168 Tortuosity, 167 Transportation costs, 123 Transportation of liquids, 101 Triangular phase diagram, 62 232 Tie Inustrial Practice of Clell1 ical Process Ellgineerill Underwood equations, 147 Vacuum distillation, 138 Van Heerdon criterion, 45 van't Hoff relationship, 9 Vapor-liquid equilibrium, 9, 57, 132 Variables, critical, 10 selection of, 60 Venture analysis, 12 Viscosity of gases, estimation of, 164 Visual aids, 14 Volatility, relative, 9, 134 Writing, technical, 14 Yield, reaction, 40, 152, 192 Documents Similar To The Industrial Practice of Chemical Process EngineeringSkip carouselcarousel previouscarousel nextSeparation Processes 2nd EditionChemical Engineering Calculation DeskbookChlorobenzene FinishedChlorobenzene Material 2520BalanceProcess Design Induction - 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