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Common Misconceptions Concerning Graduate School, J.L. Duda ( PDF )
Book Reviews ( PDF ) Applied Mathematics in Chemical Engineering, Douglas Lauffenburger, Elizabeth Susan V., Lyle Ungar ( PDF ) Chemical Engineering Practice: Graduate Plant Design, Paul Marnell ( PDF ) Colloid and Surface Science, John F. Scamehorn ( PDF ) Transport Phenomena, D.B. Shah ( PDF ) Heterogeneous Catalysis Involving VideoBased Seminars, Mark G. White ( PDF ) Linear Algebra for Chemical Engineers, Kyriacos Zygourakis ( PDF ) Catalysis, Calvin H. Bartholomew, William C. Hecker ( PDF ) BioChemical Conversion of Biomass, Alvin O. Converse, Hans E. Grethlein ( PDF ) Separations Research, James R. Fair ( PDF ) Graduate Residency at Clemson: A Real World MS Degree, Dan D. Edie ( PDF ) Semiconductor Processing, Carol McConica ( PDF ) Simulation and Estimation by Orthogonal Collocation, Warren E. Stewart ( PDF ) 
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chemical engineering education VOLUME XVIII NUMBER 4 FALL 1984 4d GRADUATE EDUCATION ISSUE APPLIED MATHEMATICS IN ChE . Lauffenburger, Dusan V., Ungar ChE PRACTICE: GRADUATE PLANT DESIGN . Mamell COLLOID AND SURFACE SCIENCE . Scamehorn TRANSPORT PHENOMENA Shah HETEROGENEOUS CATALYSIS WITH VIDEOBASED SEMINARS . White LINEAR ALGEBRA FOR ChEs . Zygourakis Reddach aw .. CATALYSIS . BIOCHEMICAL CONVERSION OF BIOMASS SEPARATIONS RESEARCH . GRADUATE RESIDENCY AT CLEMSON . . SEMICONDUCTOR PROCESSING . Bartholomew, Hecker Converse, Grethlein . Fair . Edle McConica Gad a a COMMON MISCONCEPTIONS CONCERNING GRAD SCHOOL . . 4wa0d .,mc * SIMULATION AND ESTIMATION BY ORTHOGONAL COLLOCATION Warren E. Stewart Duda eCC achanawledesa wand tlhans.... 3M FOUNDATION CHEMICAL INGININEG EDUCATION Cddo.,s Il At This is the 16th Graduate Issue to be published by CEE and distributed to chemical engineering seniors interested in and qualified for graduate school. As in our previous issues, we include articles on graduate courses and re search at various universities and announcements of de partments on their graduate programs. In order for you to obtain a broad idea of the nature of graduate work, we encourage you to read not only the articles in this issue, but also those in previous issues. A list of the papers from recent years follows. If you would like a copy of a pre vious Fall issue, please write CEE. AUTHOR Davis Sawin, Reif Shaeiwitz Takoudis ValleRiestra Woods Middleman Serageldin Wankat, Oreovicz Bird Thomson, Simmons Hightower Mesler Weiland, Taylor Dullien Seapan Skaates Baird, Wilkes Fenn Abbott Butt, Kung Chen, et al Gubbins, Street Guin, et al Thomson Bartholomew Hassler Miller Wankat Wolf Ray Fahien, Editor, CEE University of Florida TITLE Fall 1983 "Numerical Methods and Modeling" "Plasma Processing in Integrated Circuit Fabrication" "Advanced Topics in Heat and Mass Transfer" "Chemical Reactor Design" "Project Evaluation in the Chemical Process Industries" "Surface Phenomena" "Research on Cleaning up in San Diego" "Research on Combustion" "Grad Student's Guide to Academic Job Hunting" "Book Writing and ChE Education" "Grad Education Wins in Interstate Rivalry" Fall 1982 "Oxidative Dehydrogenation Over Ferrite Catalysts" "Nucleate Boiling" "Mass Transfer" "Funds. of Petroleum Production" "Air Pollution for Engineers" "Catalysis" "Polymer Education and Research" "Research is Engineering" Fall 1981 "Classical Thermodynamics" "Catalysis & Catalytic Reaction Engineering" "Parametric Pumping" "Molecular Thermodynamics and Computer Simulation" "Coal Liquefaction & Desulfurization" "Oil Shale Char Reactions" "Kinetics and Catalysis" "ChE Analysis" "Underground Processing" "Separation Processes" "Heterogeneous Catalysis" Bird Edgar, Schecter Hanratty Kenney Kerchenbaum, Perkins, Pyle Liu Peppas Rosner Lees Senkan, Vivian Culberson Davis Frank Morari, Ray Ramkrishna Russel, et al. Russell Vannice Varma Yen Aris Butt & Peterson Kabel Middleman Perlmutter Rajagopalan Wheelock Carbonell & Whitaker Dumesic Jorne Retzloff Blanch, Russell Chartoff Alkire Bailey & Ollis DeKee Deshpande Johnson Klinzing Lemlich Koutsky Reynolds Rosner Fall 1980 "Polymer Fluid Dynamics" "In Situ Processing" "Wall Turbulence" "Chemical Reactors" "Systems Modelling & Control" "Process Synthesis" "Polymerization Reaction Engineering" "Combustion Science & Technology" "Plant Engineering at Loughborough" "MIT School of ChE Practice" Fall 1979 "Doctoral Level ChE Economics" "Molecular Theory of Thermodynamics" "Courses in Polymer Science" "Integration of RealTime Computing Into Process Control Teaching" "Functional Analysis for ChE" "Colloidal Phenomena" "Structure of the Chemical Processing Industries" "Heterogeneous Catalysis" "Mathematical Methods in ChE" "Coal Liquefaction Processes" Fall 1978 "Horses of Other ColorsSome Notes on Seminars in a ChE Department" "Chemical Reactor Engineering" "Influential Papers in Chemical Re action Engineering" "A Graduate Course in Polymer Pro cessing" "Reactor Design From a Stability Viewpoint" "The Dynamics of Hydrocolloidal Systems" "Coal Science and Technology" "Transport Phnomena in Multicom ponent, Multiphase, Reacting Systems' Fall 1977 "Fundamental Concepts in Surface In teractions" "Electrochemical Engineering" "Chemical Reaction Engineering Science" "Biochemical Engineering" "Polymer Science and Engineering" Fall 1976 "Electrochemical Engineering" "Biochemical Engr. Fundamentals" "Food Engineering" "Distillation Dynamics & Control" "Fusion Reactor Technology" "Environmental Courses" "Ad Bubble Separation Methods" "Intro. Polymer Science & Tech." "The Engineer as Entrepeneur" "Energy, Mass and Momentum Transport" FALL 1984 .2 'iv Growth Through Responsibility YOUR CAREER WITH ROHM AND HAAS If you're the kind of person who can take the initiative and aggressively reach for increasing . responsibility, consider a careerwith Rohm and : ; Haas. We are a highly diversified major chemi ., ; al company producing over 2,500 products u sed in industry and agriculture. Because our employees are a critical ingredient in our con tjnuing success, we place great emphasis on their development and growth. When you join S Rohm and Haas, you'll receive a position with ; : substantial initial responsibility and plenty of .room for growth. And we'll provide the oppor tunities to acquire the necessary technical and  'managerial skills to insure your personal and  professional development. Our openings are in Engineering, Manufacturing, Research, STechnical Sales and Finance. For more infor ;_mation, visit your College Placement Office, or write: Rohm and Haas Company, Recruit ing and Placement #3484, Phila., PA 19105. ROHMN M S PHILADELPHIA. PA 19105 .W4w .tj hato a 16% An Equal Opportunity Employer 1 9 . ~7~' ,a~t~ r *~ _1. .1 `i  'i.r i I 3 *wlk , LV EDITORIAL AND BUSINESS ADDRESS Department of Chemical Engineering University of Florida Gainesville, Florida 32611 Editor: Ray Fahien (904) 3920857 Consulting Editor: Mack Tyner Managing Editor: Carole C. Yocum (904) 3920861 Publications Board and Regional Advertising Representatives: Chairman: Lee C. Eagleton Pennsylvania State University Past Chairman: Klaus D. Timmerhaus University of Colorado SOUTH: Homer F. Johnson University of Tennessee Jack R. Hopper Lamar University James Fair University of Texas Gary Poehlesn Georgia Tech CENTRAL: Robert F. Anderson UOP Process Division Lowell B. Koppel Purdue University WEST: William B. Krantz University of Colorado C. Judson King University of California Berkeley Frederick H. Shair California Institute of Technology NORTHEAST: Angelo J. Perna New Jersey Institute of Technology Stuart W. Churchill University of Pennsylvania Raymond Baddour M.I.T. A. W. Westerberg CarnegieMellon University NORTHWEST: Charles Sleicher University of Washington CANADA: Leslie W. Shemilt McMaster University LIBRARY REPRESENTATIVE Thomas W. Weber State University of New York Chemical Engineering Education VOLUME XVIII NUMBER 4 FALL 1984 Views and Opinions 156 Common Misconceptions Concerning Graduate School, J. L. Duda Courses in 160 Applied Mathematics in Chemical Engineering, Douglas Lauffenburger, Elizabeth Dusan V., Lyle Ungar 164 Chemical Engineering Practice: Graduate Plant Design, Paul Marnell 166 Colloid and Surface Science, John F. Scamehorn 170 Transport Phenomena, D. B. Shah 174 Heterogeneous Catalysis Involving VideoBased Seminars, Mark G. White 176 Linear Algebra for Chemical Engineers, Kyriacos Zygourakis Research on 180 Catalysis, Calvin H. Bartholomew, William C. Hecker 186 BioChemical Conversion of Biomass, Alvin O. Converse, Hans E. Grethlein A Program in 190 Separations Research, James R. Fair 196 Graduate Residency at Clemson: A Real World MS Degree, Dan D. Edie 200 Semiconductor Processing, Carol McConica Award Lecture 204 Simulation and Estimation by Orthogonal Collocation, Warren E. Stewart 153 Editorial 159 Division Activities 159, 185, 199,203 Book Reviews 195 Books Received CHEMICAL ENGINEERING EDUCATION is published quarterly by Chemical Engineering Division, American Society for Engineering Education. The publication is edited at the Chemical Engineering Department, University of Florida. Secondclass postage is paid at Gainesville, Florida, and at DeLeon Springs, Florida. Correspondence regarding editorial matter, circulation and changes of address should be addressed to the Editor at Gainesville, Florida 32611. Advertising rates and information are available from the advertising representatives. Plates and other advertising material may be sent directly to the printer: E. O. Painter Printing Co., P. O. Box 877, DeLeon Springs, Florida 32028. Subscription rate U.S., Canada, and Mexico is $20 per year, $15 per year mailed to members of AIChE and of the ChE Division of ASEE. Bulk subscription rates to ChE faculty on request. Write for prices on individual back copies. Copyright 1984 Chemical Engineering Division of American Society for Engineering Education. The statements and opinions expressed in this periodical are those of the writers and not necessarily those of the ChE Division of the ASEE which body assumes no responsibility for them. Defective copies replaced if notified within 120 days. The International Organization for Standardization has assigned the code US ISSN 00092479 for the identification of this periodical. USPS 101900 FALL 1984 NM views and opinions I COMMON MISCONCEPTIONS CONCERNING GRADUATE SCHOOL J. L. DUDA Pennsylvania State University University Park, PA 16802 * * * * * * Twentyfive years ago, I started graduate school at the University of Delaware. Looking back on that time, I can see that I was a typical graduate student in that I was both excited and terrified, confident and anxious, sure of success one day and afraid of failure the next. I did, however, harbor certain basic misconceptions about the experiences which lay ahead of me. In talking to our graduate students here at Penn State, I found that those same misconceptions are still common, and this insight prompted me to give the following introductory address to our incoming graduate students. SIKE YOU TODAY, I was also entering graduate school twentyfive years ago. My mind was also filled with questions and concerns. It was also cluttered with certain misconceptions, which are still popular today. I would like to look back on that time with you and try to tell you how my views on graduate school have changed. The first misconception I had was that gradu ate school would be a continuation of my experience as an undergraduate. This was probably my greatest misconception. First of all, graduate courses and undergraduate courses are, in general, somewhat different. You are an elite group since we only accept one out of every fifteen applicants to our graduate program. Consequently, there is no doubt in our minds that you can perform well in graduate courses since your ability in chemical engineering courses has been demonstrated by your undergraduate record. Therefore, graduate courses tend to be more re laxed, with less emphasis on evaluation and certainly no hint of being a weedingout process. We feel that you are in these courses because you Copyright ChE Division. ASEE. 1984 The key to graduate research is problem solving, not the acquisition of specific information. You will learn to solve problems by actually performing this task under the direction of an expert... want to learn, and therefore our main emphasis is on enhancing your technical expertise. You are now engineers, not just high school graduates. The main difference between undergraduate and graduate education is related to the research aspect of graduate studies. Very few of our gradu ate students fail to receive their graduate degree because of their performance in courses. The main hurdle is the ability to do independent research. Up to now, in my opinion, your educational ex periences have been somewhat artificial. You have studied in order to pass exams which cover very specific and limited areas. In the past, you worked certain problems on examinations. You knew there was an answer. You also knew you had enough data to reach that answer. Conducting research in graduate school, on the other hand, does not involve an artificial environment. You will be working on problems where no one knows the answer, and the problem itself might not even be clear. Graduate research is similar to an apprenticeship. You will be working directly with an expert and will learn by doing and ob serving how this expert approaches problems. The key to graduate research is problem solving, not the acquisition of specific information. You will learn how to solve problems by actually per forming this task under the direction of an expert, not by studying the philosophy or idealized ap proach to problem solving. What happened to me may also happen to some of you. I slowly began to realize that research was unlike anything that I had been exposed to previously. There is a natural tendency to exagger ate the difference and come to the countermis conception that research has nothing to do with your undergraduate work. This is not true either. CHEMICAL ENGINEERING EDUCATION J. L. Duda is Professor and Head of the Department of Chemical Engineering at The Pennsylvania State University. He received his BS in chemical engineering at Case Institute of Technology and his MS and PhD at the University of Delaware. He joined the staff at Penn State in 1971 after eight years in research with The Dow Chemical Company. Research is a natural extension of your learning career to date, but it is also more than that. You have been learning and obtaining information from teachers, textbooks, and independent study in libraries. But what do you do when the knowl edge you desire is not available in any book or article, or when no individual exists who knows the answer? Research in the physical sciences and engineering is the process of learning by asking nature questions. In a sense, nature becomes your ultimate teacher. When you design experiments, you are really formulating your questions for nature. Unlike your previous teachers, nature does not anticipate your question. You will get a direct and honest answer to your question as it was formulated. If you are misled or have difficulties, it will not be because nature failed to answer your question. It will be due to your failure in formulat ing the question or in interpreting the results. The best researchers are the ones who ask what appear to be very simple questions and receive earth shaking replies. At this point, one might ask how theory fits into all this if the basis of research is asking nature questions through experimentation. As J. Willard Gibbs said, "The purpose of theory is to find that viewpoint from which experimental observa tions appear to fit the simplest pattern." You want to determine this pattern so that you can generalize your experimental observations and minimize the number of experiments that have to be conducted. My second misconception concerning graduate school was that the choice of a research topic was one of the most important decisions of my life since it would determine what area I would work in for the rest of my career. New graduate students continually forget that the main purpose of research at the graduate level is to learn how to do research and to solve prob lems. The acquisition of knowledge in a particular area is of secondary importance. If you have learned how to do research in area A, it is a rela tively minor step to acquire the facts and back ground needed to conduct research in area B. Consequently, when choosing a research topic, your main concern should not be whether you like the research area, but whether this particular re search project and the director of this research have the best chance of teaching you how to con duct research. My third misconception was that my research work would follow the idealized method of scientific inquiry which involves a literature search, develop ment of a theory, design of the experiments, and interpretation of results that tested the theory. One quickly learns that research is often more like a random walk than an idealized textbook ap ... when choosing a research topic, your main concern should not be whether you like the research area, but whether this particular research project and the director of this research have the best chance of teaching you how to conduct research. proach. The young researcher is often quite upset when discovering this fact. At first it is difficult to accept this basic truth. It is much easier to arrive at one of the following conclusions: My thesis advisor is incompetent. My research topic is a real lemon; I don't know how anyone talked me into doing this. My research has nothing to do with what I have learned in the classroom. No one else has problems like me; my project is unique in its difficulty. What the young researcher fails to realize is that the way research results are presented in a paper or a seminar has nothing to do with the process that was followed in obtaining those re sults. Research cannot be planned like many other human endeavors. It is, in fact, a form of art. If you knew beforehand what your results were going to be and the path you would have to take to obtain them, it simply would not be research. FALL 1984 No matter how badly things are going, or how tortuous your route, you should always maintain a clear idea of your objective. One frustration which all faculty members face is that many funding organizations also do not realize this. As a graduate student, you must be careful not to confuse the formal presentation of results in papers or seminars with the actual pro cess. A related misconception is that the results you obtain in research should be in proportion to the time and effort you have spent. The most difficult aspect of research is that you do not usually see a steady progression of results. Instead, results come in bursts or surges. It takes tre mendous tenacity to hang in there and keep plugging away when you are not aware of any progress. Many young researchers also feel that their problem is so complex that it really cannot be ex plained to anyone else in a reasonable period of time. No matter how badly things are going, or how tortuous your route, you should always main tain a clear idea of your objective. If you cannot give a clear overview of your research project in a few short sentences, you have a good indication that part of your problem is your inability to keep things clearly defined in your own mind. My fourth misconception was that the study of chemical engineering had nothing to do with human values, ethics, morals, etc. When I started my graduate studies, I con sidered science to be ethically or morally neutral. However, as Bronowski has pointed out, this is confusing the results or findings of science with the activity of conducting science. There is no question that the results of your research will be ethically neutral; however, at the center of scien tific inquiry is the standard that facts or truth, not dogma, must dominate your research. By conduct ing research, you will be training yourself to avoid and resist every form of persuasion but the facts. The most difficult part will be to avoid deceiving yourself. In everyone's career, there comes a time when experimental observations are inconsistent with a pet theory. It will be a true test of your ma turity as a researcher to unbiasedly look at the facts and to determine if the experimental observa tions are consistent or inconsistent with the theory, independent of your personal feelings. As T. H. Huxley said, "The great tragedy of science is the slaying of a beautiful theory by an ugly fact." There is a natural tendency to formulate vague theories which cannot be proven wrong, but all good theories will eventually lead to their own demise since they will finally predict something which is inconsistent with experimental observa tion. Science does not have a Hippocratic oath or any other professionally induced ethical rule. How ever, you can be untruthful and still be a success ful doctor or lawyer. This is not a viable possibility for the scientific researcher. As you develop into a good researcher, you will develop the capability of making judgments based solely on the facts. I feel this training can have a very significant posi tive influence on the moral and ethical aspect of your life since it tends to minimize selfdeception and rationalization. My fifth and final misconception was that graduate study was all hard work and the rewards would come later when I had an interesting job and was making a lot of money. After I received my advanced degrees, I realized that some of the best years of my life were those I spent in graduate school. I found that the pleasure and sense of accomplishment that came with learning and creating far outweighed the other pleasures in life. As graduate students, you are among the fortunate few who will not have to spend all of your time for the next few years working to meet the material needs of your life. Until this century, the great majority of people had to spend 100% of their time just to feed their bodies. A few privileged individuals, such as the Brahmins, Mandarins, aristocrats, etc. had the opportunity to simultaneously feed their bodies and their minds. We have made great advances, but today most people still spend a major part of their lives working to fill their material needs. No matter how difficult you find the days ahead, I am confident that you will look back on these years and be grateful that you had this opportunity to devote all of your effort to learning and creating. If you are very lucky, you might, after much hard work, devotion, and frustration, be fortunate enough to be the first person to see one of those patterns to which Gibbs referred. That will be the most rewarding time of your graduate studies, not the moment you receive a piece of paper which declares that you have now earned a specific de gree or that first pay check. E CHEMICAL ENGINEERING EDUCATION 4EQ CHEMICAL ENGINEERING O E DIVISION ACTIVITIES TWENTYSECOND ANNUAL LECTURESHIP AWARD TO T. W. FRASER RUSSELL The 1984 ASEE Chemical Engineering Di vision Lecturer was T. W. Fraser Russell of the University of Delaware. The purpose of this award lecture is to recognize and encourage out standing achievement in an important field of fundamental chemical engineering theory of practice. The 3M Company provides the financial support for this annual lecture award. Bestowed annually upon a distinguished engi neering educator who delivers the Annual Lecture of the Chemical Engineering Division, the award consists of $1,000 and an engraved certificate. These were presented to this year's Lecturer at the Annual Chemical Engineering Division Ban quet, held at the University of Utah on June 26, 1984. NOMINATIONS FOR 1984 AWARD SOLICITED The award is made on an annual basis with nominations being received through February 1, 1985. The full details for the award preparation are contained in the Awards Brochure published by ASEE. Your nominations for the 1985 lecture ship are invited. They should be sent to Professor E. Dendy Sloan, Colorado School of Mines, Golden, CO 80401. NEW DIVISION OFFICERS ELECTED The newly elected ChE Division officers are: Deran Hanesian, Chairman; D. Barker, Past Chairman; Dendy Sloan, Chairman Elect; Bill Beckwith, SecretaryTreasurer; and Lamont Tyler, Director. ChE's RECEIVE HONORS Four chemical engineering professors have recently been recognized for their outstanding achievements. Phillip C. Wankat received the George Westinghouse Award for early achieve ment as a teacher and a scholar; James E. Stice was presented with the Chester F. Carlson Award for improving instructional techniques; Peter R. Rony was the recipient of the Delos Award for excellence in laboratory instruction; and Chung King Law received the Curtis W. McGraw Re search Award for outstanding early achievement in research. book reviews ENGINEERING OPTIMIZATION: METHODS AND APPLICATIONS By G. V. Reklaitis, A. Ravindran, K. M. Ragsdell: John Wiley and Sons, NY (1983) 14 Chapters, 648 pages, $39.95 Reviewed by A. W. Westerberg CarnegieMellon University This is an excellent text from which to teach optimization techniques to engineering students. It can be used at either the senior or graduate level. All of the most important methods are pre sented that have appeared in the literature. The level of detail given on each method should allow one to see how and where to apply it to small up to moderatesized practical problems. The book concentrates on methods for solving well behaved, continuous variable optimization problems. The methods included are unconstrain ed single and multivariable optimization, linear programming, and a host of methods for equality and inequality constrained nonlinear problems. Not considered are methods directly applicable for models containing ordinary and partial differ ential equations, nor is there very much on solving problems where some or most of the variables can take on only discrete values. Also the book does not consider decomposition techniques, sparse matrix techniques and the like, concepts usually needed to allow the techniques covered to be ap plied to really large problems. The book is already lengthy so it is completely reasonable that it limits its coverage to the topics that it does. The style of presentation is generally excel lent. The authors have concentrated on appealing Continued on page 185, FALL 1984 4 o4ae iet APPLIED MATHEMATICS IN CHEMICAL ENGINEERING DOUGLAS LAUFFENBURGER, ELIZABETH DUSSAN V., and LYLE UNGAR University of Pennsylvania Philadelphia, PA 19104 A ALTHOUGH APPLIED MATHEMATICS has become increasingly important in chemical engineer ing research over the past three decades, it is still eyed with great trepidation by the typical first year graduate student. The nature of mathematics is viewed as something alien to real engineering, having little or no substance nor, curiously, logic. A prevailing opinion among firstyear students is that mathematics is more closely related to magic than it is to science. It has been presented to them during their undergraduate years mainly as a mere assortment of techniques, a "bag of tricks," from which the right method for the spe cific problem at hand must be plucked. Because the "why" of mathematics has not been learned, students lack confidence in the "how" as well. At Penn we believe that this situation must be corrected if our graduate students are to be able to productively use applied mathematics in their research careers. Therefore, our set of six core graduate courses includes a twosemester sequence ("Applied Mathematics in Chemical Engineer ing") which is required of every firstyear student. In addition, we now offer a strongly recommended elective course as a third semester in that se quence. However, it is not only the formal empha sis on mathematics, but also the content and es pecially the approach of the courses that convey our message to the students. In order to gain confidence in using mathe matics in research, a student needs to know not only how to apply some technique to solve a prob lem, but also when that technique is guaranteed to work and why, what other alternatives exist, and what methods are certain to be futile. Thus, our courses are taught with what might be termed a rather fundamental approach. That is, we empha size the internal logic and structure of mathe Copyright ChE Division, ASEE, 1984 In order to gain confidence in using mathematics in research, a student needs to know not only how to apply some technique to solve a problem, but also when that technique is guaranteed to work and why, what other alternatives exist, and what methods are certain to be futile. matics, showing that equations can possess in trinsic, inviolable properties in themselves, by providing rigorous definitions and stating and pro viding relevant theorems. It is these theorems which guarantee that certain techniques will pro vide solutions for particular problems and that others will not. Further, we show how the in trinsic properties of equations correspond inti mately with the natural behavior of the physical, chemical, or biological system being modeled mathematically by the equations. Once these properties are understood, it becomes a straight forward matter to derive a large number of solu tion techniques, both familiar and new, to the students' satisfaction. It is at this point that the students finally appreciate the power of the ab stract approach, for they now have learned why the tricks in their bag sometimes worked and sometimes did not. And they realize that they are now capable of reading applied mathematics re search literature to learn new techniques, since they have a grasp of the necessary underlying theoretical foundations. This is, of course, the ultimate aim of a graduate course in any subject not to pretend to teach the entirety of knowledge in the area but to enable the students to learn whatever is of interest to them. So, what at first may appear to be a rather im practical approach to engineering applied mathe matics turns out, in fact, to be of great utility. We make the analogy to mastery of a musical instru ment; it might seem much more practical to memorize a few songs that can readily be played at parties instead of learning to read music and practicing scales and arpeggios, but which ap proach will allow a new concerto to be faced with confidence? CHEMICAL ENGINEERING EDUCATION CONTENT The basis of our approach consists of teaching as much as possible from a linear operator point of view. The first semester course concentrates on establishing the formal structure of linear, or vector, spaces, with an emphasis on spaces of finite dimension. This allows development of solution procedures for systems of linear algebraic equations and systems of linear ordinary differ ential equations. We also establish the formal structure of nonlinear metric spaces, which leads to techniques for approximate solution of non linear equations of both algebraic and ordinary differential types. The second semester course then focuses on linear spaces of infinite dimension. Understanding of these spaces permits develop ment of solution procedures for partial differential equations. Finally, the third (elective) semester deals exclusively with nonlinear systems of ordinary and partial differential equations, utiliz ing perturbation methods and bifurcation theory. The underlying theme running throughout all three semesters is one of considering problems from within an operator framework. We stress linear theory because, simply, only linear problems can really be solved (excepting special cases). Even approximate solution techniques for non linear problems, whether analytical or numerical, can be shown to be based on transforming the non linear problem into a system of linear sub problems. (It might be noted that this point helps to disabuse the notion that the computer has made the understanding of mathematics less important to the engineer.) Thus, if a student has a firm grasp of the theory of linear problems, he or she will be able to understand how nonlinear problems may be approached. When this lesson is taken to heart, the student acquires confidence from the fact that he or she possesses sufficient mathe matical skill to attack theoretical or computa tional research problems without anxiety. In the next few paragraphs we will attempt to provide a brief summary of the course content. The first lecture is devoted to defining linear spaces rigorously, with a vector being simply an element in such a space. It is pointed out that these spaces are of importance essentially because the desired solutions to systems of equations will, in fact, be vectors in appropriately defined spaces. We then show how spaces may be comprised of linear subspaces, yielding the possibility of ob taining solution vectors as a combination of vectors from different subspaces, using the con cept of direct sums. Convenient ways of develop ing such combinations are allowed by introducing the idea of linear independence of vectors. The number of terms needed for such a combination is specified, using the notion of the dimension of a space, leading to the crucial definition of a basis for a linear space with finite dimension. Linear transformations are then defined, and it is shown that all systems of linear equations, no matter what type, can be cast as a linear transformation of a vector in one space to a vector in another. Douglas Lauffenburger is currently associate professor of chemical engineering, having arrived at Penn in 1979 after receiving his BS degree at II ' linois and his PhD at Minne sota. He spent the summer of 1980 as a Visiting Scientist at the Institute for Applied Mathe matics at Heidelberg. His re havior. (L) Elizabeth Dussan V. is presently on leave as a Guggenheim Fellow at Cambridge University, holding the position of associate professor at Penn. She received her BS degree at SUNY Stony Brook and her PhD at Johns Hopkins, coming to Penn in 1973 following a post doctoral position at Minnesota. Among her areas of investigation are included fluid mechanics and interfacial phenomena. (C) are included fluid mechanics and interfacial phenomena. (C) Lyle Ungar joined the faculty at Penn in 1984 as assistant professor, having received his BS degree at Stanford and his PhD at MIT. His research interests include application of perturbation methods, bi furcation theory, and finite element analysis to kinetic and transport problems in continuum physics. Topics of current focus include crystal growth and rapid solidification materials processing. (R) FALL 1984 The first lecture is devoted to defining linear spaces rigorously with a vector being simply an element in such a space. It is pointed out that these spaces are of importance essentially because the desired solutions to systems of equations will, in fact, be vectors in appropriately defined spaces. Thus, the solution to any linear problem can be understood in terms of solution of the general linear transformation equation Lx = y where y is the "data" vector in the range space, x is the "solution" vector in the domain space, and L is the linear transformation. Regardless of whether the problem is of algebraic, differential, or integral type, the vectors and the transforma tion can be written in component form in terms of basis vectors for the range and domain spaces, so that all problems involving finitedimensional spaces are equivalent to matrix equations. In verse transformations are now defined, fore shadowing a number of solution techniques for specific problems. This permits the uniqueness of solutions, if they exist, to be determined. Norms and inner products are introduced next in order to add geometric structure to the already present algebraic structure of linear spaces. This allows formulation of orthogonal basis vectors, which will be useful for generating the most convenient solution combinations. Ad joints can now also be discussed, leading to the Fredholm Alternative Theorem and the determina tion of existence of solutions. Finally, the concept of eigenvalues and eigenvectors is presented, and a Spectral Theorem is proved to demonstrate how orthogonal basis solution expansions can be ob tained using the eigenvectors of a selfadjoint operator. At this point, it is helpful to pull back from abstract theory and apply the principles learned so far to the solution of matrix equations. As mentioned earlier, it is stressed that such equations are actually involved in all finite dimensional problems. Given the theoretical back ground, a large number of alternative solution techniques can be derived very quickly and easily, and the student now understands the justification for, as well as the limits of, these techniques. We then step back into the realm of theory and, in fact, temporarily remove all the algebraic structure we have learned about linear spaces. This leaves us with only geometric structure; that is, the notions of size and distance generated by the presence of norms in linear spaces. In non linear spaces, the function that measures the size of an element, or the distance of it from another, is called a metric. Thus, we present an introduction to metric spaces, of which solutions to nonlinear problems may be elements. We can rigorously de termine whether a sequence of elements converges to a distinct element, a property crucial to the de velopment of approximate solution techniques (as well as analytical solution methods for infinite dimensional space problems). It takes relatively little time to move to the surprisingly powerful Fixed Point Theorem. This can be used to delineate circumstances under which an iterative approach will converge to a solution, leading to development of numerical methods for systems of nonlinear as well as linear algebraic equations. It also can be used to find regions of uniqueness and multi plicity of solutions to nonlinear equations. Finally, we can use it as a bridge to ordinary differential equations, since it is required in a simple and direct proof of Picard's Theorem for existence and uniqueness of solutions to initialvalue prob lems. Iterative schemes for obtaining approxi mate solutions to nonlinear ordinary differential equations can also be developed from the Fixed Point Theorem at this time. With the reintroduction of linear spaces, the theory of linear ordinary differential equations follows directly, because all the necessary back ground is in place. The general solution to a system of such equations can quickly be developed in terms of the fundamental matrix for the differ ential transformation. Students are pleased to see the apparently disparate variety of solution techniques they might have encountered previous ly fall out very easily from the general solution expression and development. Methods for de termining the form of the fundamental matrix are discussed next, primarily utilizing eigenvector basis expansions for constantcoefficient problems (thus explaining the "sum of exponentials" type solutions commonly seen) and for variableco efficient problems as well. The mystery is thus taken out of the use of special functions (Bessel functions, Legendre functions, etc.) for the latter types of equations, as their forms are seen to be derived in a consistent and rigorous way. The last CHEMICAL ENGINEERING EDUCATION few days of the first semester are used to intro duce the ideas of asymptotic expansions and per turbation theory as means to solve nonlinear problems by turning them into a sequence of linear ones. Linearized stability theory and a quick preview of bifurcation theory are also accessible at this point. The second semester begins with linear ordin ary differential equations of boundaryvalue type. The solution procedure for these follows directly from the fundamental matrix approach previously developed for initial value problems. The fact that solution properties are not completely specified at one value of the independent variable (providing "initial" conditions) but rather some are specified at another value (yielding "boundary" conditions) causes no breakdown of the approach. Unspecified initial conditions can be assumed to be constants as yet unknown, and the fundamental matrix pro cedure can be followed. The unknown constants can then be determined by requiring the remain ing boundary conditions to be satisfied. At this point it is useful to show how common solution techniques are related to this approach. Of prime interest is a presentation of Green's function techniques, with the Green's function for a linear differential operator demonstrated to be analogous to the fundamental matrix. We then move on to an extension of linear operator theory to linear spaces of infinite dimen sion. The most significant change is in the defini tion of a basis for an infinitedimensional space. An infinite number of vectors is now required for expansion of a solution vector, and the determina tion of the coefficients is greatly complicated. It is here that the property of selfadjointness of a linear operator becomes crucially important. For such operators the expansion coefficients can be determined individually in a straightforward manner. Thus, it is worth taking some time at this point to show how problems of unusual form can sometimes be cast as selfadjoint problems by ap propriate definition of the inner product. Linear partial differential equations can now be approached as linear operator equations on in finite dimensional spaces. Thus, solutions to these can be obtained as series expansions in terms of the infinite set of basis vectors, which will be orthogonal if the differential operator is selfad joint. For nonself adjoint operators the eigen vectors will form a biorthogonal set with the eigenvectors of the adjoint operators, although in this case the eigenvalues will be more difficult to find because they can be complex. The wellknown SturmLiouville problem is seen to be a special case of a linear selfadjoint differential eigenvalue equation, which allows eigenfunction expansion solution. Now that a foundation for series expansion techniques for solution of linear partial differential equations has been laid, we can go on to examine a series of problems of increasing complexity and subtlety. Examples include the Laplace and Poisson equations, and the diffusion and wave equations, in rectangular Cartesian, cylindrical, and spherical coordinate systems on finite and semiinfinite domains, with a variety of boundary conditions. Problems involving nonselfadjoint operators are also investigated, since the essential concepts have previously been established. ... it is useful to show how common solution techniques are related to this approach. Of prime interest is a presentation of Green's function techniques ... Examples of these include combined convection diffusion equations and the biharmonic equation. Again, we stress the development of the solution procedures from the linear operator theory frame work, emphasizing the unifying logic present despite the apparent variety of problems found. The second semester is, in a sense, more of a "techniques" oriented course than the first semest er in that there is a great emphasis on how to solve problems from a general linear operator point of view rather than primarily proving theorems. For example, proof of theorems relevant to infinite dimensional vector spaces such as the Spectral Theorem are neglected in favor of a de tailed discussion of the subtle differences between finite and infinite dimensional spaces. We revisit many of the topics developed during the first se mester with an almost exclusive focus on differ ential operators. We look at adjoint operators and examine how their form intimately depends on the choice of the inner product. We apply Fredholm's Alternative to examine the conditions under which solutions exist to Lx = y, where L is a Fredholm operator. The students are sur prised to see that the existence of a solution to a particular problem is very sensitive to the form of the boundary conditions, and that the initial value problem can be thought of as a specific type of boundaryvalue problem. The students Continued on page 214. FALL 1984 4 oa4e" ia CHEMICAL ENGINEERING PRACTICE: GRADUATE PLANT DESIGN PAUL MARNELL Manhattan College Riverdale, NY 10471 T HE OBJECTIVE OF this year long graduate plant design course [1, 2] is to provide the students with A fundamental appreciation of the profit motive that drives business activity, and the role of the chemical engineer in achieving this fundamental goal Historical and contemporary perspectives on chemical engineering practice Confidence to tackle the wide variety of problems that confront the chemical engineer The emphasis throughout the course is on why things are done the way they are. The "how to" aspects of design are implemented only after their needs have been established by a critical evalua tion of the various problems in process invention, process development, and ultimately, detailed pro cess design. The spectrum of design tools, i.e., ball park estimates, preliminary design techniques, and detailed design procedures, is integrated with the various phases in a process plant project. The rapidly changing technological and social climates demand that we produce generalists who have been schooled in the basic aspects of the de sign methodologies and who can learn fast and quickly bring themselves up to speed for a particular application. Obviously, it is not possible to teach all of the design and economic methods that practicing chemical engineers use, so a collection of procedures that will suffice for many situations is emphasized. The students are also trained to critically study the literature, including The recent recession and its disastrous effect on employment clearly illustrated the fact, which is often missed by students, that engineers provide services to companies to help them achieve the primary goal of an adequate profit. Copyright ChE Division, ASEE, 1984 E t Paul Marnell is an associate professor in the Manhattan College chemical engineering department. He initiated and helped direct the coalwater fuel technology research at Brookhaven National Laboratory from 198083. Prior to joining Manhattan in 1976, he was Director of Environmental Projects for the U.S. operations of the Lurgi Company and also held engineering positions with the Stone and Webster and Foster Wheeler Corporations. He obtained his BChE from City College, his MS (nuclear engineering) from Union College, and an EngScD (mechanical engineering) from Columbia University in 1972. patents, so that they may uncover or develop new procedures and analogies which they can use with confidence in situations that are new to them. The rationale for and some of the methods used to attain the course goals are discussed in the following. "The Chemical plant is a dollar factory." William C. Reid [3] The recent recession and its disastrous effect on employment clearly illustrated the fact, which is often missed by students, that engineers pro vide services to companies to help them achieve the primary goal of an adequate profit. Thus, technical expertise combined with engineering economic analysis is the bedrock upon which engi neering judgments are made. Engineers create devices by applying the laws of nature and mathematics and using empiricism and intuition where needed. Analysis to provide CHEMICAL ENGINEERING EDUCATION basic knowledge is the province of the scientist or mathematician. Analysis to provide insight on the performance of a device is a valuable part of the design process and one which can reduce the cost of empiricism. However, often empiricism must be used to create things within a reasonable period of time. Thus, piping systems are designed on the basis of the empirical friction factor cor relations for turbulent flow, and it will probably be many years before a truly fundamental re lationship for turbulent pressure drop in pipelines will be achieved. Similar considerations hold for mass and heat transfer correlations and reaction rate expressions. Nevertheless, chemical plants have been built and will continue to be built by the judicious blending of analysis, intuition, and em piricism. This brief essay is not the place to expand on the various aspects of engineering economic analysis that are considered in the course. How ever, two elements of critical importance are: 1. Multiple alternatives are generally available to achieve a goal, and the engineer is constantly screen ing alternatives of increasing detail with tools of increasing accuracy. The observation is valid at all levels of decision making, from the selection of a project to fund to the choice of a vendor for, say, concrete reinforcing bars. Thus, several years ago the Mobil Oil Corporation felt that buying Mont gomery Ward was an attractive venture to help maximize profits, and currently the United States Steel Corporation is shutting down more of its steel plants while increasing its real estate holdings.* Similarly, examples within the chemical process industry form a hierarchy which ranges from the general to the very specific. Which product should be made to achieve a desired result, and which re action path should be used to produce it? Given the reaction path, which separation technologies would be best, and given that distillation might be desire able, should it be done in a plate or packed tower? What type of plate tower should be used, and who should the vendor be? Alternatives abound, from broad strategic questions to very specific hardware items, and usually one is more attractive than its competitors. 2. As with engineering analysis, the tools for economic analysis range from crude to sophisticated, and the choice represents a compromise between expediency and accuracy that yields a result which is acceptable for the circumstances. "Nevertheless, it would be a mistake to suppose that the present generation can *While they are only noted here, the social and economic implications of these transactions, especially the latter, are explored in the course. The first car built did not look like today's Ferrari. Similarly, many current chemical plants are much more complicated than their predecessors. afford to ignore the labours of its predeces sors." Lord Rayleigh [4] The first car built did not look like today's Ferrari. Similarly, many current chemical plants are much more complicated than their predeces sors. Modern ethylene, ammonia, and sulfuric acid plants represent the evolution and refinement of their underlying processes. All too often, study of these highly integrated technologies can intimi date a student. It is essential to stress the fact that they represent thousands of manyears of engineering effort and decades of operating ex perience, and in no way, shape, or form were con ceived, developed, and built this way on the first try. Engineers should recognize that technological progress usually represents an evolution of pain staking improvements built upon a singular revolutionary concept. Engineers, like other creative people, design, analyze, redesign, build, and refine their artifacts. Hence, it is important to inculcate the philosophy of not reinventing the wheel. Learn from what has gone before. Minimize mistakes by learning from those of others. Understand the logic of the past to help guide the developments of the present and the future. ". . the authors .... not include in their books anything they themselves do not understand." Linus Pauling [5] The vast majority of what a chemical engineer does is included in the categories of process de velopment, process design, and process improve ment. In these activities, analysis is the hand maiden of synthesis. How does the item that has been created perform? Can it be improved? During the sixties and seventies the "hand book" engineer was criticized [6]. He is a person who presumably does not understand the basis of his system, and who can use solutions in books but cannot generate new ones for new situations. In the eighties, the handbook engineer is being replaced by the "black box" engineer, i.e., one who is adept at filling out computer input forms, but who has little understanding of the underlying Continued on page 215, FALL 1984 4CD AD SE in COLLOID AND SURFACE SCIENCE JOHN F. SCAMEHORN University of Oklahoma Norman, OK 73019 APPLICATIONS OF COLLOID and surface phe nomena in chemical engineering are becoming increasingly abundant. In the search for new technologies to solve pressing problems, such techniques as enhanced oil recovery by surfactant flooding, micellar catalysis, and surfactantbased separation techniques have emerged. Traditional technologies using surface and colloid science have aroused new research interest: examples are adsorption, detergency, and flotation. The course discussed here was designed to cover a wide range of some of the more important topics in colloid and surface science (see Table 1). Obviously, in covering this many topics, a great deal of depth could not be attained, but when the students finish the course they have a working familiarity with a wide range of phenomena and a quantitative knowledge of the more important mathematical relationships in the field. Since tra ditional chemical engineering courses essentially ignore surface and colloid phenomena, the in structor has to assume he is starting from ground level in almost all of these topics. This course was designed for chemical engi neers, chemists, and petroleum engineers. A typi cal breakdown of enrollment by the three cate gories is 70%, 20%, and 10%, respectively. The only prerequisite is chemical thermodynamics (either physical chemistry or chemical engineer ing thermodynamics). The mixture of students from different disciplines brings breadth to class room discussions and forces the instructor to search for examples of applications which are out side of his immediate interests. TEXTBOOK SELECTION Unfortunately, there is no single textbook which covers both surface and colloid science Copyright ChE Division, ASEE, 1984 sufficiently well to be a basis for this course. Therefore, required texts for the course are Physical Chemistry of Surfaces, by Adamson [1], for surface science, and Surfactants and Inter facial Phenomena, by Rosen [2], for colloid science. Numerous handouts and references are also used. COURSE DESCRIPTION As seen in Table 1, the first four major topics are related to surface phenomena. Adamson [1] is used in this part of the course, more as a refer ence than as a textbook. First, considerable effort is expended in ex plaining the physical causes of surface tension, since this is critical to future topics. One useful example is to consider the creation of a vapor liquid interface as the reduction of the number of nearest neighbors to a surface molecule in the liquid from six to five. The surface tension per John F. Scamehorn received his BSChE in 1973 and his MS in chemical engineering in 1974, both from the University of Nebraska, and worked for the Chemical Research Division of Conoco Inc. for three years before returning to graduate school. He received his PhD in chemical engineering from the University of Texas in 1980. He then spent a year and a half in Corporate Research with Shell De velopment Co. before joining the chemical engineering and ma terials science department at the University of Oklahoma in 1981. His research interests focus on applications of surface and colloid science and of membrane science. He is specifically interested in enhanced oil recovery, ultrafiltration, adsorption, electrodialysis, and interactions between dissimilar surfactants in various phenomena. CHEMICAL ENGINEERING EDUCATION unit area is then approximated as onesixth of the heat of vaporization of the surface molecules occupying a unit area. Viewing the creation of a surface as "fractional vaporization" provides physical insight to the reason surface tensions exist, and the crude calculation actually gives values for surface tension within a factor of two of the correct value. Demonstration of the actual measurement of surface tension in the instructor's lab also reinforces the concept that it takes work or energy to create a surface. Using a DuNoiiy ring tensiometer, the students can see the surface stretch under stress before breaking. One of the greatest weaknesses of Adamson [1] is the treatment of surface thermodynamics. The derivations are generally not rigorous and are often obscure. Therefore, the instructor basically needs to derive fundamental thermo dynamic relationships (like the Kelvin equation and the Gibbs equation) from scratch. The power of the Gibbs equation and the importance of the definition of the dividing surface can be illustrated by a calculation of monolayer coverage of a sur factant from dilute solution from surface tension ... when the students finish the course they have a working familiarity with a wide range of phenomena and a quantitative knowledge of the more important mathematical relationships in the field. data. When covering the third major topic, adsorp tion, the basic difference between localized and mobile adsorption must be emphasized. Inter converting 2D equations of state and mobile ad sorption isotherms using the Gibbs equation il lustrates this point. Hiemenz [3] is a useful refer ence concerning the electrical double layer. At this point in the course (about halfway through), the student has seen mostly theory and is wondering about the usefulness of the material. Even though applications are in a separate section at the end of the course, to complete the ad sorption topic, adsorber design is discussed. First, practical guidelines for selection of industrial ad sorbents for various applications are given. Then some complications of adsorber design are touched TABLE 1 Course Outline 1. CAPILLARITY Definition and Reason for the Existence of Surface Tensions Laplace Equation Capillary Rise Phenomena Measurement of Surface Tension 2. SURFACE THERMODYNAMICS Surface Thermodynamic Properties Kelvin Equation Criterion of Equilibrium in Systems with Interfaces Dividing Surface Definition of Adsorption or Surface Excess Gibbs Equation Monolayer Coverage at the AirWater Interface 3. ADSORPTION Localized vs. Mobile Adsorption Langmuir Adsorption Isotherm BET Adsorption Isotherm 2D Equations of State Potential Theory Adsorption from Solution Electrical Diffuse Double Layer DebyeHiickel Theory and Debye Length Stern Layer Practical Applications and Adsorber Design 4. CONTACT ANGLE Young Equation Measurement of Contact Angle 5. MICELLE FORMATION Classes of Surfactants Micelle Structure CMC Determination MassAction Model PseudoPhase Separation Model Shinoda Equation 6. SOLUBILIZATION IN MICELLES Locations of Solubilizate in Micelles Driving Forces for Solubilization Measurement of Solubilization 7. EMULSIONS Mechanisms of Stabilization Bancroft Rule HLB Number Breaking Emulsions 8. FOAMS Gibbs Triangle Mechanisms of Film Elasticity Mechanisms of Foam Drainage Foam Breaking and Inhibiting 9. APPLICATIONS Enhanced Oil Recovery by Surfactant Flooding Detergency Marangoni Effects Novel Separation Techniques Using Surfactants FALL 1984 on: the masstransfer zone, bed heatup due to heat of adsorption, and bed regeneration. Examples of applications using activated carbon, silica gel, and ionexchange resin are given. Handouts and suggested reading material supple ment lectures on design of adsorbers [47]. In covering the topic of contact angles, the reasons that advancing and receding contact angles may differ are explored. The physical mean ing of the Young equation in terms of the surface tensions involved is emphasized. Topics 57 are in the area of colloid science. Rosen [2] is used as the text. It is easy to read and is well organized, and the text is followed much more closely in this section of the course than in the surface science section. In the consideration of micelle formation, the variety of surfactants available is discussed, and the value of McCutcheons' [8] in finding suppliers of a certain type of detergent is stressed. The various methods of CMC determination help il lustrate the properties of solutions containing micelles and lead naturally into a discussion of the massaction and pseudophase separation models of micelle formation. The fact that these models coincide for large enough micellar aggre gation numbers is stressed. The iceberg structure of water around hydrocarbon chains in solution causing the micelle formation to be entropy driven and the subsequent concept of hydrophobic bonds is then considered in the context of micellar thermodynamics. The effect of electrolyte con centration and hydrocarbon chain length on the CMC is shown to be described by the Shinoda equation [9]. The value of Mukerjee and Mysels [10] as the standard reference for literature CMC values is useful to point out. Krafft temperature, cloud point, and liquid crystals are briefly dis cussed to show that there are limits to conditions resulting in the isotropic regions where micelles form in surfactant solutions. Under the topic of solubilization, the wide spread use of Henry's law to extrapolate solubiliza tions measured at unit activity using the maxi mum additivity method is discussed. This is followed by consideration of deviations from Henry's law and methods of measurement of solubilization (vapor pressure, osmometry, vapor phase UV, vapor phase GC, ultrafiltration) over the entire concentration range. The importance of solubilization in such applications as detergency is worth mentioning. In discussions of emulsions, the origins of barriers to emulsion breaking are described. The guidelines for the selection of surfactant by HLB Number and tabulations of this value in Mc Cutcheons' [8] for commercial surfactants are em phasized. The importance of emulsions to chemical and petroleum engineering operations is illustrated by examples such as the severe problem of separat ing oils recovered by tertiary methods from pro duced water in the field because of emulsion for mation. The existence of emulsions in everyday life in products such as milk and paint helps the student feel more comfortable with the phe nomena. The fact that emulsions are not thermo dynamically stable is heavily emphasized. How ever, it must be mentioned that the socalled "microemulsions" used in surfactant flooding can be considered as a thermodynamic phase. The fact that foams are not thermodynamically stable is also stressed: that foams are sometimes desirable (detergents) and sometimes undesirable (causing entrainment in distillation columns) is important to note. New applications of foams, such as in enhanced oil recovery for mobility control or foam fractionation, point out their im portance. The applications portion of the course is de signed to show how important the phenomena discussed are and to illustrate that many of them can be occurring at the same time and have com plex interactions. The various methods of EOR are first outlined (aided by a handout from Exxon [11]), and the mechanisms by which they function are discussed. Then surfactant flooding is focused on. Theories to explain the ultralow interfacial tensions present in these systems pro vide an opportunity to explore some subtleties of interfacial tension, surface thermodynamics, solubilization, and emulsion stability. Adsorption of surfactants on minerals and precipitation neatly show the tie between surface science and colloid science. A discussion of the stateoftheart and the major remaining problems to be solved in this technology are complimented by an outline of the instructor's approach to solving these prob lems. A tour of the instructor's research lab where the students can observe such things as middle phases, surfactant precipitate, and cloud points brings home the applications of the course to EOR. Detergency also involves both surface science (surfactant adsorption on fabrics) and colloid science (solubilization). In addition, the rollback mechanism of oil removal from fabrics provides CHEMICAL ENGINEERING EDUCATION a practical example of contact angles and wetting. Until this point in the course, equilibrium phe nomena have been almost exclusively considered. A discussion of Marangoni effects demonstrates nonequilibrium surface tension effects. A non mathematical article on tears which form on the inside of a glass of wine [12] is supplemented by passing around a wine glass containing vodka so the student can see the tears form. The reduction in liquid level in the glass after being passed around the class can not always be accounted for solely by evaporation. This practical demonstra tion of Marangoni effects is always popular. The course is completed by discussion of a favorite research topic of the lecturer: separation techniques using surfactants. Among those dis cussed are foam fractionation and micellar en hanced ultrafiltration. Since the majority of the class is composed of chemical engineers, these novel applications of colloid science to replace classical separation techniques illustrate the value of colloid science. STUDENT COMMENTS In general, the students liked the relatively high fraction of course content dedicated to practical applications. They also liked the constant emphasis on the physical significance of the ma terial. They appreciated the fact that the mathe matical content of the course was kept to a level such that physical reality was not obscured. The students had two main complaints: they did not like Adamson as a text, and they found sur face thermodynamics to be less interesting than the rest of the course. However, most of them recognized the future value of Adamson as a reference book and also realized the necessity of a firm grounding in surface thermodynamics for the later topics covered. GENERAL COMMENTS Teaching both surface and colloid science in a single course is a challenging task. Some de partments choose to cover surface science in detail with a more mathematical orientation and a mention of colloidal phenomena in passing. In order to learn surfactant science, another course is needed. The dedication of two courses to this area is not always possible or desirable (par ticularly for the MS student). This course was developed as an attempt to integrate the basics from both surface science and colloid science into one course. Response from former students in in dustry concerning the value of the material learned indicates that the course fulfills a need. O REFERENCES 1. Adamson, A. W., Physical Chemistry of Surfaces, Fourth Edition, Wiley, New York (1982). 2. Rosen, M. J., Surfactants and Interfacial Phenomena, Wiley, New York (1978). 3. Hiemenz, P. C., Principles of Colloid and Surface Chemistry, Ch. 9, Marcel Dekker, New York (1977). 4. Kovach, J. L., in Handbook of Separation Techniques for Chemical Engineers, Ch. 3.1, P.A. Schweitzer, Ed., McGrawHill, New York (1979). 5. Calgon Corporation, Pamphlet on "Basic Concepts of Adsorption on Activated Carbon," Calgon, Pitts burgh. 6. Scamehorn, J. F., Ind. Eng. Chem. Process Des. Dev., 18, 210 (1979). 7. Vatavuk, W. M., and Neveril, R. B., Chem. Eng., 90, 131 (Jan. 24, 1983). 8. McCutcheons' Emulsifiers & Detergents, North American Division, McCutcheon, Glen Rock, N.J. (1983). 9. Shinoda, K., in Colloidal Surfactants, Ch. 1, K. Shinoda, T. Nakagawa, B. Tamamushi, and T. Ise mura, Eds., Academic Press, New York (1963). 10. Mukerjee, P., and Mysels, K. J., Critical Micelle Con centrations of Aqueous Surfactant Systems, National Bureau of Standards, Washington (1971). 11. "Improved Oil Recovery," a pamphlet by Exxon Corporation, Exxon, New York, 1982. 12. Walker, J., Scientific American, 248, 163 (May, 1983). FALL 1984 FORTRAN CALLABLE REAL TIME SUBROUTINES FOR APPLE II COMPUTER APPLE II can be made to function as a data acquisition and control system for under $3000. FOR MORE INFORMATION PLEASE CONTACT Dr. P. Deshpande Professor of Chemical Engineering University of Louisville Louisville, KY 40292 A CQe44eM irz TRANSPORT PHENOMENA D. B. SHAH Cleveland State University Cleveland, OH 44115 T HE PRIMARY OBJECTIVE in a course on transport phenomena is to analyze physical problems in heat, mass, and momentum transfer. The steps involved in this process are understanding the physical aspects of the problem, making appropri ate assumptions, deriving the necessary differ ential equations, and developing analytical solu tions. In this endeavor applied mathematics plays a secondary, but a very powerful, role. Of course, many problems of interest and practical im portance are quite complex, and it is not possible to obtain analytical solutions for these cases. This does not diminish the importance of finding exact or approximate analytical solutions to the develop ed differential equations. Sometimes it is neces sary to obtain a closed form of the solution in limiting cases. Such solutions under asymptotic conditions are needed to validate the numerical solution of the differential equations. A gradu Dhananjai B. Shah has a BChE from the Department of Chemical Technology, University of Bombay, and MS and PhD (1975) from Michigan State University, both in chemical engineering. He spent two years at the University of New Brunswick, one year at McMaster University, and three years at the Indiana Institute of Technology. Since 1982, he has been an assistant professor of chemical engineering at Cleveland State University. His research interests include simulation and modelling of unsteady processes, adsorption and diffusion in zeolites and catalysis. ate course in transport phenomena, therefore, should place considerable emphasis on common methods of solution of differential equations, how they are applied, and why they work. BACKGROUND Every fall, we offer a graduate course in transport phenomena. The course meets four hours a week for ten weeks, and it is one of the three required of every master's student. It is the only course a terminal master's degree candidate will have that integrates the three transport processes. Most students take this course in the first quarter of their graduate program. We have a relatively large percentage of part time graduate students. Some have come back to school after a lapse of few years, and some have had their baccalaureate degree in chemistry. They need considerable help in solving the differential equations. However, because of their practical ex perience, they have a good feel for physical situ ations and are good at making approximations and engineering judgments. The full time students are only slightly better prepared in solving the differential equations. Many of them have not had any undergraduate course in partial differ ential equations, and they tend to be overwhelmed by the equations they come across in transport phenomena. The course strives to achieve a bal ance between exposing the students to 1) ad vanced topics in transport phenomena, pointing out similarities and differences between the three transfer processes, and 2) common methods of solving differential equations. The best way to accomplish these objectives is to solve a large number of problems. Daily homework assignments are made throughout the duration of the course. Textbooks by Bird, Stewart and Lightfoot (BSL) and by Slattery (S) are used repeatedly. Both the books abound with challenging problems which are used extensively for classroom discus sion and for homework assignments. All of the students coming into the course are expected to Copyright ChE Division, ASEE. 1984 CHEMICAL ENGINEERING EDUCATION have been exposed to the first three chapters in each of the three sections in BSL. At the end of the course, it is hoped that the students will be able to comprehend almost all the material in BSL. In addition, a number of other books and journal articles are consulted (listed in the refer ences to this paper). COURSE CONTENT AND ORGANIZATION The problems in transport phenomena are formulated and analyzed in a series of steps as outlined below. Problem Visualization The coordinate system based on the geometry of the problem is chosen first. In most cases the choice is obvious, but in some cases it is not easy. For example, in considering diffusion from a point source in a moving stream (17 K, BSL), it is not easy to decide whether to use cylindrical or spherical coordinates. After the coordinate system is chosen, the physical aspects of the problem are discussed. Any intuitive feeling about the behavior of the system under some limiting conditions is brought out. Directions of velocity, The course strives to achieve a balance between exposing the students to 1) advanced topics in transport phenomena, pointing out similarities and differences between the three transfer processes, and 2) common methods of solving differential equations. temperature, and concentration gradients are de termined. Appropriate physical assumptions are made to simplify the resulting set of equations. One such assumption is to neglect end effects in many momentum transfer problems. Another example is the absorption of a component in falling film where convective flux is neglected in the X direction and diffusive flux is neglected in the Z direction (175, BSL). Differential Equations The general equations of continuity, motion, and energy are now applied to the problem under consideration. With the help of information ob tained in the above section, the terms not applic able to the problem at hand are equated to zero. The solution of the resulting set of differential TABLE 1 Classification of Problems According to Method of Solution of Differential Equations COMBINATION OF VARIABLES SEPARATION OF VARIABLES LAPLACE TRANSFORMATION 1) Flow near a wall suddenly set 1) Velocity distribution in plate and 1) Two large blocks brought in in motion (4.11, BSL) cone viscometer (3T, BSL) contact (6.2.2.2.5) 2) Heating semiinfinite slab 2) Unsteady laminar flow in a 2) Cooling of sphere in contact with (11.11, BSL) circular tube (4.12, BSL) or in well stirred fluid (11.13, BSL) an annulus (4L, BSL) 3) Unsteady evaporation 3) Unsteady tangential flow 3) Gas absorption in a falling film with (19.11, BSL) (4Lb, BSL) chemical reaction (17L, BSL) 4) Gas absorption with rapid 4) Heating finite slab (11.12, BSL) 4) Packed adsorption column chemical reaction or semiinfinite slab with con modelling (22L, BSL) (19.13, BSL) vective boundary condition (6.2.3, S) 5) Boundary Layer Theory 5) Mass transfer within a solid 5) Unsteady diffusion with a first Exact Solution for a) Momentum sphere (9.2.11, 9.2.12, S) order homogenous reaction Transfer (3.5.1, 3.5.2, S) (9.2.2, S) b) Momentum and Heat Transfer (6.7.1, 6.7.2, S) c) Heat, mass and momentum transfer (19.3, BSL) 6) Unsteady interphase diffusion (19K, BSL) FALL 1984 equations subject to the appropriate initial and boundary conditions is attempted by using one of the following three techniques. Similarity solution by combination of variables. The differential equations which can be solved by this method are characterized by boundary con ditions where the dependent variable has the same value at different values of two independent vari ables. For example in fluid flow near a wall sudden ly set in motion (4.11, BSL), the boundary con ditions are V = 0 at t = 0 for all Z and at Z = co at all t > 0. Such boundary conditions are quite common in problems involving a semiinfinite region. A new combined variable q = Z/a t" is defined which allows the above two boundary conditions to merge, i.e. V = 0 at q = oo. The value of n is chosen such that when Y] is substi tuted into the partial differential equation, on simplification, an ordinary differential equation is obtained. The choice of a is more arbitrary but is generally taken as a reciprocal of n. When the ordinary differential equation is solved, one ends up with error functions and gamma functions. The method also gives an opportunity to introduce the concept of penetration thickness which is ex ploited later in the boundary layer approximation discussion. The method is applied repeatedly to many of the problems listed in Table 1. The empha sis is on why the method works, when it is ap plicable, and how it works. Similarity Solution by Separation of Variables. The boundary conditions in this case are such that a combined variable cannot be formulated that combines the two boundary conditions into one. The boundary condition at Z = oo is either replaced by a similar one at Z = L or is character ized by heat or mass transfer resistance. Such problems are solved by the method of separation of variables. The dependent variable is assumed to be product of separable functions, each one of which is in turn a function of one independent variable only. The method requires that the students be exposed to SturmLouiville theorem, orthogonal functions, weighting functions, and the limits of integration. Again, why the method works for these boundary conditions is empha TABLE 2 Simplification of Differential Equations SEPARATION OF VARIABLES WHERE ONE FUNCTION PSEUDO STEADY STATE IS KNOWN ASYMPTOTIC CASES APPROXIMATION 1) Cone and plate Viscometer 1) GraetzNusselt Problem 1) Squeeze film (12.4, Denn) (3.53, BSL) a) Large distances (9.8, BSL) b) Short distances (11.22, BSL) 2) Creeping flow between con 2) Short contact times 2) Unsteady evaporation from a tube centric spheres (3Q, BSL) a) (9.P, 9.R, BSL) followed by separation of b) Heat transfer from wall to variables falling film (10R, BSL) c) Diffusion into falling liquid film (17.5, BSL) d) Solid dissolution into falling film (17J, BSL) 3) Periodic heating of earth's 3) NavierStokes Equations 3) Unsteady evaporation of a drop crust (11L, BSL) a) Re>0, Creeping flow (chapter 12, Denn) b) Re > oo, potential flow Inviscid flow (3.4.1, S) c) Re> o, Boundary layer approximation (chapter 15, Denn) 4) Flow near an oscillating 4) Shrinking unreacted core model in wall (3.2.44, S) gassolid noncatalytic reaction 5) Flow between rotating discs 5) Efflux times for tank (7M, 7P, BSL) (12.2, Denn) CHEMICAL ENGINEERING EDUCATION sized by comparing the similar profiles, and how it works is illustrated by solving a number of problems, some of which are listed in Table 1. In some cases, not only are the functions separable, but one of the functions is easily formu lated from the boundary conditions. For example, in describing a velocity field for flow near an oscillating wall, the boundary conditions are at Y = 0, V = Vo sin (wt e) and at Y = oo, V = 0. The boundary conditions allow us to formulate the solution as V = exp[i(wt e)]f(y). There are many such cases, and some are listed in Table 2. Use of Laplace Transforms. Many of the problems solved by combination of variables or separation of variables can also be solved by using the Laplace transform. However, it is preferably applied where there are more than one partial differential equations and variable of interest can not be determined without solving for some other variables first. An excellent example of this is the cooling of a sphere in contact with wellstirred fluid (11.21; BSL). By using Laplace transforms, it is possible to evaluate the variation of solid temperature with radius and time without having to solve for the temperature history of the fluid. A number of problems where the Laplace trans form method is applied and illustrated are listed in Table 1. Simplification of Differential Equations Many times the differential equations derived are quite complicated and none of the three methods outlined above is applicable. Under these conditions, one may wish to consider a limited case where one or more terms in the differential equations are neglected. However, it is very im portant to indicate how these approximations are made and how a simplified set of differential equa tions is derived. This is illustrated with the classic problem in fluid mechanics. The NavierStokes equations are written in dimensionless form using characteristic quantities. This introduces the Reynolds number into the NavierStokes equations. The behavior of these equations in the following three cases is then investigated. Creeping flow in the limit as Re 0 Potential flow in the limit as Re oo. This corres ponds to inviscid fluid flow far from the boundary Boundary layer approximation in the limit as Re > oo for fluid flow in the immediate neighbor hood of a boundary Excellent discussion of these topics is provided Many times the differential equations derived are quite complicated and none of the three methods outlined ... is applicable. TABLE 3 List of Additional Topics Covered in the Course A) Potential flow and stream function Creeping flow around sphere (2.6, 4.21, BSL; 3.3.3, S) B) NonNewtonian fluid flow Introduction to tensor algebra Cone and plate viscometer (3.43, 3T, BSL; 3.3.2, S) Flow in simple geometry (3.2.23.2.4, S) C) Turbulent flow (Chapter 5, BSL) Time averaged NavierStokes equations Approximations to Reynolds Stresses Velocity profiles in simple geometry (5E, 5F, 5D, 5H, BSL) D) Exact solution of NavierStokes equations Converging flow in a channel Other examples (Chapter 5, Schlichting) E) Nusselt and Sherwood numbers in laminar and turbulent flow (Ref. 2, 3) F) Steady State multicomponent diffusion with homo geneous and heterogeneous reactions (18Q, 18S, BSL; 9.2.3, 9.2.7, S) G) Diffusion from a point source in a moving stream (10.2, S) H) Macroscopic Balances Pressure distribution in a manifold (7Q, BSL) Heat exchangers (15J, BSL) Heating of a liquid in an agitated tank (15M, 15.51, BSL) Packed bed absorber and adsorber (22.51, 22.62, BSL) by Slattery and Denn. It is also pointed out to students that the number of asymptotic cases considered for large distances or short contact times treated in BSL and Slattery represent another way of simplifying the differential equations. Many cases of short contact times let us assume that the depth of pene tration is much smaller than the length of region of interest. This allows one to shift the boundary condition at, say, Z = L to Z = oo. The students immediately see the benefit of doing this as the problem becomes solvable by the combination of variables as outlined earlier. Various problems of this type are listed in Table 2. Another common concept used to simplify the differential equations is the concept of pseudo steady state approximation. The problems listed in Table 2 are used to illustrate the application of Continued on page 213. FALL 1984 4 Cowsce on HETEROGENEOUS CATALYSIS INVOLVING VIDEOBASED SEMINARS MARK G. WHITE Georgia Institute of Technology Atlanta, GA 303320100 .& WE HAVE OFFERED, for the past three years, a specialized seminar course entitled "Seminars in Heterogeneous Catalysis" to students in our research groups on alternating quarters, usually fall and spring. The original purpose of these seminars was to bring about a feeling of unity to our program of heterogeneous catalysis and to help educate our students on the nature of catalysis outside the formal graduate lecture course we offer once a year under the same name: Catalysis. After the initial startup of this seminar course we ex plored the benefits of such a communicationsbased course which included the transfer of information between graduate students working on similar problems and the improvement upon communica tion skills. The next logical extension of the course was to formalize the feedback mechanism by which students could learn of their strengths and weaknesses. Our first attempt at this feed back was rating sheets on which the audience would mark the performance of the presenter as "good" to "poor" for various aspects of the seminar presentation, such as clarity of ideas, organization, and the mechanics of the presenta tion (including quality of visual aids, nervous mannerisms, etc.). As a result of this rating sys tem, we noticed a significant improvement in the quality of the presentations, in both the content and the style of presentation. An integral part of the seminar program was a questionandanswer period that followed the formal talk. As with all novice speakers, the reaction to such interrogation The setting of the video seminar was a classroom equipped with cameras in discrete locations and with classroomtype tables having small monitors located on them. ( Copyright ChE Division, ASEE. 1984 Mark G. White received his BSChE degree from the University of Texas at Austin, his MSChE degree from Purdue University, and was graduated with a PhD degree from Rice University. For the last six years he has been teaching at the Georgia Institute of Technology. His industrial experience includes a position as a summer engineer with the Amoco Oil Company (Texas Division) and as a research engineer with the Amoco Oil Research in Whiting, Indiana. His re search interests include heterogeneous catalysis and reaction kinetics. ranged from fright to morbid fear. However, the more experienced students began to see the value of such questioning which forced the speaker to defend his research and resulted in a better under standing of the work. In time, a fraction of the students began to look forward to such question andanswer periods, except when they were the presenters. As a result of the success of the feed back rating procedure and through a desire to have further improvements in the seminar pre sentations, we chose the videobased format to affect such improvements. MECHANICS OF THE COURSE The videotaping of a formal presentation shows both similarities to and differences from the familiar seminar format. Among the similarities, the speaker must convey thoughts through words and illustrations which must be organized into a cohesive unit. In one sense, the videobased format demands better organization of the talk because of the time limit imposed by rental of the on campus taping studio. The setting of the video seminar was a classroom equipped with cameras CHEMICAL ENGINEERING EDUCATION Sin discrete locations and with classroomtype tables having small monitors located on them. An audience was present for all the tapings, and the lighting was only slightly brighter than normal room conditions. These "familiar" conditions help put the presenter at ease. However, the differences associated with video taping are significant. Usually there were one or two operators present in a control booth behind the classroom to focus the remotecontrolled cameras and to record the talk. The students be came aware of the importance of communication between the operators and themselves to ensure the proper camera position when illustrations were used in a presentation. In essence, the student became both the star and the director in taping the talk. Finally, fear of the unknown, coupled with the excitement created by the medium of television, made this experience something quite different. We tried to meet some of these differences with some preproduction planning and prepara tion. During the quarter immediately before the taping, the students were given an article entitled "The Video Performer," by Norm Herman (Edu cational and Industrial Television), which is aimed at helping the firsttime TV star to avoid some common mistakes. Additionally, the students were asked to submit titles and onepage abstracts of their talks before the quarter began, to facili tate early planning of the seminar content. Dave Edwards, Assistant Director of the Department of Continuing Education at Georgia Tech, suggest ed we have two class sessions of planning and preparation before the actual seminars were taped. The first session would involve Dave giving a short lecture on the dos and don't of video taped presentations, followed by a short presenta tion by this author demonstrating some of the ideas. The students seemed to appreciate my feeble attempt to make them feel at ease by blundering my way through the presentation. The second session was a threeminute taping of each student giving his seminar topic and abstract; this taping was followed by a review of all the presentations. This preliminary taping session was a good way of demonstrating how difficult it is to produce an errorfree talk with only one shooting. Additional preproduction preparation in volved a series of meetings between the student and this author to determine the scope of the 20 minute presentation, to write a sketchy outline (followed by a detailed outline), and finally to re view the illustrations for content and quality. We have found that these preproduction meetings are essential to producing a quality seminar for taping. Finally, each student met with the camera operators to review the illustrations on camera and to discuss the camera angles, etc. The studio was equipped with three cameras operated by remote control from the booth. Two of these cameras afforded shots of the commenta tor while the third, an overhead camera, was used exclusively for the illustrations. The side camera could be used to give angle shots of the speaker, whereas the main camera gave headon shots. When appropriate, the side camera was used to give better definition of three dimensional models. Titles and names could be superimposed under the speaker and splitscreens could be used for extend ed discussions of illustrations. Although not used in these seminars, splitscreens and chromekey facilities are available in our campus studio; needless to say, these exotic techniques require more preproduction planning and direction on the part of the student. Our experience shows that the most successful talks, in terms of clarity and An integral part of the seminar program was a questionandanswer period that followed the formal talk. freedom of errors, were those which used a mini mum of visuals and few exotic techniques; as the speakers mature, these other techniques will certainly enhance the professional nature of their talks. The review of these seminars commenced im mediately following the talk. The objective of this review was to show the student the success/failure of his attempt to communicate a technical subject in a formal setting. Success could be evaluated in terms of how clearly the student told his story. Did he connect the major points of the topic with good transition sentences? Was the logic sound? Did the illustrations convey the essence of the thought with a minimum of information? In short, did the student give a talk which was enjoyed by his peers? During the review process I would comment on the positive and negative aspects of only the more subtle points; there was no need to comment on the obvious blunders. Also, the students became aware of distractive mannerisms such as throatclearing, nervous handwaving, Continued on page 189. FALL 1984 AR AL A Fe iCH LINEAR ALGEBRA FOR CHEMICAL ENGINEERS KYRIACOS ZYGOURAKIS Rice University Houston, TX 77251 A FIRSTYEAR GRADUATE course (or sequence of courses) in applied mathematics has become an integral part of the curriculum in a large number of chemical engineering departments. Among the diverse subjects taught in these courses, linear algebra usually enjoys a prominent position. The reason for this popularity perhaps lies in the fact that linear algebra is as central a subject and as applicable as calculus. The pioneer ing work of Neal Amundson, and of his students and disciples as well as other prominent scholars, has established beyond any doubt that many sig nificant and complex chemical engineering prob lems may be solved by advanced linear algebra techniques [1]. Linear algebra can also serve as an ideal stepping stone for introducing the firstyear graduate student to the formal mathematical language of functional analysis. The basic con cepts of matrix algebra, already familiar to the student, can be formulated using the abstract framework of linear vector spaces. The same abstraction can also be used to unify apparently diverse problems in finite dimensional spaces under this common framework. Thus, the ground work is laid out for the introduction of functional analysis in infinite dimensional spaces, which is necessary for the study of differential and integral operator problems [2]. Our linear algebra course strives to combine both elements of mathematicsabstraction and application. Many of the fundamental theorems of linear algebra are rigorously derived in class. Student responses to the course evaluation questionnaire indicate that they particularly enjoy the computational part of the course since it points out some of the real problems to which linear algebra theory can be applied. c Copyright ChE Division, ASEE. 1984 TABLE 1 Course Materials COURSE TEXTBOOK Strang, G., Linear Algebra and Its Applications, 2nd Edition, Academic Press, (1980). ADDITIONAL COURSE REFERENCES 1. Amundson, N. R., Mathematical Methods in Chemical Engineering: Matrices and Their Application, Pren tice Hall, (1966). 2. Braun, M., Differential Equations and Their Applica tions, 2nd Edition, SpringerVerlag (1975). 3. Dahlquist, G., A. Bjorck and N. Anderson, Numerical Methods, Prentice Hall (1974). 4. Friedman, B., Principles and Techniques of Applied Mathematics, John Wiley (1956). 5. Hirsch, M. W. and S. Smale, Differential Equations, Dynamical Systems and Linear Algebra, Academic Press (1974). 6. Noble, B. and J. W. Daniel, Applied Linear Algebra, 2nd Edition, Prentice Hall (1977). 7. Steinberg, D. T., Computational Matrix Algebra, Mc GrawHill (1974). The theory, however, is motivated and reinforced by examples derived from a wide range of chemi cal engineering problems. Particular emphasis is placed upon the important aspects of computa tional linear algebra. In our opinion, it is impera tive to expose the students to some fundamental computational methods and to study their efficiency as well as their convergence problems. Student responses to the course evaluation questionnaire indicate that they particularly enjoy the compu tational part of the course since it points out some of the real problems to which linear algebra theory can be applied. COURSE ORGANIZATION Eleven weeks (out of a total of fifteen) of the fall semester course, "Applied Mathematics for Chemical Engineers I," are devoted to the study of linear algebra and its applications. The remaining time is devoted to a brief review of complex analysis and complex integration, which is the final preparation step for the second course in applied mathematics taught at Rice. This CHEMICAL ENGINEERING EDUCATION Kyriacos Zygourakis received his diploma in chemical engineering from the National Technical University of Greece in 1975 and his PhD from the University of Minnesota in 1980. He is presently an assistant professor in the Department of Chemical Engineering at Rice Uni versity. His main research interests are in the areas of reaction engineering, applied mathematics and numerical methods. second course covers the theory of differential and integral operators, again using the functional analysis approach. The course meets twice a week for two hours and runs largely as a lecture, although active student participation is encouraged by frequent questions from the instructor. The lectures are accompanied by tutoring sessions which are de signed to help the students with their computer projects as well as for the discussion of home work assignments in an informal way. The students are urged to keep a complete set of notes, which are regularly supplemented by handouts providing lengthy theorem proofs or summarizing the results established up to that point. The assigned textbook is Linear Algebra and its Applications (2nd Edition), by Gilbert Strang. Although it is an extremely wellwritten book, it is not followed closely (especially in the first part of the course). The students are strongly en couraged to consult additional references (see Table 1). Homework problems are assigned almost every week. In addition, the students are required to complete one or two computational projects. They also have to take a midsemester and a final exam, which consist of both open and closedbook parts. COURSE CONTENTS The linear algebra part of the course (see Table 2) consists of four parts: Vector spaces and linear transformations The solution of systems of linear equations TABLE 2 Topical Outline of the Linear Algebra Course 1. VECTOR SPACES AND LINEAR TRANSFORMATIONS Overview of the problem of solving systems of linear equations. Which applications give rise to such systems? Which are the theoretical porblems that must be answered? Vector spaces and subspaces. Linear dependence, basis and dimension. Linear transformations between finitedimension al spaces and their matrix representation. Rank and nullity of linear transformations. Elementary matrices and the computation of the rank of a matrix. The theory of simultaneous linear equations. Homogeneous and nonhomogeneous systems. The Fredholm alternative. 2. SOLUTION OF SYSTEMS OF LINEAR EQUATIONS A x = b Gaussian elimination. LUdecomposition, pivot ing, operation count. Error analysis. Illconditioned matrices. Band matrices and how they arise in practice. Finite differences solution of partial differ ential equations. Overview of iterative methods for solving linear equations. Comparison of the various numerical algorithms. 3. THE EIGENVALUE PROBLEM A x = Xx Determinants. Inner products, norms, orthogonality. Eigenvalues and eigenvectors of matrices. Diagonalization and similarity transformations. Systems of difference equations. Functions of matrices. Solution of systems of ordinary differential equations. Stability. Unitary transformations. Normal matrices. Spectral decomposition of operators. 4. QUADRATIC FORMS AND VARIATIONAL PRINCIPLES Positive definite quadratic forms. Minimization problems. Least squares. Rayleigh quotient. Maximum and minimax principles. Numerical computation of eigenvalues and eigenvectors. Overview of the finite elements method. FALL 1984 The students are thus presented with our objectives for the first part of the course. A brief review of the algebra of matrices follows, reminding the student of the familiar concepts of multiplying a matrix by a scalar to obtain another matrix and of summing two matrices to obtain a third one. Th Elgnvale prble The Eigenvalue problem Quadratic forms and variational principles The Linear Equation Problem A x = b The course starts with an introduction to the problem of solving systems of linear equations of the form A x = b. Several applications that give rise to such large systems are discussed and the three fundamental questions are introduced: Do these problems have a solution? If they do, is the solution unique? How can the solution be computed? The students are thus presented with our ob jectives for the first part of the course. A brief review of the algebra of matrices follows, remind ing the student of the familiar concepts of multi plying a matrix by a scalar to obtain another matrix and of summing two matrices to obtain a third one. It is also pointed out that these opera tions satisfy certain properties such as associativi ty, commutativity, distributivity, etc. This dis cussion serves as the motivation to introduce the notion of abstract linear vector spaces. Several examples of vector spaces are then presented, covering sets of functions, polynomials, solutions of differential or integral equations, etc. The students come to realize that seemingly different mathematical systems may be considered as vector spaces and that this abstract framework can unify these diverse phenomena into a single study. The basic concepts of linear combinations, basis sets, and dimension are then discussed. Thus, the abstract quantities called vectors can be repre sented now in terms of their coefficients of ex pansion with respect to a particular basis set. The first milestone is reached with the intro duction of linear transformations between finite dimensional spaces and their matrix representa tion. Most of the important theorems here are rigorously derived in class and the concepts of rank and nullity of transformations are formally introduced. Armed with the conclusion that all the results established for linear transformations can be used for matrices (and conversely), we can then establish the conditions for existence and uniqueness of solutions of the first fundamental problem of linear algebra A x = b. This is ac complished in one lecture using the previously derived theorems. Throughout this part of the course, emphasis is placed on the generality of this approach, and the students have the opportunity to see how the results apply to linear differential and integral operators, as well as to chemical engineering problems. Such examples include firstorder re action systems and the determination of the number of independent chemical reactions in a closed system using experimental measurements. The practical problem of efficiently computing the solution of systems of linear equations can now be considered. The Gauss elimination procedure and the LU decomposition are introduced, which lead naturally to the idea of the operation count as a measure of the computational effort required. An important application which gives rise to large systems of linear equations is then studied by introducing the finitedifference method for solv ing ordinary and partial differential equations subject to specified boundary conditions. The students learn how to take advantage of the matrix structure (band or positivedefinite matrices) in order to speed up the computational process and how to use the LUdecomposition for the efficient solution of iterative problems that arise in the solution of nonlinear differential equa tions. The problem of illconditioned matrices is outlined in sketchy form, along with a rudimentary introduction to error analysis. Iterative methods for the solution of linear systems of equations are also briefly covered. At this point a computer project is assigned. The students are asked to solve a twodimensional partial differential equation using finite differ ences. They must use different grid sizes and compare the numerical results to the true solutions in each case. The students must demonstrate that they can correctly formulate the system of linear equations. Following that, they use the library programs available at our computer center to obtain the results. The library programs LINPACK and ITPACK (for the direct and iterative solution of linear systems) have proven to be invaluable aids. CHEMICAL ENGINEERING EDUCATION Thus, the emphasis is shifted from the drudg ery of computer programming to the analysis of the results. The numerical simulations permit the students to evaluate the relative efficiency of numerical schemes (i.e. execution speeds, memory requirements) and to determine which ones must be used for the various structures and sizes of the resulting matrices. Thus, the theoretical results derived in class are reinforced and justified. The second part of the computer assignment exposes the students to the pitfalls which may be fall the unwary and uninstructed user of computer software packages. The students are asked to solve a system of equations for which the matrix of the coefficients of the unknowns is badly ill conditioned (the notorious Hilbert matrix has served as the perfect example in this respect). The students are asked to compute the known solution of a system of equations using single and double precision computer arithmetic. They are then asked to explain why the solution deteriorates as the order of the system increases by monitoring the magnitude of the pivoting elements, the con dition number of the matrix, and using the theory presented in class. The Eigenvalue Problem A x = Xx The second part of the course starts with a brief review of the theory of determinants. Their properties are presented along with the basic formulas for their computation. The operation count for solving systems of linear equations using Cramer's rate is derived and most of the students are surprised to find out that even the most power ful computer would need about 10145 years to solve a 100 x 100 system using this method. They are reminded, however, that determinants give a very useful invertibility test for square matrices, whose main application will be used later on in the course for the development of the theory of eigen values. The concepts of inner products of vectors and of the norm of a vector are then presented as abstract mappings of vectors into the field of real (or complex) numbers and are related to the familiar notions of angle between vectors and of magnitude respectively. A discussion of the solution of a simple 2 x 2 system of linear ordinary differential equations motivates the introduction of the eigenvalues of a matrix A. The main emphasis here is on the de velopment of the theoretical results needed for the solution of systems of difference and ordinary differential equations. The cases of operators with distinct and nondistinct eigenvalues are treated in detail, although the case of defective matrices and the Jordan canonical form are only briefly covered. Throughout this part of the course it is con tinuously emphasized that the eigenvalues are the most important feature of any dynamical system. The students have the opportunity to solve a large variety of chemical engineering problems. They study: The difference equations describing a cascade of CSTR'S. The differential equations describing isothermal and nonisothermal CSTR's and their stability. The problem of N firstorder chemical reactions taking place in a catalyst pellet. The difference equations resulting when a con tinuous system is subject to piecewise constant inputs, which provides them with an introduction to sampled data system theory. The problem of N firstorder reactions taking place in a batch reactor. This is a long assignment, which Throughout this part of the course it is continuously emphasized that the eigenvalues are the most important feature of any dynamical system. leads the students in a stepbystep fashion to derive the theoretical results necessary to determine all the rate constants, through a set of carefully designed experiments [3]. This problem encompasses almost everything the students have learned so far in the course. As such, it has come to be known as the "Everything you always wanted to know about first order reactions in batch (. . and more!)" assign ment. The final part of the course introduces the students to the concept of formulating the two main problems of linear algebra, namely A x = b and A x = Xx, as minimization problems. The emphasis now shifts to pointing out the ad vantages of this approach for numerical computa tions. The problem of minimization of a multi variable function serves as the starting point for an introduction of the concepts of quadratic forms and positive definite matrices. The least squares method is then developed formally, and its practi cal implications are considered. The course closes with the formulation of the eigenvalue problem as a minimization one. The Rayleigh and the mini max principles are presented, followed by a brief Continued on page 213. FALL 1984 ReAeatcWk oa CATALYSIS CALVIN H. BARTHOLOMEW AND WILLIAM C. HECKER Brigham Young University Provo, UT 84602 CATALYSIS IS A developing science which plays a critically important role in the gas, petroleum, chemical, and emerging energy industries. It com bines principles from the diverse disciplines of kinetics, chemistry, materials science, surface science, and chemical engineering. Catalysis re search at universities is typically pursued in de partments of chemical engineering and chemistry, although some of the most successful centers of catalysis research employ surface scientists, ma terial scientists, and physicists as well. Catalysis research at Brigham Young Uni versity (BYU) had its beginning about eleven years ago when Professor Bartholomew joined the chemical engineering faculty and has since evolved into an interdisciplinary program referred to as the BYU Catalysis Laboratory. The Catalysis Laboratory currently involves three faculty, two postdoctoral fellows, two visiting scholars, and fifteen students in basic investigations of hetero geneous catalysts. OBJECTIVES AND PHILOSOPHY The long term objectives of the laboratory are to: Pursue basic research in the following catalysis related areas: adsorption, supported metal catalysis, catalyst preparation, catalyst characterization, and catalyst deactivation. Obtain a basic understanding of catalyst functions in energy and air pollutionrelated processes such as methanation, FischerTropsch synthesis and nitric oxide reduction which can be used by industry Our guiding philosophies are that a basic understanding of these relationships will lead to the development of better catalyst technology and that university laboratories are best suited to carry out fundamental investigations ... Copyright ChE Division. ASEE, 1984 to develop new and better catalyst technology. Develop new and improve existing methods and tools for catalyst study, e.g. adsorption techniques, calori metry, infrared and Moessbauer spectroscopies. Train and educate 1015 students on a continuous basis in the science and art of catalysis research. The emphasis in our laboratory is on basic research relating the physical and chemical properties of catalysts to their activity and se lectivity properties. Our guiding philosophies are (i) that a basic understanding of these relation ships will lead to the development of better catalyst technology, and (ii) that university laboratories are best suited to carry out funda mental investigations of catalysts and catalytic reactions while industry is better equipped to undertake catalyst screening and development ac tivities. We subscribe to the "multitool approach"; namely, utilizing as many scientific techniques as can be usefully applied to the study of a particular catalyst or catalytic reaction. RECENT AND CURRENT RESEARCH ACTIVITIES Work over the past five years has focused on preparation, characterization, activity/selectivity, deactivation, and kinetic studies of cobalt, nickel, and iron catalysts in methanation and Fischer Tropsch synthesis. Publications of the Catalysis TABLE 1 Current Laboratory Research Projects 1. Investigation of Boron Promoted Cobalt and Iron Catalysts in FischerTropsch Synthesis: Sponsors, DOE Fossil Energy, Pittsburgh Energy Technology Center 2. Effects of Support on Adsorption, Activity/Selectivity and Electronic Properties of Cobalt: Sponsor, DOE Basic Energy Sciences, Division of Chemical Sciences 3. Investigation of CarbonylDerived FischerTropsch Catalysts: Sponsor, Atlantic Richfield Co. 4. Carbon Deposition on Fluidized Bed Methanation Catalysts: Sponsor, BCR 5. Mathematical Modeling of Methanation on Monolithic Nickel Catalysts: Sponsor, BYU 6. Infrared and Reaction Studies of Rhodium and Rhod iumMolybdenum Nitric Oxide Reduction Catalysts: Sponsor, BYU CHEMICAL ENGINEERING EDUCATION Calvin H. Bartholomew received his BS degree from Brigham Young University and his MS and PhD degrees in chemical engineering from Stanford University. He spent a year at Corning Glass Works as a Senior Chemical Engineer in Surface Chemistry Research and a summer at Union Oil as a visiting consultant. In 1973 he joined the chemical engineering department at Brigham Young University and was recently promoted to professor. He has authored over 60 scientific papers and 3 major reviews in the fields of heterogeneous catalysis and catalyst deactivation. Active in both teaching and research, he has also con sulted with 12 different companies and is currently President of the California Catalysis Society. His major research and teaching interests are heterogeneous catalysis (adsorption, kinetics, and catalyst character ization), Moessbauer spectroscopy, and air pollution chemistry. (L) William C. Hecker received his BS and MS degrees from Brigham Young University and his PhD degree from the University of California, Berkeley (1982). He has considerable industrial experience, having worked for Chevron Research, Occidental Research, Dow Chemical, Exxon, and Columbia Gas Systems. His research and teaching interests include heterogeneous catalysis, chemical kinetics, heat transfer, and infrared spectroscopy. (R) Laboratory since 1982 are listed in the References section to this paper. A complete list of publica tions and areas of current investigation may be had by contacting the authors. Recent investiga tions have considered metal boride catalyst prepa ration chemistry; adsorption of CO, H, and H2S on nickel, cobalt, and iron and of 02 on reduced and sulfided molybdenum catalysts; activities and selectivities of cobalt, iron and nickel in CO and CO, hydrogenation reactions; kinetics of CO and CO2 methanation on nickel; interactions of co balt, iron, and nickel with various supports; ac tivities of monolithic nickel catalysts; and de activation of nickel catalysts by sulfur poisoning, carbon deposition or sintering. Current research projects (Table 1) are directed toward the under standing of activity and selectivity properties of boronpromoted and carbonylderived cobalt and iron catalysts in FischerTropsch synthesis,; effects of support and dispersion on the adsorp tion, activity, and selectivity properties of cobalt; mathematical modeling of CO hydrogenation on cobalt, iron, and nickel catalysts; and infrared/ reaction studies of NO reduction on Rh and RhMo catalysts. From the above brief description it is ap parent that BYU's efforts in catalysis are diverse in terms of the reactions and catalyst types studied (i.e., methanation, FischerTropsch, NO reduction; metals, oxides, and sulfides). Never theless, the experimental approach in most of these studies has a common feature, namely an empha sis on the characterization of these systems using adsorption techniques and spectroscopy combined with laboratory reactor studies to determine spe cific activity/selectivity properties. The breadth of research interests in the Catalysis Laboratory is further illustrated by the previous work with nickel methanation catalysts which included studies of CO and H2 adsorption stoichiometry, activity/selectivity properties for CO2 and CO methanation, CO and CO, methanation kinetics, metalsupport interactions, TPD of H2 desorption for nickel on different supports, sulfur poisoning, carbon deposition, sintering of nickel on different supports and modeling of monolithic Ni reactors. The following brief description of four recent or ongoing studies illustrates the nature of cataly sis research at BYU. The first example concerns a study of Oa adsorption on unsupported MoS2, carried out by Bernardo Concha (M.S. candidate) under the direction of Professor Bartholomew. Oxygen adsorption uptakes and methanation ac tivities were determined for a series of MoS2 catalysts having a range of surface areas. The ex cellent linear correlation of the data (Fig. 1) indi 120 to 0 400 "C 6o 0 s o 0 40 0 0C 60 C 0 0 Z, * 20 o aoo'C 0 5 10 15 20 25 02 UPTAKE (pmnole/g) FIGURE 1. Oxygen uptake of MoS2 catalysts after re action for 1520 h versus steadystate methane pro duction (sulfiding temperatures are designated for each catalyst). (Paper Ref. 10) FALL 1984 to the number of oxygen adsorption sites. These results have important application in the develop ment of techniques for characterizing sulfide hydrotreating catalysts used to remove sulfur from sour petroleum and synthetic crude feed stocks. The second example is the result of a joint effort by Professors Bartholomew, Brewster, and Philip J. Smith in cooperation with PhD candi dates Edward Sughrue and Philip R. Smith to model both pellet and monolithic, fixed bed methanators. This stateoftheart model includes complete kinetic rate expressions for CO and CO2 methanation reactions, for the watergasshift re action, and for inhibition by steam. It also in corporates the appropriate reaction rate terms to account for pore diffusion, heat transfer, and external mass transfer. Using this model it is possible to predict reactor temperature profiles and conversiontemperature profiles in good agreement with experimental data for pellet or monolithic packed bed methanators (see Fig. 2). The third example, an ongoing study con ducted by Bruce Breneman (MS candidate) and HuoYen Hsieh (PhD candidate) under the di rection of Professor Hecker, involves the use of infrared spectroscopy to investigate NO reduction catalysts. (NO reduction is an important function of auto emissions catalysts.) A series of support ed rhodium catalysts have been prepared using various preparation techniques and various amounts of molybdenum in an effort to improve their activity and selectivity. Activity/selectivity measurements and two types of IR measurements are made on each catalyst. In the first type, the quantity and stoichiometry of various adsorbate molecules (e.g. CO) adsorbed on the catalyst sur face at room temperature are determined. This 500 550 600 650 Temperature (K) FIGURE 2. Comparison of experimental conversion temperature profile for 3% Ni/Al04/monolith with model calculations. (E. L. Sughrue, Ph.D. Dissertation, Brigham Young Univ., 1983) cates that hydrogenation activity is proportional information is used to determine useful correla tions with activity and selectivity. In the second type, IR spectra are obtained under reaction con ditions and reveal important information regard ing the state of the catalyst surface and the nature of the reaction intermediates. This information is important in determining reaction mechanisms. The fourth study, carried out by Robert Reuel (MS graduate) under the direction of Professor Bartholomew, involved the measurement of spe cific activities and product selectivities of cobalt on different supports. These catalysts were found to have a range of cobalt dispersions (fractions of cobalt atoms exposed to the surface) which varied over 2 orders of magnitude. While prepara tion, support, and cobalt loading influenced the activity and selectivity properties, these data were best correlated with dispersion (see Figs. 3 and 8 7 6 5 4 3 2 1 Ln (Nco) FIGURE 3. Percentage dispersion (percentage of atoms exposed to the surface) versus CO turnover frequency (rate of CO conversion per site per second) at 2250C for supported cobalt catalysts. (Paper Ref. 20) 4). These results indicate that the specific activity of cobalt and its selectivity to high molecular weight products both decrease with increasing dispersion. One important dimension of scientific work is the careful technical communication of the results. It is, in our opinion, the necessary finishing touch to any project. The laboratory has been reasonably productive in this regard. For example, during a twoyear period from 1981 to 1983, the personnel of the laboratory participated in 8 different pro jects, published 42 papers and reports, completed 7 theses and dissertations, and presented 26 papers and seminars. CHEMICAL ENGINEERING EDUCATION Lu W 0. 0 13 13 A 0 Z uJ co/s102 5 C0 c.o Average Carbon Number (wt. basis) FIGURE 4. Average carbon number of hydrocarbons pro duced at 2250C and 1 atmosphere for 3 and 10 wt.% supported cobalt catalysts as a function of dispersion. (Paper Ref. 20) EDUCATIONAL OPPORTUNITIES The most important objective of our research is to educate and train students in the science and art of catalysis research. Th sis accomplished at BYU in a number of ways: through participa tion in research projects and special courses, by participation in the biweekly catalysis seminars, and by attendance at regional and national meet ings. In addition to our basic graduate course on kinetics and catalysis (see Chem. Eng. Ed., Fall, 1981), advanced graduate courses are offered bi yearly on special topics related to catalysis, e.g., catalyst deactivation, industrial catalysis, and re actor design. The laboratory is host to roughly 1012 visitors each year of whom about 56 pre sent seminars. Graduate students are also pro vided with opportunities to attend and present papers at regional and national catalysis meetings. RESEARCH FACILITIES The Catalysis Laboratory is located in the Clyde Building, which houses the engineering disciplines. It presently includes 6 laboratories (3,000 ft2) and the basic equipment listed in Table 2 to carry out adsorption, reaction, infrared, and Moessbauer spectroscopy studies. Our facilities for studying adsorption processes (two vacuum systems, one flow system, a TGA system, and two TPD systems) are scarcely equalled even by in dustrial laboratories. The temperatureprogram meddesorption (TPD) systems have proven to be particularly valuable in determining the states and energetic of H2 and CO adsorptions on cobalt, iron, and nickel catalysts. The Moessbauer spectro meter has been extremely useful in determining phase composition and oxidation states of iron in FischerTropsch catalysts while our new FTIR infrared spectrometer is proving its worth in the study of NO adsorption and reactions on Rh catalysts. Having this variety of adsorption, re action and spectroscopic techniques at our dis posal makes it possible for us to pursue the multi tool approach. SOURCES OF RESEARCH SUPPORT The Catalysis Laboratory has weathered the recent turbulent times of increased competition and declining federal support through diversifica tiol of funding from both industry and govern ment agencies (see Table 2 and acknowledg ments). We presently receive about $200,000 $250,000 in yearly support from sources outside the university. A new fund raising effort, the Industrial Affiliates program, was initiated about two years ago. The objectives of this program are to establish closer ties with our industrial col TABLE 2 Facilities and Equipment of the BYU Catalysis Laboratory CATALYSIS LABORATORY Six laboratories3,000 ft2 with catalyst preparation areas and preparation equipment Three lab reactors including a Berty Autoclave reactor Two vacuum adsorption systems One flow adsorption system Five chromatographsincluding HP5830 and Sigma I systems TGS2 thermogravimetric balance Two TPD/TPR systems with mass spectrometer and TC detection Moessbauer spectrometer system Nicholet 5MX FTIR infrared spectrometer system Sage II, 68000 computer system; 2 Macintosh and one Lisa II5 computers Vacuum Atmospheres HE432 DriLab glove boxb UNIVERSITY Six large computers (several VAX 750 and 780 systems, IBM4341) Transmission electron microscopes (Botany): Phillips EM400 (with EDAX) and Hitachi HU11E. (Both microscopes have been used for catalyst work; TEM sample preparations have been developed.) Calorimeters (The Thermochemical Institute) GCMS (Chemistry) Xray fluorescence spectroscopy (Chemistry) aThree new laboratories added in 198283. bEquipment added in 1983. cEquipment added in 1984. FALL 1984 leagues and obtain fellowship support for gradu ate students through annual subscriptions of $5,000$15,000. Affiliates of our program receive advance copies of our publications and a special annual study on some aspect of catalysis. Thus far, three companies (Atlantic Richfield Co., Phillips Petroleum Co., and Union Oil Co. of California) have joined our program. SUMMARY Catalysis at BYU is a growing cooperative effort of faculty and students engaged in diverse areas of basic research in heterogeneous catalysis. While the Catalysis Lab is unusually productive in terms of publications, its most important pro ducts are students well trained in the multitool, multidisciplinary approach to catalysis research. Looking ahead, members of the laboratory are hoping to expand into other areas of catalysis re search including homogeneous catalysis and sur face science with the addition of a senior scientist in each of these areas. O ACKNOWLEDGMENTS The authors gratefully acknowledge financial support from the AMAX Foundation; DOE, Fossil Energy; DOE, Office of Basic Energy Sciences; NSF; Atlantic Richfield Co.; Phillips Petroleum Co.; Union Oil Foundation; and Brig ham Young University. REFERENCES: Laboratory Publications since 1982 A. Contributions to Books 1. C. H. Bartholomew and J. R. Katzer, "Sulfur Poison ing of Nickel in CO Hydrogenation," in Catalyst De activation ed. B. Delmon and G. F. Froment, Elsevier Sci. Pub. Co., Amsterdam, 1980. 2. C. H. Bartholomew, P. K. Agrawal, and J. R. Katzer, "Sulfur Poisoning of Metals," Advances in Catalysis, 31, 136 (1982). B. Journal Publications 1. C. H. Bartholomew, "Carbon Deposition in Steam Re forming and Methanation," Catalysis ReviewsSci. Eng., 24(1), 67 (1982). 2. C. H. Bartholomew and R. B. Pannell, "Sulfur Poison ing of H2 and CO Adsorption on Nickel," Appl. Catal., 2, 39 (1982). 3. E. L. Sughrue and C. H. Bartholomew, "Kinetics of CO Methanation on Nickel Monolithic Catalysts," Appl. Catal., 2, 239 (1982). 4. A. D. Moeller and C. H. Bartholomew, "Deactivation by Carbon of Nickel, NickelRuthenium, and Nickel Molybdenum Methanation Catalysts," I & EC Prod. Res. & Develop., 21, 390 (1982). 5. C. H. Bartholomew and A. H. Uken, "Metal Boride Catalysts in Methanation of Carbon Monoxide, III. Sulfur Resistance of Nickel Boride Catalysts Com pared to Nickel and Raney Nickel Catalysts," Appl. Catal., 4, 19 (1982). 6. G. D. Weatherbee and C. H. Bartholomew, "Hydro genation of CO2 on Group VIII Metals, II. Kinetics and Mechanism of CO2 Hydrogenation on Nickel," J. Catal., 77, 460 (1982). 7. C. H. Bartholomew, "Response to Comments on Nickel Support Interactions: Their Effects on Particle Morphology, Adsorption, and Activity Selectivity Properties," I & EC Prod. Res. Develop., 21(3), 523 (1982). 8. T. A. Bodrero, C. H. Bartholomew, and K. C. Pratt, "Characterization of Unsupported NiMo Hydrode sulphurization Catalysts by Oxygen Chemisorption," J. Catal., 78, 253 (1982). 9. C. H. Bartholomew, R. B. Pannell, and R. W. Fowler, "Sintering of AluminaSupported Nickel and Nickel Bimetallic Catalysts in H2/H20 Atmospheres," J. Catal., 79 34 (1983). 10. B. E. Concha and C. H. Bartholomew, "Correlation of O, Uptake with CO Hydrogenation Activity of Unsupported MoS2 Catalysts," J. Catal., 79, 327 (1983). 11. E. J. Erekson and C. H. Bartholomew, "Sulfur Poisoning of Nickel Methanation Catalysts, II. Effects of H,S Concentration, CO and H20 Partial Pressures and Temperature on Deactivation Rates," Appl. Catal., 5, 323 (1983). 12. C. H. Bartholomew and W. L. Sorensen, "Sintering Kinetics of Silica and AluminaSupported Nickel in Hydrogen Atmosphere," J. Catal., 81, 131 (1983). 13. J. M. Zowtiak, G. D. Weatherbee, and C. H. Bartholo mew, "Activated Adsorption of H2 on Cobalt and Effects of Support Thereon," J. Catal., 82, 230 (1983). 14. J. M. Zowtiak and C. H. Bartholomew, "The Kinetics of H, Adsorption on and Desorption from Cobalt and the Effects of Support Thereon," J. Catal., 83, 107 (1983). 15. C. K. Vance and C. H. Bartholomew, "Hydrogenation of Carbon Dioxide on Group VII Metals, III. Effects of Support on Activity/Selectivity and Adsorption Properties of Nickel," Appl. Catal., 7, 169 (1983). 16. R. M. Bowman and C. H. Bartholomew, "Deactiva tion by Carbon of Ru/A1203 During CO Hydro genation," Appl. Catal., 7, 179 (1983). 17. T. A. Bodrero and C. H. Bartholomew, "Oxygen Chemisorption on MoS2 and Commercial Hydrotreat ing Catalysts," J. Catal., 84, 145 (1983). 18. C. H. Bartholomew, "Finding Keys to Selectivity in FischerTropsch Synthesis," Industrial Chemical News, 4(10), 1 (1983). 19. R. C. Reuel and C. H. Bartholomew, "The Stoichio metries of H2 and CO Adsorptions on Cobalt: Effects of Support and Preparation," J. Catal., 85, 63 (1984). 20. R. C. Reuel and C. H. Bartholomew, "Effects of Sup port and Dispersion on the CO Hydrogenation Ac tivity/Selectivity Properties of Cobalt," J. Catal., 85, 78 (1984). 21. G. D. Weatherbee and C. H. Bartholomew, "Effects of Support on Hydrogen Adsorption/Desorption Kinetics of Nickel," J. Catal. 87(1), 55 (1984). CHEMICAL ENGINEERING EDUCATION REVIEW: Engineering Optimization Continued from page 159. to common sense to understand each of the op timization methods considered. Also, every method is followed with an example to illustrate it. This format is exactly right as the focus is on how to use the methods. As the jacket flyer states, ". . proofs and derivations are included only if they serve to explain key steps and properties of algorithms." The authors also offer their opinions as to the strengths and weaknesses of the various methods, and I found myself agreeing with them in virtually all cases. The book occasionally stops rather abruptly on a topic, perhaps most noticeably with the chapter on linear programming. The theory be hind sensitivity analysis for linear programming is not that difficult to present, yet the text simply presents some of the 'how to' aspects of this useful subject. Also it does not develop generalized duality theory, which can actually be done rather agreeably at a level consistent with the rest of the book. This theory is useful when attempting to understand a number of concepts, such as the saddlepoint conditions and dual bounding. The variety of methods covered in the first 11 chapters is impressive. The authors have ob viously scoured the engineering literature for the methods that have found their way into practical use for engineering problems. Included are direct and gradient based methods for unconstrained op timization problems; a simple presentation of the simplex algorithm for linear programming; the important theorems for constrained optimality; both ordinary and generalized penalty function methods; successive linearization methods; the very effective generalized reduced gradient me thod; gradient projection methods; and very im portantly the ideas behind successive quadratic programming methods, perhaps the best of the methods developed so far for nonlinear constrain ed optimization. The final chapter on methods, Chapter 11, covers briefly mixed integer linear pro gramming, quadratic programming and geometric programming. The last three chapters of the book, Chapters 12 to 14, are a chapter on studies which have been performed to compare many of the methods pre sented, a very readable and important chapter of the issues one must worry about when embarking on an optimization study, and finally a chapter de scribing three larger case studies, obviously one per author. The first of these chapters emphasizes what the authors feel must be included in a com, parison study for methods if the study is to be meaningful. The homework problems are plentiful and seem appropriate for the topics covered. Students using this book will be much better off if they have had a course on linear algebra. The material could be taught in one semester, if one is careful about not overdoing the detail on some of the methods. O PNEUMATIC AND HYDRAULIC CONVEYING OF SOLIDS by O. A. Williams Marcel Dekker, Inc., 1983, 319 pages. Reviewed by T. D. Wheelock Iowa State University This volume is the 13th in a special series of reference books and textbooks relating to the chemical industries. It treats pneumatic and hydraulic conveying as separate and independent subjects with seven chapters devoted to the former and ten chapters to the latter. An additional chapter is devoted to solid waste disposal areas, landfills, and sluice ponds. The volume is based largely on the author's considerable experience as a designer and user of conveying systems. In line with the author's statement that "the design of a pneumatic conveying system is almost as much of an art as it is in engineering function," the treat ment is largely descriptive and highly empirical. Various types of conveying systems and their operating characteristics are described. Also dis cussed are important features of system com ponents such as bins, feeders, exhausters, blowers, pumps, piping, gates, and control units. In ad dition two chapters are devoted to detailed design calculations for a number of different systems. Since the volume provides a broad and rather detailed introduction to the layout, design, and operation of pneumatic and hydraulic conveying systems, it will be of particular value to engineers responsible for the design and/or operation of such systems. It may also serve as a useful reference for collegelevel process design courses. In ad dition, because it illustrates the highly empirical nature of solids conveying technology, it may stimulate further research and development in this important field. D FALL 1984 R6eceacih o#4 BIOCHEMICAL CONVERSION OF BIOMASS ALVIN 0. CONVERSE and HANS E. GRETHLEIN Dartmouth College Hanover, NH 03755 T HE OBJECTIVE OF OUR WORK is to contribute to the development of new practical processes for the conversion of the cellulose found in biomass to fuels, chemicals, and foods. Industrial scale plants for the dilute acid catalyzed hydrolysis of the cellulose in wood are currently operated in USSR, and in the past both concentrated HC1 and dilute HSO, processes have been developed in Europe and the USA. However, these processes have not been commercially viable in competition with petrochemicals and soybean protein. ACID HYDROLYSIS Our work in this area began in 1967 when Andrew Porteous, then a student in the DE pro gram, recommended in the solution to his qualify ing examination (a design problem on which the "A A. O. Converse is Associate Dean and professor of engineering at the Thayer School of Engineering, Dartmouth College. He holds a BS degree in chemical engineering from Lehigh University and the MS and PhD degrees from the University of Delaware. Currently he is involved in research associated with the conversion of biomass to fuels and chemicals. (L) H. E. Grethlein is professor of engineering at the Thayer School of Engineering, Dartmouth College, where he specializes in biomass hydrolysis with acid or enzymes, water treatment with membranes and microorganisms, and process development in biotechnology. He has his BSChE degree from Drexel University and his PhD degree from Princeton University. (R) Obviously the costs and corrosion problems associated with higher temperatures limit the practical temperature, and mixing and heating requirements established a lower limit on the residence time. student has 30 days to work) that a continuous plug flow reactor be used to carry out dilute acid hydrolysis of the cellulosic material found in municipal wastes. Compared to the percolation re actor that had been developed for woody materials by the Forest Products Laboratory at Madison, Wisconsin [10], Porteous reasoned that the plug flow reactor would be able to handle materials, such as waste paper, that would not be porous enough for percolation, and furthermore the pro cess would be fully continuous [9]. The kinetics for Douglas fir [10] indicated that the yield of glucose would increase as the temperature is increased and the residence time is reduced. This is of par ticular importance because the yields obtainable in a percolation reactor are inherently greater than in a plug flow reactor. With support from EPA, Fagen [2], for his ME thesis, conducted batch hydrolysis experi ments and measured the kinetics constants for paper, the principal cellulosic component of municipal wastes. He found that they were similar to those for Douglas fir and hence a plug flow re actor should be operated at high temperature and a short residence time. Subsequent studies on many biomass substrates have shown this conclusion to hold true in general. Obviously the costs and corrosion problems as sociated with higher temperatures limit the practi cal temperature, and mixing and heating require ments established a lower limit on the residence time. Hence, we set out to develop a flow reactor to determine the yields that could in fact be ob tained. From a more scientific point of view, the flow reactor has another attraction: it allows one to study the kinetics of hydrolysis under more severe conditions than can accurately be studied Copyright ChE Division, ASEE, 1984 CHEMICAL ENGINEERING EDUCATION in a batch reactor because short residence times can be obtained without the heat up transients in volved in a batch reactor. Lay [6], Thompson [11], and McParland [8] (supported first by NSF and later by DOE), in their respective ME theses, developed the present flow reactor, shown in Fig. 1, and studied the kinetics of several substrates. Currently the acidi fied slurry is pumped into the reactor along with high pressure steam which condenses, mixes with, and heats the mixture to reaction temperature in, we estimate, about 0.7 sec. The minimum resi dence time used thus far is 7 sec. and the maxi mum temperature, 260 C. Under these conditions the glucose yield is 5560%. Current modifications should permit operation at 280 C where a 70% yield is expected. Several other approaches are being taken in an effort to increase the yield from acid hydroly sis. The glucose yields are reduced by the fact that glucose decomposes under the same conditions as it forms. Ward is currently studying whether the presence of acetone, through the formation of glu coseacetone complexes, can be used to reduce the glucose decomposition. Holland is currently de signing a reactor which is to have a shorter resi dence time for the liquid, and hence less glucose decomposition, than for the solids. Vick Roy [12] has recently explored the use of SO2 catalyzed hydrolysis under supercritical conditions. Because of the difficulty in pumping slurries containing a high concentration of wood, and the practice of injecting live steam into the flow re actor, the sugar concentrations in the reactor effluent are low. By using a nonaqueous immiscible carrier fluid in place of water, we have found it possible to increase the concentration of sugar in the aqueous phase. This also permits another means for separating the products. Woods have small amounts of rosins and oils, and they would be expected to concentrate in the nonaqueous phase. Of course, these advantages must justify the cost of any carrier fluid which is not recovered as well as additional processing steps. Further study is needed to allow such evaluation. ENZYMATIC HYDROLYSIS As an alternative to acid catalyzed hydrolysis, enzymes can be used to catalyze the reaction. In this case, the glucose yields, with proper pretreat ment of the substrate, are in the range of 95 100%, considerably higher than is obtained with acid hydrolysis. The reaction, however, is much slower; 2448 hrs. rather than 7 sec. Grethlein [3] compared these two methods, using data from Berkeley [13], and concluded that at that time acid hydrolysis appeared more attractive. This process evaluation is currently being updated through a set of process studies sponsored by DOE/SERI. In her DE thesis, Knappert [4] (with support from NSF and International Harvester Corp.), showed that by operating the flow reactor under somewhat milder conditions (1% HSO, 710 sec., 200 C) an effective pretreatment could be ob tained. Upon enzymatic hydrolysis of these pre treated solids, the glucose yield was >90% in 24 hrs. compared to 35% in 48 hrs. from unpretreated solids. Knappert showed that this pretreatment FIGURE 1. Flow reactor equipment. increases the fraction of pores that are larger than the enzyme molecule. Subsequent studies by Allen [1] and others have shown that the crystallinity of the cellulose remains unchanged and that the lignin is not removed. The pores are increased by the removal of a fraction of the hemicellulose, and contrary to the prevailing view, we now believe this to be the essential feature of an effective pre treatment. Grous is currently extending this study to include other methods of pretreatment. BYPRODUCTS Although glucose is the principal sugar (maxi mum yield = 42% of dry hardwood), a significant amount of xylose can be produced (maximum yield = 18% of dry hardwood). Whereas glucose is easily fermented to ethanol, xylose is not. Natural ly, efforts are underway at a number of labora tories to develop yeasts than can effectively carry out such a fermentation. However, xylose can be used to produce singlecell protein. Furthermore, its decomposition product, furfural, has a con FALL 1984 These theses include both process design and development, and basic research in applied science, in keeping with our two sets of graduate degrees... siderable value, albeit to a small market. In his PhD thesis, Kwarteng [5] (supported by Dow Chemical Co. and DOE/SERI), reformulated Root's kinetic model for the formation and de composition of furfural from xylose, and redeter mined the constants from experiments in the flow reactor. He also extended the model to include the formation of xylose from the xylan in the biomass. In contrast to xylose and glucose decomposition, furfural decomposition is second order. Hence, the furfural yield is increased by using a more dilute feed. This is countered by acid costs, product concentration, and heating costs, all of which favor a more concentrated feed. Process optimization studies are underway to evaluate the optimum feed concentration of biomass. Even at half the current market price furfural is two to three times more valuable than the sugars produced; hence its pro duction could have an important impact on the profitability of the overall process. Lignin is another byproduct that we plan to study in the future. Some of it is solubilized in the flow reactor, and the solubility of the residue in solvents is increased. Furthermore, the short residence time followed by flash quenching em ployed in the flow reactor is expected to give it unique properties. PRODUCT SEPARATION The overall process has three main parts: hydrolysis of the biomass to produce sugars and furfural, fermentation of the sugars to ethanol or possibly other chemicals, and separation of the ethanol to an anhydrous product if the ethanol is to be added to gasoline. Even though it requires a considerable amount of energy, distillation still appears to be the preferred means of separation. In his ME thesis, Lynd [7] proposed a new means of combining heat pumps with distillation that sig nificantly reduces the energy requirement, par ticularly for dilute feeds which are usually en countered when fermentation is used to generate the feed. The azeotrope formed between ethanol and water makes their separation more difficult, and even if a salt such as potassium acetate (KAc) is added to break the azeotrope, with normal distilla tion the reflux (and hence energy) must remain high if the feed is dilute, e.g. 110 wt. %. Lynd's innovation helps to overcome this requirement. Hence, the use of KAc looks much more attractive. Work is getting underway to test out the critical aspects of this process experimentally. FERMENTATION STUDIES Tricoderma reesei is a fungus which produces the extracellular enzymes used in our enzyme hydrolysis work described above. It must be grown on a cellulosic substrate in order to produce these cellulase enzymes, but unfortunately can not be present during the main hydrolysis step since it would consume the glucose product. Hence, the enzymes must be produced in a separate step. Since the pretreatment is effective in the hydrolysis step, we are now testing its effectiveness in the kinetics of the enzyme production step. Some thermophylic bacteria have the ability to ferment cellulose directly to ethanol. As the name implies, they live at relatively high tempera tures and hence the likelihood of contamination of this fermentation by other organisms is low. However, they also have some limitations: they ferment natural biomass, which contains lignin as well as cellulose, very slowly; they have a low tolerance compared to yeast for the ethanol that they produce and hence produce dilute beers, and they produce other products that compete for the substrate. We think that it may be possible to overcome these limitations through the use of mild acid hydrolysis in the flow reactor as a pre treatment, combined with simultaneous fermenta tion and product removal using Lynd's distillation scheme to remove the ethanol from the dilute beer as it is formed thus altering the product distribu tion in the favor of ethanol. Lynd will undertake a study of this in his DE thesis. In order to emphasize the role of the students in this work, the references cited are primarily student theses rather than papers in the litera ture. These theses include both process design and development, and basic research in applied science, in keeping with our two sets of graduate degrees ME and DE for those interested primarily in design and MS and PhD for those interested pri marily in research. The distinction is one of de gree since many theses involve both elements. The undergraduate programs of the students in volved in this work have included biology, chemis try, engineering science, and civil engineering as well as chemical engineering, in keeping with non CHEMICAL ENGINEERING EDUCATION departmental organization of the Thayer School. O REFERENCES 1. Allen, D. C., "Enzymatic Hydrolysis of Acid Pre treated Cellulosic Substrate: Substrate Hydrolysis, Process Development & Process Economics," ME thesis, Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, 1983. 2. Fagan, R. D., "The Acid Hydrolysis of Refuse," ME thesis, Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, 1969. 3. Grethlein, H. E., "Comparison of the Economics of Acid and Enzymatic Hydrolysis of Newsprint," Bio tech Bioeng, Vol. XX, 503, 1978. 4. Knappert, D. R., "Partial Acid Hydrolysis Pretreat ment for Enzymatic Hydrolysis of Cellulose: A Pro cess Development Study for Ethanol Production," DE thesis, Thayer School of Engineering, Dart mouth College, Hanover, NH 03755, 1981. 5. Kwarteng, I. K., "Kinetics of Dilute Acid Hydrolysis of Hardwood in Continuous Plug Flow Reactor," PhD thesis, Thayer School of Engineering Dartmouth College, Hanover, NH 03755, 1984. 6. Lay, J. R., "The Acid Hydrolysis of High Solid Content Cellulose Slurries," ME thesis, Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, 1978. 7. Lynd, L. R., "Energy Efficient Distillation with In novative Use of Heat Pumps," MS thesis, Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, 1984. 8. McParland, J. J., "The Acid Hydrolysis of Cellulosic Biomass: A Bench Scale System and Preliminary Plant Design," ME thesis, Thayer School of Engi neering, Dartmouth College, Hanover, NH 03755, 1980. 9. Porteous, A., "Improved Manufacture of Polyure thane Foam," DE thesis, Thayer School of Engineer ing, Dartmouth College, Hanover, NH 03755, 1967. 10. Saeman, J. F., "Kinetics of Wood Saccharification," Industrial and Engineering Chemistry, 37, 32, 1945. 11. Thompson, D. R., "The Acid Hydrolysis as a Means of Converting Municipal Refuse to Ethanol: Process Kinetics and Preliminary Plant Design," ME thesis, Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, 1978. 12. Vick Roy, J. R., "Biomass Hydrolysis with Sulfur Dioxide," ME thesis Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, 1984. 13. Wilke, C. R., R. D. Yang and U. Von Stockar, Bio tech. Bioeng. Symp., 6, 155, 1976. VIDEOBASED SEMINARS Continued from page 175. and use of noncommunicative words such as "uh", etc. Sometimes the review sessions were absolutely devastating for the presenter since these manner isms are greatly "amplified" by the video camera and, of course, preserved for posterity. However, I was pleasantly surprised by the lighthearted attitude with which all students received the re view process. There was much goodnatured kidding about the errors, and no one seemed to be embarrassed or hurt by the review. The two best presentations (i.e. free from errors) were edited, together with my brief com ments, into one tape which we shall use as a means of external communication to industry and to other academic institutions. For example, I plan to send this tape to some industry contacts to intro duce our research group and to precede my visit to a group I have yet to meet. Secondly, this tape may be used as a subtle recruiting aid at academic institutions which I may visit. Students seem to listen intently to their peers regarding graduate research experiences. REACTIONS TO THE VIDEO SEMINARS The student reactions to this new format were varied. Some met the videobased seminar course with enthusiasm, some with fear, and some with indifference. A few were cynical about the value of a seminar course which did not allow a tough questionandanswer session. Many felt that furth er refinement of their seminar mechanics was un necessary. The professors showed the opposite feelings, perhaps as a result of years of teaching and giving technical presentationsseminars. However, after the taping all were of the same accord. Moreover, the students became more aware of the original intent of this experiment: to pro vide a new format which would allow instant feed back on a seminar presentation. The videobased format best satisfies that need for instant feed back. CONCLUSIONS In conclusion, this brief experiment with videobased seminars was successful with regard to the original intent of improving visual com munication skills in a formal seminar setting. This format is suitable for use as an occasional tool, preferably with students who have had some ex perience in seminar presentation. We may not repeat this experience until at least six to eight quarters have elapsed. O ACKNOWLEDGMENTS We acknowledge the generous help offered by David Edwards and the crew in our Media Center and the monetary support offered by Rohm and Haas Company to cover the taping and studio costs. FALL 1984 4 PSEPAS Ria in R SEPARATIONS RESEARCH JAMES R. FAIR The University of Texas Austin, TX 78712 A LL CHEMICAL ENGINEERS understand the im portance of separation processes in the manu facture of chemical products. Raw materials must be purified, catalyst poisons eliminated, unreacted materials separated for recycle, and endproducts refined to meet specifications. Further, waste streams must undergo separations before they can be discharged into the environment. Separation processes pervade not only the classical chemical/ petroleum process industries but other ones as well, such as electronics, food and biological, metals, and so on. Investment in separation equip ment represents a large fraction of the industry total, and the processes consume very large amounts of energy. It is not surprising that there is much interest in developing improved methods for separating mixtures, not just for improved economics but also for simply enabling isolation of a material that is tightly bound in some parent mixture. It is surprising, however, that there is not more easilyidentifiable research of a generic type that can support the needs of an industry so dependent on separations. In fact, there is a great deal of research in pro gress that supports the development of improved industrial separation processes. In academia, such research covers areas of thermodynamics, trans port processes in various media, and reaction se lectivity. In industry, the research is often directed toward specific problems that occur in the develop ment of new processes or products. In many re spects, there has been too little collaboration be tween the academicians and the industrialists who The research areas targeted were: distillation, adsorption, liquidliquid extraction, supercritical fluid extraction, membrane processes for separating both gaseous and liquid mixtures, chromatographic separations, electrochemical separation methods, and separations employing chemical reactions. Copyright ChE Division, ASEE 1984 James R. Fair joined the chemical engineering faculty at The Uni versity of Texas in 1979, after many years with Monsanto Company. At Texas he holds the Ernest & Virginia Cockrell Chair and also is Head of the Separations Research Program. He has received numerous awards from the AIChE and was honored as an Eminent Chemical Engineer at the Diamond Jubilee meeting in November 1983. He is a Fellow of AIChE and a member of National Academy of Engineer ing. He holds BS, MS and PhD degrees from Georgia Institute of Technology and the Universities of Michigan and Texas, as well as an honorary ScD degree from Washington University. share common interests in separations ranging from the fundamental to the applied. This paper describes one attempt to foster greater industry university collaboration in the separations tech nology area, the attempt being identified as our Separations Research Program at The University of Texas at Austin. DEVELOPMENT OF THE PROGRAM A number of UT faculty had been conducting separationsrelated research for several years when in 1983 they were invited to participate in an industryfunded consortium sponsored by the Center for Energy Studies at UT. The center had a lineitem budget from the State of Texas and had as one of its purposes the development of new programs that could impact the efficiency of energy usage by industry. Since the chemical and petrole um industries represent two of the three largest energyconsuming segments of the total industry, and since within them separations are the largest energyusers, it was logical for the center to be interested in industrial separation processes. This CHEMICAL ENGINEERING EDUCATION led to a seed money grant that enabled the hiring of a fulltime program manager, Dr. J. L. Humph rey, to pursue the planning and organization of the consortium. At the same time, a large (145,000 square feet) new research facility was approved by the UT administration, and arrangements were made for the separations work to utilize a signifi cant amount of the space. The research areas targeted were: distillation, adsorption, liquidliquid extraction, supercritical fluid extraction, membrane processes for separat ing both gaseous and liquid mixtures, chromato graphic separations, electrochemical separation methods, and separations employing chemical re actions. All of these areas had some coverage by faculty in the chemical engineering and chemistry departments. The industries targeted were: chemi cal, petroleum refining, gas processing, biologi cal, pharmaceutical, food, and textile. Informal talks were held with UT faculty members, uni TABLE 1 ParticipantsSeparations Research Program* ABCOR, Inc./Koch Engineering Air Products and Chemicals, Inc. Albany International Corp. Aluminum Company of America Amoco Oil Company ARCO Petroleum Products Company The BOC Group, Inc. Celanese Chemical Company Combustion Engineering, Inc. Dow Chemical Company Dow Corning Corporation E. I. duPont de Nemours & Co. Ethyl Corporation Exxon Research & Engineering Co. Glitsch, Inc. B. F. Goodrich Company HoffmanLa Roche, Inc. M. W. Kellogg Company Koppers Company, Inc. Monsanto Company Neste Oy Norton Company Nutter Engineering/ChemPro Corporation Osmonics, Inc. Perry Gas Companies, Inc./Separex Corporation Phillips Petroleum Company Rohm & Haas Company Shell Development Company A. E. Staley Manufacturing Co. Standard Oil of Ohio Texaco, Inc. Union Carbide Corporation *As of June 1984 Since the chemical and petroleum industries represent two of the three largest energyconsuming segments of the total industry, and since within them separations are the largest energyusers, it was logical for the center to be interested in industrial separation processes. versity administration, and representatives of a number of companies. A charter was written, and the plan was further developed and published as an 89page prospectus. This document was mailed widely to industry, and during the developmental period twentytwo companies visited the UT campus to learn more about the proposed pro gram. In May 1983 an informational meeting was held, and 101 representatives from sixty com panies attended. A research participation agree ment was drawn up and mailed to companies with an invitation to join the program. Formal opera tion was to begin in January 1984. It should be mentioned that the cost of the prospectus, the in formational meeting, and the preparation of state oftheart reports on the several separations areas was underwritten by the Electric Power Research Institute through a grant. At this writing, thirtytwo companies have signed twoyear participation agreements. They are listed in Table 1. CURRENT RESEARCH AREAS The plan was for the research to be supervised largely by regular UT faculty members. Thus, it was necessary for the research area coverage to be compatible with the interests of these people. It was recognized that additional areas could be covered by faculty yet to be hired, or by fulltime research scientists and engineers, but these were deferred until a later time when resources and in dustry interests could justify the expansion. In the following sections brief sketches will describe the current work in progress. Membrane Separations. This work is divided into the separation of gaseous and liquid mix tures. For gases, direction is under D. R. Paul and W. J. Koros. Both of these people have had active programs in membrane separations for several years, Dr. Paul at UT and Dr. Koros at North Carolina State University. Arrangements were made for Koros to move to UT as a fulltime re searcher initially, followed by a faculty appoint ment. It is clear that the use of membranes for gas separation is an industrial reality, with the promise of a large expansion of the areas of FALL 1984 application. It is equally clear that many im portant questions regarding application cannot be answered with today's knowledge, and thus there is the opportunity for more rapid expansion of membrane technology through the support of generic research. The current program has thrusts in the following directions: pure gas sorption and transport, mixed gas sorption and transport, mem brane durability, separation of vapors, asymmetric SRP researcher William J. Koros measures the weight gained by a tiny membrane sample as it sorbs, or takes in, gas. A weight gain of 500 millionths of a gram indicates a highly sorbent material. membrane formation and characterization, and module simulation/performance. As might be ex pected, emphases such as the foregoing can shift as more knowledge is gained. The liquidmixture membrane program is under the direction of D. R. Lloyd, who began his research in this area at Virginia Polytechnic Institute and State University before moving to UT a few years ago. The program includes the synthesis of polymers, the preparation of sheet and hollowfiber membranes, transport studies, and the investigation of possible applications in the petrochemical, biochemical, pharmaceutical, biomedical, and genetic industries. The unifying theme of the research is the need to understand the physicochemical factors that govern the sepa ration process. Distillation. This old friend, and its associates absorption and stripping, is being studied under the direction of J. R. Fair. As is well known, it is the dominant separation method in the process industries and for many good reasons is likely to remain so. The work at UT is directed primarily to the mass transfer efficiency of common types of contacting devices for distillation columns. Of the several segments of distillation technology (phase equilibria, mass and energy balances, efficiency, and equipment design), understanding of the mass transfer process is in the lowest stage of development. Two particular devices are being studied: the crossflow sieve tray and highefficien cy packing. The sieve tray is widely used and is uniquely amenable to mechanistic modeling. The highefficiency packing types, only recently de veloped, are making possible large energy savings in vacuum fractionations. The ultimate goal of this work is to have the form of mechanistic models that enable the reliable prediction of per formance for both new and retrofitted distillation columns. Supercritical Fluid Extraction. This work is under the direction of K. P. Johnston. Supercriti cal fluid extraction (SFE) is a hybrid process that uses benefits from both distillation and liquid ex traction. The process has the additional advantage that slight changes in temperature and pressure near the critical point cause extremely large changes in the solvent density and thus its dis solving power. In comparison with conventional separation processes, SFE offers considerable flexibility for an extractive separation through the control of pressure, temperature, choice of solvent and cosolvent ("entrainer"). There are a few SFE processes that have reached commercial ization, but in general the method still awaits better understanding of phase behavior as well as the transport processes that take place in SFE equipment. The program at UT is directed toward the acquisition of fundamental thermodynamic data and the development of predictive models that can guide solvent selection and processing con ditions. Of particular interest is the use of co solvents which in small amount can greatly en hance the separation factors. LiquidLiquid Extraction. This work is under the direction of J. R. Fair and J. L. Humphrey. Liquidliquid extraction (LLE) is another old friend, though not nearly as old as distillation. It has gained increased attention recently as an alternative to distillation that for some cases can CHEMICAL ENGINEERING EDUCATION result in distinct energy savings. For temperature labile mixtures, LLE can also offer advantages if the labile species do not undergo high tempera ture conditions in the solvent stripper. As for distillation, little is known about the mass transfer processes that take place in LLE equipment, and this is partly due to the dominance of proprietary type extraction devices in commercial practice. Under study at UT are sieve tray extractors and highefficiency packed columns, both of which are nonproprietary and amenable to mechanistic modeling. It is expected that with the new under standing gained there will be resulting develop ments in more energyefficient extraction device design. In a related area, work is underway to deter mine the mass transfer characteristics of a con tinuousflow supercritical fluid extraction system using a counterflow solvent/feed arrangement. Adsorption. Drs. Fair and Humphrey are also directing work in this area. Interest in the area is high because of breakthroughs in the applica tion of pressureswing adsorption to separating gas mixtures such as air into their components without excessive thermal gradients. There are two areas of initial study at UT: mechanisms of thermal and pressure regeneration steps for con ventional fixed bed gas adsorbers, and break through relationships for liquidphase adsorption. There is future interest in the study of moving bed and fluid bed adsorption processes. Progress in adsorption technology has been largely through the development of improved adsorbents such as zeolite and carbon molecular sieves. The work at UT is centered on the kinetics of adsorption and desorption on and from these adsorbents as well as the more traditional adsorbents (where new process applications may be envisioned). ElectricBased Processes. This work comes under the direction of A. J. Bard of the UT chemis try department. Two areas are currently being studied: electrochemistry in critical aqueous solu tions and electrically controlled adsorption. Funda mental research on electrochemical processes in critical aqueous solutions has not been performed previously. Thermodynamic (PVT) and conduct ance studies have illustrated that the structure of water solutions changes dramatically near the critical point (375C and 220 atmospheres for pure water). Since the dielectric constant of water decreases to that of a "normal" fluid at high temperatures and pressures, critical and super critical water becomes a good solvent for nonionic At poster session representatives from companies listen to program manager J. L. Humphrey describe the sepa rations test facilities to be installed in the new research laboratories. organic species. However, a wide range of super critical temperatures and pressures is accessible for which water is still a good electrolytic solvent. The electrochemical study of these systems there fore provides a unique opportunity to examine se lectively soluble, electroactive species in situ. With respect to electrosorption, the extent of adsorption of substances at the solid/liquid inter face depends upon the potential difference across this interface. Thus, the adsorption of organic species on conductive carbon particles can be con trolled by the potential applied. This type of sepa ration has not been exploited, mainly because the fundamental data have not been obtained and be cause of construction problems associated with largescale adsorbers where a uniform applied po tential could be used. Separations with Chemical Reactions. This pro gram represents an expansion of work started several years ago at UT by G. T. Rochelle, the director of the present work. His quite compre hensive program has dealt largely with the re moval of sulfur dioxide from stack gases, common ly called flue gas desulfurization (FGD). The technology of FGD dominates commercial ap proaches to pollution abatement in fossilfired FALL 1984 Newer programs deal with the more general area of acid gas removal from gas mixtures and involves basic absorption/reaction modeling studies. power plants but is expensive, presents operating problems, and produces byproducts of limited in dustrial use. However, it is unlikely to be dis placed by other technologies and by its nature suggests that there are many possible improve ments. The program at UT has involved enhance ment of SO, absorption by buffer additives to the CaCOs slurry scrubbing medium, and has pro duced mechanistic models for the total diffusion/ reaction process. Studies have included the use of dry CaO and "dry" Ca(OH), scrubbing media. Simulation work is underway that encompasses the entire process, including regeneration and re cycle. Newer programs deal with the more general area of acid gas removal from gas mixtures and involves basic absorption/reaction modeling studies. Mass transfer in such separations is fre quently enhanced by fast chemical reactions and at the very least is accompanied by nonlinear equilibria associated with chemical reactions. Thus, technical quantification of such separations can require measurements of chemical kinetics, equilibria, and mass transfer at representative conditions. Chromatographic Separation Processes. The use of highpressure liquid chromatography (HPLC) or gelpermeation chromatography (GPC) for the separation of macromolecular solu tions is being studied under the direction of D. R. Lloyd. Aqueous and organic solutions containing synthetic polymers, natural polymers, proteins, pharmaceuticals, and the like are under investiga tion. The objective here is to study the design con siderations that are required to scale up from laboratory to pilot plant. It is clear that this work will have an important bearing on developing bio technologytype processes. OPERATION OF THE PROGRAM The Separations Research Program is ad ministered by a program head, J. R. Fair, and a program manager, J. L. Humphrey. One repre sentative from each participating company makes up the SRP Industrial Advisory Committee, which meets twice a year to review and advise the pro gram. Separate study groups meet twice yearly to review individual programs in detail; for example, in May 1984 there were separate study group meetings for membranes, distillation, ex traction (conventional and supercritical), and chemical reaction separations. The Industrial Ad visory Committee receives overviews of programs, whereas the study groups interact closely with faculty, graduate students and, very importantly, with themselves. An effort is made to obtain in puts from the companies that can influence the directions that some programs can take, even though the principal investigators (faculty/staff) retain final control over specific research studies. An example response from the companies to a questionnaire is shown in Table 2. A question often asked both by academicians and industry people, with regard to consortia of this type, is "What advantage does a participant have over a nonparticipant, since the research results will eventually be placed in the public domain through theses, dissertations and pub lished articles ?" The response to this question can be quite positive, and follows these lines: (1) the participant receives results early, in the way of progress reports, discussions with the researchers, theses and dissertations that can be delayed for publication; (2) the participant receives a royalty free license to practice any patents resulting from the program; (3) the participant has a mechanism TABLE 2 Research TopicsParticipating Company Interest (26 companies reporting) Degree of Interest Separation of gas mixtures by membranes Separation of liquid mixtures by membranes Supercritical fluid extraction Distillation/absorption /stripping Liquid/liquid extraction Adsorption Separation by chemical reaction Electrochemical separation methods High Mod. 19 6 Low 1 Weighted Rating* 44 17 8 1 42 16 8 2 40 14 7 5 35 10 12 4 32 11 9 6 31 9 7 10 25 7 7 12 21 *Weighted rating: high = 2, moderate = 1, low = 0 CHEMICAL ENGINEERING EDUCATION Panel discussion at Industrial Advisory Committee meet ing, with members, from left, James R. Fair, program head; Herbert H. Woodson, director, Center for Energy Studies; Jimmy L. Humphrey, program manager; Donald R. Paul, principal investigator and chairman, Depart ment of Chemical Engineering. for keeping up to date in separations areas where there is not justification for doing so inhouse for example, in an area of only peripheral interest presently but possibly more active in the future; (4) the participant benefits from interaction of its people with those in other organizations with kindred interests. In some ways, the lastnamed benefit can be the greatest of them all, if the par ticipant works it carefully. FUTURE DIRECTIONS We expect the separations field to continue in the forefront of chemical processing technology, along with the allied areas of reaction engineer ing and transport processes. Developing interest in specialty chemicals, such as those in the bio technology and electronics industry segments, carries with it the critical need for recovery and purification, often under nonclassical operating conditions. Tonnage chemicals will remain under continuous pressure to reduce costs and conserve energy, and this means retrofitting a like separa tion technique, substituting a new separation tech nique, or adopting novel combinations of separat ing methods. Much of the timehonored technolo gy, for example in distillation, is still not well understood and thus may be difficult to exploit economically. In summary, chemical engineers will continue to deal heavily with separation prob lems, and we expect to provide them with some answers. The future of the Separations Research Pro gram at The University of Texas also seems bright. Along with the new research laboratory space will come new equipment provided by the university, some of it of a fairly large scale. A number of companies have recently expressed interest in becoming participants. Plans are de veloping for the use of visiting scholars and full time research personnel. We have outside grants and contracts in the separations field that serve to leverage the funding provided by the industrial participants. Importantly, the entire program is being staffed with excellent graduate students, and the learning experience for them and the principal investigators is, indeed, the raison d'etre for the entire effort. D books received Gas Tables: International Version, Joseph H. Keenan, Jing Chao, Joseph Kaye. John Wiley & Sons, Somerset, NJ 08873; 211 pages, $37.95 (1983) )Vetering Pumps: Selection and Application, James P. Poynton. Marcel Dekker, Inc., New York 10016; 216 pages, $29.75 (1983) Chemical Grouting, Reuben H. Karol. Marcel Dekker, Inc., New York 10016; 344 pages, $45.00 (1983) Basic Chemical Thermodynamics, Third Edition, E. Brian Smith. Oxford University Press, New York 10016; 160 pages, $21.95 (1983) Los Alamos Explosives Performance Data, Charles L. Mader, James N. Johnson, Sharon L. Crane. University of California Press, Berkeley, CA; 811 pages, $45.00 (1983) Practical Quality Management in the Chemical Process Industry, Morton E. Bader. Marcel Dekker, Inc., New York 10016; 160 pages, $27.50 (1983) Fourth Symposium on Biotechnology in Energy Pro duction and Conservation, Charles D. Scott, Editor; John Wiley & Sons, Inc., Somerset, NJ 08873; 495 pages, $65.00 (1983) NMR and Chemistry: An Introduction to the Fourier TransformMultinuclear Era, Second Edition, J. W. Akitt. Chapman & Hall, 733 Third Avenue, New York, NY 10017; 263 pages, $16.95 (paperback) (1983) Waste Heat: Utilization and Management, S. Sengupta and S. S. Lee; Hemisphere Publishing Co., New York 10036; 1010 pages $125.00 (1983) Journal: Particulate Science and Technology, Vol. 1, No. 1, J. K. Beddow, Editor; Hemisphere Publishing Co., New York, NY 10036; $27.50/year indiv. rate. Prudent Practices for Disposal of Chemicals in Labora tories, Nat. Academy Press, 2101 Constitution Ave., Wash ington, DC 20418; 282 pages, $16.50 (1983) The Chemistry and Technology of Coal, James G. Speight, Marcel Dekker, New York 10016; 544 pages, $69.75 (1983) FALL 1984 4 Pfaym /e, GRADUATE RESIDENCY AT CLEMSON "A Real World MS Degree" DAN D. EDIE Clemson University Clemson, SC 29631 "I would like to get an MS degree but I first want to see what industry is like." W E HAD HEARD this statement (or some varia tion of it) over and over as we tried to con vince quality undergraduate students to seek ad vanced training after graduation. It was especially hard for me to counter this statement since I felt the same way when I completed my Bachelor of Science degree. Of course, most undergraduates cannot realize how truly difficult it is to leave in dustry and return to graduate school. Also, they do not fully appreciate the problems that the shortage of American graduate students is causing as universities and industry attempt to fill teaching and research positions. This desire for industrial experience and the decline in the number of American graduate students was extensively discussed in the fall 1980 meeting of the Clemson Department of Chemical Engineering faculty and the depart ment's Industrial Advisory Board. The discussions led to a new approach to graduate funding and training at Clemson called the Graduate Residency Program. This program seems to be that rare in stance where the student, industry, and the uni versity all benefit through cooperation in gradu ate education. The Graduate Residency Program offers an increased level of financial support for the student and, at the same time, provides the This is the third year of the Industrial Residency program. Thus far, eight students have completed their MS, four are presently in their final work period completing their MS thesis research, and three are just beginning the program. C Copyright ChE Division, ASEE. 1984  Dan Edie is professor of chemical engineering at Clemson Uni versity. He received his BS degree from Ohio University and his PhD degree from the University of Virginia. Before joining Clemson he was employed by NASA and the Celanese Corporation. At Clemson he has served as Graduate Program Coordinator and his research interests include rheology and polymer processing. student with an opportunity to gain significant industrial research experience. DESCRIPTION OF THE PROGRAM First, companies submit proposed research projects to the faculty, and these projects are re viewed for their suitability as thesis topics. The approved topics are then given to the Graduate Residency Program applicants who have pre viously applied to the graduate program and who typically have a 3.5/4.0 or better undergraduate grade point average. The applicants indicate their preference of both the thesis topic and company. Next, the applicants and company representatives are invited to the Clemson campus for one day of interviews during which the applicants can ask further questions about both the companies and the research topics. The companies can evaluate the applicants at the same time. Finally, the com panies indicate their preference, and applicants are informed of this selection. The applicant can either accept or reject the residency research position offered. CHEMICAL ENGINEERING EDUCATION A student graduating with a BS degree in chemical engineering in May would begin this master's degree program immediately. The Gradu ate Residency Program begins with an initial threemonth summer work period with the spon soring company. The student normally spends this first summer getting to know the company pro cedures as he or she begins to work on the research project proposed by the company and agreed upon by the student. The student meets biweekly with the faculty advisor and company advisor. At the end of this first summer the research project is FIGURE 1. Bill Thornton of Milliken and Company (L) and Kyle Veatch (R) discussing Graduate Residency projects. fairly well defined, and the student returns to the Clemson campus for two consecutive semesters. During these two semesters, the twentyfour se mester hours of formal lecture courses required for the MS degree are completed. Also during this period of fulltime study, the student is able to interact academically and socially with the full time graduate students in the university. Six hours of research credits taken during the work periods complete the 30 hours required for the degree. Upon completion of the formal course work, the student returns to the sponsoring company and resumes work on the project begun the previous summer. The project is supervised by an industrial and a faculty advisor through biweekly meetings with the student. At the completion of this seven month work period, a formal thesis based on the project is presented to an advisory committee composed of the faculty advisor (committee chair man), the industrial advisor, and two faculty members from the department of chemical engi neering. After committee approval of the thesis, the student receives the Master of Science degree in December, thus obtaining the degree nineteen months after completion of the BS degree. The sponsoring company provides financial support for the student by providing Clemson with a grant of approximately tenmonths salary for a BSlevel chemical engineer (the time period the student is actually working on the research project). The university then awards this support to the student in the form of a fellowship. Thus, the student receives a stipend of approxi mately $1000 per month throughout the nineteen month master's degree program. This is signifi cantly higher than typical financial support for graduate students and, coupled with the oppor tunity to obtain ten months of industrial ex perience, has allowed us to attract topnotch undergraduates to our graduate program. The program offers several advantages to the student, the company, and the faculty. Advantages to the Graduate Student The student can obtain a master's degree in nineteen months, with ten months spent working on a spe cific industrial problem while compensated by a fellowship of $1000 per month. Since the student begins work on the project during the summer prior to the start of formal course work, graduate courses may be selected and tailored to his FIGURE 2. Craig Leite, holder of a Graduate Residency Fellowship, preparing an emulsion in his research into emulsion stability. FALL 1984 FIGURE 3. Dr. John Beard (L) served as the faculty ad visor for Bill Rion (R) who just completed the residency program. The thesis topic involved an energy balance on a large polymer plant. or her research needs, which increases motivation in classwork. The student is exposed to an industrial environment, including specific industrial problems, prior to decid ing the direction of his or her career. The student has excellent daytoday supervision, ex perimental facilities, and analytical equipment avail able to him or her at the company location (which is normally an industrial, technical or research center). Advantages to the Sponsoring Company The participating company can evaluate the future potential of the graduate student on a firsthand basis. The research results have more than compensated for the support paid to the student. The company is able to draw on the expertise of top level BS chemical engineers as well as Clemson University faculty to solve problems of specific interest to the company. Advantages to the Faculty Faculty members are exposed to a wide variety of industrially oriented problems in a number of companies. This helps them stay current with in dustrial needs. This, in turn, increases their prob ability of developing more industriallyoriented on campus research projects. The department has obtained a significant new source of financial support for graduate education which can supplement industrial, state, and federal grants. The department of chemical engineering now has in dustrial research facilities and resources at its dis posal which it could not otherwise afford. The department of chemical engineering at Clemson has become a more vital and productive partner with the rapidly growing chemical and polymer industries in the state of South Carolina. Even publication of results has posed no great problem. Although a couple of MS theses have been held two years before being placed in the uni versity library, most thesis topics have been based on nonproprietary problems and the results have been freely published. PARTICIPANTS AND THESIS TOPICS Companies such as Tennessee Eastman, the Allied Corporation, DuPont, Exxon Enterprises, Celanese, and Milliken & Company are presently supporting Industrial Residency students. These students had obtained their BS degrees from several universities. Thesis topics have been excit ing and challenging to both students and faculty alike. They have covered topics such as Control of emulsion polymerization Effect of additives on theological characteristics of resin system Mathematical modeling of radial temperature effects during melt spinning Parametric studies of binary distillation columns Rheology of dye systems Solvent extraction using supercritical carbon dioxide This is the third year of the Industrial Resi dency program. Thus far, eight students have completed their MS, four are presently in their final work period completing their MS thesis re search, and three are just beginning the program. The program has had a significant impact on our MS program, not only by adding more topnotch students to our graduate program, but also by providing over $250,000 to support quality gradu ate students during these three years. The faculty and the sponsoring companies are enthusiastic about this unique blend of a fulltime Master of Science program and "real world" research. But the best measures of success is that the Industrial Residency students themselves are delighted with the program. O CHEMICAL ENGINEERING EDUCATION book reviews FLUID MECHANICS AND UNIT OPERATIONS By David S. Azbel and Nicholas P. Cheremisinoff: Butterworth Publishers, Woburn, MA (1983) $49.95 Reviewed by David B. Greenberg University of Cincinnati Fluid Mechanics and Unit Operations is de finitely not just another overworked theme on the topic of momentum transport. It is, rather, a serious attempt on the part of the authors to pres ent the subject uniquely in the language of the practitioner and in a fashion that bridges the ob vious gap between theory and practice or, more appropriately, between classroom and application. It is relatively detailed in the subject matter treat ed and massive in size (over 1100 pages). The book is, however, focused solely on those opera tions that are based primarily on momentum transport. These include single and multiphase fluid flow, fluid transport by pumps and compres sors, separation techniques such as filtration, fluidization, sedimentation and centrifugation, and the theory and application of mixing. Those operations which require detailed knowledge of the remaining transport science trilogy, namely heat and mass transport coupled with fluid dy namics are not covered in this work but, as the authors suggest, are best treated separately in additional volumes. One might assume, therefore, that the authors ambitiously intend to complete the trilogy at some point in the future. The text naturally partitions into several sections. The first of these includes the funda mental development of the subject of fluid dy namics and covers introductory and descriptive material on the thermodynamic and transport properties of fluids, similitude, modelling and di mensional analysis, hydrostatics and a section which the authors denote as internal problems of hydrodynamics. This latter portion is actually an elementary development of the associated con servation equations of fluid dynamics and their application to flow in pipes and conduits. The treatment here is far from complete but adequate for an introductory sophomore or junior course, or as a reference for the practicing engineer. The text is easy to read, the diagrams are clear, and the example problems are detailed in scope and effectively presented. It is clear that this section, which covers about onethird of the book, is roughly equivalent to many of the elementary texts available on the subject. In the second section of the book the authors apply the theoretical concepts developed earlier to fluid transport in pumps and compressors. Here, the reader is guided through a detailed de scription and classification of the various basic pump designs, their associated operational details, and where each of these designs is best used. There is also a section on selection and special applica tions as well as a set of practical problems at the end of each chapter. The practitioner should es pecially appreciate the fashion in which the ana lytical and descriptive material is synergistically presented. Moreover, the student, whose knowl edge of the subject is more application limited, will gain considerably, not only by the theory practice blend but also through the examples and problems which are well couched in an industrial atmosphere. The last two sections of the book deal with the application of fluid flow to external problems of hydrodynamics and heterogeneous systems. The authors introduce the topic of physical separations briefly and then develop the topics of sedementa tion, gravity settling, filtration, electrostatic pre cipitation, and centrifugal techniques from con sideration first of singleparticle motion in liquid solid and gassolid systems. Emphasis is placed on the requisite theoretical concepts which lead the student directly to the salient design considera tions of the topic. The theory is well supported by useful practical examples and problems which cover a range of contemporary unit operations. The chapter on fluidization which is especially descriptive will be quite useful to the engineer in industry who is concerned with the design of such equipment. Practical treatment of complicated phenomena in multiphase systems is presented in a clear, concise fashion with some needed detail devoted to the effects of such parameters as hold up, classification, bubble size effects and entrain ment upon the design of these systems. Moreover, the authors devote a final chapter to the hydro dynamics of gasliquid flow. Much of this ma terial is quite new and relevant, and is probably not available in earlier texts on fluid dynamics. Because twophase flow is still a most complex and Continued on page 212. FALL 1984 PSEMICONR in SEMICONDUCTOR PROCESSING CAROL M. McCONICA Colorado State University Fort Collins, CO 80523 CHEMICAL ENGINEERING includes the science of reactor design and optimization. As any pro duction environment becomes process limited, the role of chemical engineering increases in im portance. Semiconductor manufacturing is an ideal example of a maturing process ready for re actor optimization and design. As we break into the technology of Very Large Scale Integration (VLSI) and Ultra High Speed Integrated Circuits (UHSIC), yields in the fabrication facility be come very important. Highthroughput, highyield processes must be developed so that our industries will be viable in a marketplace filled with over whelming foreign competition. Such processes can only be developed after the fundamental physics and chemistry of the chemical reactions are well understood. At Colorado State University (CSU), the de partments of chemical engineering, electrical engineering, physics, and chemistry have respond ed to industry's need by creating a graduate pro gram in integrated circuit (IC) process engineer C. M. McConica received her PhD (1982) in chemical engineering from Stanford University. She spent three years with Hewlett Packard (19791982) developing stateoftheart deposition/etching processes for their 128Kb RAM and 640Kb ROM, all fabricated with 1 micron NMOS doublelayer metal technology. The chips utilizing this tech nology are now sold in the HP 9000. TABLE 1 National Average Monthly Salary Offers (BSChE)** Total Offers ELECTRONICS % of Offers Salary PETROLEUM % of Offers Salary CHEMICALS % of Offers Salary 1984* 1983 1982 1981 827 2023 6952 11695 11.5 15.8 4.4 2.9 $2173 $2109 $2112 $1915 13.0 16.6 36.7 41.5 $2358 $2329 $2329 $2068 47 34.5 $2304 $2260 39 36 $2241 $2016 *1984 data through June only **CPC Salary Survey, The College Placement Council ing. A student trained in most classical BSEE programs lacks the background in fluid mechanics, heat transfer, reaction kinetics and chemistry which is essential to integrated circuit manu facturing. While students with BSChE degrees have the best education for processing integrated circuits, they lack an understanding of circuit de sign, device physics, and EE language. The gradu ate programs in integrated circuit processing at CSU give students an opportunity to broaden their background while pursuing research on a state oftheart level. EMPLOYMENT OF CHEs BY ELECTRONICS INDUSTRIES The electronics industries have recently begun to recognize the value of hiring chemical engineers to fulfill their processing needs. Table 1 lists cur rent salary offers and the percentage of the total number of offers made by the electronics, petrol eum, and chemical industries to BSChE gradu ates. The statistics were compiled annually from the College Placement Council (CPC) Salary Survey between 1980 and 1984. The actual number of offers made by both the electronics and petroleum industries declined, but more so for Copyright ChE Division, ASEE. 1984 CHEMICAL ENGINEERING EDUCATION While students with BSChE degrees have the best education for processing integrated circuits, they lack an understanding of circuit design, device physics, and EE language. The graduate programs in integrated circuit processing at CSU give students an opportunity to broaden their background while pursuing research on a stateoftheart level. PERCENT PERCENT 100 90 s80 10  1980 1981 1982 1983 1984 YEAR FIGURE 1. Percent of BSChE offers from microelectronics industries in the USA. the latter. The table clearly shows the growing importance of the electronics industry for chemi cal engineers. In 1981, only 3% of all offers to BSChE graduates came from electronics, while 40% came from the petroleum industry. By 1983, however, 13% of all offers were coming from electronics firms and only 17% from petroleum industries. The chemical industries have con sistently made 30% to 50% of all job offers to graduating chemical engineers. Fig. 1 presents the hiring trend by the electronics industry in bar graph form. At CSU the hiring rate by electronics firms has increased much more rapidly than the national rate (Fig. 2). This is a reflection of the proximity of microelectronics companies to CSU. Many companies have western headquarters and locate their research and fabrication facilities in appeal ing locations. While there is little petroleum re fining or chemical production in Colorado, micro electronics is pervasive and growing. This is also true for Arizona, New Mexico, Idaho, Utah, Ore gon, Washington, Minnesota and, most obviously, California. Other states with active microelec tronics industries also have active petrochemical or traditional chemical industries. These industries are still hiring the majority of chemical engineers in those states. The salaries offered to BSChE graduates by electronics companies since 1981 are an average of $196/month less than offers given by petroleum companies, and $127/month less than those offered by chemical companies. This is simply the result of hiring into an EEdominated discipline where salaries have traditionally been lower. Many high tech companies believe that their remote locations, informal dress requirements, flexible work hours and stock optionprofit sharing plans compensate for this salary differential. Female engineers in microelectronics firms enjoy the support of a relatively young professional work force and a primarily female fabrication work force. The employment statistics listed are for BSChE graduates and clearly reflect the high de mand for chemical engineers in electronics. We believe this demand would extend to the MS and PhD level if graduate students could be given the opportunity to pursue research relevant to micro electronics. The following sections describe the coursework and the research topics and facilities currently available to graduate students interested in integrated circuit fabrication. INTEGRATED CIRCUIT PROCESSING PROGRAM The presumed prerequisites for MSChE candidates are given in Table 2. Students with out an engineering background may enter the pro gram and complete these undergraduate courses at CSU. The MS program for a student with a BS PERCENT 100 30 20 1980 1981 FIGURE 2. Percent of CSU chemical engineering gradu ates working in the field of microelectronics. FALL 1984 TABLE 2 Prerequisites for M.S. ChE Organic Chemistry Physical Chemistry Fluid Mechanics Unit Operations Thermodynamics Electrical Circuits Reactor Design Chemical Engineering Design in chemical engineering normally contains 26 hours of coursework. An additional 46 credits are earned for the thesis. Chemical engineers in the IC processing program are required to take four core chemical engineering courses, and then are allowed to choose the remainder of their credits from courses offered by EE and other depart ments. A typical twoyear MS course schedule is given in Table 3. The PhD program is an ex tension of the MS program, requiring more credits of coursework and successful defense of a dis sertation based on original research. Many of the electrical engineering courses emphasize material properties, fabrication technologies, and solid state physics. No special prerequisites are required of the BSChE student. Chemical engineers do quite well in these courses because of their solid back ground in thermodynamics and transport phe nomena. Students have the option to pursue courses which emphasize device design and de vice physics. These are not required of chemical engineers due to their more classical EE prerequi sites. INTEGRATED CIRCUIT PROCESSING RESEARCH At Colorado State University there is an active solid state research group in the departments of chemical engineering, electrical engineering, and physics. Work is sponsored by the Department of Defense, the Department of Energy, the National Science Foundation, and the Colorado Micro electronics Industry. The focal point of the re search work is a clean semiconductor fabrication laboratory. Current research activities include selective chemical vapor deposition of refractory metals (C. M. McConica), oxides and interfaces of silicon and compound semiconductors (C. W. Wilmsen), photovoltaic devices (J. Sites), transi tion metal silicides (J. E. Mahan), and polycrystal line silicon devices (J. E. Mahan). The major research facilities supporting the research are Solid state device fabrication facility (class 100 clean room, metallization, diffusion, oxidation, photo lithography, wet chemistry, plasma etching, ion beam sputtering). Electron microscopy (ISI SuperII, ISI 100B and Hitachi HHS2R scanning electron microscopes, Hitachi HU200F transmission electron micro scope). Xray diffraction (GE diffractometer, Laue camera). Transport properties measurements (galvanomag netic effects, thermoelectric power, temperature controlled cryostat). Surface analysis facility (Auger electron spectro scopy, ESCA, UPS, SIMS analysis). The current semiconductor research effort in chemical engineering emphasizes an understand ing of the kinetics of low pressure chemical vapor deposition. Metallic films are deposited on single wafers in a high vacuum system which can be used as a differential flow reactor. Classical methods of kinetics and catalysis are utilized to determine the kinetic parameters which govern TABLE 3 M.S. ChE Course Schedule FALL Mathematical Modeling Thermodynamics Semiconductor Devices I Seminar Thin Film Phenomena SPRING Advanced Reactor Design SolidGas Kinetics Seminar Principles of Semiconductors 3 credits 3 credits 3 credits 1 credit 3 credits 13 credits 3 credits 3 credits 1 credit 3 credits 10 Credits Remaining courses in second year (39 credits) to be chosen from: Introduction to Electron Microscopy Organometallic Chemistry Technique in Inorganic Chemistry Surface Chemistry Advanced Process Control Advanced Mass Transfer Semiconductor Devices II VLSI Plasma Processing Microelectronics Semiconductor Materials Optical Materials and Devices VLSI Processing Topics in Plasma Dynamics Solid State Physics I Solid State Physics II THESIS46 credits CHEMICAL ENGINEERING EDUCATION the deposition reactions. The deposited films are then analyzed for electrical and physical proper ties. Through cooperation with local industries the students fabricate devices using the latest thin film technology. Other students are using CSU's kinetic results to model the behavior of industrial reactors. Again, local industries cooperate by al lowing the comparison between our models' pre dictions and their deposition results. The Department of Chemistry actively partici pates along with the previously mentioned de partments in Colorado State University's Con densed Matter Sciences Laboratory. Current re search activities include the study of molecular condensed phases (E. R. Bernstein), electrode surface modification (C. M. Elliott), techniques of elemental analysis and the chemical characteriza tion of surfaces (D. E. Leydon), and NMR studies of solids (G. E. Maciel). CONCLUSIONS Chemical engineers are currently contributing to the electronics industry in growing numbers. Colorado State University has responded to in dustry demand for chemical engineers by offering a graduate program emphasizing integrated cir cuit processing. The program utilizes courses from several departments while allowing the student to apply chemical engineering techniques to an integrated circuit fabrication research topic. Graduates are receiving multiple offers from top quality semiconductor companies throughout the United States. O S book reviews COMPUTATIONAL METHODS FOR TURBU LENT, TRANSONIC, AND VISCOUS FLOWS Edited by J. A. Essers Hemisphere Publishing Corp., 1983; 360 pages, $49.95 Reviewed by G. K. Patterson University of Arizona This book consists of six contributions in the general field of numerical simulation of turbulent flows. Each article is a strong contribution on the topic covered. Those topics are: "Numerical Methods for Coordinate Generation Based on a Mapping Technique," by R. T. Davis; "Intro duction to Multigrid Methods for the Numerical Solution of Boundary Value Problems," by W. Hackbusch; "HigherLevel Simulations of Turbu lent Flows," by J. H. Ferziger; "Numerical Methods for Two and ThreeDimensional Re circulating Flows," by R. I. Issa; "The Computa tion of Transonic Potential Flow," by T. J. Baker; and "The Calculation of Steady Transonic Flow by Euler Equations with Relaxation Methods," by E. Dick. To the novice attempting to learn the basics of numerical turbulence simulation, the organiza tion of the book is not optimum. Although it is logical thematically to present grid generation, multigrid solution methods, and higherlevel simulation in the first half of the book to lay a theoretical basis for the more practical topics to follow, the novice would feel more comfortable reading first about general methods for Reynolds averaged modeling as presented for recirculating flows and transonic flows in the fourth through sixth chapters. The book offers much to those who already have some knowledge of numerical simulation of turbu lent flows. The treatment is not general and comprehensive for the entire turbulent and transonic flow modeling field. Each chapter pre sents a rather narrow topic from the author's par ticular viewpoint. Even though the collection represents the notes for a course presented at the von Karman Institute, no effort was made to link the presentations. Indeed, only one chapter was supplied with a nomenclature list, and each chapter has a different set of symbols. The book would be valuable to those with some familiarity with numerical simulation of flow but without expertise in numerical modeling of turbulent, transonic flow. They should probably read the chapters in the order: 4, 5, 6, 2, 1, 3. That order corresponds to problem complexity and so is easier for nonexperts. The book probably does not present much in each topic that an expert on that topic does not already know, so it should not be expected to provide much that is new if only that chapter is read. Its value is in its possible intro duction of experts in one field, say coordinate generation and mapping, to another field where that expertise can be used, say external, transonic, turbulent flows. Having known little about tran sonic flows but much about incompressible turbu lent flow modeling, I learned much from the last two chapters. O FALL 1984 hwad 2.ectue SIMULATION AND ESTIMATION BY ORTHOGONAL COLLOCATION The Chemical Engineer ing Division Lecturer for 1983 is Warren E. Stewart of the University of Wis consin. The 3M Company provides financial support for this annual lectureship award. A native of Wisconsin, Warren Stewart began his chemical engineering studies at the University of Wiscon sin, attaining the BS degree in 1945 (as a Navy V12 trainee) and the MS in 1947 after completion of his naval service. He received his ScD in 1951 from the Massachusetts Institute of Technology, where he worked with Harold Mickley on interactions of heat, mass, and momentum transfer in boundary layers. He joined Sinclair Research Inc. in 1950, and worked there for six years, participating in the development of a catalytic reforming process and in early work on com puterized process simulation. His continuing interests in chemical process modelling and numerical methods date from this industrial research experience. In 1956 he joined the chemical engineering faculty of the University of Wisconsin where he was department chairman from 1973 to 1978. He has held two visiting ap pointments at the Mathematics Research Center of the university, and is now a regular member of the center. In 1957, Professors R. Byron Bird, Warren E. Stewart, and Edwin N. Lightfoot began work on a textbook for a new course in chemical engineering. The resulting book, Transport Phenomena, published in 1960, has had a wide influence in engineering education. Professor Stewart is a Fellow of AIChE, and received their Alpha Chi Sigma Award for Chemical Engineering Research in 1981. He also received the Benjamin Smith Reynolds Teaching Award of the College of Engineering at the University of Wisconsin in 1981. He is an associate editor of the Journal of Computers and Chemical Engineer ing and an honorary advisor to the Latin American Journal of Chemical Engineering and Applied Chemistry. Stewart's research emphasizes new mathematical ap rpoaches to practical analysis of chemical process systems. He has worked extensively in the areas of fluid mechanics, transport properties, chemical reactor modelling, and weighted residual methods. WARREN E. STEWART University of WisconsinMadison Madison, WI 53706 T IS A PLEASURE to talk and write on a favorite theme to my fellow chemical engineers. My theme for today is orthogonal collocationits origins, its relation to other approximate methods, and some examples of its use in engineering. Orthogonal collocation is a technique for solv ing transport problems efficiently by fitting a trial solution at selected points. The points are chosen by use of orthogonal functions to minimize the approximation error over the given region. The speed of the method has proved valuable in modelling and controlling chemical reactors, and shows similar promise for staged separation systems. Two kinds of approximations are important in process modelling: approximations of the problem and of the solution. Examples of each kind are listed in Table 1. Orthogonal collocation belongs in the second category, among the weighted residual methods now to be described. PROBLEM STATEMENT Consider a generalized problem statement, typical in process modelling and in physical theory. A vector y of unknown functions of coordinates x is to be found by solving the equations Lvy = fv(x,y) in V (1) Lsy = fs(x,y) on S (2) in which Lv and Ls are the local parts of a linear operator L. Eq. (1) denotes the equations (differ ential or other) to be solved in the main region of the problem, and Eq. (2) denotes any needed initial and boundary conditions. The regions V and S may be continuous (as in distributed models of re actors) or physically lumped (as in stagewise models of plate columns). We assume that any desired approximations of the original problem have been done, so that Eqs. (1) and (2) are to be CHEMICAL ENGINEERING EDUCATION Copyright ChE Division, ASEE, 1984 solved as given. APPROXIMATION OF THE SOLUTION Weighted residual methods employ an approxi mating function for y in Eqs. (1) and (2). A popular form is n1 y = yo(x) + 1 ai (x) (3) i=0 with chosen functions yo(x), (o(x), ... ,n_ (x) and adjustable coefficients a, .. a.,. Often the ai are treated as functions of one of the coordinates, as in the method of Kantorovich [11] for reducing twodimensional problems to ordinary differential form. If each basis function q (x) is nonzero only within a corresponding subdomain, Eq. (3) is called a spline or finiteelement approximation. Approximation of y by y in the problem gives the residual functions Lvy fv(x,y) = ev in V (4) Lsyfs(x,y) = Es onS (5) which locally measure the errors incurred. For given choices of the functions yo and 0i, the residuals depend on x and on a, . an1. If a general solution of Eq. (1) or (2) is known, we can use it in (3) and thus eliminate ev or es. Elimination of E, is often possible, and yields an interior approximation (only Ev appears). Elimination of Ev may be possible when fv = 0; this yields a boundary approximation (only Es ap pears). Examples of the latter are the eigen function expansions used in problems of potential theory, heat conduction, and Newtonian creeping flow. If such general solutions are not available, or are not used in y, both ev and Es will appear; the TABLE 1 Kinds of Approximation Methods 1. Approximation of the problem A. Linearization B. Asymptotic methods and perturbations C. Physicochemical assumptions and simplifications 2. Approximation of the solution A. Weighted residual methods Least squares Orthogonality method Variational methods of Rayleigh and Ritz Galerkin method Collocation methods Finite element methods B. Finite difference methods The following poem was submitted by R. B. Bird to commemorate Warren Stewart's birthday on July 3, 1984, and was accompanied by the observation that "I don't quite understand how such a young chap got to be so old so fast, do you?" TO WARREN EARL STEWART on his 60th birthday A student came in to see Warren And said in voice quite forlorn "I can't find a path Through this quagmire of math These nablas to me are quite foreign." So Warren, who's also called Earl, Decided to help this young girl. Without using a book He unflinchingly took The Laplacian of grad div curl curl. r. b. bird result will then be a mixed approximation. A weighted residual method (projection method) is then used to determine the coefficients ao, . an1. Standard criteria [8, 11, 12, 16, 19, 24] include least squares S (E,) = 0 Dai i = 0 ,.... n1 the method of moments (here weight functions g, (x) must be chosen) (e,gi) = 0 i = 0,... n1 (7) the method of Galerkin [7] (which includes the variational methods of Raleigh [4] and Ritz [6] when the latter are applicable) (e, i) = 0 i = 0... n1 (8) and the method of collocation or selected points. e(xi= 0 i = 1,...n (9) The inner product (e,g,) denotes the sum or inte gral of the product Egi over all points of V and S. Egs. (6), (8) and (9) can be regarded as special forms of Eq. (7), with the weights gi chosen as aE/Zai, Oi(x), and 8(xxi+1), respectively. ORTHOGONAL COLLOCATION Eq. (9) is the most convenient criterion, but to make it reliable one needs a way of choosing good collocation points. A simple way is to approximate Eq. (5), (6) or (7) by use of an optimal npoint FALL 1984 quadrature of the inner product. This leads to Eq. (9) directly, with the xi now chosen as the quadra ture abscissae. The points thus found are always zeros of one or more orthogonal functions; this prompted the name orthogonall collocation" given to this method in [18]. This approach was initially proposed by the writer to Lou Snyder in 1964 during his research on flow in packed beds [17], and was implemented with John Villadsen [18] beginning in 1965. The theory of optimal quadratures, begun by Gauss [1], has yielded good points and weights for approximating many kinds of integrals in one dimension [14, 15] and in several [15, 23]. One can This leads to Eq. (9) directly, with the xi now chosen as the quadrature abscissae. The points thus found are always zeros of one or more orthogonal functions; this prompted the name orthogonall collocation"... use these points directly for collocation with cor responding regions and approximating functions. Quadratures over discrete point sets have ap parently not been studied, but good grid points can be found, as in [55] and [57], by use of classical polynomials orthogonal on such regions [5, 10]. A more analytical approach is to write inter polation functions Qnv(x,x1, . xn) and/or Qns(x,x, .. Xn) for the collocated residuals. Then the residual functions, or their effects, can be ap proximately minimized by doing the collocation at those points which minimize a suitable measure of Qnv and Qs. For example, replacement of E by Qn in Eq. (6), (7) or (8) yields a gridpoint criterion for a correspondingly weighted orthog onal collocation scheme. This method makes clear the restrictions implied by collocation at standard quadrature points, and also yields collocation points for other criteria or basis functions as de sired. Examples of this approach to collocation may be found in Lanczos [13], DeBoor and Swartz [27], Carey and Finlayson [34], and in several of our papers [18, 26, 37, 48, 50, 55, 56, 57]. Lanczos [13] chose Q,v in one dimension as the polynomial (xxi) ... (xx,) with least maximum magnitude on the interval [1, 1]. The resulting polynomial is Tn(x) = cos(n cos1 x), as found by Tschebychef [2]. This choice of grid points, xi = cos[i 1/2)rr/n], gives a minimal upper bound on the residual in collocation [13], just as in ordinary interpolation [9], provided that the residual and its first n derivatives are continuous. Different grid points should be used for collocation, as shown in [50], if one wishes to minimize the maximum deviation y yl. SYMMETRIC PROBLEMS IN ONE DIMENSION Consider a system of symmetric secondorder differential equations in one space dimension Lvy = f(x2,y) for 0 < x2 < 1 (10) The region considered is the interior of a slab, long cylinder, or sphere. The boundary conditions are y = y(l) at x2 = 1 and (for a cylinder or sphere) dy 0 at x = 0 dx (11) (12) The solution is symmetric [y = y(x2)], and is as sumed to be continuous. This kind of problem and extensions of it are important in fluid mechanics and reactor modeling. A polynomial approximant y(x2) consistent with Eqs. (11) and (12) is S+ 1 .n y = y(1) + (1x) I ax" (13) Thus the boundary residuals are zero, and the de termination of ao,... a,_ is an interior approxima tion problem. The interior residual Ev is computable, for any particular form of Eq. (10), by inserting y in place of y. The result will depend on x2 and on the un known coefficient vectors ai. Thus, it will be tedious to apply Eq. (6), (7) or (8) unless Eq. (10) is simple. Suppose we collocate y with Eq. (10) at some set of points, x,2 < x22 < ... Xn2. Then the residual vanishes at those points, and assuming continuity, it can be approximated throughout the interval by ev = (x2 x12) ... (x2 x2) [bo + blx2 + ...] (14) according to Weierstrass' theorem [14]. Here bo, b1, etc., are bounded constants. We can now choose x2, . xn2 by requiring that the leading term of Ev satisfy Eq. (7) for arbitrary bo. This gives the orthogonality conditions f gi(x) Q(x2) d(xa) =0 i = 1,...n (15) for the polynomial Q (x2) whose zeros are x,2, ... CHEMICAL ENGINEERING EDUCATION x,2. Here d(x") is a generalized volume element, with a = 1 for a slab, 2 for a long cylinder, or 3 for a sphere. Eq. (15) determines the grid points uniquely, provided, of course, that the functions g, (x2), . g(x2) are linearly independent on the interval of integration. To get a Galerkinlike collocation method from Eq. (15), as in [18], we choose g (x2) = (x2) (1 x2)X2 and obtain (1 (1 x2) x2 Qn(X2) d(xa) = 0 i=l n 1 f (Galerkin analog) (16) From this it follows that Q. is one of the Jacobi polynomials, derived in [3] and given in [15], [18] and [38]. For the slab geometry (a = 1), the points xi, .. .. x+, at which (1 x2) Qn(x2) vanishes are the abscissae of a (2n + 2)point symmetric Radau quadrature formula (or Lobatto formula). The interior points xl, . x are used as collocation points for Eq. (10), and the point xn+, = 1 is used for the outer boundary condition. To get a leastsquares collocation method for Eq. (10), we choose weights consistent with Eq. (6) and the leading term of Eq. (14). Noting that the collocation makes ao, ... a,_n implicit functions of x2, ... Xn2, we obtain the relations 1  f [(x2x2) .. (x2X.)]2d(xa) = 0 i = ,... n (17) which may be rearranged to give Sx2i Qn(x2) d(xa) = 0 i = 0,...n1 o (least squares analog) (18) and yield another kind of Jacobi polynomial. Ex plicit formulas for the Q. of Eq. (18) are given in [15] and [38]. For the slab geometry (a =1), Qn is a Legendre polynomial and the interior grid points x, ... Xn are the positive abscissae of a 2n point Gauss quadrature formula. The point Xn.+ = 1 must be added for collocation of the outer boundary condition. For numerical work it is convenient to rewrite Eq. (13) as a Lagrange interpolant y = S lj(x2)yj (19) j=l n+1 3 (x2) 0+ (X Xk2) k=j (Xj2 Xk) (20) k~j ... consider the steadystate performance of a tubular isothermal catalyticwall reactor of radius R and catalytic length L, fed with pure reactant A in developed laminar flow with centerline velocity Vmax. in which yj stands for y (xj). Derivatives and inte grals of y then follow readily; for example, dy dx xi xi S( dlj (x2) j=1 dx xi n+l 1 Aij j=l jn+1 I 2 V'2x2) Yi= ii>  i (21) n+1 Y BijYj j=l (22) f f(x2)xadx = n+1 n+1 I1 j f (x)x"dx f(xj2) = 1 j=1 f=1 0 Wifi (23) The final polynomial, 10.+(x2), in Eq. (19) is pro portional to Q,(x2). This gives a simplification of Eq. (23) when (18) is used, since Q.(x2) is then orthogonal to x0 and consequently W,,0 vanishes exactly. Eq. (23) is exact for f(u) of degree 2n (here u = x2) when Eq. (16) is used, and 2n 1 when Eq. (18) is used. The constants xi, Aij, Bi, and Wi are tabulated in [18] for the criterion in Eq. (16). Tables for both criteria, (16) and (18), are given by Finlayson [24]; subroutines are given by Villadsen and Michelsen [38]. EXAMPLE As a simple example, consider the steadystate performance of a tubular isothermal catalyticwall reactor of radius R and catalytic length L, fed with pure reactant A in developed laminar flow with centerline velocity vmax. The catalytic wall, which begins at z = 0, induces a firstorder hetero geneous reaction A > B with rate constant k," cm/s. The fluid is considered Newtonian with constant density p, viscosity t, and binary diffusivity DAB. Longitudinal diffusion is neglected. An expression for the flowmean fractional con version as a function of z is desired. The continuity equation for species A under these conditions can be written in dimensionless FALL 1984 form as (32) [12] 2DY aZ 1 D DY x (x x ax 'xax 0 x<1 (24) in which y = ACAF/C, x = r/R, and Z = zDAB/R2Vmax. The boundary conditions are y=l for 0 Yi = 1 at Z = 0 4y + 4y = Ky, for 0 < Z < ZL (33) 4y + 4y2 = 0 for Z > ZL (34) Insertion of Eqs. (33) and (34) into Eq. (31) gives DY =0 at x=0 for Z>0 Dx (26) ay Ky at x=1 for 0 Y =0 at x=l for Z>ZL (28) Dx Eq. (27) is a reactant mass balance on an element of catalytic surface. It contains two dimensionless parameters: K = kl"R/DAB and ZL = LDAB/ R vmax. Finally, let (1x2) [1 y(x,Z)] xdx (29) (1x2) xdx denote the flowmean reactant conversion at Z. For a quick, approximate answer we will use collocation with n = 1. For this twodimensional problem, we extend Eq. (19) as follows n+l , y = (x) yj (Z) (30) j=l thus immediately satisfying Eq. (26) and the symmetry of the problem. Since y is not known at x = 1, we will choose the points according to Eq. (18). The collocation constants then become, with a = 2 and n = 1: [xi] = [V\112 [Ai] = 2V2 2V2 [Bjl] = 8 [W,] = 1/2 8 8 L 0 Collocation of Eq. (24) at the interior locus x = x, gives the ordinary differential equation 1 dy = 8y' + 8y2 2 dZ (31) Collocation of Eqs. (25), (27) and (28) gives _ 16Ky, for 0 dy, =0 for Z > ZL dZ The solution for the gridpoint states is 4 = 4 exp yJ 4 + K for 0 < Z < ZL YL = 1 ( 16K Y1 exp 4+ Y2 L 4 (35) (36) 16KZ) 4 + K} (37) S)for Z> Z (38) and values at other radii can be interpolated with Eq. (30). The flow mean conversion, computed from Eqs. (23) and (29), is X= 1 yfor all Z> 0 (39) since the quadrature weight W2 is zero for the grid points used here. The inlet profile in Eq. (25) is approximated only roughly here since y(x,0) is a parabola satisfying Eq. (27). Eq. (32) causes the parabola to give the correct flowmean inlet composition. The inlet condition would be better approximated if a larger n were used; however, a much better fit could be obtained by use of a properly singular function y,, as in (56). This problem can also be worked via Eq. (13), with y(1,Z) and a,(Z) as the unknown coefficients. Several examples of this approach are given in [18] and [21]. We prefer the method based on ordinates yi, because it is less affected by round ing errors at large n [49] and also handles initial conditions more directly. The collocation method also gives quick solu tions with axial diffusion included, or with other forms of kinetics. Nonlinear kinetics will usually call for numerical treatment of Eq. (31) and of CHEMICAL ENGINEERING EDUCATION the wall boundary condition; several pocket com puters now have this capability. An interesting correspondence exists between traditional reactor models and collocation approxi mations to Eq. (24). Collocation with n = 1 yields Eq. (31), which has the same form as a plugflow reactor model. The collocation solution also gives expressions for the radial profile and wall transfer coefficient, which the plug flow model does not provide [22, 38]. Collocation solutions with n > 2 reveal dis persion effects [51, 52] through the presence of unequal velocities v. (xi) at the interior grid points. In developed laminar flow no artificial term is needed to describe the dispersion, and no feed back of material is predicted other than longi tudinal molecular diffusion. APPLICATIONS OF ORTHOGONAL COLLOCATION Orthogonal collocation has been used extensive ly in chemical reactor simulation and design. A survey of early work is given in [31]. Applications have ranged from onepoint radial collocation of catalyst particle models [20] and tubular reactor models [22] to detailed simulations of multidimen sional reactors [25, 26, 49]. Electrochemical re actors have also been treated [35], with major re ductions in computing time. Fig. 1 shows temperature profiles from a simu lated startup of an oxylene oxidation reactor [26, 49]. Orthogonal collocation was used, with piecewise polynomials in the axial direction and global polynomials in the radial coordinates of the particles and tube. Improvements in the algorithms since the original work [26] have reduced the computation time from 240 s to 40 s on a Univac 1100 for the first 600 s of reactor operation [49]. Various approximations for reactor engineer ing have been developed, and existing models test ed. Onepoint collocation of intraparticle transport problems [20] has given useful insight regarding particle shape effects, ignition and extinction phe nomena, as well as proper particle sizes for. measurements of intrinsic kinetics. Onepoint col location of the radial derivatives in twodimension al models of tubular reactors [22, 38] yields equa tions formally similar to the plugflow model, but provides also the radial profiles and wall transfer coefficients, as in the example of the preceding section. Multipoint simulations of catalyst par ticles [28] show that the ignition and extinction limits are somewhat sensitive to the particle shape, and are often well approximated by one 400 390 500 T 400 (C) 300 380 200 370 =r100s .5 I. I.5m z FIGURE 1. Bulk temperature profiles during startup of an oxylene oxidation reactor [26, 49]. The first 0.8 m of the bed is diluted to 50% catalyst; the re mainder is 100% catalyst. point collocation. Collocation analyses of packed bed reactors have been made by Young and Finlay son [30] to determine when axial dispersion may be neglected. Collocation studies of multiple re actions in porous particles [48] have shown sig nificant effects of catalyst pore size distribution. Collocation has also proved effective in solving multicomponent reactor problems with dispersion [52], and has made it clear that the dispersion co efficients are rather complicated functions of the chemical kinetics. Orthogonal collocation has proved useful in nonlinear estimation problems where extensive parameter spaces need to be explored. A useful shortcut, given in [36], is the direct computation of parametric sensitivities by a simple extension of the Newton solution algorithm. Bayesian esti mation algorithms are demonstrated in [36] and [46] for multiresponse reactor data. Computer aids to formulation and testing of reaction models are described in [41] and [45]. Pulseresponse experi ments and collocation analysis are used in [39] to determine the thermal conductivity and heat ca pacity of an extruded catalyst. Transport problems in various geometries have been analyzed. Paper [29] analyzes the sensitivity of ClusiusDickel column performance to imperfect centering of the heated rod or wire. Papers [32] and [33] deal with the Graetz problem for tubes and for packed beds, with longitudinal conduction in cluded; a fuller analysis for tubes is given in [38]. Paper [56] tests a model of viscoelastic fluids by comparing predicted and observed flow fields in a cavity with a rotating lid. Fast reactions and boundary layers give rise to steep solutions, which are hard to fit with global polynomials. Basis functions derived by lineariza tion have proved effective in several such cases FALL 1984 [37, 44, 48, 49] when used in orthogonal collocation schemes. For example, Table 2 shows multicom ponent profiles for catalytic reforming in a spheri cal particle, computed by orthogonal collocation with hyperbolic functions [48]. These functions are tailormade for the given problem, thus permitting good accuracy with a small set of collocation points. Piecewise polynomials (finite elements) are widely used in computing steep solutions. They are commonly fitted by orthogonal collocation on each element [27, 34, 40, 43, 51, 54]. Integral methods such as least squares, however, are applicable to polynomial elements of lower order, and have been used in [47] to derive a robust algorithm with moving finite elements. Finiteelement schemes are attractive for systems with localized action, whereas global schemes are still the most efficient for computing smooth solutions. Orthogonal collocation has been applied re cently to large plate columns [42, 53, 55, 57] to obtain reasonable simulations in shorter comput ing times. The states in each module of the column are interpolated by polynomials of low order n, and these are fitted by applying the column model at n collocation points. The preferred points [55, 57] are obtained by a leastsquares principle in which the sum of squares (Qn,Q,) over the stages is mini mized with respect to the gridpoint locations x1, ... x, (which can have noninteger values). The resulting orthogonal polynomial was dis covered by Tschebychef [5] in a different context, and rediscovered by Hahn [10], for whom it is " C3 t 2.0 hr S8.6 FEED 8.4 e.2 8. 0 li S 5 1t 15 2e 25 38 35 STAGE NUMBER FIGURE 2. Transient response of the liquid states in a binary 32stage still to a step change in boilup rate [55, 57]. Solid curves: interpolated full 32stage solu tion. Points and dashed curves: nodal states and inter polated profiles found by 8point orthogonal collocation. named. Fig. 2 shows the nice results achieved by this method when eight nodes are used to describe the transient response of a 32stage column to a step change in boilup rate. The collocation method closely approximates the full solution, and takes about 1/12 as long. This method should be useful in the design and control of distillation systems, and it has interesting possibilities for particulate modelling of reactors. There are many excellent applications in the literature. Only a sample is reported here. I ask TABLE 2 Profiles for Catalytic Reforming in a Spherical Particle of Radius R = 0.9 mm* Concentrations, mole cm3.106 nHeptane Isoheptanes Naphthenes Hydrogen Toluene Cracked Products 1.0000 15.84 0. 15.84 237.6 15.84 0. 769.24 0.9904 15.50 0.69 13.00 238.2 17.88 0.07 768.80 0.9488 14.13 2.79 5.70 239.6 23.17 0.38 767.64 0.8718 11.99 4.88 1.47 240.5 26.35 0.89 766.92 0.7578 9.62 6.52 0.44 240.7 27.34 1.52 766.70 0.6074 7.56 7.69 0.33 240.8 27.67 2.17 766.63 0.4250 6.10 8.40 0.32 240.8 27.88 2.73 766.59 0.2188 5.28 8.72 0.32 240.8 28.01 3.11 766.56 *Computed by orthogonal collocation with the grid points shown, and a bimodal pore size distribution [48]. CHEMICAL ENGINEERING EDUCATION Radial Position ri/R Temp. K the understanding of the reader for the sparse selection that has been made. CONCLUSION Orthogonal collocation is an approach designed to minimize problem size and computation time. It is adaptable to basis functions of global or piece wise form, and to various weighted residual cri teria; thus the user's insights can be built in. The gridpoint strategy can be summarized simply as follows: do to the interpolant Qn (x,x, . x,) as you would to the residual e, if you had unlimited time. OE ACKNOWLEDGMENT Thanks are due to the 3M Company for spon soring this lecture, and to my chemical engineer ing friends at Washington University, Virginia Tech, CarnegieMellon and Ohio State University for their hospitality. Above all, I thank my students and John Villadsen for their collaboration in this and other areas of research. LITERATURE CITED 1. Gauss, C. F., "Methodus Nova Integralium Valores per Approximationem Inveniendi," Comm. Soc. Reg. Sci. Gottingen, III, 165 (1816) ; Werke, 3, 163. 2. Tschebychef, P. L., "Sur les Questions de Minima, qui se Rattachant a la Representation Approximative des Fonctions," Mim. Acad. sc. Petersb., Ser. 6, Vol. 7, 199 (1859); Oeuvres, 1, 271. 3. Jacobi, C. G. J., "Untersuchungen fiber die Differ entialgleichung der hypergeometrischen Reihe," J. reine angew. Math., 56, 149 (1859); Werke, 6, 184. 4. Rayleigh, Lord J. W. S., "Some General Theorems Re lating to Vibrations," Proc. London Math. Soc., IV, 357 (1873). 5. Tschebychef, P. L., "Sur l'Interpolation des Valeurs Equidistantes," Zapiski Imperatorski Akademii Nauk, 25 (1875); Oeuvres, 2, 217. 6. Ritz, W., "tTber eine neue Methode zur LUsung ge wisser Variationsprobleme der mathematischen Physik," J. reine angew. Math., 135, 1 (1908). 7. Galerkin, B. G., "Rods and Plates. Series Occurring in Various Problems of Elastic Equilibrium of Rods and Plates," Vestnik Inzhenerov i Tekhnikov, 19, 897 (1915). Translation 6318924, Clearinghouse, Fed. Sci. Tech. Info., Springfield, VA. 8. Frazer, R. A., W. P. Jones and S. W. Skan, "Approxi mations to Functions and to the Solutions of Differen tion Equations," Gt. Brit. Air Ministry Aero. Res. Comm. Tech. Rept. 1, 517 (1937). 9. Lanczos, C., "Trigonometric Interpolation of Em pirical and Analytic Functions," J. Math. Phys., 17, 123 (1938). 10. Hahn, W., "tUber Orthogonalpolynome, die qDifferen zengleichungen genfigen," Math. Nachrichten, 2, 4 (1949). 11. Kantorovich, L. V., and V. I. Krylov, Approximate Methods in Higher Analysis, Gostekhizdat (1949). English translation, Interscience, New York (1958). 12. Crandall, S. H., Engineering Analysis, McGrawHill, New York (1956). 13. Lanczos, C., Applied Analysis, p. 504, PrenticeHall, Englewood Cliffs, NJ (1956). 14. Kopal, Z., Numerical Analysis, Second Edition. Chap man & Hall, London (1961). 15. Abramowitz, M., and I. Stegun, Handbook of Mathe matical Functions, National Bureau of Standards Applied Mathematics Series 55, Washington, DC (1964). 16. Finlayson, B. A., and L. E. Scriven, "The Method of Weighted ResidualsA Review," Appl. Mech. Rev., 19, 735 (1966). 17. Snyder, L. J., and W. E. Stewart, "Velocity and Pres sure Profiles for Newtonian Creeping Flow in Regu lar Packed Beds of Spheres," AIChE J., 12, 167, 620 (1966). 18. Villadsen, J. V., and W. E. Stewart, "Solution of Boundary Value Problems by Orthogonal Colloca tion," Chem. Eng. Sci., 22, 1483 (1967); 23, 1515 (1968). 19. Krasnosel'skii, M. A., G. M. Vainikko, P. P. Zabreiko, Ya.B. Rutitskii, and V.Ya. Stetsenko, Approximate Solution of Nonlinear Operator Equations, Russian Edition, Moscow (1969). English translation by D. Louvish, WoltersNoordhoff, Groningen, The Nether lands (1972). 20. Stewart, W. E., and J. V. Villadsen, "Graphical Calcu lation of Multiple Steady States and Effectiveness Factors for Porous Catalysts," AIChE J., 15, 28, 961 (1969). 21. Stewart, W. E., "Solution of Transport Problems by Collocation Methods," Chapter 4 in Lectures in Trans port Phenomena, by R. B. Bird, E. N. Lightfoot, T. W. Chapman and W. E. Stewart, AIChE Continuing Education Series No. 4 (1969). 22. Finlayson, B. A., "Packed Bed Reactor Analysis by Orthogonal Collocation," Chem. Eng. Sci., 26, 1081 (1971). 23. Stroud, A. H., Approximate Calculation of Multiple Integrals, PrenticeHall, Englewood Cliffs, NJ (1971). 24. Finlayson, B. A., The Method of Weighted Residuals and Variational Principles, Academic Press, New York (1972). 25. Kjaer, J., Computer Methods in Catalytic Reactor Calculations, Haldor Tops6e, Vedvaek, Denmark (1972). 26. Stewart, W. E., and J. P. Serensen, "Transient Re actor Analysis by Orthogonal Collocation," Fifth European Symposium on Chemical Reaction Engineer ing, pp. B875, C28, C29, Elsevier, Amsterdam (1972). 27. De Boor, C., and B. Swartz, "Collocation at Gaussian Points," SIAM J. Numer. Anal., 10, 582 (1973). 28. Sorensen, J. P., E. W. Guertin, and W. E. Stewart, "Computational Models for Cylindrical Catalyst Particles," AIChE J., 19, 969, 1286 (1973); 21, 206 FALL 1984 (1975). 29. Serensen, J. P., M. S. Willis, and W. E. Stewart, "Effects of Column Asymmetry on Thermal Diffusion Separations," J. Chem. Phys., 59, 2676 (1973). 30. Young, L. C., and B. A. Finlayson, "Axial Dispersion in Nonisothermal Packed Bed Chemical Reactors," Ind. Eng. Chem. Fund., 12, 412 (1973). 31. Finlayson, B. A., "Orthogonal Collocation in Chemi cal Reaction Engineering," Catal. Rev., 10, 69 (1974). 32. Sorensen, J. P., and W. E. Stewart, "Computation of Forced Convection in Slow Flow through Ducts and Packed BedsI. Extensions of the Graetz Problem," Chem. Eng. Sci., 29, 811 (1974). 33. Serenson, J. P., and W. E. Stewart, "Computation of Forced Convection in Slow Flow through Ducts and Packed BedsIII. Heat and Mass Transfer in a Cubic Array of Spheres," Chem. Eng. Sci., 29, 827 (1974). 34. Carey, C. F., and B. A. Finlayson, "Orthogonal Col location on Finite Elements," Chem. Eng. Sci., 30, 587 (1975). 35. Caban, R., and T. W. Chapman, "Rapid Computation of Current Distribution by Orthogonal Collocation," J. Electrochem. Soc., 123, 1036 (1976). 36. Stewart, W. E., and J. P. Serensen, "Sensitivity and Regression of Multicomponent Reactor Models," Fourth International Symposium on Chemical Re action Engineering, DECHEMA, Frankfurt, 112 (1976). 37. Guertin, E. W., J. P. Sorensen, and W. E. Stewart, "Exponential Collocation of Stiff Reactor Models," Comp. Chem. Engng., 1, 197 (1977). 38. Villadsen, J. V., and M. L. Michelsen, Solution of Diferential Equation Models by Polynomial Approxi mation, PrenticeHall, Englewood Cliffs, NJ (1978). 39. Stewart, W. E., J. P. Sorensen, and B. C. Teeter, "PulseResponse Measurement of Thermal Properties of Small Catalyst Pellets," Ind. Eng. Chem. Fundam., 17, 221 (1978); 18, 438 (1979). 40. Finlayson, B. A., Nonlinear Analysis in Chemical Engineering, McGrawHill, New York (1980). 41. Serensen, J. P., and W. E. Stewart, "Structural Analysis of Multicomponent Reactor Models: Part I. Systematic Editing of Kinetic and Thermodynamic Values," AIChE J., 26, 98 (1980). 42. Wong, K. T., and R. Luus, "Model Reduction of High Order Multistage Systems by the Method of Orthogonal Collocation," Can. J. Chem. Eng., 58, 382 (1980). 43. Ascher, U., J. Christiansen, and R. D. Russell, "Col location Software for Boundary Value ODEs," ACM Trans. on Math. Software, 7, 209 (1981). 44. Caban, R., and T. W. Chapman, "Solution of Bound aryLayer Transport Problems by Orthogonal Col location," Chem. Eng. Sci., 36, 849 (1981). 45. Stewart, W. E., and J. P. Serensen, "ComputerAided Modelling of Reaction Networks," in Foundations of ComputerAided Process Design, R. S. H. Mah and W. D. Seider, Eds., Engineering Foundation, New York, II, 335 (1981). 46. Stewart, W. E., and J. P. Serensen, "Bayesian Estimation of Common Parameters from Irregular MultiResponse Data," Technometrics, 23, 131 (1981); 24, 91 (1982). 47. Miller, K., and R. N. Miller, "Moving Finite Elements. I, II.," SIAM J. Numer. Anal., 18, 1019, 1033 (1981). 48. Serensen, J. P., and W. E. Stewart, "Collocation Analysis of Multicomponent Diffusion and Reaction in Porous Catalysts," Chem. Eng. Sci., 37, 1103 (1982). 49. Sorensen, J. P. Simulation, Regression, and Control of Chemical Reactors by Collocation Techniques. Dr. Techn. Thesis, Technical University of Denmark, Lyngby (1982). 50. Co, A., and W. E. Stewart, "Viscoelastic Flow from a Tube into a Radial Slit," AIChE J., 28, 644 (1982). 51. Wang, J. C., and W. E. Stewart, "New Descriptions of Dispersion in Flow through Tubes: Convolution and Collocation Methods," AIChE J., 29, 493 (1983). 52. Wang, J. C., and W. E. Stewart, Coupled Reactions and Dispersion in PulseFed Tubular Reactors, Paper 57e, AIChE National Meeting, Los Angeles (1982). 53. Cho, Y. S., and B. Joseph, "ReducedOrder Steady State and Dynamic Models for Separation Processes," AIChE J., 29, 261, 270 (1983). 54. Davis, M. E., Numerical Methods and Modelling for Chemical Engineers, Wiley, New York (1984). 55. Stewart, W. E., K. L. Levien, and M. Morari, "Col location Methods in Distillation," in Proceedings of the Second International Conference on Foundations of ComputerAided Process Design, A. W. Wester berg and H. H. Chien, Eds., CACHE Corporation, New York (1984), page 535. 56. Nirschl, J. P., and W. E. Stewart, "Computation of Viscoelastic Flow in a Cylindrical Tank with a Rotat ing Lid," J. NonNewtonian Fluid Mech. (in press). 57. Stewart, W. E., K. L. Levien, and M. Morari, "Simu lation of Fractionation by Orthogonal Collocation," Chem. Eng. Sci. (in press). REVIEW: Fluid Mechanics Continued from page 199. difficult phenomena to quantitate, this chapter pro vides a reasonable summary of the key features of this topic. Again the emphasis is primarily on the design aspects. It provides, in effect, a point ofdeparture for someone who wishes to gain an initial insight into the area. In summary, therefore, the authors have written a comprehensive text that covers those unit operations which have a unique basis in fluid, dynamics. The book is generally well written and liberally laced with pertinent detailed examples drawn from industrial situations. Although the material covered extends well beyond that normal ly found in a first course in fluid dynamics, it does include the requisite essence and could easily be used as a text in such a course. I suspect, however, that it will find much more use as a handy refer ence for the practicing engineer. I do hope that the authors complete the trilogy. O] CHEMICAL ENGINEERING EDUCATION TRANSPORT PHENOMENA Continued from page 173. this method. However, emphasis is placed on when such an approximation can be invoked by develop ing ideas on multiple time scale analysis. The method is illustrated by considering shrinking unreacted core model in gassolid reactions and evaporation of a drop in a stagnant fluid. Additional topics covered in the course are listed in Table 3. These include nonNewtonian fluid flow, turbulent flow, some cases of exact solution of NavierStokes equations, evaluations of Nussclt and Sherwood numbers in laminar and turbulent flow, and some cases of mass transfer where no analogs in heat transfer are available. Finally, some examples of macroscopic balances are also solved. SUMMARY The course is essentially a survey in transport processes. An attempt is made to give students a thorough understanding of the topics covered, so that they can formulate the necessary differential equations. They are given sufficient insight into some of the powerful tools available to analyze and solve these equations. It is emphasized that the answers obtained must be checked to see if the assumptions made in deriving them are ful filled. It is also stressed that in most cases, knowing the distribution of velocity, temperature, and con centration is not as important as knowing the fluxes at the interface. These in turn are then' related to friction factor, Nusselt, and Sherwood numbers respectively. The course as described here has been well received by the students. Good students tend to feel they are ready to tackle more difficult topics. Terminal master's students feel they have a solid foundation in transport phe nomena on which they can continue to build their practical experience. O REFERENCES 1. Bird, R. B., W. E. Stewart, E. N. Lightfoot, Transport Phenomena, 7th printing, Wiley, New York, 1960. 2. Bird, R. B., W. E. Stewart, E. N. Lightfoot, and T. W. Chapman, AIChE Continuing Education Series, No. 4, 1969. 3. "Selected Topics in Transport Phenomena," Chem. Eng. Symp. Ser., No. 58, 61, 1965. 4. Denn, M. M., Process Fluid Mechanics, PrenticeHall, Inc., Englewood Cliffs, N.J., 1980. 5. Schlichting, H., BoundaryLayer Theory, 7th Edition, McGrawHill, New York, N.Y., 1979. 6. Slattery, J. C., Momentum, Energy and Mass Transfer in Continue, Robert E. Kreiger Publishing Company, 2nd Edition, Huntington, N.Y., 1981. LINEAR ALGEBRA Continued from page 179. discussion of simple numerical methods for the computation of eigenvalues. In order to further establish the importance of the variational methods, the finite element method is briefly out lined at the end of the course, using tools that the students already possess. CONCLUDING REMARKS Our course attempts to introduce the students to the essentials of linear algebra and, at the same time, to convey the fact that these elegant results can be applied to a wide range of engineer ing problems. Significant emphasis is placed upon the development of basic and efficient compu tational methods. There is hardly any need to stress again the importance of exposing the chemi cal engineering graduate student to the basics of numerical analysis. Our experience indicates that the essentials of computational linear algebra can be successfully integrated into an applied mathe matics course. A large number of students go on to take a rigorous numerical analysis course given by the Mathematical Sciences Department at Rice, which covers methods for the solution of ordinary and partial differential equations. They have dis covered that their background in computational linear algebra was adequate. We plan to introduce still another computer project in future offerings of this course, in order to familiarize the students with some of the most useful methods for the numerical computation of eigenvalues and eigenvectors of large matrices. The emphasis will again be on the understanding of the physical problem and the resulting mathe matical one, and on the study of the relative ad vantages of the various algorithms. E ACKNOWLEDGMENT The author wishes to acknowledge the in fluence of his mentors, Rutherford Aris, Neal Amundson and D. Ramkrishna, who have shown him that applied mathematics can also be enjoy able and who have shaped his ideas about teach ing. REFERENCES 1. Amundson, N. R., Chem. Eng. Edn., 3, 174 (1969). 2. Ramkrishna, D., Chem. Eng. Edn., 13, 172 (1979). 3. Wei, T. and C. D. Prater, Adv. Catalysis, 13, 204 (1962). FALL 1984 APPLIED MATHEMATICS Continued from page 163. also enjoy seeing the connection between the non existence of a solution determined by the applica tion of a mathematical theorem to a physically generated problem to be equivalent to a violation of a basic conservation principle such as mass, energy, or momentum. This helps them develop a further appreciation for the practical importance and usefulness of mathematical theorems. When we present partial differential equations, we begin by emphasizing the characteristics of the "typical" problem which can readily be solved by pointing out the restrictions that must be placed on the shape of the domain, the boundary conditions, and the form of the operator. This brings together many of the concepts developed over the first two semesters. Then we proceed to analyze a number of specific problems which violate in one form or another these restrictions and show that the manipulations that must be performed to make these problems solvable, which might have ap peared as "tricks," can be rationalized and under stood based upon their indepth knowledge of the structure and properties of vector spaces. Thus, the students have developed a deeper appreciation for the key role played by mathematical theory in being a creative applied mathematician. The third semester covers the solution struc tures of nonlinear equations and the perturbation methods used to analyze them. Three different areas of perturbation analysis are studied: bound ary layer theory, bifurcation theory, and finite ele mentbased numerical methods. The semester starts with a general introduction to perturba tion techniques. Following a rigorous definition of order and asymptotic series, a variety of ex pansion techniques can be seen to be different formalisms for singular perturbation. The bulk of the course covers bifurcation theory: a set of perturbation techniques for de termining the multiple solutions to nonlinear algebraic, ordinary differential, and partial differ ential equations, their stability, and their de pendence on parameters. Theoretical concepts de veloped in the first two semesters, such as Fred holm's Alternative and the Implicit Mapping Theorem, are central to bifurcation analysis. Spe cific examples from fluid mechanics and reactor design show how the theory may be used to analyze transitions between the multiple steady states which frequently arise. The course concludes by covering computer implementation of perturbation techniques using the Finite Element Method. Computeraided analysis relies heavily on the same local ex pansions covered earlier in the course. Any ana lytical technique can be implemented on a com puter, but the ability to trade off more steps and unknowns for simpler calculations at each step en courages the use of lower order expansions and local basis functions rather than, for example, eigenfunction expansions. Using linear operator notation highlights the similarities between com puterbased techniques for analyzing the ordinary differential equations that arise upon discretizing partial differential equations and analytical per turbation techniques for studying the original partial differential equations. TEXTS Though it is difficult to find a text that presents the necessary concepts in the manner we have just described, it is important for the students to learn to read applied mathematics literature. Therefore, we do require a few texts and assign correspond ing sections from them. For the first semester course, we have used either Mathematical Founda tions in Engineering and Science by Michel and Herget or Linear Operator Theory in Engineering and Science by Naylor and Sell as the major text. We make up our own homework problems, how ever, which include extending theoretical concepts and proving theorems as well as solving problems arising from chemical engineering applications. For the section on matrices, readings from Mathe matical Methods in Chemical Engineering, Vol. I: Matrices and Their Application by Amundson and Linear Algebra and its Application by Strang are assigned. For the section on metric spaces, we find helpful supplemental reading in Green's Functions and Boundary Value Problems by Stakgold and Introductory Functional Analysis with Applica tions by Kreysig. In the second semester, the aforementioned book by Stakgold is the major text. Other references include Principles and Techniques of Applied Mathematics by Friedman, and the text by Naylor and Sell mentioned pre viously. For the third semester, the principal texts are Perturbation Methods in Applied Mathe matics by Cole and Elementary Stability and Bi furcation Theory by loos and Joseph. CONCLUSION We are convinced that our approach to teach ing applied mathematics for chemical engineer ing graduate students has been very successful. CHEMICAL ENGINEERING EDUCATION 214 Despite the rigorous and initially abstract per spective, student reaction has been overwhelming ly favorable. Probably the primary reason for this is that we try very hard to stress the "why" of applied mathematics, so that the "how" of solving problems is seen to follow logically and naturally from an understandable conceptual framework. The major criticism of our approach might be that fewer specific techniques can be included because of the time devoted to the underlying theory. How ever, we strongly believe that this is no real short coming because the students are now equipped to learn a wider assortment of new techniques on their own because they have the background necessary to comprehend the basis of unfamiliar methods. And this, after all, is the objective of graduate education. O GRADUATE PLANT DESIGN Continued from page 165. theory and its limitations and those of the numerical procedure utilized to reach a solution. The proliferation of engineering software houses is alarming. Are they becoming the de facto engi neering companies of the future? It appears that in the headlong rush to utilize the computer, the art of creating a reasonable and useful model of physical reality may be declining. The measure of the sophistication of a mathemati cal model is not what you include but, rather, what you leave out. However, the capability of computers to crunch complicated differential equations and systems of equations encourages overly complex models that can conceal the sig nificant variables and their relationship. Often, simple models and simple procedures are all that are required for the problem at hand. With the bewildering array of software being marketed and the significant use of computer design in industry, it is extremely important that the student appreciate the roles of the various levels of analysis in his work. Using a sledge hammer when a tack hammer would suffice is a cardinal sin which demonstrates a serious lack of judgment and/or knowledge. Students are en couraged to keep it as simple as possible, con sistent with the results desired. Concerning analysis itself, all too often the student is faced with papers and texts that pre sent skimpy discussions of the physical aspects of the model, and pages and pages devoted to solving the resulting equations. They are both important, especially when the model is not correct. A good example of a meager discussion about the physical basis of a model is the no slip boundary condition of fluid mechanics. Consult a modern text on fluid mechanics and it is probable that this boundary condition is stated with no dis cussion, as if it were a selfevident truth. Consider the student who has seen mercury flow in a glass thermometer; would he not question the validity of this statement? If Coulomb, Poisson, Navier, and Stokes and others of similar scientific stature debated this point during the 19th century [7], does it not deserve some textbook discussion so that the student can appreciate the turmoil that is often encountered in creating a good physical model? In addition to the current information ex plosion problem, misinformation is also trouble some. For example, in one year, in just one journal, at least three authors [8, 9, 10] discussed the mis application of Le Chatelier's Principle, while Pauling [5] describes some recent textbook errors he has detected. To help the students develop confidence in their understanding of the literature and their creative and analytical abilities, they are required to rigorously justify the rationales for their de signs, the bases for their design calculations, and the expected accuracies of their results. If our students achieve these three primary goals, then I have no doubt that they will be able to design the bioengineering and materials pro cesses of the future as well as the innovative petro chemical processes required to retain the vitality of the chemical process industries. O REFERENCES 1. Kelleher, E. G. and N. Kafes, Chem. Eng. Ed., Fall, 1972: 178180. 2. Kelleher, E. G., Chem. Eng. Prog. 68, No. 8: 3536. August, 1972. 3. Reid, W. C., Chemical Engineering, Dec. 14, 1970. 147 150. 4. Strutt, J. W. (Lord Rayleigh), Scientific Papers, Vol. 1, pp. 196198. Cambridge, University Press. 1899. 5. Pauling, L., Chemtech. 14, No. 6: 326327. June 1984. 6. Churchill, S. W., Chem. Eng. Prog. 66, No. 7: 8690. July 1970. 7. Goldstein, S. (ed.), Modern Developments in Fluid Dynamics, Vol. 2, pp. 676680. New York, Dover Publications. 1965. 8. Treptow, R. S., J. Chem. Ed. 57, No. 6: 417420. June 1979. 9. Mellon, E. K., J. Chem. Ed. 56, No. 6: 380381. June 1979. 10. Bodner, G. M., J. Chem. Ed. 57, No. 2: 117119. Febru ary 1980. FALL 1984 :m I I k 1  I1 :1 1L'i !%, Ir 5i 4. =! *"1 Chemical Engineering at UNIVERSITY OF ALBERTA EDMONTON, CANADA FACULTY AND RESEARCH INTERESTS I.G. DALLA LANA, Ph.D. (Minnesota): Kinetics, Heterogeneous Catalysis. D.G. FISHER Ph.D. (Michigan): Process Dynamics and Control, RealTime Computer Applications. M.R. GRAY Ph.D. (Cal. Tech.): Chemical Kinetics, Characterization of Complex Organic Mixtures, Bioengineering, Natural Gas Processing. D.T. LYNCH, Ph.D. (Alberta): Catalysis, Kinetic Modelling, Numerical Methods, ComputerAided Design. J. MARTINSANCHEZ, Ph.D. (Barcelona): Process Control, AdaptivePredictive Control, Systems Theory. J.H. MASLIYAH Ph.D. (British Columbia): Transport Phenomena, Numerical Analysis, ParticleFluid Dynamics. A.E. MATHER, Ph.D. (Michigan): Phase Equilibria, Fluid Properties at High Pressures, Thermodynamics. A.J. MORRIS, Ph.D. (NewcastleUponTyne): Process Control, Real Time Use of Microcomputers, Process Simulation. K. NANDAKUMAR, Ph.D. (Princeton): Transport Phenomena, Process Simulation, Computational Fluid Dynamics. W.K. NADER Dr. Phil. (Vienna) Heat Transfer, Transport Phenomena in Porous Media, Applied Mathematics. F.D. OTTO, (CHAIRMAN), Ph.D. (Michigan): Mass Transfer, GasLiquid Reactions, Separation Processes, Heavy Oil Upgrading. D. QUON Sc.D. (M.I.T.), PROFESSOR EMERITUS: Energy Modelling and Economics. D.B. ROBINSON, Ph.D. (Michigan), PROFESSOR EMERITUS: Thermal and Volumetric Properties of Fluids, Phase Equilibria, Thermodynamics. J.T. RYAN Ph.D. (Missouri): Energy Economics and Supply, Porous Media. S.L. SHAH Ph.D. (Alberta): Linear Systems Theory, Adaptive Control, Stability Theory, Stochastic Control. S.E. WANKE Ph.D. (CaliforniaDavis): Catalysis, Kinetics. R.K. WOOD Ph.D. (Northwestern): Process Dynamics and Identification, Control of Distillation Columns, ComputerAided Design. For further information contact: CHAIRMAN, Department of Chemical Engineering, University of Alberta, Edmonton, Canada T6G 2G6 THE UNIVERSITY OF ARIZONA TUCSON, AZ The Chemical Engineering Department at the University of Arizona is young and dynamic with a fully accredited undergraduate degree program and M.S. and Ph.D. graduate programs. Financial support is available through government grants and contracts, teaching, and research assistantships, traineeships and industrial grants. The faculty assures full opportunity to study in all major areas of chemical engineering. Graduate courses are offered in most of the research areas listed below. THE FACULTY AND THEIR RESEARCH INTERESTS ARE: HERIBERTO CABEZAS, Asst. Professor University of Florida, 1984 Liquid Solution Theory, Solution Thermodynamics Polyelectrolyte Solutions WILLIAM P. COSART, Assoc. Professor Ph.D., Oregon State University, 1973 Heat Transfer in Biological Systems, Blood Processing JOSEPH F. GROSS, Professor Ph.D., Purdue University, 1956 Boundary Layer Theory, Pharmacokinetics, Fluid Mechanics and Mass Transfer in The Microcirculation, Biorheology SIMON P. HANSON, Asst. Professor Sc.D., Massachusetts Inst. Technology, 1982 Coupled Transport Phenomena in Heterogeneous Systems, Com bustion and Fuel Technology, Pollutant Emissions, Separation Processes, Applied Mathematics GARY K. PATTERSON, Professor and Head Ph.D., University of MissouriRolla, 1966 Rheology, Turbulent Mixing, Turbulent Transport, Numerical Modelling of Transport DON H. WHITE, Professor THOMAS W. PETERSON, Assoc. Professor Ph.D., California Institute of Technology, 1977 Atmospheric Modeling of Aerosol Pollutants, LongRange Pollutant Transport, Particulate Growth Kinetics, Combustion Aerosols ALAN D. RANDOLPH, Professor Ph.D., Iowa State University, 1962 Simulation and Design of Crystallization Processes, Nucleation Phenomena, Particulate Processes, Explosives Initiation Mechanisms THOMAS R. REHM, Professor Ph.D., University of Washington, 1960 Mass Transfer, Process Instrumentation, Packed Column Distillation, Computer Aided Design FARHANG SHADMAN, Assoc. Professor Ph.D., University of CaliforniaBerkeley, 1972 Reaction Engineering, Kinetics, Catalysis, Coal Conversion JOST O. L. WENDT, Professor Ph.D., Johns Hopkins University, 1968 Combustion Generated Air Pollution, Nitrogen and Sulfur Oxide Abatement, Chemical Kinetics, Thermodynamics, Interfacial Phe nomena Ph.D., Iowa State University, 1949 Polymers Fundamentals and Processes, Solar Energy, Microbial and Enzymatic Processes Tucson has an excellent climate and many recreational opportunities. It is a growing, modern city of 450,000 that retains much of Ihe old Southwestern atmosphere. For further information. write to: Dr. Farhang Shadma.n Graduate Stady Con m ittee Department of Chem ical Engitine ring ULniversity, of A rizona. Tucson, A r:izona 85 ^21 The Uniers.i/ of Ar.zona .. an equal opporlunily educal.onal instftul;on'equal opporluntry employer ARIZONA STATE UNIVERSITY Graduate Programs for M.S. and Ph.D. Degrees in Chemical and Bio Engineering Research Specializations Include: ENERGY CONSERVATION ADSORPTION/SEPARATION * BIOMEDICAL ENGINEERING TRANSPORT PHENOMENA * SURFACE PHENOMENA REACTION ENGINEERING * CATALYSIS ENVIRONMENTAL CONTROL * ENGINEERING DESIGN PROCESS CONTROL * Our excellent facilities for research and teaching are complemented by a highlyrespected faculty: James R. Beckman, University of Arizona, 1976 Lynn Bellamy, Tulane University, 1966 Neil S. Berman, University of Texas, 1962 Llewellyn W. Bezanson, Clarkson College, 1983 Timothy S. Cale, University of Houston, 1980 William J. Crowe, University of Florida, 1969 (Adjunct) William J. Dorson, Jr., University of Cincinnati, 1967 R. Leighton Fisk, MD, University of Alberta, Canada, 1972 (Adjunct) K. Kumar Gidwani, New York University, 1978 (Adjunct) Eric J. Guilbeau, Louisiana Tech University, 1971 Robert Kabel, Pennsylvania State University, (Visiting) James T. Kuester, Texas A&M University, 1970 Gregory Raupp, University of Wisconsin, 1984 Castle O. Reiser, University of Wisconsin, 1945 (Emeritus) Vernon E. Sater, Illinois Institute of Technology, 1963 Robert S. Torrest, University of Minnesota, 1967 Bruce C. Towe, Pennsylvania State University, 1978 Imre Zwiebel, Yale University, 1961 Fellowships and teaching and research assistantships are available to qualified applicants. ASU is in Tempe, a city of 120,000, part of the greater Phoenix metropolitan area. More than 38,000 students are enrolled in ASU's ten colleges; 10,000 of whom are in graduate study. Arizona's yearround climate and scenic attractions add to ASU's own cultural and recreational facilities. FOR INFORMATION, CONTACT: Imre Zwiebel, Chairman, Department of Chemical and Bio Engineering Arizona State University, Tempe, AZ 85287 JW W IN=WSi Auburn University Auburn t r  Engineering W* L.A THE FACULTY RESEARCH AREAS R. P. CHAMBERS (University of California, 1965) Biomedical/Biochemical Engineering Process Simulation C. W. CURTIS (Florida State University, 1976) Biomass Conversion Reaction Engineering J. A. GUIN (University of Texas, 1970) Coal Conversion Reaction Kinetics L. J. HIRTH (University of Texas, 1958) Environmental Pollution Separations A. C. T. HSU (University of Pennsylvania, 1953) Heterogeneous Catalysis Surface Science Y. Y. LEE (Iowa State University, 1972) Oil Processing Transport Phenomena R. D. NEUMAN (Inst. Paper Chemistry, 1973) Process Design and Control Thermodynamics T. D. PLACEK (University of Kentucky, 1978) Interfacial Phenomena Pulp and Paper Engineering C. W. ROOS (Washington University, 1951) A. R. TARRER (Purdue University, 1973) THE PROGRAM B. J. TATARCHUK (University of Wisconsin, 1981) D. L. VIVES (Columbia University, 1949) The Department is one of the fastest growing in the Southeast and D. C. WILLIAMS (Princeton University, 1980) offers degrees at the M.S. and Ph.D. levels. Research emphasizes both experimental and theoretical work in areas of national FOR INFORMATION AND APPLICATION, WRITE interest, with modern research equipment available for most all Dr. R. P. Chambers Head types of studies. Generous financial assistance is available to Chemical Engineering qualified students. Auburn University, AL 36849 Auburn University is an Equal Opportunity Educational Institution CHEMICAL ENGINEERING EDUCATION  I~ I GrAD A.E ISTUDIES [C] ,MICA, ENG:ll INEEING ; , BRIGHAM YOUNG UNIVERSITY PROVO,UTAH Ph.D., M.S., & M.E. Degrees ChE. Masters for Chemists Program Research Programs Biomedical Engineering Catalysis Coal Gasification * Faculty Combustion Electrochemical Engineering Fluid Mechanics Fossil Fuels Recovery Thermochemistry & Calorimetry D. H. Barker, (Ph.D., Utah, 1951) C. H. Bartholomew, (Ph.D., Stanford, 1972) M. W. Beckstead, (Ph.D., Utah, 1965) D. N. Bennion, (Ph.D., Berkeley, 1964) B. S. Brewster, (Ph.D., Utah, 1979) J. J. Christensen, (Ph.D., Carnegie Inst. Tech, 1958) R. W. Hanks, (Ph.D., Utah, 1961) W. C. Hecker, (Ph.D., U.C. Berkeley, 1982) P. O. Hedman, (Ph.D., BYU, 1973) J. L. Oscarson, (M.S., Michigan, 1972) R. L. Rowley, (Ph.D., Michigan State, 1978) P. J. Smith, (Ph.D., BYU, 1979) L. D. Smoot, (Ph.D., Washington, 1960) K. A. Solen, (Ph.D., Wisconsin, 1974) Beautiful campus located in the rugged Rocky Mountains Financial aid available Address Inquiries to: Brigham Young University, Dr. Douglas N. Bennion, Chemical Engineering Dept., 350 CB, Provo, Utah 84602 FALL 1984 THE UNIVERSITY OF CALGARY ,... ~ . *... ~ GRADUATE STUDIES IN CHEMICAL AND PETROLEUM ENGINEERING The Department offers programs leading to the M.Sc. and Ph.D. degrees (fulltime) and the M. Eng. degree (parttime) in the following areas: ThermodynamicsPhase Equilibria Heat Transfer and Cryogenics Kinetics and Combustion Multiphase Flows in Pipelines FluidizationGrid Region Transport Phenomena Environmental Engineering Ultra Pyrolysis of Heavy Oils Enhanced Oil Recovery InSitu Recovery of Bitumen and Heavy Oils Natural Gas Processing and Gas Hydrates Antibiotic Production in Immobilized Cells Biorheology and Biochemical Engineering Computer Control and Optimization of Engineering Processes Fellowships and Research Assistantships are available to qualified applicants. FACULTY The University is located in the City of Calgary, the oil capital of Canada, the home of the world famous Calgary Stampede and the 1988 Winter Olympics. The city combines the traditions of the Old West with the sophistication of a modern urban centre. Beautiful Banff National Park is 110 km west of the City and the ski resorts of the Banff, Lake Louise and Kananaskis areas are readily accessible. FOR ADDITIONAL INFORMATION WRITE Dr. M. F. Mohtadi, Chairman Graduate Studies Committee Dept. of Chemical & Petroleum Eng. The University of Calqary Calgary, Alberta T2N 1N4 Canada R. A. HEIDEMANN, Head A. BADAKHSHAN L. A. BEHIE D. W. B. BENNION P. R. BISHNOI R. M. BUTLER M. FOGARASI M. A. HASTAOGLU J. HAVLENA A. A. JEJE N. E. KALOGERAKIS A. K. MEHROTRA M. F. MOHTADI R. G. MOORE P. M. SIGMUND J. STANISLAV W. Y. SVRCEK E. L. TOLLEFSON (Wash. U.) (Birm. U.K.) (W. Ont.) (Penn. State) (Alberta) (Imp. Coll. U.K.) (Alberta) (SUNY) (Czech.) (MIT) (Toronto) (Calgary) (Birm. U.K.) (Alberta) (Texas) (Prague) (Alberta) (Toronto) CHEMICAL ENGINEERING EDUCATION r I ~ I CA THE UNIVERSITY OF CALIFORNIA, BERKELEY... RESEARCH INTERESTS ENERGY UTILIZATION ENVIRONMENTAL PROTECTION KINETICS AND CATALYSIS THERMODYNAMICS POLYMER TECHNOLOGY ELECTROCHEMICAL ENGINEERING PROCESS DESIGN AND DEVELOPMENT SURFACE AND COLLOID SCIENCE BIOCHEMICAL ENGINEERING SEPARATION PROCESSES FLUID MECHANICS AND RHEOLOGY ELECTRONIC MATERIALS PROCESSING PLEASE WRITE: ... offers graduate programs leading to the Master of Science and Doctor of Philosophy. Both pro grams involve joint facultystudent research as well as courses and seminars within and outside the department. Students have the opportunity to take part in the many cultural offerings of the San Francisco Bay Area, and the recreational activities of California's northern coast and moun tains. FACULTY Alexis T. Bell (Chairman) Harvey W. Blanch Elton J. Cairns Morton M. Denn Alan S. Foss Simon L. Goren Edward A. Grens Donald N. Hanson Dennis W. Hess C. Judson King Scott Lynn James N. Michaels John S. Newman Eugene E. Petersen John M. Prausnitz Clayton J. Radke Jeffrey A. Reimer David S. Soong Charles W. Tobias Charles R. Wilke Michael C. Williams Department of Chemical Engineering UNIVERSITY OF CALIFORNIA Berkeley, California 94720 UNIVERSITY OF CALIFORNIA DAVIS Course Areas Applied Kinetics and Reactor Design Applied Mathematics Biotechnology Colloid and Interface Processes Fluid Mechanics Heat Transfer Mass Transfer Process Dynamics Rheology Semiconductor Device Fabrication Separation Processes Thermodynamics Transport Processes in Porous Media Program UC Davis, with 19,000 students, is one of the major campuses of the University of California system and has developed great strength in many areas of the biological and physical sciences. The Department of Chemical Engineering emphasizes research and a pro gram of fundamental graduate courses in a wide variety of fields of interest to chemical engineers. In addition, the department can draw upon the expertise of faculty in other areas in order to design individual programs to meet the specific interests and needs of a student, even at the M.S. level. This is done routinely in the areas of environmental engineering, food engineering, bio chemical engineering and biomedical engineering. Excellent laboratories, computation center and electronic and mechanical shop facilities are available. Fellowships, Teaching Assistantships and Research Assistantships (all providing additional summer support if desired) are available to qualified applicants. Degrees Offered Master of Science Doctor of Philosophy Faculty RICHARD L. BELL, University of Washington Mass Transfer, Biomedical Applications ROGER B. BOULTON, University of Melbourne Enology, Fermentation, Filtration, Process Control BRIAN G. HIGGINS, University of Minnesota Fluid Mechanics, Coating Flows, Interfacial Phenomena, Fiber Processes and Refining ALAN P. JACKMAN, University of Minnesota Environmental Engineering, Transport Phenomena BEN J. McCOY, University of Minnesota Separation and Transport Processes AHMET N. PALAZOGLU, Rennsselaer Polytechnic Institute Process Synthesis and Control ROBERT L. POWELL, The Johns Hopkins University Rheology, Fluid Mechanics DEWEY D. Y. RYU, Massachusetts Inst. of Technology Biochemical Engineering, Fermentation JOE M. SMITH, Massachusetts Institute of Technology Applied Kinetics and Reactor Design PIETER STROEVE, Massachusetts Institute of Technology Mass Transfer, Colloids, Biotechnology STEPHEN WHITAKER, University of Delaware Fluid Mechanics, Interfacial Phenomena, Transport Processes in Porous Media Davis and Vicinity The campus is a 20minute drive from Sacramento and just over an hour away from the San Francisco Bay area. Outdoor sports enthusiasts can enjoy water sports at nearby Lake Berryessa, skiing and other alpine activities in the Sierra (2 hours from Davis). These rec reational opportunities combine with the friendly in formal spirit of the Davis campus to make it a pleasant place in which to live and study. Married student housing, at reasonable cost, is located on campus. Both furnished and unfurnished one and twobedroom apartments are available. The town of Davis (population 36,000) is adjacent to the campus, and within easy walking or cycling distance. For further details on graduate study at Davis, please write to: Graduate Advisor Chemical Engineering Department University of California Davis, California 95616 or call (916) 7520400 CHEMICAL ENGINEERING UNIVERSITY ALIFORNIA OS PROGRAMS UCLA's Chemical Engineering Depart ment maintains academic excellence in its graduate programs by offering diversity in both curriculum and research opportunities. The department's continual growth is demon strated by the newly established Institute for Medical Engineering and the National Center for Intermedia Transport Research, adding to the already wide spectrum of research activities. Fellowships are available for outstand ing applicants. A fellowship includes a waiver of tuition and fees plus a stipend Located five miles from the Pacific Coast, UCLA's expansive 417 acre campus extends from Bel Air to Westwood Village. Students have access to the highly regarded sciences programs and to a variety of expe riences in theatre, music, art and sports on campus. CONTACT Admissions Officer Chemical Engineering Department NGELES 5405 Boelter Hall Los Angeles CA 90024 Los Angeles, CA 90024 FACULTY D.T. Allen Yoram Cohen S. FathiAfshar T.H.K. Frederking S.K. Friedlander E.L. Knuth Ken Nobe L.B. Robinson 0.I. Smith W. D. Van Vorst V. L. Vilker A.R. Wazzan F.E. Yates RESEARCH AREAS Thermodynamics and Cryogenics Reverse Osmosis and Membrane Transport Process Design and Systems Analysis Polymer Processing and Rheology Mass Transfer and Fluid Mechanics Kinetics, Combustion and Catalysis Electrochemistry and Corrosion Biochemical and Biomedical Engineering Aerosol and Environmental Engineering UNIVERSITY OF CALIFORNIA SANTA BARBARA *, ." .p *: ; .tz '._ : T *, :.. ..2":, . FACULTY AND RESEARCH INTERESTS PROGRAMS AND FINANCIAL SUPPORT SANJOY BANERJEE Ph.D. (Waterloo) (Chairman) Two Phase Flow, Reactor Safety, Nuclear Fuel Cycle Analysis and Wastes PRAMOD AGRAWAL Ph.D. (Purdue) Biochemical Engineering, Fermentation Science HENRI FENECH Ph.D. (M.I.T.) Nuclear Systems Design and Safety, Nuclear Fuel Cycles, TwoPhase Flow, Heat Transfer. OWEN T. HANNA Ph.D. (Purdue) Theoretical Methods, Chemical Reactor Analysis, Transport Phenomena. SHINICHI ICHIKAWA Ph.D. (Stanford) Adsorption and Heterogeneous Catalysis GLENN E. LUCAS Ph.D. (M.I.T.) Radiation Damage, Mechanics of Materials. DUNCAN A. MELLICHAMP Ph.D. (Purdue) Computer Control, Process Dynamics, RealTime Computing. JOHN E. MYERS Ph.D. (Michigan) (Dean of Engineering) Boiling Heat Transfer. G. ROBERT ODETTE Ph.D. (M.I.T.) Radiation Effects in Solids, Energy Related Materials Development. A. EDWARD PROFIO Ph.D. (M.I.T.) Bionuclear Engineering, Fusion Reactors, Radiation Transport Analyses. ROBERT G. RINKER Ph.D. (Caltech) Chemical Reactor Design, Catalysis, Energy Conversion, Air Pollution. ORVILLE C. SANDALL Ph.D. (Berkeley) Transport Phenomena, Separation Processes. DALE E. SEBORG Ph.D. (Princeton) Process Control, Computer Control, Process Identification. The Department offers M.S. and Ph.D. de gree programs. Financial aid, including fellowships, teaching assistantships, and re search assistantships, is available. Some awards provide limited moving expenses. THE UNIVERSITY One of the world's few seashore campuses, UCSB is located on the Pacific Coast 100 miles northwest of Los Angeles and 330 miles south of San Francisco. The student enrollment is over 14,000. The metropoli tan Santa Barbara area has over 150,000 residents and is famous for its mild, even climate. For additional information and applications, write to: Professor Sanjoy Banerjee, Chairman Department of Chemical & Nuclear Engineering University of California, Santa Barbara, CA 93106 CHEMICAL ENGINEERING EDUCATION PROGRAM OF STUDY Distinctive features of study in chemical engineering at the California Institute of Tech nology are the creative research atmosphere and the strong emphasis on basic chemical, physical, and mathematical disciplines in the program of study. In this way a student can properly prepare for a productive career of research, development, or teaching in a rapidly changing and ex panding technological society. A course of study is selected in consultation with one or more of the faculty listed below. Required courses are minimal. The Master of Science degree is normally com pleted in one calendar year and a thesis is not required. A special M.S. option, involving either research or an inte grated design project, is a feature to the overall program of graduate study. The Ph.D. degree requires a minimum of three years subsequent to the B.S. degree, consisting of thesis research and further advanced study. JAMES E. BAILEY, Professor Ph.D. (1969), Rice University Biochemical engineering; chemical reaction engineering. GEORGE R. GAVALAS, Professor Ph.D. (1964), University of Minnesota Applied kinetics and catalysis; process control and optimization; coal gasification. ERIC HERBOLZHEIMER, Assistant Professor Ph.D. (1979), Stanford University Fluid mechanics and transport phenomena L. GARY LEAL, Professor Ph.D. (1969), Stanford University Theoretical and experimental fluid mechanics; heat and mass transfer; suspension rheology; mechanics of nonNewtonian fluids. MANFRED MORARI, Professor Ph.D. (1977), University of Minnesota Process control; process design FINANCIAL ASSISTANCE Graduate students are sup ported by fellowship, research assistantship, or teaching assistantship appointments during both the academic year and the summer months. A student may carry a full load of graduate study and research in addition to any assigned assistantship duties. The Institute gives consideration for admission and financial assistance to all qualified applicants regardless of race, religion, or sex. APPLICATIONS Further information and an application form may be obtained by writing Professor G. N. Stephanopoulos Chemical Engineering California Institute of Technology Pasadena, California 91125 It is advisable to submit applications before February 15, 1985. C. DWIGHT PRATER, Visiting Associate Ph.D. (1951), University of Pennsylvania Catalysis; chemical reaction engineering; process design and development. JOHN H. SEINFELD, Louis E. Nohl Professor, Executive Officer Ph.D. (1967), Princeton University Air pollution; control and estimation theory. FRED H. SHAIR, Professor Ph.D. (1963), University of California, Berkeley Plasma chemistry and physics: tracer studies of various environmental and safety related problems. GREGORY N. STEPHANOPOULOS, Associate Pro fessor Ph.D. (1978), University of Minnesota Biochemical engineering; chemical reaction engineering. NICHOLAS W. TSCHOEGL, Professor Ph.D. (1958), University of New South Wales Mechanical properties of polymeric materials; theory of viscoelastic behavior; structure property relations in polymers. W. HENRY WEINBERG, Chevron Professor Ph.D. (1970), University of California, Berkeley Surface chemistry and catalysis. Oan Stereo E PROFESSORS! A New Release from Pittsburgh's High Performance Group The UNIVERSITY OF CINCINNATI  CHEMICAL REACTION ENGINEERING AND HETEROGENEOUS CATALYSIS Modeling and design of chemical reactors. Deactivating catalysts. Flow equipment. Laser induced effects. PROCESS SYNTHESIS GRADUATE STUDY in Chemical Engineering M.S. and Ph.D. Degrees FACULTY Stanley Cosgrove Robert Delcamp Joel Fried Rakesh Govind David Greenberg Daniel Hershey SunTak Hwang YuenKoh Kao SoonJai Khang Robert Lemlich William Licht Joel Weisman pattern and mixing in chemical Computeraided design. Modeling and simulation of coal gasifiers, activated carbon columns, process unit operations. Prediction of reaction byproducts. POLYMERS Viscoelastic properties of concen trated polymer solutions. Thermodynamics, thermal analysis and morphology of polymer blends. AIR POLLUTION Modeling and design of gas clean ing devices and systems. TWOPHASE FLOW Boiling. Stability and transport properties of foam. THERMODYNAMIC ANALYSIS OF LIVING HUMAN AND CORPORATE SYSTEMS Longevity, basal metabolic rate, and Prigogine's and Shannon's entropy formulae. FOR ADMISSION INFORMATION Chairman, Graduate Studies Committee Chemical & Nuclear Engineering, #171 University of Cincinnati Cincinnati, OH 45221 MEMBRANE SEPARATIONS Membrane gas separation, continuous membrane reactor column, equilibrium shift, pervaporation, dy namic simulation of membrane separators, membrane preparation and characterization. ar sonl O M.S. and Ph.D. programs O Friendly atmosphere O Vigorous research programs supported by government and industry O Proximity to Montreal and Ottawa O Skiing, canoeing, mountain climbing and other recreation in the Adirondacks O Variety of cultural activities with two liberal arts colleges nearby O Twentyone faculty working on a broad spectrum of chemical engineering research problems Research Projects are available in: o Colloidal and interfacial phenomena O Computer aided design O Crystallization O Electrochemical engineering and corrosion O Heat transfer 0 Holographic interferometry O Mass transfer O Materials processing in space O Optimization O Particle separations O Phase transformations and equilibria O Polymer processing O Process control O Reaction engineering 0 Turbulent flows O And more... Financial aid in the form of: O instructorships 0 fellowships O research assistantships 0 teaching assistantships O industrial coop positions 6r For more details, please write to: Dean of the Graduate School Clarkson University Potsdam, New York 13676 CHEMICAL ENGINEERING EDUCATION I6i 001 010 Graduate Coorcdnator ^. Chemical Engitneering Dept. SCLEMSO U nVERSITY Clemson., SC 29651 FALL 1984 231 li: i FAL 198 231iirii COLORADO SCHOOL / OF I 1874 MINES CoR0 THE FACULTY AND THEIR RESEARCH A. J. Kidnay, Professor and Head; D.Sc., Colorado School of Mines. Thermodynamic properties of coalderived liquids, vaporliquid equilibria in natural gas systems, cryogenic engineering. J. H. Gary, Professor; Ph.D., University of Florida. Up grading of shale oil and coal liquids, petroleum re finery processing operations, heavy oil processing. E. D. Sloan, Jr., Professor; Ph.D., Clemson University. Phase equilibrium thermodynamics measurements of natural gas fluids and natural gas hydrates, thermal conductivity measurements for coal derived fluids, adsorption equilibria measurements, stagewise pro J *cesses, education methods research. V. F. Yesavage, Professor; Ph.D., University of Michigan. Thermodynamic properties of fluids, especially re lating to synthetic fuels. Oil shale and shale oil processing; numerical methods. R. M. Baldwin, Associate Professor, Ph.D., Colorado School of Mines. Mechanisms of coal liquefaction, kinetics of coal hydrogenation, relation of coal geochemistry to liquefaction kinetics, upgrading of coalderived asphaltenes, supercritical gas extrac tion of oil shale and heavy oil. M. S. Graboski, Associate Professor; Ph.D., Pennsylvania State University. Coal and biomass gasification pro cesses, gasification kinetics, thermal conductivity of coal liquids, kinetics of SNG upgrading. M. C. Jones, Associate Professor; Ph.D., University of California at Berkeley. Heat transfer and fluid me chanics in oil shale retorting, radiative heat transfer in porous media, free convection in porous media. M. S. Selim, Associate Professor; Ph.D., Iowa State University. Flow of concentrated fine particulate .. "suspensions in complex geometries; Sedimenta ' ; tion of multisized, mixed density particle suspensions. A 1' A. L. Bunge, Assistant Professor; Ph.D., University of ~ . _. California at Berkeley. Chromatographic processes, t enhanced oil recovery, minerals leaching, liquid membrane separations, ion exchange equilibria. For Applications and Further Information On M.S., and Ph.D. Programs, Write S5 i Chemical and Petroleum Refining Engineering Colorado School of Mines _ t ,ii Golden, CO 80401 CHEMICAL ENGINEERING EDUCATION Colorado State University Location: CSU is situated in Fort Collins, a pleasant community of 80,000 people located about 65 miles north of Denver. This site is adjacent to the foothills of the Rocky Mountains in full view of majestic Long's Peak. The climate is excellent with 300 sunny days per year, mild temperatures and low humidity. Opportunities for hiking, camping, boating, fishing and skiing abound in the immediate and nearby areas. The campus is within easy walking or biking distance of the town's shopping areas and its new Center for the Performing Arts. Degrees Offered: M.S. and Ph.D. programs in Chemical Engineering Financial Aid Available: Faculty: Teaching and Research Assistantships paying Fc4 a monthly stipend plus tuition reimbursement. Larry Belfiore, Ph. D., I. University of Wisconsin Bruce Dale, Ph.D. Purdue University Jud Harper, Ph.D., Iowa State University Naz Karim, Ph.D., University of Manchester Terry Lenz, Ph.D., Iowa State University Jim Linden, Ph.D., Iowa State University Carol McConica, Ph.D. Stanford University Vince Murphy, Ph.D., University of Massachusetts Research Areas: Alternate Energy Sources Biochemical Engineering Catalysis Chemical Vapor Deposition Computer Simulation and Control 7 Fermentation Food Engineering Polymeric Materials Porous Media Phenomena Rheology Semiconductor Processing Solar Cooling Systems Thermochemical Cycles Wastewater Treatment For Applications and Further Information, write: Professor Vincent G. Murphy Department of Agricultural and Chemical Engineering Colorado State University Fort Collins, CO 80523 FALL 1984 Chemical Engineering at CORNELL UNIVERSITY A place to grow... with active research in biochemical engineering applied mathematics/computer simulation energy technology environmental engineering kinetics and catalysis surface science heat and mass transfer polymer science fluid dynamics rheology and biorheology reactor design molecular thermodynamics/statistical mechanics with a diverse intellectual climategraduate students arrange individual programs with a core of chemical engineering courses supplemented by work in other outstanding Cornell departments including chemistry biological sciences physics computer science food science materials science mechanical engineering business administration and others with excellent recreational and cultural opportunities in one of the most scenic regions of the United States. Graduate programs lead to the degrees of Doctor of Philosophy, Master of Science, and Master of Engineering (the M.Eng. is a professional, designoriented program). Financial aid, including attractive fellowships, is available. The faculty members are: Douglas S. Clark, Joseph F. Cocchetto, Claude Cohen, Robert K. Finn, Keith E. Gubbins, Peter Harriott, Robert P. Merrill, William L. Olbricht, Ferdinand Rodriguez, George F. Scheele, Michael L. Shuler, Julian C. Smith, Paul H. Steen, William B. Street, Raymond G. Thorpe, Robert L. Von Berg, Herbert F. Wiegandt. FOR FURTHER INFORMATION: Write to Professor Claude Cohen Cornell University Olin Hall of Chemical Engineering Ithaca, New York 14853 The University of Delaware awards three graduate degrees for studies and practice in the artand science of chemical engineering. An M.Ch.E. degree based upon course work and a thesis problem. An M.Ch.E. degree based upon course work and a period of in dustrial internship with an experienced senior engineer in the Delaware Valley chemical process Industries. A Ph.D. degree for original work presented in a dissertation. THE REGULAR FACULTY ARE: G. Astarita (1/2 time) M. A. Barteau C. E. Birchenall K. B. Bischoff C. D. Denson P. Dhurjati B. C. Gates M. T. Klein A. M. Lenhoff R. L. McCullough A. B. Metzner J. H. Olson M. E. Paulaitis R. L. Pigford T. W. F. Russell S. I. Sander (Chairman) J. M. Schultz A. B. Stiles (1/2 time) R. S. Weber A. L. Zydney CURRENT AREAS OF RESEARCH INCLUDE: Thermodynamics and Separ ation Process Rheology, Polymer Science and Engineering Materials Science and Metallurgy Fluid Mechanics, Heat and Mass Transfer Economics and Management in the Chemical Process Industries Chemical Reaction Engi neering, Kinetics and Simulation Catalytic Science and Technology Biomedical Engineering Pharmacokinetics and Toxicology Biochemical Engineering Fermentation and Computer Control FOR MORE INFORMATION AND ADMISSIONS MATERIALS, WRITE: GraduateAdvisor Department of Chemical Engineering University of Delaware Newark, Delaware 19716 UNIVE RS ITY FLORIDA Gainesville, Florida Graduate study leading to ME,MS &PhD F A C U L T Y FACULTY Tim Anderson Thermodynamics, Semiconductor Processing/ Seymour S. Block Biotechnology Ray W. Fahien Transport Phenomena, Reactor Design/ Gar Hoflund Catalysis, Surface Science Lew Johns Applied Mathematics/ Dale Kirmse Process Control, Computer Aided Design, Biotechnology/ Hong H. Lee Reactor Design, Catalysis/ Gerasimos K. Lyberatos Optimization, Biochemical Processes/ Frank May Separations Ranga Narayanan Transport Phenomena/ John O'Connell Statistical Mechanics, Thermodynamics Dinesh O. Shah Enhanced Oil Recovery, Biomedical Engineering/ Spyros Svoronos Process Control/ Robert D. Walker Surface Chemistry, Enhanced Oil Recovery/ Gerald WestermannClark Electrochemistry, Transport Phenomena Graduate Admissions Coordinator Department of Chemical Engineering University of Florida Gainesville, Florida 32611 0 F TEC If '4I: Graduate Studies in Chemical Engineering ... GEORGIA TECH Atlanta Ballet Center for Disease Control Commercial Center of the South High Museum of Art All Professional Sports Major Rock Concerts and Recording Studios Sailing on Lake Lanier Snow Skiing within two hours Stone Mountain State Park Atlanta Symphony Ten Professional Theaters Rambling Raft Race White Water Canoeing within one hour For more information write: Dr. Gary W. Poehlein School of Chemical Engineering Georgia Institute of Technology Atlanta, Georgia 30332 Chemical Engineering Air Quality Technology Biochemical Engineering Catalysis and Surfaces Electrochemical Engineering Energy Research and Conservation Fine Particle Technology Interfacial Phenomena Kinetics Mining and Mineral Engineering Polymer Science and Engineering Process Synthesis and Optimization Pulp and Paper Engineering Reactor Design Thermodynamics Transport Phenomena Graduate Programs in Chemical Engineering University of Houston The Department of Chemical Engineering at the University of Houston has developed research strength in a broad range of areas: Chemical Reaction Engineering, Catalysis Biochemical Engineering Electrochemical Systems Semiconductor Processing Interfacial Phenomena, Rheology Process Dynamics and Control Twophase Flow, Sedimentation Solidliquid Separation Reliability Theory Petroleum Reservoir Engineering The department occupies over 75,000 square feet and has over $3 million worth of experimental apparatus. Financial support is available to fulltime graduate students through re search assistantships and special industrial fellowships. The faculty: For more information or application forms write to: Director, Graduate Admissions Department of Chemical Engineering University of Houston Houston, Texas 77004 (Phone 713/7494407) N. R. Amundson O. A. Asbjornsen V. Balakotaiah H.C. Chang E. L. Claridge J. R. Crump H. A. Deans A. E. Dukler R. W. Flumerfelt C. F. Goochee E. J. Henley D. Luss R. Pollard H. W. Prengle, Jr. J. T. Richardson F. M. Tiller F. L. Worley, Jr. CHEMICAL ENGINEERING EDUCATION GRADUATE STUDY AND RESEARCH The Department of Chemical Engineering Graduate Programs in The Department of Chemical Engineering leading to the degrees of MASTER OF SCIENCE and DOCTOR OF PHILOSOPHY THE UNIVERSITY OF ILLINOIS AT CHICAGO FACULTY AND RESEARCH ACTIVITIES Francisco J. BranaMulero Ph.D., University of Wisconsin, 1980 Assistant Professor T. S. Jiang PhD., Northwestern University, 1981 Asssitant Professor John H. Keifer Ph.D., Cornell University, 1961 Professor G. Ali Mansoori Ph.D., University of Oklahoma, 1969 Professor Sohail Murad Ph.D., Cornell University, 1979 Assistant Professor Satish C. Saxena Ph.D., Calcutta University, 1956 Professor Stephen Szepe Ph.D., Illinois Institute of Technology, 1966 Associate Professor Raffi M. Turian Ph.D., University of Wisconsin, 1964 Professor The MS program, with its optional thesis, can be completed in one year. Evening M.S. can be completed in three years. The department invites applications for admission and support from all qualified candidates. Special fellowships are available for minority students. To obtain application forms or to request further information write: Process synthesis, operations research, optimal process control, optimization of large systems, numerical analysis, theory of nonlinear equations. Interfacial Phenomena, multiphase flows, flow through porous media, suspension rheology Kinetics of gas reactions, energy transfer processes, laser diagnostics Thermodynamics and statistical mechanics of fluids, solids, and solutions, kinetics of liquid reactions, solar energy Thermodynamics and transport properties of fluids, computer simulation and statistical mechanics of liquids and liquid mixtures Transport properties of fluids and solids, heat and mass transfer, isotope separation, fixed and fluidized bed combustion Catalysis, chemical reaction engineering, energy transmission, modeling and optimization Slurry transport, suspension and complex fluid flow and heat transfer, porous media processes, mathematical analysis and approximation. Professor S. C. Saxena The Graduate Committee Department of Chemical Engineering University of Illinois at Chicago Box 4348, Chicago, Illinois 60680 UNIVERSITY OF ILLINOIS AT URBANACHAMPAIGN The chemical engineering department  offers graduate programs leading to the M.S. and Ph.D. degrees "' 0 The combination of distinguished faculty, outstanding facilities and a diversity of E research interests results in exceptional opportunities for graduate education. I S9300 50 629I Faculty 579 Richard C. Alkire I I I I I Harry G. Drickamer Charles A. Eckert Thomas J. Hanratty Jonathan J. L. Higdon Walter G. May Richard I. Masel Anthony J. McHugh Mark A. Stadtherr James W. Westwater Charles F. Zukoski, IV Fe+2 For Information and Application Forms Write S.l' O Department of Chemical Engineering University of Illinois Box C3 Roger Adams Lab 1209 W. California Street Urbana, Illinois 61801 Graduate Studies in Chemical Engineering Illinois Institute of Technology Chicago, Illinois I  i i   iFaculty ... R.L. Beissinger A. Ci nar  D. Gidaspow IDT.' Hatziavramidis iJ.R. Selman S.M. Senkan I .. iB.S.i Swanson I D.T. Wasan W.A. Weigand C.V. Wittmar Research Areas 'Biochemical and Biomedical  Chemical Reaction Engineering Combustion .  ComputerAided Design Electrochemical Engineering . Environmental Fluid Mechanics .  Interfacial and Colloidal Phenomena .... .  !Process Dynamics and C Transport Phenomenai' i _. ....... .. .i..... . " .....i .. "". '". .."' _ l . . 4 \ r t r, .......i .... I i l , i ! irv , s I~...._. I.. _ /m. K \ U S/ N I I A> I I 'I I I I  I I I I  I ~  SI Sr1 &' For Mor Information Write to: Chemical engineering Department  Graduate admissions Committee Illinois Ins tute of Technology j I.I.T. Cen r Chicago Illinois 60616 I I U.S. S _ . ~_II _ i I T 7 THE INSTITUTE OF PAPER CHEMISTRY is an independent graduate school. It has an interdisciplinary degree program designed for B.S. chemical engineering graduates. Fellowships and full tuition scholarships are available to qualified U.S. and Canadian Citizens. Our students receive S9,000.00 fellowships each calendar year. Our research activities span the papermaking process including: plant tissue culture surface and colloid science fluid mechanics environmental engineering polymer engineering heat and mass transfer process engineering simulation and control separations science and reaction engineering For f,.rrher nformal'on contfOt: D.recior of Admissions The Insi.iule of Paper Chem;slr, P Bo. 1039 Appleion WI 54912 Telephone 414 734J9251 242 CHEMICAL ENGINEERING EDUCATION M" la F iZ~_* B i ll ll in lll el l Graduate Program for *M.S. and Ph. D. Degrees in Chemical and Materials Engineering __Research Areos Bi _* Kinetics and Cotalysis Biomass Conversion Membrane Separations Particle Morphological Analysis Air Pollution MassTransfer Operations Numerical Modeling Particle Technology Atmospheric Transport Bioseparations and Biotechnology Process Design J Surface Science I Transport In PorousMedia For additional information and application write to: Graduate Admissions Chemical and Materials Engineering The University of Iowa Iowa City, Iowa 52242. 319/3536237 1 NI THE UNIVERSITY OF IOWA THE UNIVERSITY OF IOWA _ _ IOWA STATE UNIVERSITY William H. Abraham Thermodynamics, heat and mass transport, process modeling Lawrence E. Burkhart Fluid mechanics, separation process, process control George Burnet Coal technology, separation processes Charles E. Glatz Biochemical engineering, processing of biological materials Kurt R. Hebert Electrochemical engineering, corrosion James C. Hill Fluid mechanics, turbulence, convective transport, air pollution control Kenneth R. Jolls Thermodynamics, simulation Terry S. King Catalysis, surface science, catalyst applications Maurice A. Larson Crystallization, process dynamics Allen H. Pulsifer Solidgas reactions, coal technology Peter J. Reilly Biochemical engineering, enzyme and fermentation technology Glenn L. Schrader Catalysis, kinetics, solid state electronics processing Richard C. Seagrave Biological transport phenomena, biothermo dynamics, reactor analysis Dean L. Ulrichson Solidgas reactions, process modeling Thomas D. Wheelock Chemical reactor design, coal technology, fluidization Gordon R. Younquist Crystallization, chemical reactor design, polymerization For additional information, please write: Graduate Officer Department of Chemical Engineering Iowa State University Ames, Iowa 50011 ..': * "P1. Y. 'v, "z _  ..... S t, _. y .  " . owt3r: 11t !!:: =4.p A F S'THE UNIVERSITY OF KANSAS Department of Chemical and Petroleum Engineering Offers graduate study leading to the M.S. and Ph.D. degrees For further information, write to Professor George W. Swift, Graduate Advisor Department of Chemical and Petroleum Engineering 4006 Learned Hall The University of Kansas Lawrence, Kansas 66045 Faculty and Areas of Specialization * Kenneth A. Bishop, Professor (Ph.D., Oklahoma); reser voir simulation, interactive computer graphics, optimization John C. Davis, Professor and chief of geology research section, Kansas Geological Survey (Ph.D., Wyoming); probabilistic techniques for oil exploration, geologic computer mapping Kenneth J. Himmelstein, Adjunct Professor (Ph.D., Maryland); pharmacokinetics, mathematical model ing of biological processes, cell kinetics, diffusion and mass transfer Colin S. Howat, III, Assistant Professor (Ph.D., Kansas); applied equilibrium thermodynamics, process de sign Don W. Green, Professor and Codirector Tertiary Oil Recovery Project (Ph.D., Oklahoma); enhanced oil recovery, hydrological modeling James O. Maloney, Professor (Ph.D., Penn State); technology and society Russell B. Mesler, Professor (Ph.D., Michigan); nucleate and film boiling, bubble and drop phenomena Floyd W. Preston, Professor (Ph.D., Penn State); geo logic pore structure Harold F. Rosson, Professor and Department Chairman (Ph.D., Rice); production of alternate fuels from agri cultural materials Bala Subramaniam, Assistant Professor (Ph.D., Notre Dame); kinetics and catalysis, insitu characterization of catalyst systems George W. Swift, Professor (Ph.D., Kansas); thermo dynamics of petroleum and petro chemical systems, natural gas reservoirs analysis, fractured well analysis, petrochemical plant design John E. Thiele, Assistant Professor (Sc.D., MIT); struc ture/property relationships of polymers, polymer chemistry and physics, polymer viscoelasticity Shapour Vossoughi, Associate Professor (Ph.D., U. of Alberta); enhanced oil recovery, thermal analysis, applied rheology and computer modeling Stanley M. Walas, Professor Emeritus (Ph.D., Michigan); combined chemical and phase equilibrium G. Paul Willhite, Professor and Codirector Tertiary Oil Recovery Project (Ph.D., Northwestern); enhanced oil recovery, transport processes in porous media, mathematical modeling FALL 1984 Graduate Study in Chemical Engineering KANSAS STATE UNIVERSITY DURLAND HALLNew Home of Chemical Engineering M.S. and Ph.D. programs in Chemical Engineering and Interdisciplinary Areas of Systems Engineering, Food Science, and Environmental neering. Financial Aid Available Up to $12,000 Per Year FOR MORE INFORMATION WRITE TO Professor B. G. Kyle Durland Hall Kansas State University Manhattan, Kansas 66506 Engi AREAS OF STUDY AND RESEARCH TRANSPORT PHENOMENA ENERGY ENGINEERING COAL AND BIOMASS CONVERSION THERMODYNAMICS AND PHASE EQUILIBRIUM BIOCHEMICAL ENGINEERING PROCESS DYNAMICS AND CONTROL CHEMICAL REACTION ENGINEERING MATERIALS SCIENCE SOLIDS MIXING CATALYSIS AND FUEL SYNTHESIS OPTIMIZATION AND PROCESS SYSTEM ENGINEERING FLUIDIZATION ENVIRONMENTAL POLLUTION CONTROL UNIVERSITY OF KENTUCKY DEPARTMENT OF CHEMICAL ENGINEERING M.S. and Ph.D. Programs THE FACULTY AND THEIR RESEARCH INTERESTS J. Berman, Ph.D., Northwestern Biomedical Engineering; Cardiovascular Transport Phenomena; Blood Oxygenation D. Bhattacharyya, Ph.D. Illinois Institute of Technology Novel Separation Processes; Membranes; Water Pollution Control G. F. Crewe, Ph.D., West Virginia Catalytic Hydrocracking of Polyaromatics; Coal Liquefaction C. E. Hamrin, Ph.D., Northwestern Coal Liquefaction; Catalysis; Nonisothermal Kinetics R. I. Kermode, Ph.D., Northwestern Process Control and Economics E. D. Moorhead, Ph.D., Ohio State Electrochemical Processes; Computer Measurement Techniques and Modeling L. K. Peters, Ph.D., Pittsburgh Atmospheric Transport; Aerosol Phenomena A. K. Ray, Ph.D., Clarkson Heat and Mass Transfer in Knudsen Regime; Transport Phenomena J. T. Schrodt, Ph.D., Louisville Simultaneous Heat and Mass Transfer; Fuel Gas Desulfurization T. T. Tsang, Ph.D., TexasAustin Aerosol Dynamics in Uniform and NonUniform Systems Fellowships and Research Assistantships are Available to Qualified Applicants For details write to: E. D. Moorhead Director for Graduate Studies Chemical Engineering Department University of Kentucky Lexington, Kentucky 405060046 FALL 1984 ~tF~ 7~E~"~' ii r "~ru~YYisslll$l~s~" ~l~lldl Loutsiana Unhtrstty CHEMICAL ENGINEERING GRADUATE SCHOOL THE CITY Baton Rouge is the state capitol and home of the major state institution for higher educationLSU. Situated in the Acadian region, Baton Rouge blends the Old South and Cajun Cultures. The Port of Baton Rouge is a main chemical shipping point, and the city s economy rests heavily on the chemical and agricultural industries. The great outdoors provide excellent recreational activities year round, additionally the proximity of New Orleans provides for superb nightlife, especially during Mardi Gras. THE DEPARTMENT M.S. and Ph.D. Programs Approximately 70 Graduate Students DEPARTMENTAL FACILITIES IBM 434 I with more than 50 color graphics terminals Analytical Facilities including GC/MS, FTIR, FTNMR, LC's, GC's... Vacuum to High Pressure Facilities for kinetics, catalysis, thermodynamics, supercritical processing Shock Tube and Combustion Laboratories Laser Doppler Velocimeter Facility Bench Scale Fermentation Facilities TO APPLY, CONTACT: EDWARD McLAUGHLIN, CHAIRMAN Department of Chemical Engineering Louisiana State University Baton Rouge, LA 70803 FACULTY A. B. CORRIPIO (Ph.D., LSU) Control, Simulation, Computer Aided Design K. M. DOOLEY (Ph.D., Delaware) Heterogeneous Catalysis, Reaction Engineering M. F. FRENKLACH (Ph. D., Hebrew Univ.) Combustion, Kinetics, Modeling F. R. GROVES (Ph.D., Wisconsin) Control, Modeling, Separation Processes D. P. HARRISON (Ph.D., Texas) Fluid Solid Reactions, Hazardous Wastes A. E. JOHNSON (Ph.D., Florida) Distillation, Control, Modeling M. HJORTSO (Ph.D., Univ. of Houston) Biotechnology, Applied Mathematics F. C. KNOPF (Ph.D., Univ. of Purdue) Computer Aided Design, Supercritical Processing E. McLAUGHLIN (D.Sc., Univ. of London) Thermodynamics, High Pressures, Physical Properties R. W. PIKE (Ph.D., Georgia Tech) Fluid Dynamics, Reaction Engineering, Optimization J. A. POLACK (Sc.D., MIT) Sugar Technology, Separation Processes G. L. PRICE (Ph.D., Rice Univ.) Heterogeneous Catalysis, Surfaces D. D. REIBLE (Ph.D., Caltech) Transport Phenomena, Environmental Engineering R. G. RICE (Ph.D., Pennsylvania) Mass Transfer, Separation Processses D. L. RISTROPH (Ph.D., Pennsylvania) Biochemical Engineering C. B. SMITH (Ph. D., Univ. of Houston) Nonlinear Dynamics, Control A. M. STERLING (Ph.D., Univ. of Washington) Biomedical Engineering, Transport Properties, Combustion D. M. WETZEL (Ph.D., Delaware) Physical Properties, Hazardous Wastes FINANCIAL AID Taxfree fellowships and assistantships with tuition waivers available Special industrial and alumni fellowships with higher stipends for outstanding students Some parttime teaching positions for graduate students in high standing State 0 University of Maine at Orono M.S. AND PH.D. PROGRAMS IN CHEMICAL ENGINEERING * Sponsored projects val ued at$1 million peryear are in progress. * Faculty is supported by extensive stateoftheart facilities. * Relevancy of the Depart ment's research is in sured by continuous liai son with engineers and scientists from industry who help guide the fac ulty concerning emerg ing needs and activities of other laboratories. * Research and teaching assistantships are avail able. * Outstanding candidates (GPA between 3.75 and 4.00) wishing to pursue the Ph.D. are invited to apply for President's Fel lowships which provide $4000 per year in addi tion to regular stipend and free tuition. THE GRADUATE FACULTY AND THEIR RESEARCH William H. Cockler Sc.D., MIT, 1960 * Heat Transfer * Pressing & Drying Operations * Energy from Low Btu Fuels * Process Simulation Albert Co Ph.D., Wisconsin, 1979 * Transport phenomena * Polymeric Fluid Dynamics * Rheology Arthur L. Fricke Ph.D., Wisconsin, 1962 * Properties of Polymeric Systems * Polymer Processing and Design * Rheology of Polymeric Fluids Joseph M. Genco Ph.D., Ohio State, 1965 * Process Engineering * Pulp & Paper Technology * Wood Delignification Marqueta K. Hill Ph.D., University of California, 1966 * Black Liquor Chemistry * Pulping Chemistry * Ultrafiltration John C. Hassler Ph.D., Kansas State, 1966 * Process Analysis and Numerical Methods * Instrumentation and RealTime Computer Applications John J. Hwalek Ph.D., University of Illinois, 1982 * Heat Transfer * Process Control Systems Erdogan Kiran Ph.D., Princeton, 1974 * Polymer Physics and Chemistry * Thermal Analysis and Pyrolysis * Supercritical Fluids James D. Lisius Ph.D., University of Illinois, 1984 * Transport Phenomena * Electrochemical Engineering * Mass Transfer Kenneth I. Mumm6 Ph.D., Maine, 1970 * Process Modeling and Control * System Identification & Optimization Hemant Pendse Ph.D., Syracuse, 1980 * Colloidal Phenomena * Particulate Systems * Porous Media Modeling Ivar H. Stockel Sc.D., MIT, 1959 * Pulp & Paper Technology * Droplet Formation * Fluidization Edward V. Thompson Ph.D., Polytechnic Institute of Brooklyn, 1962 * Polymer Material Prop erties * Membrane Separation Processes * Pressing & Drying Operations Douglas L. Woerner Ph.D., University of Washington, 1983 * Concentration Polariza tion * Ultrafilter Operation * Light Scattering University of Maryland Faculty: Robert B. Beckmann Theodore W. Cadman Richard V. Calabrese Kyu Y. Choi Larry L. Gasner James W. Gentry Albert Gomezplata Randolph T. Hatch Juan Hong Thomas J. McAvoy Thomas M. Regan Wilburn C. Schroeder Theodore G. Smith Location: The University of Maryland is located approximately 10 miles from the heart of the nation, Washington, D.C. Excellent public transportation permits easy access to points of interest such as the Smithsonian, National Gallery, Congress, White House, Arlington Cemetery, and the Kennedy Center. A short drive west produces some of the finest mountain scenery and recreational opportunities on the east coast. An even shorter drive east brings one to the historic Chesapeake Bay. "3'^ "I^ ~Degrees Offered. SM.S. and Ph.D. programs in : '~l j Chemical Engineering. Financial Aid Available: Teaching and Research Assistantships I. :. at $9,640/yr.  " *~. .:" ,' . Research Areas: Aerosol Mechanics Air Pollution Control Biochemical Engineering Biomedical Engineering Fermentation Laser Anemometry Mass Transfer Polymer Processing Process Control Risk Assessment Separation Processes Simulation For Applications and Further Information, Write: Professor Thomas J. McAvoy Department of Chemical and Nuclear Engineering University of Maryland College Park, Md. 20742 
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