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Angelo J. Perna, of the New Jersey...  
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Developing a course in chemical...  
An introduction to equilibrium...  
Book reviews  
We hold these truths to be...  
A course in immobilized enzyme...  
A secondyear undergraduate course...  
Removal of chlorine from the chlorinenitrogen...  
Undergraduate education: Where...  
Book reviews  
Purdueindustry computer simulation...  
Crystallization: An interesting...  
Principles of stagewise separation...  
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Front Cover 1 Front Cover 2 Table of Contents Page 61 Angelo J. Perna, of the New Jersey Institute of Technology Page 62 Page 63 UCLA Page 64 Page 65 Page 66 Page 67 Developing a course in chemical engineering ethics: One class' experiences Page 68 Page 69 Page 70 Page 71 Page 72 Page 73 An introduction to equilibrium thermodynamics: A rational approach to its teaching: Part 1. Notation and mathematics Page 74 Page 75 Page 76 Page 77 Page 78 Book reviews Page 79 We hold these truths to be selfevident Page 80 Page 81 A course in immobilized enzyme and cell technology Page 82 Page 83 Page 84 Page 85 Page 86 Page 87 A secondyear undergraduate course in applied differential equations Page 88 Page 89 Page 90 Page 91 Removal of chlorine from the chlorinenitrogen mixture in a film of liquid water Page 92 Page 93 Page 94 Page 95 Undergraduate education: Where do we go from here? Page 96 Book reviews Page 97 Purdueindustry computer simulation modules: The Amoco Resid Hydrotreater process Page 98 Page 99 Page 100 Page 101 Crystallization: An interesting experience in the ChE laboratory Page 102 Page 103 Page 104 Page 105 Principles of stagewise separation process calculations: A simple algebraic approach using solvent extraction Page 106 Page 107 Page 108 Page 109 Books received Page 110 Page 111 Computation of multiple reaction equilibria Page 112 Page 113 Page 114 Page 115 Page 116 Back Cover Back Cover 1 Back Cover 2 

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ceia education EDITORIAL AND BUSINESS ADDRESS: Chemical Engineering Education Department of Chemical Engineering University of Florida Gainesville, FL 32611 EDITOR: Ray W. Fahien (904) 3920857 ASSOCIATE EDITOR: T Anderson (904) 3922591 CONSULTING EDITOR: Mack Tyner MANAGING EDITOR: Carole Yocum (904) 3920861 PUBLICATIONS BOARD CHAIRMAN * E. Dendy Sloan, Jr. Colorado School of Mines PAST CHAIRMEN Gary Poehlein Georgia Institute of Technology Klaus Timmerhaus University of Colorado MEMBERS * South Richard M. Felder North Carolina State University JackR. Hopper Lamar University Donald R. Paul University of Texas James Fair University of Texas Central I. S. Dranoff Northwestern University West Frederick H. Shair California Institute of Technology Alexis T. Bell University of California, Berkeley Northeast Angelo J. Perna New Jersey Institute of Technology Stuart W. Churchill University of Pennsylvania Raymond Baddour Massachusetts Institute of Technology Northwest Charles Sleicher University of Washington Canada Leslie W. Shemilt McMaster University Library Representative Thomas W. Weber State University of New York Spring 1991 Chemical Engineering Education Volume XXV Number 2 Spring 1991 EDUCATOR 62 Angelo J. Perna, of the New Jersey Institute of Technology, Deran Hanesian DEPARTMENT 64 UCLA, D.T. Allen, S.M. Senkan CURRICULUM 68 Developing a Course in Chemical Engineering Ethics: One Class' Experiences, James C. Watters, Dominic A. Zoeller 74 An Introduction to Equilibrium Thermodynamics: A Rational Approach to Its Teaching; Part 1, Notation and Mathematics, Donald F. Williams, David Glasser 82 A Course in Immobilized Enzyme and Cell Technology, William E. Lee, III CLASSROOM 88 A SecondYear Undergraduate Course in Applied Differential Equations, Thomas Z. Fahidy 106 Principles of Stagewise Separation Process Calculations: A Simple Algebraic Approach Using Solvent Extraction, Barry D. Crittenden 112 Computation of Multiple Reaction Equilibria, Alan L. Myers RANDOM THOUGHTS 80 We Hold These Truths to be SelfEvident, Richard M. Felder CLASS AND HOME PROBLEMS 92 Removal of Chlorine From the ChlorineNitrogen Mixture in a Film of Liquid Water, Sarwan S. Sandhu VIEWS AND OPINIONS 96 Undergraduate Education: Where Do We Go From Here? Richard G. Griskey LABORATORY 98 PurdueIndustry Computer Simulation Modules: The Amoco Resid Hydrotreater Process, R.G. Squires, G.V. Reklaitis, N.C. Yeh, J.F. Mosey, LA. Karimi, P.K. Andersen 102 Crystallization: An Interesting Experience in the ChE Laboratory, Te6filo A. Graber S., Maria E. Taboada M. 79 Call for Papers 79,97 Book Review 110 Books Received CHEMICAL ENGINEERING EDUCATION (ISSN 00092479) is published quarterly by the Chemical Engineering Division, American Society for Engineering Education and is edited at the University of Florida. Correspondence regarding editorial matter, circulation, and changes of address should be sent to CEE, Chemical Engineering Department, University of Florida, Gainesville, FL 32611. Advertising material may be sent directly to E.O. Painter Printing Co., PO Box 877, DeLeon Springs, FL 32130. Copyright 1991 by the Chemical Engineering Division, 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, ASEE, which body assumes no responsibility for them. Defective copies replaced if notified within 120 days of publication. Write for information on subscription costs and for back copy costs and availability. POSTMASTER: Send address changes to CEE, Chem. Engineering Dept., University of Florida, Gainesville, FL 32611. 61 educator ) ANGELO J. PERNA of the c New Jersey Institute of Technology T First... the student (1950) and then... the teacher (1991) f k DERAN HANESIAN New Jersey Institute of Technology Newark, NJ 07102 A ngelo J. Perna (or Angie, as he is more familiarly known to friends and colleagues) was born in Brooklyn, New York, in 1931, to Vito and Marie Perna, who had immigrated to the United States from Italy. He was the fourth child in a family of eight children. Although Angie's early years paralleled the great depression in the United States, the Perna family was never unduly affected since Vito was selfem ployed and was able to continuously provide for his family. Education was always highly stressed in the Perna household, and the children were encouraged to help one another to excel in academics. Angie enjoyed, and was accomplished in, both academics and sandlot sports as he was growing up. He participated in baseball and football activities and was on several championship teams in each sport. He says that he always knew he would even tually go to college and become a teacher, but during his early years he was undecided whether to pursue engineering or history as a careeralthough he en joyed chemistry and mathematics, it was in history that he received early academic recognition. When Angie was a junior in high school his fa ther passed away after a long bout with cancer. The lengthy siege of illness had created such a serious fi nancial drain on the family resources that when Angie graduated from high school the following year, he had to postpone his plans for college and join the workforce instead. He worked first for the Motion Picture Association of America and later in the gar ment industry before being drafted into the United States Army in January of 1952. Angie was sent to Camp Breckenridge, Kentucky, for basic training before being sent to Korea in June of 1952, where he served with Company K of the 279 RCT attached to the 45th Division until August of 1953. While in Korea he rose to the rank of staff sergeant and earned several battle stars and the Combat Infantryman's Badge. Angie was honorably discharged in November of 1953 and through the GI assistance program he was finally able to begin his postponed college education. It is interesting to hear how he made the decision to attend Clemson and take up chemical engineering: When Igot out of the service Ifelt I could not go to a school in the immediate area and live at home. I really wanted to go to Brooklyn Poly, but since all of my friends were now working, I knew I would be socializing with them, and I could never have undertaken a course of study while continuing to intermingle with my friends; therefore, the school I attended had to be one which was far enough away so that I had to live Copyright ChE Division, ASEE 1991 Chemical Engineering Education r *~ ~ there instead of at home. In addition, it had to be inexpensive enough so that my savings and my GI support could see me through the studies. Insofar as to why I chose chemical engineering this was simple. I happened to read an article in the New York Times which gave a salary survey for all engineers, and chemical engineers were paid the most. This fact appealed to me, and since I had done fairly well in chemistry, my field of study was now fixed. As for Clemson, a cousin of mine had gone there prior to the second world war and a high school classmate of mine was currently attendingand both of them were enthusiastic about the place. So I thought, 'Why not?" In addition, I remembered they had a pretty good football team (even in those days). I saw in the college catalog that they offered chemical engineering and that it was fairly inexpensive, so I applied for admission, and I was accepted. I entered the school in January of 1954. These decisions were the most fortuitous ones I have ever made, and I have been thankful to the fates ever since. I found a school I respect, a profession I love, and I met not only a great group of classmates, but also Dr. Charles E. Littlejohn. Dr. Littlejohn was a dedicated teacher who in stilled a sense of pride and professionalism in his students, and he had a marked effect on Angie's life. Even in the face of all of Angie's eventual technical accomplishments in teaching and research, it is the area of service to his colleagues and his profession in which he places the greatest value. He credits Char ley Littlejohn with instilling in him a sense of re sponsibility toward both his chosen field of endeavor and its related professional organizations. After graduation from Clemson, Angie joined Un ion Carbide where he worked at the Y12 plant in Oak Ridge, Tennessee. While there he worked as a production engineer, as a researchdevelopment en gineer, and finally as a production scheduler. He found himself working on innovative powdered met allurgy techniques and isostatic pressinginterest ing work, but classified since it dealt with thermo nuclear weapons. After more than three years at Union Carbide he decided to return to school to work on his Master's degree and to continue with his plan to enter the teaching profession, so in September of 1960 he re turned to Clemson and became a member of the ini tial graduate class in chemical engineering. During this period of time Angie became inter ested in the environmental area through his inter Spring 1991 action with George Meenahan, a professor in chemi cal engineering, and Gene Rich, chairman of the civil engineering department and author of Unit Op erations of Sanitary Engineering. Angie helped Dr. Rich by reviewing his book and (together with a classmate, Bill Huffman) by solving the text prob lems. This period of time had a great influence on his strong belief that chemical engineers are ideally suited by their training to be a force in solving the challenges that the environment presents. It was Even in the face of all of Angle's eventual technical accomplishments in teaching and research, it is the area of service to his colleagues and his profession in which he places the greatest value. during this time that Angie also began his associa tion with the unit operations laboratory when, as a graduate assistant, he was given the responsibility for the lab. After obtaining his Master's in 1962, he went to VPI to teach metallurgy for a year before going on to the University of Connecticut for his PhD degree. His classmates at UConn were an unusual group since, like Angie himself, all of them had been out of college for a period of time prior to returning to college to pursue advanced degrees, and all of them eventually went into teaching. The group consisted of Herb Klei and Mike Howard of UConn, George Knepple of William Patterson, and Pat Marino. While at UConn, Angie was an instructor in chemical engineering and taught the unit operations laboratory. He did his research under Dr. L.F. Stutzman in the area of distillation dynamics and control. After receiving his PhD, Angie joined the Depart ment of Chemical Engineering and Chemistry at Newark College of Engineering in Newark, New Jersey, and he and I began what was to be a long co operative effort. In the late 1960s we worked to gether on a fivestory unit operations lab and a sepa rate process dynamics and control lab, and in addi tion to designing about thirty experiments, we suc cessfully wrote proposals and received funding from NSF, the State of New Jersey, and the industrial sector, amounting to approximately onehalf million dollars. We developed a new teaching format that included a sixhour onceaweek lab with three dif ferent types of lab reports and oral student presen Contined on page 86 Prtment ChE at U C D.T. ALLEN, S.M. SENKAN University of California Los Angeles, CA 90024 The University of California at Los Angeles, founded in 1929, is located in rolling green hills just five miles from the ocean, in one of the most at tractive areas of Southern California. It is bordered on the north by the residential community of BelAir and the Santa Monica mountains. Its southern bound ary is Westwood Village, which serves as a shopping and entertainment center for Los Angeles. The at tractive campus on 419 acres is the home of about 2000 faculty and 35,000 students. The UCLA Department of Chemical Engineering is part of the School of Engineering and Applied Science, which was originally established as the Col lege of Engineering in 1944. The school has grown steadily in stature and reputation and now ranks among the top ten schools of engineering nationwide and is among the top five schools of engineering at public universities. Chemical engineering is a rela tively young department, officially established in 1983 and accredited by ABET shortly thereafter. Prior to 1983 the department was part of a unified undergraduate engineering program. Since its establishment and accreditation in 1983, the department has undergone steady growth in stat ure and reputation. At present the department of fers BS, MS, and PhD degrees in chemical engineer ing, and the current total enrollment is about 150 undergraduate and 50 fulltime graduate students. The department offices and most of the research laboratories are housed in Boelter Hall, which is currently undergoing a major renovation that will double the available floor space. At present the department offers BS, MS, and PhD degrees in chemical engineering, and the current total enrollment is about 150 undergraduate and 50fulltime graduate students. ... the annual research budget is over 2 million dollars Hoyce Hall, one of the four buildings that made up the original UCLA campus in Westwood The number of faculty has also increased stead ily, to a current level of twelve. This has led to a spectacular increase in graduate research activity; at present the annual research budget of the depart ment is over 2 million dollars, placing it in the top fifteen in the nation in federal research funding. These funds support our fifty graduate students, numerous undergraduate research assistants, and postdoctoral research associates. The department typically admits about fifteen new graduate students each year, including both domestic and international scholars. THE FACULTY AND THEIR RESEARCH The design of clean, environmentally compatible technologies is a key challenge facing modern indus try and the profession. The UCLA chemical engi neering department is playing a leading interna tional role in developing the research and design fundamentals needed for a rational approach. The department presently houses two highlyvisible na Copyright ChE Division, ASEE 1991 Chemical Engineering Education gl11ep tional research centers: the National Center for In termedia Transport (sponsored by the US Environ mental Protection Agency since 1981), directed by Yoram Cohen, and the National Science Foundation Engineering Research Center for Hazardous Sub stances Control (established in 1987), directed by Sheldon Friedlander. Although many of our faculty members participate in the activities of these cen ters, the research conducted in the department is diverse, as can be seen in the following paragraphs and in the Table 1 summary. Reaction Engineering Reaction engineering and kinetics is one of the major research areas in the department. The research programs undertaken by Professors Allen, Hicks, and Senkan seek a better understanding of the mechanisms of homogeneous and heterogeneous reactions at the molecular level. David Allen's research emphasizes the application reaction en gineering principles to energy and environmental issues. His current interests include the molecular modeling of petroleum processing (particularly catalytic cracking) as well as gastoparticle reaction pathways in urban atmos pheres, and development of catalytic hydrodechlorination processes. In his research, Robert Hicks studies the cata lytic oxidation of hydrocarbons using Pt and Pd as cata lysts, with the objective of developing more efficient auto mobile catalytic converters that will lead to reduced pol lutant emissions at coldstart conditions. Selim Senkan's research in reaction engineering is directed toward the de velopment of detailed chemical kinetic mechanisms (DCKM) describing hightemperature processes such as hydrocarbon pyrolysis, oxidation, and combustion. DCKMs developed by Professor Senkan involve the participation of hundreds of species in thousands of elementary reac A1 tions, and rely on the use of largescale computing. The data needed in the development of DCKMs are derived from experiments conducted jointly with physical chem ists and theoretically via the use of computational qiuan tum mechanics. Materials Processing The research of Yoram Cohen involves the develop ment of novel materials and resins using polymer adsorp tion, polymer grafting, and surface silyation processes. Traugott Frederking's research in thermodynamics and transport phenomena at low temperatures (i.e., cryogen ics) is paving the way for the development and better utilization of superconductors. Sheldon Friedlander is investigating the development of new technologies involving ultrafine particles, including the design of aero sol reactors and the engineering of submicron agglo merate structures composed of multicomponent aero sols. The deposition of semiconductor and metal thin films for microelectronic devices using organometallic chemical vapor deposition is an expanding area of re search of Robert Hicks. Combustion At present, combustion and combustionrelated activi ties are underway in the departments of chemical engi neering, mechanical engineering, and chemistry. Eldon Knuth developed one of the first Molecular Beam Mass Spectrometer systems in the world to study flame struc ture. He is currently exploring relaxation processes in molecular beams and cluster formation in lowtempera ture freejets. Selim Senkan is investigating the effects of halogens in hydrocarbon combustion, and in particular their role in the formation of toxic combustion byprod ucts. His research has important applications to hazard ous waste incineration. In addition, his research empha  Students can enjoy swimming, skiing, and mountain climbing... on the same day! Spring 1991 sizes the use of combustion as a manufacturing process to synthesize useful chemicals from abundant natural resources by partial oxidation. Owen Smith's research in combustion emphasizes the development of non intrusive optical diagnostics, such as particle image veloci metry and laser induced fluorescence. He recently de veloped a twodimensional resonantlystabilized dump combustor which promises to be particularly useful in waste incineration. Transport Phenomena Yoram Cohen and Sheldon Friedlander study the transport of pollutants in air, water, soil, and other envi ronmental media, particularly through the National Cen ter for Intermedia Transport. These studies are not con fined merely to dispersion within single environmental media; rather, they focus on processes occurring at inter faces (particularly airsoil and airwater interfaces) and the incorporation of these intermedia transport processes into multimedia studies of pollutant impact on the envi ronment. The application of transport phenomena at cryo genic temperatures is the specialty ofTraugott Freder king. He is currently working on screen and perforated plate compact cryocooler systems at liquidhelium tem peratures, with the objective of developing a basic under standing of thermal boundary layer conditions at super conductorliquid interfaces. Electrochemistry Fundamental and applied electrochemistry is the ma jor research thrust of Ken Nobe. Typical industrial appli cations that are addressed in his laboratory include reduc tion of corrosion rates in marine environments, reduction of hydrogen embrittlement of highstrength steels, and improvement of the efficiency of electrochemical manufac turing operations like the electrodeposition of specialized metals like Invar. Along with the late Manuel Baizer, Pro fessor Nobe and his group have also pioneered paired electroorganic syntheses in flow reactors. In a collabora tive activity, Vincent Vilker and Nobe are exploring elec troenzymology as a method for the synthesis of fine chemi cals and for the development of biosensors. TABLE 1 Chemical Engineering Faculty and Research Interests at UCLA DAVID T. ALLEN Environmental Reaction Engineering Atmospheric Aerosol Chemistry Processing of Heavy Fuels and Hazardous Waste Molecular Models of Catalytic Cracking Chemistry YORAM COHEN Polymer Science and Transport Phenomena Polymerization Reaction Engineering Brownian Dynamics ofMacromolecules Polymer Grafting and Adsorption * NonNewtonian Fluid Mechanics Water Purification * Multimedia Transport of Toxic Chemicals and Exposure Analysis TRAUGOTT H. K. FREDERKING Cryogenics Low Temperature Transport in Porous Media, Phase Separ ation, Thermomechanical Devices Heat Transfer Cryo cooler Components, SuperconductingDevices and Related Transport Phenomena SHELDON K. FRIEDLANDER Aerosol Technology and Air Pollution Formation and Behavior of Submicron Particles Source Allocation and Receptor Modeling Air Pollution Control * Mass Transfer and Diffusion Particle/Surface Interactions ROBERT F. HICKS Surface and Interface Engineering Catalysis Reaction Engineering of Organometallic Vapor Deposition ELDON L. KNUTH Molecular Dynamics in Gas Flow Vibrational, Rotational, Translational Relaxations Conden sation and Evaporation Chemical Relaxations VASILIOS MANOUSIOUTHAKIS Process Design, Dynamics and Control Linear and Nonlinear Control Systems Design Integration of Design and Control Process and Control Systems Design for Microelectronic Material Manufacturing Waste Minimi zation Through Chemical Process Synthesis Separation Network Synthesis HAROLD G. MONBOUQUETTE Biochemical Engineering Biomimetic Membrane Systems Culture of Microbes that Thrive at Extremes of Temperature, pH, and Salt Concen tration Biosystems for Heavy Metal Recovery Immobil izedCell Fermentations KEN NOBE Electrochemistry Catalysis Battery and Fuel Cells Corrosion and Electro deposition of Metals and Semiconductors Bioelectro chemistry SELIM M. SENKAN HighTemperature Chemical Kinetics and Reaction Eng. Combustion, Gas Kinetics, Flame Chemistry Incineration of Hazardous Materials Computational Quantum Mechan ics Synthesis of Useful Chemicals by Combustion OWEN I. SMITH Combustion HighTemperature Chemical Kinetics Reaction Mechan isms in Combustion, Incineration and Chemical Vapor Deposition Optical Methods for Combustion Diagnostics VINCENT L. VILKER Biochemical Engineering Colloid and Interfacial Phenomena Proteins, Virus, and Bacteria Bioelectrochemical Catalysis 6 Chemical Engineering Education Biochemical Engineering Professors Monbouquette and Vilker form the chemi cal engineering component of a strong collaborative re search program in biochemical engineering. Collaborating with faculty in pharmacology, biological chemistry, mo lecular biology, microbiology, public health, and civil engi neering, they are working on problems related to the cleanup of groundwater contamination, chemical synthe sis, and chemical sensors via the use of modern biochemi cal methods. Vincent Vilker's research is focused on bio catalysis of bacterial redox enzymes. He is developing processes to detoxify trace contaminants in water, to syn thesize oxygenated hydrocarbons and fuel additives and is undertaking research to optimize the production of en zyme system proteins in natural or cloned host bacteria. Harold Monbouquette is pioneering the use of archaebacteria (i.e., bacteria that thrive under extreme conditions, such as temperatures in excess of 100 C and pH levels below 1 and above 10) to synthesize highly stable enzymes for use in the treatment of toxic wastes and for the synthesis of new biomaterials. Process Design and Control The design and control of chemical processes for mini mal environmental impact is an underlying theme in much of Vasilios Manousiouthakis' work. He has developed the concept of massexchange networks, which is extremely important in chemical process industries. He has also developed approaches for estimating the waste minimiza tion potential of chemical processes. His research in proc ess control involves studies on the dynamic behavior and control of generalized linear and nonlinear systems using algebra, topology, functional analysis, differential geome try, and optimization. Separations The overall goal of the separations program, guided by Yoram Cohen and Harold Monbouquette, is the de velopment of novel separations processes, including highly selective membranes and sorbent media, through chemical tailoring of the phase interface. Current projects include the construction and study of new polymersilica resins for selective sorption of organic and heavy metals and biomimetic membranes for metal recovery. They have recently initiated a collaborative proj ect involving the creation and testing of novel ceramic supported polymer membranes for applications in perva poration and hyperfiltration. As is evident from the foregoing discussion, re search activities undertaken by chemical engineer ing faculty at UCLA span studies from the molecu lar level (characterized by length scales on the order of Angstroms) to the design and control of large scale systems (characterized by length scales on the order of meters to kilometers). As indicated, many of the studies deal with environmental issues. An im portant outgrowth of these coupled activities is that the students not only receive training in the funda Spring 1991 mental and applications of science and technology, but they are also sensitized to the needs of society at a time when crucial questions are being asked on how to grow and innovate in an era of economic, environmental, and energy constraints. The environmental theme in the department's research has also had a significant impact on under graduate education. Specialized courses in pollution control technology, mass transfer of pollutants in the ambient environment, and combustion, energy, and the environment have been developed or are in the planning stages. An undergraduate course on toxic substances control (designed for nonengineers) has also been created. In addition to the development of specialized courses, the department has focused on incorporat ing environmental issues into all parts of the cur riculum. Examples include design of a wasteto energy incinerator in the capstone design course and the development of chemical reactors with minimal byproduct formation in the chemical reaction engi neering course. The department also offers a variety of addi tional specialty courses, reflecting the breadth of the research activities of the faculty. These courses are complemented by hundreds of science and engineer ing courses offered in other departments. Exposure to worldclass researchers in chemistry, molecular biology, atmospheric sciences, and other disciplines provides exciting opportunities for the intellectual growth of our students. LIFE IN SOUTHERN CALIFORNIA The faculty and students of UCLA enjoy a wealth of cultural and recreational opportunities, both on campus and in greater Los Angeles. Mountain climb ing and skiing, as well as surfing and sailing cen ters, are all easily accessible from campus and are available virtually at any time of the year. World renowned artists in dance, music, and the arts regu larly perform both on campus and at the nearby Los Angeles Music Center. And of course, there is Holly wood, Universal Studios, Disneyland... As LA has become one of the leading metropoli tan areas on the Pacific Rim, the city has become a melting pot of many cultures. Los Angeles has a Chinatown, a Little Tokyo, a Koreatown and many other ethnic communities, together with an outstand ing selection of restaurants. These communities of fer students a window on the world which is avail able in few other cities. O curriculum DEVELOPING A COURSE IN CHEMICAL ENGINEERING ETHICS One Class' Experiences JAMES C. WATTERS, DOMINIC A. ZOELLER University ofLouisville Louisville, KY 40292 The 198889 ABET accreditation guidelines'"I for engineering programs in the United States state, "An understanding of the ethical, social, economic, and safety considerations in engineering practice is essential for a successful engineering career." This tenet obliges engineering programs to incorporate a minimum amount of coursework on engineering eth ics into what is already a tightlypacked curriculum. The manner in which ethics are introduced into the curricula allows for a number of choices. One choice is to incorporate a discussion of ethics into the context of an existing course or courses; another choice is to develop a separate course that deals ex clusively with ethical and other closelyrelated is sues. Then the decision must be made as to what level in the curriculum to place the course. Finally, a curriculum must be developed which meets not only the requirements of ABET but also the needs of the students and the instructor. INTEGRATION VS. STANDALONE APPROACH The pros and cons of integrating "new" material into existing courses versus devising a standalone course to present the material, have long been de bated. In recent years, with the emphasis on incor porating developing technologies into our curricula, there have been many champions of the integration approach. Integration has the obvious advantage of not adding any extra credits or courses to an already demanding courseload. However, we believe that for A standalone course in ethics has advantages an instructor... can be given free rein to develop the curriculum without being confined by the boundaries of a traditional theory or practice course. James C. Watters is an associate professor of chemical engineering at the University of Louisville, and is currently the Acting Department Chair. He received his BE in chemical engineering from the National University of Ireland, University College (Dublin, Ireland) and his MS and PhD degrees from Y < the University of Maryland. His research interests are in novel separation processes, membranes, poly mer synthesis, and methods of teaching and learn ing. Dominic A. Zoeller (photo unavailable) received the Master of Engineering degree in chemical engi neering from the University of Louisville in 1989. He is currently a production engineer in the specialty monomers plant of the Dow Chemical Company in Midland, Michigan. the integration approach to work, the topic must be included in more than one existing course and thus would probably be taught by more than one faculty member. It has been our experience (in several engi neering disciplines) that many engineering faculty members are uncomfortable with the area of ethics as a subject to be included in their existing technical courses. This discomfort may stem from their own lack of knowledge or fear of ethical issues, or their disdain for "diluting" the traditional courses with "soft" topics. In any event, while the integration approach may look like a good idea at first blush, we contend that it is difficult to carry out in practice. As a result of such delibertaions, at Louisville we insti tuted a twocredit course devoted to "Ethical Issues in Chemical Engineering." A standalone course in ethics has advantages. From a teaching perspective, an instructor with a genuine interest in the topic can be given free rein to develop the curriculum without being con fined by the boundaries of a traditional theory or practice course. Also, the student in such a course can dwell on the course topics without worrying that the "nontechnical" issues are taking time from the Copyright ChE Division, ASEE 1991 Chemical Engineering Education seemingly "more important" technical topics of an integrated course. A disadvantage of the standalone course may be the inability of students to integrate ethical issues into technical coursework areas. Both students and educators tend to neatly segment learning into sepa rate courses, with almost sacrosanct boundaries that are not to be crossed. However, this problem can be overcome by judicious placement of the course into the curriculum. WHEN TO TEACH Once we had decided to introduce a separate course in ethics, the next hurdle was to decide where it belonged in the curriculum. Should it be early (for example in the sophomore year), before the student has been exposed to many of the technical areas of the profession and is still "fresh" or "naive"? Or, should it be later (perhaps in the senior year) when the more knowledgeable and, presumably, more mature and "streetwise" student can better synthesize his or her experiences in the profession to decisionmaking? The University of Louisville is unique among chemical engineering programs in the United States in that our accredited degree is the Master of Engi neering, a fiveyear program with mandatory coop erative internship training. We included the "Ethi cal Issues in Chemical Engineering" course in the final semester of the fifth year, although it could easily fit into the final semester of the fourth year in a school with a more traditional program. We con sidered it most beneficial to approach ethical issues from the more mature viewpoint of a fourth or fifth year student. This was particularly helpful for our students since they had all had coop internships. Many had already experienced or witnessed the grey areas of realworld situations. In fact, many of them identified with some of the classic case studies we discussed and volunteered that they had experienced similar quandries in their internships. We elected to offer a twocredit course, meeting once a week for one hour and fortyfive minutes. This framework ensured that students would take the course seriously (since two credits were at stake), and it allowed for the inclusion of class exercises and films that would be difficult to use in a standard, fiftyminute, time slot. The course was taught by one of the authors (JCW), an Associate Professor in the chemical engineering department who has an inter est in, and commitment to, teaching professional responsibility. The pros and cons of using engineer ing faculty to teach ethics have been debated,'12,3 but in our case, financial considerations dictated that it be taught by one of our own faculty. CONTENT AND FORMAT The course, first taught in the spring of 1988, originally took a philosophical and historical per spective on ethics, an approach that the present author was uncomfortable with. He elected instead to use a casestudy approach that was loosely based on a now discontinued, crossdisciplinary course called "Technology and Society" with which he had been involved in the early 1980s.'4' Table 1 lists the content of "Ethical Issues in Chemical Engineering" as presented in the spring of 1989. Class format included lectures, discussions, TABLE 1 Course Outline: Ethics and Values in Engineering The course will examine the foundations of our value sys tems and how these relate to our decisions as engineers. In this context we will examine codes of ethics as proposed by the various engineering societies, classic ethics case studies from the literature, whistleblowing and beyond, and our rights and responsibilities as professionals. The format will include lectures, videotapes, discussions, and presentations by class members. Grading will be based on successfully completing assigned homework and on participation in class discussion. SCHEDULE * Introduction * Why engineers should be concerned with ethics * Film: What You are Now is What You Were When * Class discussion: Origin of our value systems * Class exercise: Where do you draw the line? * Codes of ethics: Advantages and drawbacks * Ethics case studies: UTexas film and discussion * Ethics case studies: Discussion of assigned problems * EthicsThe Law: Professional societies * Classic ethics cases: Student presentations * Classic ethics cases: Student presentations * Film: "Do Scientists Cheat?" (NOVA) * Whistleblowing: What, When, How * Films: "Enemy of the People" (60 Minutes) "Pomeroy File" (60 Minutes) * Whistleblowing: Support, discussion * Responsibility: Film, Toxic Trials Summary and Conclusions  Spring 1991 Integration has the obvious advantage of not adding any extra credits or courses to an already demanding courseload. However, we believe that for the integration approach to work, the topic must be included in more than one existing course and thus would probably be taught by more than one faculty member. videotapes, and presentations by students. Class ma terials included texts, films, and experiential exer cises. Appendix A presents a brief annotated bibliog raphy of the materials used and referenced during the semester. Topics addressed included the founda tion of our individual value systems, codes of ethics and their limitations, whistleblowing and its conse quences, and the whole concept of responsibility for one's actions. Grades were based on weekly home work assignments, participation in classroom dis cussions, and presentations of assigned materials. No examinations were giventhe authors firmly believe that a topic such as ethics is best taught and best received by students in a nonthreatening, semi informal format. The first weeks of the course are devoted to an examination of what each student believes on ethi cal and moral issues, where those beliefs came from, and why such issues should be of concern. The film What You are Now is What You Were When presents a perspective that relates one's moral philosophy to the major features of one's early upbringing. Stu dents are encouraged to apply this model to people they know, such as parents, teachers, ministers, poli ticians, etc., and to discuss how applicable it is to their own lives. The next segment of the course deals with profes sionalism and the concept of ethics codes. Many codes, such as those ofAIChE, IEEE, and NSPE, are exam ined for thoroughness, applicability, etc. Students quickly learn that some codes (such as AIChE's) are very vague, while others (such as NSPE's) are much more detailed. Yet even the detailed ones do not come close to addressing every situation and, in fact, some of the tenets are potentially contradictory. The student who is looking for a "quick fix" in the codes soon realizes that absolution of personal decision making is rarely to be found. The concept of taking responsibility for one's own actions also starts to develop at this point in the course. Students are asked to discuss the case stud ies presented by Kohn,'5' with particular reference to the ethics codes, and they quickly realize that even some of the seemingly simpler situations involving ethical decisionmaking lack easy black andwhite answers. When the student responses are compared with those of employed engineers (tabu lated by Hughson and Kohn'61' the diverse opinions are readily apparent. The comparison also allowed us to see how opinions have changed over a period of ten years. The culmination of this segment of the course was a discussion, based on Unger,[71 of the inter faces between ethics and the law, and between eth ics and professional societies. Students are struck by the widely different levels of support afforded by the various professional societies for engineers with ethical dilemmas. The last segment of the course deals with whistleblowing and its consequences. This topic ac tually weaves a thread through the whole course, since many of the case studies evolved from someone "blowing a whistle" or from someone having been the victim of such action. The excellent NOVA film, "Do Scientists Cheat?" demonstrates the consequences of not blowing a whistle as well as what happens when one does. The two 60 Minutes segments, "Enemy of the People" and "The Pomeroy File," outline the histories of a whistleblower and of one who "dared" to speak out in public on a contro versial issue. Each week students had to carry out a homework assignment that consisted primarily of discussion questions, many culled from Ethics in Engineering 8. Around midsemester, the students (working in pairs) developed an indepth study of a major ethics case. Topics included Bhopal, the Challenger, BART, the Corvair, the Pinto gas tank, Hooker Chemicals, etc. In addition to a written report, the teams presented their findings orally, either formally or in a role playing format. OBSERVATIONS OF A STUDENT (DAZ) As a fifthyear student in engineering, I felt a great deal of apprehension in attending my first ethics class. It seemed strange that after spending five years honing my skills in making cold, calculat ing, rightorwrong decisions, the administration now felt it necessary to train me in ethics. Unfortunately, this attitude was shared by most of my classmates. However, I found that several aspects of the course Chemical Engineering Education enabled me to take the concepts and theories beyond the walls of the classroom. The first tool was the textbook,r7 which was clear cut and easy to read. In some cases, the author ad mitted that there were no right answers, even with the aid of hindsight. This was refreshing. By using current and semicurrent examples from the engi neering field, the author was able to keep the inter est of the reader. In many cases the incidents pre sented were already common knowledge, while other events had taken place prior to our collective mem ory. It was interesting to compare class reactions to these two different stimuli. In the first case, the class usually had preconceived notions about the case, but when the incident was unfamiliar they were at the mercy of the materials presented for making their conclusions. In most cases the class easily formed a consensus on ethical issues. The second tool for generating interest in the class was the syllabus. Dr. Watters recognized that it would be impossible to alter the psychological constitution of the students and sought instead to raise our level of consciousness in the area of ethical questions. By working through several scenarios, reading the text and several handouts, watching some video presentations on ethical issues, and hold ing candid discussions, he hoped we might recognize our position in the ethical loop. The effect of this candid approach to what could have been a boring dotherightthing course was profound. We began to view the class as a lively forum rather than a waste of time. As we prepared for each class through the reading assignments and our weekly reports, we were intrigued by the ques tions we could not answer. We explored the difficulty of enforcing a uniform code of ethics in a predomi nantly freewill society. We discovered the moral dilemma of selfpreservation versus doing what is right, and we discussed legislative efforts to man date morals. We discovered that being ostracized by your peers and associates is often the penalty of being ethical. Dr. Watters realized that such a class does not lend itself to the general form of the engineering curriculum and that he could not simply spout platitudes to the class. Instead he allowed us to "discover" the ethical questions of which we were ignorant. There was also an investigative assignment for the class to carry out. Transcripts of several ethical incidents were distributed to the class and were to be researched by teams of two. The students were required to research their individual case and pres ent to the class the ethical issues involved, the mis takes that were made, where the blame lay, and, if possible, where the players are now. The selection of cases consisted of three major types. First was the historical case. The incident was usually common knowledge to all participants, the data were available from simple research, and a We explored the difficulty of enforcing a uniform code of ethics in a predominantly freewill society. We discovered the moral dilemma of self preservation versus doing what is right, and we discussed legislative efforts to mandate morals. conclusion had in most cases been made. For such a case, the students were able to perform all of the tasks of the investigation unless some of the infor mation had been lost in history. The second form was a historical case which was not common knowledge. Like the previous example, there is a great deal of information available and a conclusion has probably been made. However, their lack of familiarity with the incident allows the stu dents to arrive at their own conclusions. Care must be taken, however, that the students do not simply write a book report, but rather that they seek out sources for several viewpoints. The third type of case was the current event, and it was the most difficult to research. Since ethics, or the lack thereof, is a popular subject in the press, there are usually several general examples from which to select. However, it may be difficult to get enough information to make legitimate deci sions since in many cases the incidents are still under investigation. When that is the case, the sce nario may better serve the class as a source of im promptu discussion. From my perspective as a student, there are sev eral effective ways to spark interest: Emphasize participation over a letter grade Promote openended discussions Moderate discussion in an unoffensive manner Use reading and AV materials as a starting point for dialogue, not as an end unto itself Keep all of the students involved in the discussions Use interactive exercises where possible Allow time for dialogue Instructors should be openminded about students' opinions and, if need be, avoid subjects on which they have a strong personal bias Some important concepts taken from the class Spring 1991 include the following: Personal convictions dictate the level of an individual's ethics. IEEE is a model for a professional organization's support of its members on ethical issues. Persistent and tactful communication is the most powerful weapon available to the subordinate engineer for the prevention of serious ethical blunders. In many cases ethical dilemmas are "loselose" situations: to be a whistleblower can result in firing and/or blackballing, but allowing an unethical practice to persist poses personal problems as well as leads to the possibility of being fired, blackballed, or imprisoned. The most common and most difficult dilemma is faced when one must choose between survival and "doing the right thing." MUSINGS OF AN INSTRUCTOR (JCW) When I first volunteered to teach the ethics course I experienced some feelings of trepidation. After all, how was I going to have any impact on the ideas and ideals of a group of young adults, in their early to midtwenties, who had known me for several years socially as well as in the classroom? However, this uncertainty actually led me to the approach I took. Because we knew each other, I felt we could be hon est with each other and refrain from juding each other by each other's opinions. We could be critical of those opinions and we could try to change or influ ence them, but we would not judge a classmate sim ply by his or her opinion on some topic. This ap proach led to some initial reticence, but everyone soon became comfortable with talking in our group, and some excellent discussions resulted. A feature which aided the giveandtake of our discussions was the removal of the pressures of an examination. Class goals, objectives, and require ments were clearly spelled out from the beginning, and the students knew what they had to do to "make the grade." They came to look upon the ethics class not only as a break from the normal routine of the ory and research, but also as something which would be important in their future. Just how topical and current an ethics course can be was illustrated by an incident which happened during the course of the semesterthe vessel, Exxon Valdez, hit a reef in Alaska. For several weeks the class followed this developing story, and we dis cussed the ethics of supertankers, drunkdriving pi loting, complacency on safety issues, progress ver sus the environment, the rising price of gas at the pumps, etc. It was invaluable as a learning experi ence, it reinforced theory, and it illustrated that a welldesigned ethics course should be flexible enough to capitalize on current events. Overall, the course was well received by the stu dents. The discussions were lively and the effort they put into the assigned projects was excellent. To involve all the students in the discussion, class size should be small (preferably less than twenty stu dents). This type of course requires that students be treated as adults, and students thus treated will generally respond favorably. The result is a satisfy ing and fulfilling experience for all concerned. REFERENCES 1. Accreditation Board for Engineering and Technology, Inc., (ABET), Criteria for Accrediting Programs in Engineering in the United States, New York, NY (1987) 2. Tucker, W.H., "Dilemmas in Teaching Engineering Ethics," CEP, p. 20 April (1983) 3. Wilcox, J.R., "The Teaching of Engineering Ethics," CEP, p. 15, May (1983) 4. Lindauer, G.C., and D.J. Hagerty, "Ethics Simulation in the Classroom," CEP, p 17, July (1983) 5. Kohn, P.M., "Perplexing Problems in Engineering Ethics," Chem. Eng.,, p. 96, May 5 (1980) 6. Hughson, R.V., and P.M. Kohn, "Ethics," Chem. Eng., p. 132, September 22 (1980) 7. Unger, Controlling Technology: Ethics and the Responsible Engineer, Holt, Rinehart, Winston, New York, NY (1982) 8. Martin, M.W., and R. Schinzinger, Ethics in Engineering, McGrawHill, New York, NY (1989) APPENDIX ANNOTATED BIBLIOGRAPHY The following is a list of materials (books, films, articles, etc.) used or usable in an ethics course. It is by no means complete. The opinions expressed are those of the senior author (JCW) and are intended to aid an instructor formulating a new course in ethics. * Books Unger, Stephen H., Controlling Technology: Ethics and the Responsible Engineer, Holt, Rinehart, and Winston, New York (1982) A concise survey of many aspects of the ethics question, including the codes of ethics, the role of engineering societies, ethics and the law, and how to avoid conflict. The author takes a downtoearth approach to his topic and the text is liberally laced with case studies which illustrate the theory. The book is biased towards electrical engineering (reflecting the background of the author), so there is heavy emphasis on the IEEE code and EE case studies. The book was generally well received by the students in my class, though the value for money was questioned ($20* for a 190page paperback). Martin, M.W., and R. Schinzinger, Ethics in Engineering, McGrawHill, New York, NY (1983, 1989) This book is subdivided into four sections: The Scope of Chemical Engineering Education Engineering Ethics; The Experimental Nature of Engineering; Engineers, Management and Organizations; and Career Choice and Future Issues. The approach is more philosophical in nature than Unger's, especially in the first section. However, the text is generally readable and has a broader scope than Unger's. It contains excellent discussion problems for homework or inclass analysis. There are some problems in the first edition which are omitted from the second, and the second edition includes some recent case studies such as Bhopal and Challenger, along with some new problems. Flores, A., Ethical Problems in Engineering, Vol. One: Readings, Rensselaer Polytechnic Institute, Troy, NY (1980) This volume consists of a series of essays by several authors on the general topics of professionalism, codes of ethics, competitive practice, employed professionals, and social responsibility. As with any series of papers, this one lacks the continuity of a monograph and the entries sometimes overlap. The resulting text tends to drag and makes very dry reading. However, a short, judiciouslychosen selection could enhance a lecture course. Baum, R.J., Ethical Problems in Engineering, 2nd ed., Vol. Two: Case Studies, Rensselaer Polytechnic Institute, Troy, NY (1980) This is the companion volume to the book by Flores. It presents analyses of, and essays on, many of the classic ethical cases from about 1960 to 1980. Included are the BART case, the Pinto gas tank, the Corvair, Hooker Chemicals, and many others, some of which are not so well known. They serve as excellent starting points for student research and classroom discussion. Some of the studies are quite brief, while others extend to twenty or more pages. SFilms "What You are Now is What You Were When" This film, about ninety minutes long, is a monologue by Dr. R. Massey, formerly of the University of ColoradoBoulder, which examines the origins of our value systems by looking at influences in our past lives, such as family, church, schools, peers, media, etc. His model is then applied to different generations to see how events in their teens and twenties influence their outlook and actions today. Massey is a dynamic presenter who talks "a mile a minute" with a strong Texas twang. Students either love him and find him hilarious, or loathe him and find him nauseous. My version of the film is somewhat dated (1976), but I understand there is a more recent edition available. The film contains some mild profanity, but nothing the students haven't heard in the movies, or indeed in the AIChE room! "Do Scientists Cheat?" NOVA (1989) This excellent film examines if and how practitioners of science cheat in presenting research results. The pressures put on young scientists to publish and win grants are cited as major causes for this errant behavior. Some classic and recent cases are examined in detail. The consequences for one scientist who "blew the whistle" on another's falsified data are discussed, leading to the seeming conclusion that neither of them escaped from the situation unscathed. The film makes a good jumpingoff point for classroom discussion of whistle blowing, ethics in academe, falsifying of data, etc. (lasts about one hour). "Enemy of the People," 60 Minutes An examination of the case of an employee of Lockheed Georgia who made an issue of cost overruns in government contracts. He was ostracized byhis community (a onecompany town), his church, and his employer. When he was fi.,ally reinstated in the company, it was in a "paperpushing" position. The issue of whistle blowing as a loselose situation is very evident in this film (lasts about twenty minutes). "The Pomeroy File," 60 Minutes This film examines the case of a pilot for Continental Airlines who spoke up at a town meeting against a proposed nuclear power plant and later found out that a national security file had been compiled on him, citing him as a subversive. The issues of freedom of speech, national security files on individuals, "subversives," and the use of such files as leverage with an individual's employer, are discussed. Ethics Case Studies, Chemical Engineering Department, University of Texas. Contact: D.M. Himmelblau This film features roleplaying of five of the cases presented by Kohn (1980), including analysis by a panel of "experts." While the acting leaves something to be desired and the dialogue and roles are highly sexist, it is helpful to see these case studies portrayed as "real life" situations (lasts about thirty minutes, about five to seven minutes per case). The concept of responsibility within the chemical industries is highlighted in many recent NOVA and Frontline films. Some examples are "Toxic Trials" (concerning chemicals in the groundwater being linked to abovenormal incidences of leukemia in Woburn, Massachusetts), "Who's Killing Calvert City?" (about pollution problems and local politics in Calvert City, Kentucky), and "Nuclear Legacy" (about the nuclearwaste disposal problem). Each film lasts about one hour. * Simulations / Games Where Do You Draw the Line? An Ethics Game (Simile II, Del Mar, CA 1977) Five (or less) groups of participants make ethical judgments about the behavior of people described in a variety of situations. Each group makes decisions about different sets of situations and as the results are tabulated some interesting discussions occur. Once it is made apparent that each group was considering different situations, discussion can be directed towards discovering the assumptions which the groups used to make their judgments and the implications of those assumptions. The issues raised are stealing, income tax evasion, and withholding of information (takes about ninety minutes, including discussion time). Whistleblowing Case (Lindauer and Hagerty, 1983) A young engineer is presented with an ethical dilemma and is forced to make a decision on blowing the while on his employer. A cast of ten to twelve characters, representing various interests in the case, provide him/her with support or harassment (takes about one hour to complete, with up to another hour for discussion). O Spring 1991 curriculum AN INTRODUCTION TO EQUILIBRIUM THERMODYNAMICS A Rational Approach to Its Teaching PART 1: Notation and Mathematics' DONALD F. WILLIAMS, DAVID GLASSER University of the Witwatersrand Johannesburg, South Africa traditionally, undergraduate students of thermo dynamics have difficulty understanding the sub ject and its material. While we do not deny that there are conceptual difficulties to overcome, it seems to us that there are two factors in the usual ap proach that make a student's introduction to ther modynamics more difficult than is necessary. First, there is the underlying mathematics of the state functions and the notation associated with it. This often seems to suggest that the "state func tions" and their mathematics are different from the functions which the student has already met in his previous mathematical education. Second, the way in which the state functions (internal energy, entropy, and temperature) are introduced is not easily related to the students' previous background in physics. In order to address these two problems, we devel oped an approach which has now been taught to thirdyear chemical engineering undergraduates for the last six to seven years. It has been our experi ence that the students have been able to relate the material to their previous work in mathematics and physics with relative ease, and that they have been able to assimilate the subject without undue diffi culty. As a result, the general level of understand ingof both the students and the teachershas been significantly improved. Since the approach tackles the two factors men tioned above, which have applicability in quite dif ' Part 2 of this paper, "Internal Energy, Entropy, and Tempera ture," will appear in the next issue of CEE. Donald Williams has taught at the University of the Witwatersrand since 1967. He has a special interest in teaching chemical engineering to students at the junior end of the curriculum and has recently devised a new course to be taught to firstyear students. His m n itl irl et llJpruvniy itha tahinsiy ui a trimuodynamics was first aroused while being taught by David Glas ser in one of his earliest efforts. David Glasser is a professor of chemical engineering at the University of the Witwatersrand. He holds de grees from the University of Cape Town and Imperial College (London). His main areas of interest are reac tion engineering and mathematical modeling. He has been interested in teaching thermodynamics eversince he first became involved after being "made an offer" as the mostjunior member of the academic staff. ferent areas, it is convenient to divide our presenta tion into two parts. Part 1 will consider notation and the mathematical development, and Part 2 (which will appear in the next issue of CEE) will be concerned with the introduction of the state func tions. The notation which we introduce was developed by Harris,11,21 and the axiomatic approach adopted in Part 2 is based on Callen,131 who suggested this method as long ago as 1960. We find it surprising that Callen's approach has not found more favor with educators. It is the pur pose of this paper to show how these ideas can be combined to form a logical and consistent introduc tion to thermodynamics. Notation and Mathematical Development Thermodynamics traditionally employs a deriva tive notation which is rarely used elsewhere and which is not obviously consistent with the mathe matics which students learn and use in other courses. Thus, the conceptual difficulties are compounded by the need to learn a sort of thermodynamicc mathe Copyright ChE Division, ASEE 1991 Chemical Engineering Education x ~z matics" which has special kinds of partial deriva tives and nonexact differentials. The mere manipu lation of the notation becomes such an arcane proc ess that this ability is in itself regarded as "thermo," and purely mathematical results are confused with the results of thermodynamics. These nonstandard forms arise for historical reasons and from the problems which arise in using the same symbol to denote a value as well as a function. We will outline below an alternative method of presenting the material which is entirely consis tent with the mathematics of functions to which students are accustomed. We start by emphasizing that the development at this stage is purely algebraic, and no physical significance is intended to be attached to any of the variables we use. Everything could, in fact, be devel oped in terms of x, y, and z. However, we prefer to adopt a set of symbols in which the equations we develop will turn out (when at a later stage we do give significance to some of the symbols) to be di rectly useful. Notation Consider a variable H which may be expressed as a mathematical function (that is a rule for obtain ing a value for a dependent variable from given values of a set of independent variables) of two other variables T and P. For example, we might write that H=T2 +2Tlog(P) (1) Now suppose that another variable V may also be expressed as a function of T and P; suppose, for example, that V = T/P. Since we can solve this rela tionship to give P = T/, we can substitute in Eq. (1) to express H as a function of T and V H = T2 + 2T log(T / V) (2) We thus have two possible functions for H. The first gives us the rule for calculating a value of H from given values of T and P. The second is the rule for calculating a value of H from values of T and V. We might be tempted to indicate these two possible functions for H by some such notation as H(T,P) and H(T,V). However, this is contrary to all the rules for functions we have learned in mathematics, where if H(T,P) is given by Eq. (1), then it follows that H(T,V) = T2 + 2T log(V) (3) which is not the same as Eq. (1) and will not give the required value for H as Eq. (2) will when the state of the system is given by corresponding values of the variables P, V, and T. To keep to the mathematical Spring 1991 We find it surprising that Callen's approach has not found more favor with educators. It is the purpose of this paper to show how these ideas can be combined to form a logical and consistent introduction to thermodynamics. formulation to which we are accustomed, we need to write something like for Eq. (1), and H = f(T,P) H = g(T,V) for Eq. (2), the corresponding relationship in terms of T and V, where we use f and g to indicate that different functions are involved. It is clear that we need to avoid confusion between the value of H at certain conditions and its functional form in terms of the chosen independent variables. The difficulty in thermodynamics arises from two factors. First, the actual functional relationships are rarely known explicitly, and we are usually forced to work only with their derivatives and other proper ties. Second, given the large number of dependent variables of interest (H) and the even larger possible number of combinations of independent variables (P,T,V, . .), there are not really enough function symbols (f,g, . .) to go around. Even if there were enough, it would be very tricky to remember which function symbol represented which variable as a function of which independent variables. We solve this problem by adopting a notation where f and g are replaced, respectively, by HTP and HTV. We may then write equations such as H = HTP(T,P) and H = H"(T,V), where the super scripts remind us both that we are dealing with in dependent functional forms and of the independent variables with which we are concerned, while the terms in brackets tell us the values of these vari ables at which to evaluate the function. For the example above, we will now have the functions HTP = T2 +2T log(P) (4a) HV = T2 + 2T log(T / V) (4b) Note also that values such as HTP(273,1) and HT(273,22.4) are clear and unambiguous. Derivatives Of course, we usually find in thermodynamics that we are concerned not so much with the func tions, that is f or g or HTP (which indeed often turn out to be unknown), but with their derivatives. For 75 the function f of Eq. (1) there are two possible de rivatives: f and f aT aP These derivatives are defined in the usual fashion. For example f li (f(T + AT, P) f(T,P) (5) aT m0 AT (5)T Using our superscript function notation, we may write the two derivatives of f as TP and TP aT aP This notation is found to be considerably less confusing for the student than the conventional one in which the first of the above derivatives is written as ( aT )p where the P is usually read as "at constant P." Be side being somewhat clumsy, this (as we all know) can lead the student into the confusion shown by many classic 'howlers,' such as denying the existence of this derivative at a point in a process in which P is not constant. In fact, of course, as the superscript notation emphasizes, P is not a con stant, but is an independent variable of both H"T and aHTP/aT, of exactly the same status as T. We stress the need to understand the usual nota tion, which the students will, of course, find in texts and other sources which they consult, even if (in the initial stages at least) this understanding is reached by translating into our own notation in order to clarify the functional dependencies. It is, in fact, interesting to note that students may frequently be observed using the superscript notation for this pur pose when working with the differential equations of other courses, such as transport phenomena. Differentials Consider now the equation y = f(x). We define dy and dx to be any two variables which satisfy the equation dy = dx (6) and we call dy and dx differentials. (We need to write the derivative with the symbol a to avoid con fusion with the differentials using the symbol d.) Note that dy and dx are any quantities which satisfy this equation; in particular, there are no implica tions about the "smallness" of these quantities. It is clear that dx and dy define a line which is tangent to the f(x) curve at the point (x,y). Similarly, for our function H"P we define the dif ferentials dT, dH, and dP as quantities which satisfy HTP HTP dH = H dT+ H pdP (7) aT aP If we divide Eq. (7) by dT, we obtain dH aH HTP dP (8) dT 3T P dT where we emphasize that the first and last terms are merely the ratios of two differentials, not deriva tives. Notice that from Eq. (7), if dP is zero (which is perfectly acceptable since we have not divided through by dP at any stage), we obtain dH aHTP dT dP T (9) Just as the differentials of Eq. (6) define a tangent line to the curve y = f(x), the differentials of Eq. (7) represent movement on a plane which is the tangent plane at the point (P,T) to the H = H"r(P,T) surface. The important point to note is that the lefthand side of Eq. (9) is an algebraic expression, not a limit as in Eq. (5). This is a direct consequence of the definition of Eq. (7) and the fact that the differen tials are not necessarily small quantities. The im portant result is that all future manipulations will be algebraic; the limit process only occurs in the definition of the derivative in Eq. (5). We need to note, however, that when we place a constraint such as dP = 0 on an expression such as the quotient on the left of Eq. (9), the values of dH and dT are no longer arbitrary, as we have con strained their variation. Using these concepts (especially that of Eq. 9), the student may develop all of the familiar relation ships using only simple and unambiguous algebra. For example, consider the two differentials dH and dT. It is clear that d /d (10) dHT dT where we emphasize that the two terms are ratios of differentials, not derivatives. Now, consider Eq. (10) when dP = 0. From Eq. (9) we obtain aTHP ( aHTP H 1 T )11 If we consider the following ratios of differentials: dH dH dV (12) dT dV dT12) we may, from the situation when dP = 0, obtain the wellknown relation aHTP aHVP aVTP dH dH dV (13q T V 3T (13) Chemical Engineering Education Shorthand Notation for Derivatives The notation which we have adopted for deriva tives, although clear, makes for slightly tedious writ ing and somewhat more tedious typing or typeset ting (although certainly no more so than the tradi tional notation). We may save some effort and space by adopting a shorthand in which aHTP is replaced by H aT Although useful for simple statements and equa tions, this notation is somewhat more difficult for the novice to use in performing algebra. It may be preferable to use the expanded form, especially in handwriting, to perform manipulations such as those of Eqs. (10) to (13) above. This notation may easily be extended to higher derivatives, as the functions of thermodynamics are sufficiently "smooth" that the order of differentiation is not important. (Alterna tively, if the order of differentiation is important, we may use notation such as HT'P' and HP'T' to indicate the difference.) Integrals We define an integral in the usual way as the limit of a sum. That is, over some path V = V(S) from S, to S2 S2 / N fTSdS= lim Tsv S.V Si[5 ASi I ASi o i=l x 1 N+ where NASi = S, S2. (There is no ambiguity about dS when used in conjunction with the integral sign.) Canonical Variables Consider a function USV. This function leads to differentials given by dU= o dS+ dvdV (14) or, expressed more concisely in the shorthand nota tion explained above dU= Us dS+Usv dV (15) If we define the functions TsV = Us and PSV =USV (16) then obviously dU = TdS PdV (17) We may now regard this equation as being a differential relationship between U and four vari ables (T, P, V, and S), only two of which are inde pendent. As many readers will know, we can show that Spring 1991 there is a "special" relationship between U and the pair of variables, S and V, which is not shared by the other variables, T and P. The reasoning is outlined as follows. Consider the (known) relation T = USv TSV Assume that from the function TSV we may uniquely solve for S; that is S = S (19) We may substituted S = S'v into U = Usv to get =U SV(s Vv)= U (20) By similar arguments, we may obtain UsP, U"", UTs and all the other various combinations of inde pendent variables. We now note, however, that the reverse processes are not possible. If we have U"T we cannot uniquely obtain Usv. This is because in the process of differen tiating Usv to obtain T or P we lose information. Suppose, for example, that the functional form of Usv is such that Usv = K+As + Bv + Cs (21) Then in the process of differentiating U with respect to S in order to obtain Tsv as defined by Eq. (18), we lose all information about K and the function Bv. It is therefore not possible to reconstruct USV from U', since the integration process which reverses the dif ferentiation involves the addition of arbitrary "con stants" (they may be functions of V) about which we have no information from UTV. This special nature of Usv is expressed by saying that S and V are the canonical variables of U. The question obviously arises: Is this behavior peculiar to UsV, or are there other functions which have different canonical variables? It turns out that there are such functions. If we invent a new function A = U TS, then A can be shown (by a similar argument to the one above) to have canoni cal variables T and V. By a similar process, if we let H = U + PV and G = U TS + PV, then H has as its canonical variables S and P, while G has T and P. These new functions HSP, GTP, and A" are the only new ones we can define with these properties among the four variables T, P, S, and V, and so they have a special significance. (For students with suitable mathematical backgrounds, one may of course ob tain H, G, and A directly by Legendre transforms; for others, the argument above may suffice.) Useful Relations We may notice from the definition of H above 77 (18) that the quantity T, which we defined by T = Us, will also be equal to HS'P. We may thus obtain the familiar relationships for T, P, S, and V, such as T = U = Hs P (22) Maxwell Relations These relationships may be obtained as shown in the following example, where we have set the de rivatives out in full for clarity. Since Tsv = Us (23) S then, provided the functions are twice continuously differentiable, it follows that aTSV 2 SV a2USV av av (24) Ts a I (1Usv j ap sv as (25) (26) This result may be written more succinctly as TSv' = ps'. By similar methods, we may obtain the usual other results, known as Maxwell Relations, or CrossDifferentiation Identities. PathDependent Functions Consider the difference AU between the values U1 and U2 of the function USV at two points (S,,V,) and (S2,V2). This is given by AU = U2 U1 (27a) where U= Usv(Si,Vi) (27b) and U2 =USV(S2,V2) (27c) We may also calculate AU from dU = TdS PdV as 2 2 2 2 2 AU= dU= TdSjPdV= UsvdSjUsvdV (28) 1 1 1 1 1 We see that the term TdS is a function of S and V, and will in general therefore have different val ues at different points on the (S,V) plane. The JTdS term is a line integral whose value will depend upon the path from (S1,V,) to (S2,V2) along which we evalu ate it. The same applies to the term JPdV. The student might see this more clearly if it is explained in the following fashion. At every point on the (S,V) plane, there is a value of P, since we may write P = Psv. We may therefore draw the path on 78 the (P,V) plane corresponding to the path on the (S,V) plane along which we are integrating from point 1 to point 2. On the (P,V) plane, the term JPdV is simply the area under the curve, which obviously depends upon the PV path we are considering. For future convenience we shall define these two pathdependent integrals as Q= ITdS W=IPdV (29) (30) so that Eq. (28) becomes AU=Q+W (31) We note that while the value of AU depends only on the initial and final states (S,,V,) and (S2,V2), the values of Q and W depend on the path between those two states along which we evaluate their defining integrals. Functions of More Variables All the functions which we have considered above have been functions of two variables. The reasoning may be extended in a straightforward fashion to functions of a larger number of variables. Although there is nothing radically new here, experience sug gests that in the classroom situation it is better to start, as we have done above, with only two inde pendent variables. Once the concepts are grasped for these functions, students have no trouble under standing the similar results for functions of more variables. Let us then consider n further independent variables. We shall give these the symbols N1, N2, ... N. . Nn. The symbolism [N] represents this whole set of variables. We shall aiso need the set of n1 variables [N ] that is N1, N2, ... N_1, Ni+ , Nn excluding N1. We may then consider the function U UsV[Nj (32) from which we may write the differential S V[N.] SV['N. SVN.IN. ji dU=U Sv[dS +U dV+ U dNi (33) We may then define We may then define SV [Nj] T=U P=uSV LNj (34) (35) (36) Substituting these definitions into Eq. (33), we ob tain Chemical Engineering Education dU=TdSPdV + idNi (37) i The above definitions of T and P are no different to those we have used previously. We may define the functions A, H, and G as we have done before. Thus TVINj 1 A=UTS= ATV[N and H and G are defined in an analogous fashion. There are also many new functions we could de fine with canonical variables involving one or more of our new variables [N]. For instance B= Ug 1N1 = B 1 (38) but these in general do not turn out to be useful functions, so we shall not explore this avenue fur ther. We may also obtain, as we did above, a set of Maxwell relations. For example, from the second derivatives of U, we may obtain SV'[N S V[Nj] T = P (39) while from A we may obtain TV'[Nj] T'V[Nj S =P (40) Many other relationships are of course possible. For example TPNj [Njkj] TPN [Nk i] (41) It perhaps needs to be stressed again at this point that all the above development is purely mathe matical. All the relations we have developed follow from the properties of functions and their deriva tives and from our (arbitrary) definition of the sym bols P and T in terms of the derivatives of Usv. We have not yet done any "thermodynamics"! The development that may be referred to as "thermo" (including the identification of our symbols T and P with their usual meaning) will form the sub ject of Part 2 of this paper. We may also note that in this approach the mathe matics we use is entirely consistent with that which a student has learned in the standard mathematics course. In particular, we have no need for any spe cial kinds of derivatives. We have found in our teach ing that students readily assimilate this material and do not appear to have the same problems of understanding that the authors did when they were undergraduates. REFERENCES 1. Harris, W.F., ChemSA, 7(12), 259 (1981) 2. Harris, W.F., ChemSA, 8(7), 82 (1982) 3. Callen, H.B., Thermodynamics, John Wiley & Sons, New York, NY (1960) 0 book review A GUIDE TO CHEMICAL ENGINEERING PROCESS DESIGN AND ECONOMICS by Gael D. Ulrich John Wiley & Sons; 472 pages, $33.95 (1984) Reviewed by Andrew N. Hrymak McMaster University This book is intended as a reference text for a course using case studies such as those from the AIChE design competition. Topics covered in the book fall into three main categories: process design, economics, and technical report writing. Extensive references to wellknown chemical engineering texts and handbooks are found throughout the book. The first section is entitled "Process Design." The chapters within this half of the book cover the design process, process conception, flowsheets, and the speci fication and design of individual pieces of equip ment. In Chapter 2, the reader is introduced to the importance of understanding the process and ob taining typical flowsheets from the literature and Chapter 3 summarizes flowsheet preparation and common symbols. Chapter 4 is a lengthy chapter devoted to the specification and design of individual pieces of proc ess equipment. Separate sections cover different classes of units (such as heat exchangers, pumps, reactors, etc.). Each section gives a brief overview of Continued on page 95. Spring 1991 REQUEST FOR FALL ISSUE PAPERS Each year Chemical Engineering Education publishes a special fall issue devoted to graduate education. It consists of 1) articles on graduate courses and research, written by professors at various universities, and 2) ads placed by chemical engineering departments describing their graduate programs. Anyone interested in contributing to the editorial content of the 1991 fall issue should write to the editor, indicating the subject of the contribution and the tentative date it will be submitted. SDeadline is June 1, 1991. Random Thoughts... WE HOLD THESE TRUTHS TO BE SELFEVIDENT RICHARD M. FIELDER North Carolina State University Raleigh, NC 276957905 Being engineering professors, we all know about the need to make assumptions . and we also know that if the assumptions are invalid, the results can be worthless. We learn early in our careers to check our results (Does the model fit the data? Does the algorithm converge? Does the product meet qual ity specifications?) and if they are not satisfactory, to question our assumptions (Is the solution ideal? Is the reactor isothermal? Is flow laminar?), and we try to develop the same critical, questioning mentality in our students. When it comes to education, however, our men tality changes. We generally do whatever it is we do without much critical evaluation of how well or how poorly it is working, and we accept without question what Armando Rugarcial2' calls academic myths assumptions that have never been shown to have any basis in reality and often defy common sense. Here are some of them. MYTHS ABOUT ... FACULTY RECRUITMENT People who (1) don't have Ph.D.'s, or (2) have spent their careers in industry and have no research publications, are not qualified to be engineering professors. When filling faculty vacancies, an engineering department benefits most by selecting the can didates in the hottest and currently most fund able research areas. How much grant money they attract in the next five years is more important than whether they know enough engineering to teach the core courses and to change research areas if their present one goes out of fashion. The best way to handle required courses that Copyright ChE no one wants to teach, such as the unit opera tions laboratory or the capstone design course, is to rotate them among the faculty so that no one gets stuck with them too often. An inferior solution is to fill a vacant faculty po sition with someone who has the desire to teach these courses and the expertise to teach them well. When selecting a department head, the faculty benefits most by choosing the candidate with the strongest research record, regardless of administrative experience or ability. How he or she runs the department in the next five to ten years is less important than what he or she does in research after that. MYTHS ABOUT... RESEARCH AND TEACHING Excellence in research and excellence in teach ing are highly correlated. Requiring EVERY faculty member to build up a strong research program as a condition for promotion and tenure is in the students' (professors', department's) best interests. Excusing new professors from teaching re sponsibilities so they can write proposals is a good thing to do. Excusing them from re search responsibilities so they can develop a couple of good courses makes no sense. Professors who are excellent at research and mediocretoadequate at teaching deserve ten Richard M. Felder is a professor of chemical eng neering at North Carolina State University, where h has been since 1969. He received his BChE fro. City College of C. U.N. Y. and his PhD from Princeto. "" He has worked at the A.E.R.E., Harwell, an Divson, ASEE 1991 i ne m n. id oDI uuna, l I vaI na aL aty, anIICIU a prseU b lt courses on chemical engineering principles, reactor design, process optimization, and effective teaching to various American and foreign industries and insti tutions. He is coauthor of the text Elementary Prin ciples of Chemical Processes (Wiley, 1986). Chemical Engineering Education ure. Professors who are excellent at teaching and mediocretoadequate at research don't. MYTHS ABOUT... CURRICULUM DESIGN AND PEDAGOGY Our graduates routinely say they never use 907c of what we taught them. Since we're engineering professors, 90% of what they're doing must not be engineering. It makes sense educationally to teach stu dents a generalized theory (e.g., transport theory) before teaching them anything about the specific phenomena and devices that the theory was invented to describe (e.g., unit operations). Tensor calculus, quantum chemistry, and statistical mechanics should be taught to every chemical engineering undergraduate; statis tical process control, project management, and technical writing they can pick up on their ownthere's no room for those subjects in our crowded curriculum. The best thing to do with ethics, safety, envi ronmental science, and all those other impor tant things ABET says we have to teach, is stick them all in the capstone design course. I accomplish something useful when I spend fifty minutes in class writing detailed deriva tions on the chalkboard for the students to copy. We can't teach students to think critically or creativelyither they can do it or they can't. Students who complain that our lectures have nothing to do with the real world don't know anything about the real worldand we do. IfI have covered the syllabus, I have done my job successfully. MYTHS ABOUT... EVALUATION OF STUDENTS (GRADING) How well our students will do as engineers correlates highly with (a) their undergradu ate GPA; (b) their ability to solve problems with unfamiliar twists on 50minute exams; (c) anything else that we typically use to evalu ate them. An average score of 40 on my final exam proves (a) I set high standards; (b) they didn't understand the material. There is no possi Spring 1991 ability that it proves (c) the test was lousy. An average score of 85 on your final exam proves (a) it was a trivial test; (b) you're a soft grader; (c) there was widespread cheating. There is no possibility that the result proves (d) they learned the material. Performance on the written Ph.D. qualifying examination correlates with anything except performance in courses on the same material. MYTHS ABOUT... EVALUATION OF TEACHING All methods of evaluating teaching are unre liable, and student evaluations are the most unreliable of all. If you get consistently outstanding student evaluations, it must be because you are (a) an easy grader; (b) an "entertainer." It is cer tainly not because you are (c) an outstanding teacher. Ifl get consistently rotten student evaluations, it is because (a) the students are ignorant and lazy; (b) I don't water down the ma terial for them; (c) they don't understand what I am doing for them now but in later years they'll come back and thank me. It is definitely not because (d) I am doing a rot ten teaching job. I could go on, but you get the idea. When I classify these points as myths I am not saying there's nothing to them; it's just that as far as I know they've never been scientifically or even empirically validated. (Mentioning someone who is great at both teaching and research, for instance, doesn't quite do it.) If you can justify one or another of these assumptions, let me know and I'll set the record straight. If, on the other hand, you conclude that the assumptions might be faulty, then how about considering whether some alternative assumptions might lead to better ways of doing things? Couldn't hurt. 1 'Before you attempt it, though, you might want to check out the literature: McKeachie'l provides invaluable summaries of the research on most of the topics in question, and Rugarcia'' makes some interesting points specifically on the research/teaching di chotomy. 1. McKeachie, W.J., Teaching Tips: A Guidebook for the Be ginning College Teacher, 8th ed., Toronto, D.C. Heath & Co. 119861 2. Rugarcia, A., "The Link Between Teaching and Research: Myth or Possibility?" Engineering Ed.. 81, 20 (1991) curriculum A COURSE IN IMMOBILIZED ENZYME AND CELL TECHNOLOGY WILLIAM E. LEE III University of South Florida Tampa, FL 33620 Courses addressing topics in biotechnology are becoming more common in the chemical engi neering curriculum. Many departments offer a sen ior or firstyear graduate course in biochemical en gineering fundamentals, often following the curricu lum developed by Bailey and Ollis.'2'1 Tavlarides'I3 also describes a course in enzyme and biochemical engineering for graduate students. However, the text of Baily and Ollis, now in its second edition,141 ap pears to be the book of choice, due to the fact that its orientation is towards chemical engineering while most other books are aimed at biochemists or bio technologists. The only exception to this might be the text of Aiba, et al.,'" which is (unfortunately) out of print. There has been an increase in the number of potential texts during the last few years, such as the text by Bu'lock and Kristiansen.'"' Basic enzyme technology is often addressed in such an introductory course, and it usually includes enzyme kinetics in some detail along with some ref erence to immobilized enzymes. More advanced courses in enzyme kinetics are quite often handled by chemistry departments at the graduate level. However, selected advanced enzyme technology con cepts within chemical engineering are frequently in cluded as special topics in courses such as advanced William E. Lee III is an assistant professor of chemi cal engineering at the University of South Florida. He is the coordinator of the biotechnology and biomedical programs between chemical engineer ing, the College of Natural Science, and the College of Medicine. His current research interests involve the application of chemical engineering principles to problems in the life and medical sciences, including research in sensory perception, metabolic aspects of disease processes, and problems in citrus proc essing. kinetics and reactor design. In most of these cases, the topic of immobilized cells is given only passing reference at best. One application example that is sometimes addressed relates to biofilms which im mobilize microbes that form on the walls of fermen tation vessels, including the aeration tanks in waste water treatment. Biosensors may also be discussed. Otherwise, applications are often only briefly cov ered, if at all. The technology of immobilized enzymes and cells has grown tremendously over the last decade. Chemi cal engineers are involved in the immobilization proc esses themselves in addition to the ultimate utiliza tion in some bioreactor configuration. The descrip tion of the kinetics and mass transfer aspects of immobilized systems depends on a good foundation in chemical engineering transport phenomena and reaction engineering. Many enzyme applications involve the enzyme in an immobilized form due to a number of advantages (versus the free form) such as ease of recovery, maintenance of the active form at higher levels for longer times, more freedom in reac tor operation, and less potential product contamina tion problems."7 Economic considerations often favor the immobi lized system'8" for the same reasons stated above in addition to the higher throughput rates (relative to the free form) that can often be realized. However, a detailed economic analysis must consider the costs of the immobilization process itself since prepara tion for the more sophisticated techniques may be expensive. Immobilized cells enjoy many of the same bene fits as immobilized enzymes. In the case of mam malian cells, immobilization is often the only way SC(0pyriight ChE Diriim. ASEE 1991 Chemical Engineering Education Immobilization technology has found its way into a variety of applications, including organic chemical production, food processing, pharmaceutical production, environmental engineering, and (receiitly) biomedical situations.... This article describes a course in chemical engineering which addresses, in some detail, the technology of immobilized enzymes and cells. that cells can be used in most reactor systems, due in most cases to their fragility. For example, mam malian cells may not be able to tolerate even the gentlest of mechanical agitation. Immobilization technology has found its way into a variety of applications, including organic chemical production, food processing, pharmaceutical produc tion, environmental engineering, and (recently) bi omedical situations. Increased employment of this technology will probably parallel the continuing suc cesses of molecular biology. Immobilized enzymes and cells are also important in the biosensor area, where very specific probes are now possible as a result of this technology. This article describes a course in chemical engi neering which addresses, in some detail, the tech nology of immobilized enzymes and cells. It is meant to be an elective course for advanced seniors or gradu ate students in chemical engineering or some other technical discipline. The course has been offered twice at this writing, and will be offered in the future as part of a series of chemical engineering electives in the biotechnology area. COURSE OUTLINE Table 1 presents the course outline. As can be seen, the onesemester course (3 semester credits) covers a variety of topics, including the basic immo bilization methods, transport phenomena and kinet ics of immobilized systems, reactor configurations, and applications. An important application area which received special attention involved biosensors. The topic of basic microbe physiology and the impact of immobilization procedures on viable organisms was also addressed. Two texts were required for the course. Process Engineering Aspects of mmobilized Cell Systems, by Webb, et al.,19' was used along with Immobilized Microbial Systems: Principles, Techniques, and In dustrial Applications, by Kolot."101 In addition, a number of journal articles and other readings (see Table 2, next page) were utilized. Each class meeting typically started with the presentation of an application example, either by one of the students or by the instructor. The presen tation and following discussion were limited to ten TABLE 1 Course Outline 1. Introduction to immobilized enzyme and cell technology 2. Immobilization methods A. Entrapment gels fibers microencapsulation other methods B. Binding Carrier binding physical adsorption onto surfaces (including physical aspects of various carriers) ionic binding chelation or metal binding covalent binding C. Crosslinking D. Analytical methods used to study the effectiveness of immobilitation 3. Immobilized cell physiology A. Importance of cell physiology prior to immobilization B. Effect of immobilization on cell physiology C. Activity of immobilized cell particles, including mass transfer and control of cell growth and metabolism 4. Immobilized system kinetics A. External mass transfer resistances B. Intraparticle diffusion and chemical reaction C. Simultaneous internal and external resistances 5. Reactor design considerations A. Basic enzyme kinetics B. Reactor configurations used for immobilized biocatalysts C. Miscellaneous topics biofilm formation mixing and agitation approaches oxygen supply control schemes 6. Biosensors A. Types of sensors and underlying principles B. Applications Spring 1991 minutes. The two texts included a number of appli cation discussions and were eventually addressed as part of this series. Additional examples, beyond those in the texts, were presented by the instructor during the course and are listed in Table 3. There were also a few supplementary exercises. In the first exercise, students were instructed to con tact an industrial supplier of immobilized enzymes and, if the supplier was cooperative, to obtain a sample of the product along with any descriptive literature. The samples thus obtained were displayed in one session for all to see. We also viewed some of the samples under a scanning electron microscope. The second exercise involved the analysis of US Patents involving immobilized systems, specifically "Process for Preparing Biomass Attached to a Car rier" (Patent No. 4,560,479) and "Immobilization of Microorganisms on a Plastic Carrier" (Patent No. 4,696,901). For the final exercise, students presented three inclass presentations on the following topics: A method of physical adsorption of an enzyme or cell onto a surface, including the underlying physical principles An analytical procedure which could be used to determine the extent of success of an immobilization procedure An application example Students were told that the presentations should last ten to fifteen minutes. The general class was allowed to direct questions to the presenter follow ing the presentation. The students also did simple experiments involv ing the immobilization process itself. They formed alginate gels (no enzyme or microbe involvement) starting with sodium alginate solutions,"1I and they formed Kcarrageenan gels by dissolving the mate rial in physiological saline, warming, and contacting with a gelinducing agent.1101 DISCUSSION The two texts used in the course were good selec tions. Their technical depth is satisfactory, and they are reasonably priced (the combined price is less than $70). Neither book addresses immobilization methods in any depth. Also, analytical procedures to establish the success (or lack thereof) of an immobi lization procedure are not cited. As a result, both of these important topics were addressed via outside sources (see Table 2). Additionally, the topic of bio sensors is not considered in either text, so outside supplementation in that area was also necessary (noted in Table 2). The discussion on biosensors stressed the underlying enzymatic principles involved and did not emphasize any associated electronics or probe hardware aspects. Finally, the texts do not consider engineering economic analysis at all, but this was easily handled by additional materials. Application examples were presented through out the course, some by the students themselves but most of them by the instructor. I found that mixing in the applications with the technical material was effective, and it helped the students to focus on the concept that there are many real applications, i.e., that the topic is not just theoretical in nature. The students also found the discussion on the patents to be interesting, both as to the technical content and as to the nature of the patent and patenting process TABLE 2 Selected Additional References General Materials Enzyme Engineering Case Study: Immobilized Lactasel141 Industrial Applications of Immobilized Enzymes: A com mercial Overview18] Immobilized Enzymes: A Survey[15" Immobilization Methods Preparation and Properties of Gel Entrapped Enzymes1'lo Microbial Adhesion in Perspective'17' Adherence of Marine MicroOrganisms to Smooth Surfaces[t18 Mechanisms involved in Sorption of Microorganisms to Solid Surfaces191 MicrocarrierBound Mammalian Cells'201 A Range of Ceramic Biosupports[21' Carriers for Immobilized Biologically Active Systems[221 Immobilization of Enzymes by Adsorption'23' Covalent Linkage III: Immobilization of Enzymes by Intermolecular CrossLinking1241 Some Techniques Involved in Study of Adsorption of Microorganisms to Surfaces[251 Mass Transfer and Kinetics Mass Transfer in Immobilized Cellsl261 Oxygenation of Processes Involving Immobilized Cells127] Diffusion and Kinetics with Immobilized Enzymes[28] Reactor Technology Design and Operation of Immobilized Enzyme Reactors[291 Reaction Engineering Parameters for Immobilized Biocatalysts[301 Biosensors Biosensors[311 Membrane Systems: Analysis and Designl321 Immobilized Enzymes for Clinical Analysis'331 Chemical Engineering Education itselfsomething most of the students knew little about. Most students who selected this course had pre viously taken the senior chemical engineering class titled "Theory and Design of Bioprocesses," a course which uses the text of Bailey and Ollis. However, there are always some students who have nottypi cally, students in the environmental engineering sequence of civil engineering. Their participation in the course required several lectures on basic enzyme kinetics. Also, the section on intraparticle transport phenomena and kinetics required a presentation of some preliminary background (Bailey and Ollis give a good elementary treatment) in order to bring all the students up to speed. The weakest area of the course involved the labo ratories. Ideally, several experiments should be done (at least as demonstrations) which cover a variety of immobilization methods. A minimal series could in clude an example of gel entrapment, covalent cross linking, microencapsulation, and physical absorp tion. These should be supported by SEM or some other appropriate analytical inspection procedure. Several recipes are presented by Trevan'121 and by Rosevear."113 Another good experiment could involve a comparison of free and immobilized enzymes in a simple reaction experiment. I intend to improve the laboratory aspect of the course in future offerings. Finally, the inclass presentations were effective for two reasons: it made students more aware of the available sources of information on the subject, and it gave students good practice in organizing and orally presenting a technical topic, something in which most of them did not have much experience. TABLE 3 Selected Application Examples (in addition to examples in the texts) Antibody Production[341 Separation of LAmino Acids from Mixtures of the L and DAmino Acids'35,361 Hybridoma and Monoclonal Antibody Productiont37' Drug Production from Immobilized Plant Cells381 Hydrolysis of Lactosel39 Encapsulation of Vaccines and Hormones1401 HighFructose Corn Syrup Production[41' Bioconversion of Lipophilic Compounds'42' Effect of Biofilm Presence on Reactor Performance'41 In summary, the course effectively presents a va riety of new information regarding immobilized en zyme and cell technology. All the students claim to have received new knowledge, and all could see the potential and demonstrated significance of the tech nology. While this is a good standalone elective, it is especially effective when the students have previ ously taken an introductory course in biochemical engineering. REFERENCES 1. Bailey, J.E., and D.F. Ollis, "Biochemical Engineering Fun damentals," Chem. Eng. Ed., 10,162 (1976) 2. Bailey, J.E., and D.F. Ollis, "Biochemical Engineering Fun damentals (Revisited)," Chem. Eng. Ed., 19, 168 (1985) 3. Tavlarides, L.L., "Enzyme and Biochemical Engineering," Chem. Eng. Ed., 8,188 (1974) 4. Bailey, J.E., and D.F. Ollis, Biochemical Engineering Funda mentals, McGrawHill Book Co., New York, NY (1986) 5. Aiba, S., A.E. Humphrey, and N.F. Millis, Biochemical Engi neering, Academic Press, New York, NY (1973) 6. Bu'lock, J, and B. Kristiansen, Basic Biotechnology, Aca demic Press, London, England (1987) 7. Atkinson, B., "Immobilized Cells, Their Application and Po tential," in Process Engineering Aspects of Immobilised Cell Systems, by C. Webb, G.M. Black, and B. Atkinson, eds., Pergamon Press, Inc., Elmsford (1986) 8. Sweigart, R.D., "Industrial Applications of Immobilized En zymes: A Commercial Overview," App. Biochem. Bioeng., 2 209(1979) 9. Webb, C., G.M. Black, and B. Atkinson, Process Engineering Aspects of Immobilised Cell Systems, Pergamon Press, Inc. Elmsford (1986) 10. Kolot, F.B., Immobilized Microbial Systems:Principles, Tech niques, and Industrial Applications, Robert E. Krieger Pub lishing Co., Malabar, FL (1988) 11. Mattiasson, B., "Immobilized Systems," in Immobilized Cells and Organelles, B. Mattiasson, ed., CRC Press, Inc., Boca Raton, FL (1983) 12. Trevan, M.D., Immobilized Enzymes, John Wiley and Sons, New York, NY (1980) 13. Rosevear, A., J.F. Kennedy, and M.S. Joaquim, Immobilized Enzymes and Cells, A. Hilger, Philadelphia, PA (1987) 14. Ford, J.R., and W.H. Pitcher, "Enzyme Engineering Case Study: Immobilized Lactase," in Immobilized Enzyme Tech nology, J.J. Weetall, S. Suzuki, eds, Plenum Press, New York, NY (1975) 15. Goldstein, L., and E. KatchalskiKatzir, "Immobilized En zymes: A Survey," in Applied Biochemistry and Bioengineer ing. Volume 1, Immobilized Enzyme Principles, L.B. Win gard, E. KatchalskiKatzir, and L. Goldstein, eds, Academic Press, New York, NY (1976) 16. O'Driscoll, KF., "Preparation and Properties of Gel Entrapped Enzymes," Adv. Biochem. Eng., 4,155 (1976) 17. Marshall, K.C., and G. Bitton, "Microbial Adhesion in Per spective," in Adsorption of Microorganisms to Surfaces, G. Bitton and K.C. Marshall, eds., John Wiley and Sons, New York, NY (1980) 18. Fletcher, M., "Adherence of Marine MicroOrganisms to Smooth Surfaces," in Bacterial Adherence, E.H. Beachey, ed., Chapman & Hall, New York, NY (1980) 19. Daniels, S.L., "Mechanisms Involved in Sorption of Microor ganisms to Solid Surfaces," in Adsorption of Microorganisms Spring 1991 to Surfaces, G. Bitton and K.C. Marshall, eds, John Wiley and Sons, New York, NY (1980) 20. Hirtenstein, M., and J. Clark, "MicrocarrierBound Mam malian Cells," in Immobilized Cells and Organelles, B. Mat tiasson, ed., CRC Press, Inc., Boca Raton, FL (1983) 21. Adams, J.M., L.A. Ash, A.J. Brown, R. James, D.B. Kell, G.J. Salter, asnd R.P. Walter, "A Range of Ceramic Biosupports," Am. Biotech. Lab., October (1988) 22. Messing, R.A., "Carriers for Immobilized Biologically Active Systems," Adv. Biochem. Eng., 10, 52 (1978) 23. Zaborsky, O.R., "Immobilization of Enzymes by Adsorption," in Biomedical Applications of Immobilized Enzymes and Proteins, Volume I, T.M. Chang, ed., Plenum Press, New York, NY (1977) 24. Zaborsky, O.R., "Covalent Linkage: III. Immobilization of Enzymes by Intermolecular CrossLinking," ibid. 25. Costerton, J.W., "Some Techniques Involved in Study of Adsorption of Microorganisms to Surfaces," in Adsorption of Microorganisms to Surfaces, G. Bitton and K.C. Marshall, eds., John Wiley and Sons, New York, NY (1980) 26. Radovich, J.M., "Mass Transfer Limitations in Immobilized Cells," Biotech. Adv., 3, 1 (1985) 27. Enfors, S.O., and B. Mattiasson, "Oxygenation of Processes Involving Immobilized Cells," in Immobilized Cells and Or ganelles, B. Mattiasson, ed., CRC Press, Boca Raton, FL (1983) 28. Engasser, J.M., and C. Horvath, "Diffusion and Kinetics with Immobilized Enzymes," in Applied Biochemistry and Bioengineering: Volume 1, Immobilized Enzyme Principles, L.B. Wingard, E. KatchalskiKatzir, and L. Goldstein, eds., Academic Press, New York, NY (1976) 29. Pitcher, W.H., "Design and Operation of Immobilized En zyme Reactors," Adv. Biochem. Eng., 10, 1 (1978) 30. Buchholz, K., "Reaction Engineering Parameters for Immo bilized Biocatalysis," Adv. Biochem. Eng., 24, 39 (1982) 31. Turner, P.F., Biosensors: Fundamentals and Applications, Oxford University Press, Oxford, England (1987) 32. Vieth, W.R., Membrane Systems:Analysis and Design, Hanser EDUCATOR: Perna Continued from page 63 stations for the twosemester senior course. For twenty years now we have continuously worked on upgrad ing the laboratory experiments and its format. During these years, together with colleagues in the civil engineering department, Angie also initi ated cooperative efforts at the graduate level in en vironmental engineering. The first joint effort was to secure an interdisciplinary waterpollution training grant for graduate civil and chemical engineers, funded by the Federal Water Pollution Control Administration. This then led to the development of an interdisciplinary program in environmental engi neering. Angie developed courses in unit operations of water treatment processes and in solid waste man agement processes. Angle and John Liskowitz developed other highly successful joint research and programs that eventu ally led to numerous EPA research grants as well as Publishers, New York, NY (1988) 33. Suzuki, S., and I. Karube, "Immobilized Enzymes for Clini cal Analysis," in Enzymes and Immobilized Cells In Biotech nology, A.I. Laskin, ed., Benjamin Cummings Publishing Co., Inc., London, England (1985) 34. Nillson, K., "Entrapment of Cultured Cells in Agarose Beads," in Large Cell Culture Technology, Hanser Publishers, New York, NY (1987) 35. Chibata, I., T. Tosa, and T. Sato, "Immobilized Biocatalysts to Produce Amino Acids and Other Organic Compounds," in Enzymes and Immobilized Cells in Biotechnology, A.I. Laskin, ed., Benjamin Cummings Publishing Co., London, England (1985) 36. Chibata, I., and T. Tosa, "Industrial Applications of Immobi lized Enzymes and Immobilized Microbial Cells," in Applied Biochemistry and Bioengineering. Volume 1. Immobilized Enzyme Principles, L.B. Windgard, E. KatchalskiKatzir, and L. Goldstein, eds., Academic Press, New York, NY (1976) 37. Goosen, M.F., "Animal Cell Culture in Microcapsules," Chem. Eng. Ed., 22,196 (1988) 38. Brodelius, P. "Immobilized Plant Cells," in Immobilized Cells and Organelles, Volume I, B. Mattiasson, ed., CRC Press, Inc, Boca Raton, FL (1983) 39. Goldberg, B.S., "A Novel Immobilized Enzyme Reactor Sys tem," paper presented at the 24th Annual Spring Sympo sium, AIChE, East Brunswick, NJ, May 10 (1984) 40. Change, T.M.S., "Biomedical Applications of Artificial Cells Containing Immobilized Enzymes, Proteins, Cells, and Other Biologically Active Materials," in Enzymes and Immobilized Cells in Biotechnology, A.I. Laskin, ed., Benjamin Cummings Publishing Co., London, England (1985) 41. Barker, S.A., and G.S. Petch, "Enzymatic Process for High Fructose Corn Syrup," in Enzymes and Immobilized Cells in Biotechnology, A.I. Laskin, ed., Benjamin Cummings Pub lishing Co., London, England (1985) 42. Tanaka, A., and S. Fukui, "Bioconversion of Lipophilic Com pounds by Immobilized Biocatalysts in the Presence of Or ganic Solvents," ibid. O an Exxon grant that funded an environmental toxi cology option under the direction of Dick Trattner. Out of all these efforts came the impetus for the Institute for Hazardous and Toxic Waste Manage ment and the NSFinitiated HazTox Center. While Angie's research efforts have been in the main environmentally oriented, his research inter ests span the spectrum from ultrasonicaided mass transfer to characterization of leachate from MSV incinerator ash. His current interest is in MSW in cinerator residue, which he has been working on jointly with Don Sundstrom and Herb Klei (Univer sity of Connecticut). This research is an outgrowth of a twoyear (198890) stint as a visiting professor of chemical engineering and a research fellow at the Environmental Research Institute at UConn. A fellow of AIChE and ASEE, he is the recipient of numerous citation certificates and awards, includ ing the ASEE/MidAtlantic Western Electric Award, the DELOS Distinguished Service Award, and the ODK Award of Merit. Chemical Engineering Education His AIChE activities include service on ten insti tute committees, Technical Program ViceChairman of the 1977 NYC Annual Meeting, and Chairman of both the Student Chapters Committee and the Edu cational Projects Committee. He has also served as a Director of the New York City AIChE local section. In ASEE he has served on numerous commit teess over the years, including Chairman of the 3M and DELOS Award Committees, in addition to hold ing ten elective offices, including Chairmanships of CHED, DELOS, and the Instrumentation Division. In addition to the above professional activities, he has also served as Chairman of the ACS Mobay Committee, and as National President of Omega Chi Epsilon (the chemical engineering honor society), and President of the Association of College Honor Societies. He is also the author of approximately thirtyfive papers, numerous presentations, coauthor of a book, and coeditor of three proceedings. Angie's role in Omega Chi Epsilon deserves spe cial attention. When Angie came to our department as a young assistant professor in 1967, I was Faculty Advisor of Omega Chi Epsilon, an honorary society with relatively few members at the time. I seized the opportunity to pass this advisorship on to our new young faculty memberI had more seniority and was being called upon with increasing frequency for other faculty business. Little did I realize what an impact this decision would have on the future of Omega Chi Epsilon. When he became advisor to our chapter in 1968, there were less than twenty na tional chapters in existence. After working inten sively with our chapter, he became National Vice President of the organization in 1974 and then Na tional President in 1978. When he completed his tenure as president he had expanded membership organization in Omega Chi Epsilon to forty chap ters. He continued to work for the organization in his capacity as past president, and there are now fortynine chapters nationwide. His role as a national leader in Omega Chi Epsi lon also led to the office of President of the Associa tion of College Honor Societies, an umbrella group for the nation's more than sixty different honor so cieties. These activities epitomize Angie's devotion to the profession. His volunteer involvement has always been intense, and he has given his time and talents happily and without thought of rewardhis real reward has been his own satisfaction in having par ticipated. Spring 1991 The multitude of people in our professional socie ties that Angie knows continually amazes meand he always remembers their names! He and I have attended these meetings together for years, and al though we were at the same sessions, he somehow always managed to meet many more colleagues than I, or anyone else, did. He never tires of meeting old, and new, friends and engaging in lengthy bullses sions with them at meeting after meeting. His en thusiasm permeates the air at checkin and lasts long after everyone else is tired and ready to go home. In addition to service on numerous department and institute committees at NJIT, Angie has been Chairman of the Faculty Council and President of the Professional Staff Association. He has also been a reviewer for NSF, EPA, AIChE, CEE, I&EC, Engi neering Education, and the IACT, jr. He has been a consultant to the municipal and industrial sector, and during the summer of 1989 he served as a con sultant and senior development officer to UNIDO in Vienna, Austria. Angie's activities in the department include a stint as Acting Department Chairman (covering for me while I was on sabbatical leave) and as indus trial fund raiser. During the 1970s his activities in fund raising led to a tripling of funds donated to the department and to the development of a Chemical Engineering Department Merit Award Program with its own endowment fund. At the present time he devotes his energies to teaching and the develop ment of a Center for Municipal Solid Waste Studies. When I was first contacted by CEE about the possibility of writing this article, I asked Angie for his permission and cooperation. He agreed with the one condition that he would be permitted to write the concluding paragraph for the article. It follows. You know, I consider myself extremely fortunate in having had a department and an institute administration that has supported my activities at a number of professional society meetings, and I am appreciative of the large number of colleagues I have had the opportunity to interact with through the years. In many cases, these associations developed into strong friendships that I have grown to treasure. To all of these individuals and their families I would like to take this moment to express my sincere appreciation for their support and for the opportunity to have served with them, but mostly for their friendship over the years. I've got to sayI'm a very lucky fellow who has had a rewarding career. o 87 classroom A SECONDYEAR UNDERGRADUATE COURSE IN APPLIED DIFFERENTIAL EQUATIONS THOMAS Z. FAHIDY University of Waterloo Waterloo, Ontario, Canada N2L 3G1 Conventional wisdom holds that loweryear courses in mathematics for engineers should be taught by mathematicians, who can supply the nec essary depth and rigor that engineering instructors, however adept in applying the subject, may lack. Reality, however, tells us otherwise. Excessive insis tence upon uniqueness, existence properties and proof of theorems, and unfamiliarity with engineering flavored problems, coupled with a reluctance to blend lectures with practical examples, is counterproduc tive in loweryear courses. A large proportion of the students lose interest in the subject; their indiffer ence, often mingled with hostility toward anything mathematical, can make the instruction of higher year engineering mathematics and process control a difficult task. There is much to be said, as a consequence, for the teaching of mathematics to undergraduate engi neering students by engineering instructors who possess the required mathematical background and motivation. Having taught thirdyear (compulsory) and fourthyear (elective) courses (including process control) over the years, I have often been frustrated by the varying and unpredictable mathematics back ground of chemical engineering students entering their third year. Depending on the whim of the mathe matician who taught the secondyear course in ap  71 ^__ fB~ Thomas Z. Fahidy received his BSc (1959) and MSc(1961) at Queen's University (Kingston, Ontario, Canada) and his PhD (1965) from the University of Illinois (UrbanaChampaign) in chemical engineer ing. He teaches courses in applied mathematics to engineenng students and conducts research in elec trochemical engineering. His major research areas are magnetolectrolysis and the development of novel electrochemical reactors. He he is the author of nu Smerous scientific articles. Excessive insistence upon uniqueness, existence properties and proof of theorems, and unfamiliarity with engineeringflavored problems,... is counterproductive in loweryear courses. plied differential equations, one stream of students may have been given a healthy dose of certain topics (notably Laplace transformation) while the next group would have received little or no instruction in the same subject. Recently, when an opportunity of putting my thoughts of what this course should con tain into practice, I seized it with alacrity. The framework and "infrastructure" was given to me: 1) the course was to be administered by the mathematics faculty (including the assignment of a teaching assistant), 2) the traditionallyused text"' was designated, and 3) the course designation code and title was assigned. All this suited me fine. I was eager to set about my goal of putting a strong em phasis on the solution of chemical engineering prob lems via ordinary differential equations (ODE) which could be handled in the second year. The strategy was to discuss the theory behind each technique in a concise manner but without a formal proof (except where the procedure was short and straight forward) and to supply a goodly number of numeri cal illustrations. Homework assignments, normally consisting of four to six nonelementary problems per set, were to be handed out and graded every week. A twohour openbook midterm and a threehour openbook fi nal examination would serve as formal measures of student performance. COURSE FRAMEWORK The course structure is summarized in Table 1. The seven major topics follow a similar sequence in the textbook.'11 In Part 1, the definitions, the gen Copyright ChE Division, ASEE 1991 Chemical Engineering Education eral, particular, and singular solutions, and the ques tion of uniqueness are briefly covered, followed by a moredetailed discussion of direction fields and isoclines (in anticipation of nonlinear analysis in future years). In Part 2 the separablevariables tech nique, transformation methods, homogeneous equa tions, exact differential equations, the integrating factor method, and Clairauttype equations are treated. This portion of the course is heavily dosed with (elementary) numerical examples taken from chemical kinetics, reaction engineering, applied bio chemistry, and heattransfer theory. Particular attention is paid to linear equations in Part 3, where Laplace transformation techniques are introduced and treated by anticipating later use in fourthyear process control courses in terms of transfer functions. Since the transfer function is the bridge in transform space between the input and output function in a linear system, its concept is in troduced early to emphasize its usefulness in solving differential equations. The basic tools for handling transform inversion (e.g., reduction to simpler forms via partial fractioning, convolution theorem, trans form tables) are treated in detail, but contour inte gration is omitted due to the students' lack of knowl edge of complex calculus in the second year. The treatment of series solutions deviates from the conventional approach in that various classical methods (e.g., the method of Frobenius) are covered briefy but sufficiently for the introduction of Bessel functions as an important technique for solving a class of secondorder linear differential equations of practical importance. Due to time limitations, only the Bessel equation of the first kind is discussed, with appropriate applications; emphasis is laid particularly on the handling of the zeroes of Bessel functions in view of physical considerations (see Example 1). In the next section, on orthogonal functions and SturmLiouville theory, the motivation for the orthogonality concept is emphasized and the general technique for the expansion of functions into or thogonal series is briefly shown (the discussion of Fourier series in solving partial differential equa tions in a subsequent thirdyear course is an exten sion of this topic). Part 6 concerns a subject of growing importance at loweryear levels but which is not traditionally taught in this course: numerical techniques. I am convinced that the numerical handling of all mathe matical problems of engineering importance should be introduced as early as possible and that an undue weighting of analytical techniques is outdated. The obsolete philosophy of neglecting numerical solutions at a loweryear level is also manifested in the text book, which deals only with the Euler techniques and the RungeKutta method (in a surprisingly short chapter). To remedy this, I added the handling of secondorder ODE's with twopoint boundary value problems (see Example 2) and initial value problems TABLE 1 Structure of SecondYear Course in Applied Differential Equations #OF ONEHOUR LECTURES ILLUSTRATIVE EXAMPLES OF ChE NATURE 1. General concepts and philosophy of ODE's 2. Firstorder and simple ODE's 3. Linear differential equations and Laplace transformation 4. Series solutions and Bessel functions 5. Orthogonal functions and SturmLiouville theory 6. The numerical solution of ODE's 7. System of ODE's and linear ODE's. Linearized systems None Firstorder irreversible batch reactors; mixing in a wellstirred tank at equal and unequal inflow and outflow rates; second order irreversible batch reactions; radial heat conduction in a cylindrical solid; flow through containers of various geometries; growth and decay in simple biochemical reaction systems; production of isotopes in a nuclear reactor Countercurrent heatercooler problems; secondorder under damped control systems; twoelement mixer cascades; elemen tary transfer function analysis Flux distribution in a cylindrical nuclear reactor; radial temp erature distribution in a cylindrical conductor; buckling of a vertical column (in an ecumenical spirit!) None None Consecutive irreversible firstorder batch reactions; mixer cascades; flow through mixers equipped with valves Spring 1991 SUBJECT as a step in (what I conceive to be) the right direc tion. (I would be happy to see a strong component of numerical approaches in earlier calculus courses.) Finally, Part 7 puts emphasis on the structural properties of linear systems, e.g., eigenvalues and eigenvectors. It introduces the statevariable and state transition matrix concept, the decoupling of state variables via canonical transformation, and the solution of nonlinear systems for small excur sions about their steady states via linearization (see Example 3). For obvious reasons, first and secondorder systems only serve for the purpose of illustration. TYPICAL CLASS ILLUSTRATION EXAMPLES EXAMPLE 1 Physical Importance of the Zeroes of Bessel Functions The energy flux distribution in an upright cylin drical nuclear reactor of radius R is given by the ODE2' 2 2 d2 + dO 2 2 (1) dr2 dr where y is a known physical parameter. At r = R, the flux 4 is zero and the maximum energy flux, called the design power level of the reactor, exists at the axis: 4Om = )(0). Since )ma is finite, the Yofunction (Bessel function of the second kind order zero) term must be suppressed in the general solution. Hence 4(r) = maxJo(yr) (2) where J is the Bessel function of the first kind order zero. It follows that Jo(yR)=0 (3) There are, in principle, an infinite number of roots which satisfy Eq. (3), but which one should be taken here? This is where the physics of the problem must be considered. We know that the flux decreases from its maximum value at r = 0 to zero at r = R: so does Jo(yr) on [0,ao], a, being the first zero of J(x). Since Jo(x) is negative between a, and the second zero a2, and negative energy flux is physically meaningless, the correct solution of Eq. (3) is yR = al = 2.4048 and the final solution to the problem is given by )(r) = AJo(2.4048 r / R) (4) The suppression of successive roots of Bessel functions past the first one due to physical con straints is an oftenencountered requirement. An other instructive example, albeit not in chemical engineering, is the stability of a vertical wire prob lem'31 involving a fractional Bessel function of the first kind (good for a homework problem?). EXAMPLE A Simple TwoPoint Boundary Value Problem Given the linear ODE 2 dy =expy/2 (5) dx2 with boundary conditions x = 0, y = 1, and x = 2, y = 1, the problem is to estimate the values of y in the interior of the [0,2] domain. Using the conven tional central difference approximation for the secondorder derivative, a grid structure with ele ments Yn 2yn + Yn1 = h exp(y 2) (6) can be constructed, where n is an arbitrary node (or mesh point) position in the grid. This is a very good problem for illustrating at the same time the useful ness of linear algebra as well as finitedifference calculus and iteration strategies. In the simplest case we take a single interior point at x = 1, and thus n = 0 and n = 2 become boundary points. Conse quently, Eq. (2) reduces to the finding of y, via the iteration scheme yL 1 + (1 / 2) exp y (7) starting with an arbitrary estimate y10o'. If we choose y(0) = 1, then yl(4' = 1.16954 and y15' = 1.16955 are obtained; with y 'O = 1, y(4' = 1.16955. If we choose two interval nodes 2/3 units apart, we obtain the 2 x 2 matrix A with elements all = a22 = 2/3 and a2 = a2, = 1/3, connecting the vector with elements y1(k+", y2k+l) to the vector with elements 1 + (2/3)2exp(y1(k)); 1 + (2/3)2exp(y2(k). It eration quickly yields the values of yl = Y2 = 1.15193. Smaller grid sizes can be assigned for a homework problem, calling upon the students' computer skills. The approach is an adaptation of Hamming's treat ment of twopoint boundary value problems.l41 EXAMPLE 3 Linearization of Flow Through a Tank With a Valve in the Effluent Line This problem is often discussed in process control texts'5' and in the author's opinion it serves as an excellent and simple example to illustrate the con cept of linearization and the usefulness of deviation variables in lowerlevel courses. The starting point is the mass balance. Adh Q h (8) dt k (8) Chemical Engineering Education where A is the uniform crosssectional area of the tank, h is the instantaneous liquid level in the tank, Qi is the liquid inflow rate, and k is the valve con stant. At steadystate conditions Qi = kV h Hence, in terms of deviation variables y = h h* and x Qi Qi*, Eq. (8) is rewritten as A = X(t) = k(h (9) For sufficiently small magnitudes of x, the nonlin earity is removed by the truncated Taylor expansion Ohh= 1 _y 2 h* and the linear approximation Ad+ k y=x(t) (10) 2y h is obtained. The constraints on the validity of lin earization are illustrated numerically under a spe cific set of conditions as shown in Table 2. Having discussed this problem in class, we then take up flow through two tanks in series and solve by elimination or elementary state variable theory, emphasizing the stability of the linearized system with negative real eigenvalues k /2A,1 h  k2 / 2A2 h2 STUDENT RESPONSE By and large, student response was what could be expected in any course in engineering mathemat ics; those with a grasp of fundamental mathematical principles were receptive to the application flavor, TABLE 2 Comparison of True and Approximate Solutions in Example 3 for Step Inputs X(t) = XoH(t) [H(t): unit step function] A = 0.28 m2; Qi, = 0.39 m3/min; k = 0.408 m3/minm1/2 h (m) time x = 0.01 x = 0.1 (min) (m/min) (m /min) Eq. 9* Eq.10 Eq. 9* Eq. 10 0.1 0.9174 0.9174 0.9483 0.9484 0.5 0.9288 0.9288 1.0632 1.0626 1.0 0.9390 0.9390 1.1678 1.1641 2.0 0.9508 0.9507 1.2963 1.2808 3.0 0.9564 0.9561 1.3638 1.3353 5.0 0.9603 0.9599 1.4195 1.3726 10.0 0.9614 0.9609 1.4416 1.3828 0.9614 0.9610 1.4423 1.3830 *Solved by an arbitrary numerical technique, covered in Section 6 (Table 1) Spring 1991 while those with a weak mathematical background were too bogged down in operational details to worry about the physical nature of the topics and problems discussed. There was, at any rate, not a single com plaint about the application side of the course, and one of the two written comments supplied with a computerized course evaluation by students states, "Nice having some semireal chemical engineering problems." On a scale of ten, 42 responding students in a class of 69 gave 6.6 to the course and 7.5 to me (secondyear course critiques often give overall scores below 5.0). Some students recognized their weak ness in linear algebra (in spite of a twoterm course taught in the first year) as a serious impediment in following Section 7 (Table 1). Orthogonal functions and SturmLiouville theory (Section 5) also proved to be a "baptism of fire" for many, and numerical techniques (Subject 6) made even the sleeping come temporarily alivea sure sign of the ubiquitousness and appreciation of computers. AFTERTHOUGHTS The real challenge in teaching this course was in finding an appropriate balance between mathemati cal theory and engineering applications when stu dents had little knowledge of either. The course con tent may thus have been a bit too ambitious. It may be more useful in the future to expand the numerical techniques portion at the expense of ODE systems, allotting at least as many formal lectures to the former as to the latter. Recentlywritten books, tuned more closely to the eighties, may also enhance the course.[61 The course was a source of great enjoyment for me, and I look forward to teaching it periodically. I hope that some of the students will subsequently explore the wonders of applied mathematics on their own. REFERENCES 1. Spiegel, M.R., Applied Differential Equations, 3rd ed., Pren tice Hall, Englewood Cliffs, NJ (1981) 2. Farrel, O.J., and B. Ross, Solved Problems in Analysis, Prob lem 6, p. 343, Dover, New York, NY (1971) 3. Relton, F.E., Applied Bessel Functions, Section 5.3, p. 62, Dover, New York, NY (1956) 4. Hamming, R.W., Introduction to Applied Numerical Analy sis, Section 8.11, p. 217, McGraw Hill, New York, NY (1971) 5. Stephanopoulos, G. Chemical Process Control:An Introduc tion to Theory and Practice, Example 6.1, p. 118, Prentice Hall, Englewood Cliffs, NJ (1984) 6. Edwards, Jr., C. H., and D.E. Penney, Elementary Differen tial Equations with Boundary Value Problems, 2nd ed., Pren tice Hall, Englewood Cliffs, NJ (1989) 0 class and home problems The object of this column is to enhance our readers' collection of interesting and novel problems in chemical engineering. Problems of the type that can be used to motivate the student by presenting a particular principle in class, or in a new light, or that can be assigned as a novel home problem, are requested, as well as those that are more traditional in nature and which elucidate difficult concepts. Please submit them to Professors James 0. Wilkes and T. C. Papanastasiou, Chemical Engineering Department, University of Michigan, Ann Arbor, MI 48109. REMOVAL OF CHLORINE FROM THE CHLORINENITROGEN MIXTURE IN A FILM OF LIQUID WATER SARWAN S. SANDHU University of Dayton Dayton, OH 454690001 In industry there are many examples of absorption of a gas with or without chemical reaction in the liquid phase. In physical absorption, a particular gaseous component is removed from a gas mixture due to its larger solubility in the liquid phase sol vent. The removal of butane and pentane from a refinery gas mixture by a heavy oil in the liquid phase is an example of physical absorption. In ab sorption with chemical reaction, the gaseous compo nent to be removed transfers across the gasliquid interface due to a difference in the bulk chemical potentials or concentrations in the two phases. The transferred gas then reacts with a liquidphase com ponent while simultaneously diffusing in the liquid phase mixture. The gas purification processes, such as removal of chlorine from nitrogen or air by means of water, removal of carbon dioxide from synthesis gas by means of aqueous solutions of hot potassium carbonate or monoethanolamine, and removal of H2S and CO2 from hydrocarbon cracking gas by means of ethanolamine or sodium hydroxide, are some ex amples of absorption with chemical reaction. Sarwan S. Sandhu is a professor of chemical engi neering at the University of Dayton. He received his PhD from the University of London (England). His teach ing and research interests are in applied mathematics, chemical engineering kinetics and reactor analysis, transport phenomena, thermodynamics, combustion, and electrochemical engineering including fuel cells. PROBLEM STATEMENT Chlorine is to be removed from a mixture of chlo rine and nitrogen by absorption and reaction of chlo rine with water in a falling liquid film, where a pseudofirstorder reaction takes place: C12(g e)+H20(0) Cl (1)+ H ()+HOCl(g) 1. Develop mathematical expressions describing two dimensional concentration profiles of C12(A) in the liquid film, the total chlorine removal rate for the entire length of the film, and the mass transfer enhancement factor defined as the ratio of the actual rate of chlorine removal to the rate of chlorine removal in the absence of chemical reaction. 2. Evaluate the twodimensional chlorine concentration profile, the total chlorine removal rate, and the mass transfer enhancement factor for the following data:12' System temperature: 24.5 C Chlorine concentration in the liquid film at the gas liquid interface: CAo = 0.1746 x 105 mole cm3 Width of the liquid film: w = 1.0 cm Thickness of the liquid film: 5 = 0.008 cm Height of the falling liquid film: L = 1.0 cm Pseudofirstorder reaction rate constant: k1'"= 13.6 s Molecular diffusivity of chlorine (A) in the liquid solution: DA = 1.477 x 105 cm2 s' The chlorine removal process is to be carried out under isothermal and steadystate conditions by gently stirring the chlorine/nitrogen mixture as de picted in Figure 1. Copyright ChE Dwiision. ASEE 1991 Chemical Engineering Education PROBLEM SOLUTION A sketch of the process is shown in Figure 1. Continuously flowing chlorinenitrogen mixture is stirred and a film of liquid water falling along the vertical nonreactive plane wall is in contact with the gas phase. The gas mixture is at temperature, T, and pressure, P. The liquid phase concentration of chlorine at the gasliquid interface can be deter mined for the evaluation of the numerical data using the methods given in References 3 and 4. The solution'1 to the momentum equation for the steadystate fully developed laminar flow gives an expression for the velocity, vZ, profile as vz(x)=vmr 1)2] (1) where vm g 2 (2) and vm = maximum velocity of liquid at the liquidfilm surface g = gravitational acceleration p = liquid density g = absolute viscosity To set up the differential model describing trans port and consumption of the species A(C12) in the liquid phase region, we follow the generally accepted approach given in Reference 1. The origin of the cartesian coordinate system x, y, z is located at the surface of the liquid film at its top end (see Figure 1). Species A is assumed to be transported in the x and z directions only. The concentration of the species A, CA, is a function of both x and z coordinates. A mole balance for component A is applied over the spatial element in the liquid region shown in Figure 1. The CHLORINE LEAN MIXTURE e CHLORINE RICH MIXTURE z'O z 0z +Az CHLORINE + NITROGEN / MIXTURE /7777777 NAZ NAXL x x+Ax / // / // Figure 1. Sketch of the chlorine removal process by absorption and chemical reaction in the falling film of liquid water (not to scale). Spring 1991 resulting differential equation is NAx NAz +kl CA=0 (3) Under the assumption of negligible transport of spe cies A by diffusion in the z direction relative to its transport by the liquid bulk flow, and no bulk flow in the x direction, NA and Nx are approximated by NA =CAV,(x) (4) NA =DA x (5) NAz and Nx represent the molar fluxes of species A in the z and x directions, respectively. Equations (1), (3), (4), and (5) are combined to result in DA2 CA +v lx CA () DA a2 +vm CAz +kCA =0 (6) ax [ o z The required boundary conditions are: at z=0 CA=O for 0 at x=0 CA =CAo for 0 aC at x=6 A =0 ax for 0 If the region of the liquid film in the direction of the x coordinate, where molecules of the species A pre vail, is thin relative to the liquid film thickness, then the liquid velocity in the downward direction in that region can be assumed to be close to the maximum velocity, vm. This approximation results in the sim plification of Eq. (6), making it suitable for obtaining an analytical solution. The simplified version of Eq. (6) is O2CA __A DA m OA2 m +k CA= 0 (8) The boundary condition, Eq. (7c), is reduced to xo, CA=0 for 0 under the condition that chlorine is rapidly removed via chemical reaction in the liquid phase relative to its diffusion perpendicular to the gasliquid inter face. Using the Laplace transform procedure,15,'6 Eq. (8) is solved to obtain the following result: CA 1 Le4erfc z + e~ p erfc12 + r }p Cz 2Szcca 2 rz a9 (10) 93 ///////// where Vmx DA " 2 k, x DA Equation (10) describes the dimensionless centration profile, CA/CA, as a function of both x z. Under the limit of z  (i.e., sufficiently lar so that erfc in the first term becomes erfc ( o) ar the second term becomes erfc (), then Eq. (10 duces to A= exp( p The molar flux of species A into the liquid film a location is given by NAx DA ( CA x=0 DA a xO x The total removal rate of species A (i.e., of C12) the gas mixture is given by z=L WA=WJ NAxx )dz z=0 k, = wCAoVm D [( u)er u) eu where k, L u= vm Error and complementary error functions were com puted using the approximation technique from Ref (lla) erence 7. It is noted that erfc (x) = 1 erf(x). The resulting twodimensional dimensionless concentra tion profiles of chlorine in the liquid film are shown (lib) in Figure 2. The calculated total chlorine removal rate is WA = 0.278 x 10' mol s1, and the resulting con mass transfer enhancement factor is Et = 1.982. and ge z) Validity of the assumption of constant velocity in d in Eq. (8) was verified by solving Eq. (6) numerically. )re Analytical solution of Eq. (8) and the numerical solu tion of Eq. (6) are compared in Figure 3 for two (z/L) locations. (12) t a z DISCUSSION OF RESULTS Figure 2 shows the profiles of the dimensionless (13) concentration, CA/CAO, of chlorine as a function of the dimensionless penetration distance, x/6, at a num from T = 0.8 0 (14a) The expression for the removal rate of species A by its absorption in the absence of chemical reaction is obtained by substituting k1 = 0 in Eq. (14) and then applying the L'Hopital's rule to determine the resulting indeterminate limit. The result is given by 1+u)erf +cu) eU} WAAo WCAoVm DA 1 dk d 1/21 k O k1 dkl =WCAoL 4DV (15) Finally, the mass transfer enhancement factor is given by Sf +u) erf + eu mts = W( = L ) The second part of the problem is answered by obtaining the numerical data by means of a Fortran program that solves the above theoretical equations. 94 t LIQUID FILM SURFACE tS SOLID WALL SURFACE Figure 2. Twodimensional concentration profiles of chlorine in the falling film of liquid water 0.9 0.8 0.7 0.6 CA  0.5 CAO 0.4 0.3 0.2 0.1 x Figure 3. Comparison of the analytical solution of Eq. (8) with the numerical solution of Eq. (6). Chemical Engineering Education ber of dimensionless depths, z/L. A rapid decrease in the chlorine concentration is interpreted in terms of its fast consumption via chemical reaction relative to its diffusion in the liquid phase. Agreement be tween the analytical solution of Eq. (8) and the numerical solution of Eq. (6) as seen in Figure 3 justifies the assumption of constant velocity in Eq. (8). The mass transfer enhancement factor value of 1.98 is indicative of about double the chlorine re moval rate via its absorption without chemical reac tion. The model predictions suggest that the con tinuously flowing liquid films can, indeed, be used for purification of gas mixtures, e.g., chlorine/nitro gen or air mixture, by absorption of trace species, e.g., chlorine, with chemical reaction in the liquid phase. REFERENCES 1. Bird, R.B., W.E. Stewart, and E.N. Lightfoot, Transport Phe nomena, John Wiley and Sons, New York, pp. 537539 (1960) 2. Rosner, D.E., Transport Processes in Chemically Reacting Flow Systems, Butterworths, Boston, MA., p. 393 (1986) 3. Smith, J.M., and H.C. Van Ness, Introduction to Chemical Engineering Thermodynamics, McGrawHill Book Co., New York, NY, p 332, 346 (1987) 4. Reid, R.C., J.M. Prausnitz, and T.K. Sherwood, The Proper ties of Gases and Liquids, McGrawHill Book Co., New York, NY, p. 361 (1977) 5. Spiegel, M.R., Advanced Mathematics, McGrawHill Book Co., New York, NY, pp. 277,100, 73 (1977) 6. Oberhettinger, F., and L. Badii, Tables of Laplace Trans forms, SpringerVerlag, New York, NY, p. 264 (1973) 7. Abramowitz, M., and I.A. Stegun (editors), Handbook ofMathe matical Functions, (9th printing), Dover Publications, Inc., New York, NY, p 299 (1970) 0 REVIEW: Process Design Continued from page 79. the major types of equipment in the class, the basic operating principle, literature references, and sketches or photographs of the units. Shortcut siz ing techniques and rulesofthumb are used through out the chapter for rough sizing. The major feature of the chapter is a set of tables which provide criteria for the preliminary specification of units within each equipment class. The selection tables are organized by principle of operation, applicable capacity range, important data to that class of equipment (i.e., par ticle size for crushing equipment), material compati bility, type of service, and any other criteria useful for differentiating alternatives within the class of equipment. Qualitative ranking of the units is pro vided when numerical comparisons are not appro priate for comparing equipment, such as past expe rience in the suitability of the unit for a particular Spring 1991 problem application. I tried to use the tables by selecting some units that I was particularly familiar with and found that they (and the text) provided enough basic information to describe the unit and give a size range. There is enough information to select a unit given the feed characteristics, but not enough information to do any analysis of the opera tion of the unit or detailed sizing. The second section of the book (approximately one hundred and fifty pages) covers "Economic Analy sis." Chapters cover capital and manufacturing cost estimation, economic optimization, and cashflow analysis. The cost estimation techniques presented are adequate for a preliminary estimate. Figures provide capital cost estimates for different types of units, but there is no information about the error or spread of data used to create the figures. The chap ter on cashflow analysis (time value of money) is brief, and the coverage on the treatment of alterna tive investments could use more examples and dis cussion. The final, brief, section is a single chapter on "Technical Reporting." There are many anecdotes to encourage the student to write effectively. It would have been useful to provide example outlines for different types of engineering design reports to give the student an idea of what information is expected, depending on the type of study being done. After I finished reading the book, there were a number of things that troubled me. The design proc ess is not emphasized as an iterative process that requires preliminary sizing and costing and then more detailed study and operations analysis (which may force changes in the original process concept). Little reference is made to modern computer pack ages that can do both the shortcut and the rigorous mass and energy balances (and sometimes the eco nomics), and which allow the student to do a second pass at the design. The overall plant design is a set of chemical operations for which one must make decisions about unit alternatives as well as the proc ess configuration itself. Process units interact through recycles so that design decisions in one unit can affect the operation, size, and economics of the rest of the plant. Some material and detailed examples on process configuration alternatives (process syn thesis) would be useful for the student to see that different process concepts are possible. If the instructor has a design course that is based on a welldefined case study, then the book provides reference material that would be useful for prelimi nary unit design and economic analysis. O 95 views and opinions UNDERGRADUATE EDUCATION Where Do We Go From Here? RICHARD G. GRISKEY Stevens Institute of Technology Hoboken, NJ 07030 Chemical engineering undergraduate education has undergone many changes and transforma tions over the years. It has moved from a curriculum best described as industrial chemistry through the unitoperations approach, to an emphasis on engi neering sciences (i.e., transport phenomena) with greatly increased mathematical sophistication, and ultimately to a heavy infusion of computerbased methods and techniques. The nature and background of the faculty has also changed. Initially, the typical professor was ori ented toward practice and to what some called a handbookapproach to teaching. Later, however, as the unit operations approach took hold, faculty (while still oriented to practice) began to involve themselves in research that was designed to provide an understanding of complex phenomena. The next permutation saw faculty becoming both more mathe matically and more scientifically oriented. Further, while engineering research had been mainly ex perimental in nature, it now began to take on a more theoretical slant. Finally, the "computer revo lution" produced a new breed of professors, with many of them geared almost exclusively to a com puter approach. In addition to the above, the relationship of the faculty to industrial practice has also greatly changed. Where it was once common to encounter faculty with industrial experience, there are now far fewer such individuals, particularly among junior profes Richard G. Griskey received his BS, MS, and PhD degrees from CarnegieMellon University. He has held both professional and administrative positions (department head, dean, provost, executive vice presi dent) at several universities. An active researcher, She has over two hundred publications and has super vised over fifty graduate theses. sors. It is not uncommon at some institutions to find many, if not all, of the departmental core courses taught by faculty whose experiences are wholly con fined to academia. The changing curriculum and changing faculty have obviously had a great impact on chemical engi neering education (in particular, on undergraduate education). There is no question that today's bacca laureate graduates are considerably different from their predecessors of twenty, ten, or even five years ago. Today's chemical engineering graduates are sharp, they are highlysophisticated mathematically, and they are quite proficient with respect to the computer. All would seem to be well. However, when engi neers in industry (including new hires) are asked to evaluate today's undergraduate chemical engineer ing education, they raise a number of questions. For example, newlyminted engineers complain about a lack of "practical information" in their training. The serious thing about this charge is that it even comes from students who have graduated from institutions which strongly emphasize practice rather than the ory. Complaints of older engineers range from an inability of new hires to carry out wellknown proce dures to their lack of even a rudimentary under standing of equipment. At this point, a number of different opinions would be elicited. One type of response would be that there is no problem and that all is well. Others, however, would probably recommend a massive reorganiza tion of chemical engineering education in order to cure any and all perceived problems. Actually, both camps are correct in their evalu ation. Massive changes in curriculum, courses, etc., are not needed; what is needed is a change in the way the material is presented. We must move from an overbalance and dependence on theory, mathe Copyright ChE Division, ASEE 1991 Chemical Engineering Education One type of response would be that there is no problem and that all is well. Others, however, would probably recommend a massive reorganization of chemical engineering education ... matics, and the computer, to a new approach that not only recognizes and maintains those gains but also clearly links them to engineering practice. How do we do this? We do it by changing the style and philosophy of teaching our undergraduate courses. At the risk of oversimplification, the follow ing points should be considered: Continue to teach fundamentals, but emphasize the first principles even more strongly. Make the greatest possible use of phenomenological approaches. Clearly delineate the progression, use, and relationships between theoretical, semiempirical, and empirical approaches. Emphasize practice by continually interlinking theory to actual or real situations. Do this quantitatively; if unable to do so, use qualitative and/ or anectodal examples. Build on first principles by using homework or examination problems that emphasize applications in different, new, or novel areas or applications (i.e., enable the graduate to move into new areas of technology). Put mathematics into its proper perspective (i.e., useful and important, but not the beall or endall). Use the computer, but emphasize that it is a means, not an end, and that garbage in gives garbage out. Work into each course the concepts of process and equipment. Emphasize innovation, creativity, and ingenuity, remembering that an engineer is a "person who carries through an enterprise by skillful or artful contrivance." A response to the preceding might be that we already do these things in academia, so why bother? It should be evident that even if we are doing them, as academics we are falling short and must there fore emphasize them even more strongly. Another comment might be that these are admit tably worthwhile objectives, but how can they be implemented? A possible scheme for implemen tation in chemical engineering departments would be to: Commit to a teaching philosophy that emphasizes the preceding points as well as others that accomplish the same goals. Take advantage of the valuable resource of faculty with industrial experience to track the undergraduate core courses so that theory and practice can be effectively interlinked. Utilize, as well, those faculty members who specialize in experimental research so that the aspects of equipment and processes can be emphasized. Develop good rapport with industry so that examples, guest lecturers, etc., can be used to enrich core courses. Build on science and mathematics, but clearly emphasize the fact that engineering is different. Evaluate all of the preceding by contacts and discussions with recent graduates and more mature practicing engineers. Keep the undergraduate curriculum dynamic, recognizing that static situations produce deterioration. Hopefully, this paper will stimulate discussion and more detailed consideration of undergraduate education in chemical engineering. This in itself would be a rewarding and beneficial exercise. 0 book review VISCOUS FLOWS: THE PRACTICAL USE OF THEORY by Stuart Churchill Butterworths, 80 Montuale Avenue, Stoneham, MA 02180; $52.95, 602 pages (1988) Reviewed by Stanley Middleman University of California, San Diego La Jolla, CA 920930310 Professor Churchill has produced a textbook aimed at the student with prior background in fluid dynamics, although he states that it has been used with "surprising success" as a first course for under graduates when the material is presented at a slower pace and with some deletion of detail. My own im pression is that this book could indeed be used in a juniorlevel fluids course, but that its success would depend to a great degree on the skill of the teacher in choosing the topics to be included, and in supple menting the material of the text with ample class room discussion so as to provide a broader context in which fluid dynamics is seen as an essential element of chemical process engineering. In the hands of a teacher whose main focus would be on the derivation of solutions to various fluid dynamics problems, the use of this text would be less successful in providing Continued on page 111. Spring 1991 laboratory PURDUEINDUSTRY COMPUTER SIMULATION MODULES The Amoco Resid Hydrotreater Process R.G. SQUIRES, G.V. REKLAITIS, N.C. YEH, J.F. MOSBY,1 I.A. Karimi,2 P.K. Andersen Purdue University West Lafayette, IN 47907 The senior chemical engineering laboratory is a required part of most accredited chemical engi neering programs and is considered a "capstone" course, drawing as it does on students' previous tech nical work. Furthermore, the senior laboratory typi cally requires the students to use their written and oral communication skills and, since lab projects are often group efforts, their interpersonal skills as well. In Purdue's laboratory course students work to gether in groups of three, consisting of a group leader, an experimentalist, and a design engineer. Each group works on three monthlong projects chosen from a list of about a dozen experiments which in volve processes such as extraction, filtration, distil lation, gas and liquidphase reaction, ion exchange, heat transfer, fluid flow, mixing, and diffusion. In our view, the ideal laboratory experiment should duplicate a real industrial process. The stu dents would use modern equipment to investigate a complex problem, and would do so under realistic time and budget constraints. Since universities can hardly afford to construct or operate industrialscale plants, the next best alternative is to devise experi ments which closely simulate the operation of indus trial processes. With this in mind, we are developing a series of computer simulations intended for use in undergraduate chemical engineering laboratories. These simulations model actual industrial chemical processes and are being produced with the assis In our view, the ideal laboratory experiment should duplicate a real industrial process. The students would use modern equipment to investigate a complex problem... ' Amoco Corporation; 2 Northwestern University Company Amoco Mobil Dow Chemical Tennessee Eastman Air Products Process Hydrodesulfurization Catalytic Reforming Latex Emulsion Polymerization Methyl Acetate from Coal Process Heat Transfer tance of various corporate sponsors. The first five are listed in Table 1. AMOCO RESID HYDROTREATER The first simulation that we have completed models a hydrodesulfurization pilot plant (see Fig ure 1) built by Amoco in its Naperville, Illinois, re search facility. The hydrotreater takes a mixture of heavy, highsulfur hydrocarbons (called "resid oil") and upgrades it by breaking the long carbon chains to form smaller chains adding hydrogen to increase the saturation removing sulfur in the form of HS gas R.cI Pump R.Acy Pu Figure 1. Amoco hydrodesulfurization pilot plant. The three ebullatedbed columns are well mixed by the recycle streams. Copyright ChE Division, ASEE 1991 Chemical Engineering Education TABLE 1 Process Simulations and Industrial Sponsors Ra orV2 Pmdlx Ravr R.dFd NonCatalytic Reactions +H, H2 +H2 +H2 R > G  D N w> L \k k2 k 3 Catalytic Reaction k Sulfur + H2  H2S Figure 2. Hydrodesulfurization reaction scheme. Each of the components R, G, D, N, and L is a mixture of many different compounds, lumped together by boiling point. The reaction scheme is shown in Figure 2. Each of the components R, G, D, N, and L is a complicated mixture of many different chemical species, the ac tual composition of which would be very difficult to specify exactly. R, G, D, N, and L are characterized by their average boiling points and their sulfur con tent (see Table 2). The hydrogenation reactions (reactions 1 through 7) are modeled as a set of sequential and parallel firstorder reactions. The net generation rates are given by R.G. Squires is a professor of chemical engineering at Purdue University. He received his BS in chemical engineering from Rensselaer Polytechnic Institute in 1957 and his MS and PhD from the University of Michigan in 1958 and 1963, respectively. His current research interests center on the educational applica tions of computer simulation. G.V. Reklaitis is Head of the School of Chemical Engineering at Purdue University. He earned a BS from Illinois Institute of Technology in 1965 and a MS and PhD from Stanford University in 1969. His research interests include process systems engineering, process scheduling methodology, and the de sign and analysis of batch processes. N.C. Yeh is a postdoctoral research in chemical engineering at Purdue University. He received a BS from National TsingHwa University (Taiwan) in 1978 and a PhD in chemical Engineering from Purdue University in 1987 His research deals with process simulation and optimization. J.F. Mosby is a Senior Research Associate at the Amoco Research Center in Naperville, IL. He received his BS and PhD in chemical engineering from Purdue University in 1959 and 1964, respectively. His research interests include petroleum refining process development and simulation. LA. Karimi is an assistant professor in the chemical engineering department at Northwestern University. He received his BS from IIT Bombay in 1980 and his MS and PhD from Purdue University in 1982 and 1984. His research has dealt with computeraided design, scheduling, and optimization of batch chemical processes. P.K. Andersen is an assistant professor in the Department of Freshman Engineering at Purdue University. He earned his BS from Brigham Young University in 1981 and his PhD from UC Berkeley in 1987, both in chemical engineering. His research has dealt with transport in multiphase flows and the educational applications of computer simulation. Spring 1991 rR =(k +k5+k + k7)R rG =k2G +CRGk1R rD =k3D + CRDk5R + CGDk2G 3 RD5 GD2 r k4 RN R + CDNk3 L CNLk4N RLk7 where R, G, D, N, and L are the weight fractions of the sulfurfree components; k1, k2 .. ., are rate constants, and CRG, CRD ... CRL are stoichiometric coefficients. The desulfurization reaction (reaction 8) is cata lytic. It is first order in hydrogen, second order in sulfur, and inhibited by resid: AktES2 r 1 + K9R Here A is a catalyst deactivation factor (A = 1 for fresh catalyst), i is the partial pressure of hydrogen, kg is a kinetic rate constant, and K, is an equilib rium constant. The rate constants for reactions 1 through 8 are given by Arrheniustype relations ki = ai exp(Ei / RT), i= 1,...,8 where a is the preexponential factor and Ei is the activation energy for the ith reaction. The reactions are carried out in well mixed, ebul latedbed reactors, which are modeled as continuous stirredtank reactors (CSTRs). Under some condi tions, the simultaneous solution of the mass and energy balances for a CSTR may exhibit multiple steady states (see Figure 3). The reactors usually operate at the intermediate steady state, which is unstable with respect to temperature; at the lower steady state the conversion is too low and at the upper steady state the temperature is too high. THE COMPUTER PROGRAM The program consists of more than 10,000 lines of FORTRAN and C code. It can simulate the steady state behavior of one, two, or three reactors in series, TABLE 2 Reactants Component Average B.P. (F) Sulfur (wt. %) Resid (R) >1200 5.0 Gas Oil (G) 827 2.0 Distillate (D) 514 1.0 Naphthas (N) 280 0.5 Light Gas (L) <200 0.0 or the dynamic behavior of a single reactor. The program currently runs on the Sun 3/60 worksta tion, although it can be readily modified to run on any machine that supports the X Window System. A graphical user interface makes the program easy to use, even for students having minimal expe rience with Sun computers. The user employs a mouse to select from options presented on "pulldown" menus. Should the user get lost or for get what to do, he or she can get help from the program itself. USE OF THE MODULES AT PURDUE Eight threehour lab periods are allotted to each project. In preparation for the first scheduled lab period, the students are asked to study a written description of the process and to view a short video taped "plant tour" supplied by the corporate spon sor. They also attend an orientation meeting with the instructor, where general questions about the process, the simulation, and the lab are answered. THE INITIAL ASSIGNMENT In keeping with our attempt to provide realism in the project, the students are given their assign ment on official Amoco stationery. They are required to do the following things: Determine the values of the preexponential factors for the hydrogenations Check activation energy for one of the hydrogenations Determine the preexponential factor a8 and activation energy E8 for the desulfurization Check the form of the catalyst deactivation equation and measure the catalyst deactivation rate The assignment letter authorizes the students to run the Naperville pilot plant and two small labora tory reactors. BUDGETARY LIMITATIONS Contributing to the sense of realism in this mod ule is a requirement that the students work within a budget. Initially they are given $150,000 (simulated money, of course!) with which to work. Table 3 lists the time and money required for various tasks in volving the pilot plant and laboratory reactor. Note that the students are charged a fee each time they seek help from the "consultant" (i.e., the instructor). THE PLANNING CONFERENCE The students spend the first two lab periods pre paring a plan of attack, which they must present to the instructor in a planning conference before the Temperature Figure 3. Mutiple steady states in a CSTR. The system usually operates at the intermediate steady time. third period. In this conference the instructor asks the students to describe, in order, the experiments they intend to carry out. At each step they must justify their plans. The instructor asks questions and gives hints where necessary, but is careful not to reveal too much about the solution to the problem. The students are faced with a number of choices regarding the type and number of reactors, the cata lyst age, the feed composition, and the reactor tem perature. In making these choices, they have to keep in mind a number of constraints: It takes five days' and $75,000 (half the budget) to clean and prepare the pilot plant. It costs another three days' and $50,000 to replace the catalyst in the pilot plant; obviously, the students cannot afford to change their minds on the catalyst selection. Each pilot plant run takes twentyfour hours.' The preexponential factors a,,..., a, must be measured in the pilot plant. Other constants can be obtained from the lab reactor, but their values must be checked in the pilot plant. It makes sense to use the lab reactors as much as possible, since they are considerably cheaper to op erate than the pilot plant. Furthermore, the lab re actors are easily refilled with catalyst, permitting the students to take data related to catalyst age. However, all constants that are determined from laboratory data must be checked in the pilot plant. (By "checked" we mean that four or five points over a reasonable range should agree with the previously determined values.) STEADYSTATE SIMULATION Once the students have demonstrated to the in structor's satisfaction that they have a good grasp of the problem, they are shown how to operate the computer program in the steadystate mode. This enables them to simulate the operation of the labo S imulated time Chemical Engineering Education ratory reactors and the pilot plant, from which they can obtain the required kinetic constants. The students are permitted to take data from the third through the sixth lab period. During the sixth period the group leader is required to give a fifteen minute oral progress report, which is videotaped and critiqued in private with the speaker. DYNAMIC SIMULATION After the group leader's progress report, the in structor shows the students how to run the simula tor in the dynamic mode. The students are then given a second assignment letter informing them that they have been selected to act as consultants during the startup of a resid hydrotreater at Amoco's Texas City refinery. They are asked to simulate the startup of a single reactor, controlling the operating conditions manually to reach steady state. Then they are to cease controlling the system and to note the time that elapses before automatic shutdown occurs. The startup problem is especially challenging because the operating conditions within the reactor can only be controlled indirectly, by setting the tem perature, flow rate, and composition of the feed stream. Furthermore, instantaneous changes in these variables are not permitted; the students must wait fifteen minutes between changes in the feed set tings, and they are limited to changing feed tem perature by no more than 100 F at a time. Finding a suitable control strategy is typically a trialand error process. (Dynamic simulation runs are not charged against the students' budgets.) Two lab periods are allotted for the startup prob lem. The students then have one week to produce a full written report, including the results of their TABLE 3 I Expenses Initial preparation and startup of pilot plant (includes cost of initial charge of catalyst Replacement of catalyst in pilot plant One pilot plant run (includes labor, materials, analysis, etc.) Three reactors in series Two reactors in series One reactor One laboratory reactor run (includes catalyst replacement) Consultation 5 days $75,000 3 days $50,000 24 hours 24 hours 24 hours $4,500' $4,000' $3,5001 24 hours $5001 ? $500 'Multiply by 1.5 for Saturday runs; by 2.0 for Sunday runs Spring 1991 steadystate experiments and an outline of their rec ommended startup procedure. ROLE OF THE INSTRUCTOR The instructor has four important parts to play in a simulation project: 1. Mother Naturesets the mean values and random variability of all parameters used in the simulation 2. Bossreceives the oral and written reports from the group 3. Consultanthelps with specific technical questions, but charges a fee that must be paid from the budget. 4. Instructorassigns the grades, of course. COMPUTER SIMULATIONS FOR EDUCATION Although it would be possible to design a senior laboratory made up entirely of computersimulated experiments, we believe that students should also gain "handson" experience by working with real laboratory equipment. For this reason, we allow only one of the three required experiments to be a com puter project. We have used the Amoco module here at Purdue for five semesters, with great success. As an alterna tive to traditional lab experiments, computer simu lation offers a number of significant advantages: Processes that are too large, complex, or hazardous for the university lab can be readily simulated on the computer. Realistic time and budget constraints can be built into the simulation, giving the students a taste of"real world" engineering problems. The emphasis of the laboratory can be shifted from the details of operating a particular piece of laboratory equipment (which may not be representative of current industrial practice) to more general considerations of proper experimental design and data analysis. Computer simulation is relatively inexpensive compared to the cost of building and maintaining experimental equipment. Simulated experiments take up no laboratory space and are able to serve large classes because the same computer can run many different simulations. AVAILABILITY OF THE MODULES Anyone interested in obtaining more information on the PurdueIndustry ChE Simulation Modules should contact Professor Squires. An NSFsponsored workshop on the modules will be held at Purdue on July 2628, 1991. ACKNOWLEDGMENTS This work has been supported by the National Science Foundation (Grant No. USE888554614). Technical assistance was provided by Amoco Oil Company and the CACHE Corporation. I laboratory CRYSTALLIZATION An Interesting Experience in the ChE Laboratory TEOFILO A. GRABER S., MARIA E. TABOADA M. Universidad de Antofagasta Antofagasta, CHILE The economy of Chile is strongly based on metal lic mining activity. However, large reserves of salt and brines available in northern Chile have led to a significant increase in the amount of research effort expended on nonmetallic mining exploitation and processing. Wealthy reserves of lithium, potas sium, nitrates, sulphates, boron, etc., including var ied crystalline forms, are found there. The Universidad de Antofagasta has played an important role in the development of these non metallic mining research projects. Crystallization has been one of the chosen subjects and has been taught during the last three terms in the department of chemical engineering. Crystallization is offered as a four semesterhour course, including lecture and laboratory work which consists of four experiments. The one described in this paper is aimed at the study of sodiumsulphate crystallization in a MSMPR continuouslyagitated crystallizer tank. It is intended for the study of crys tallization kinetics of decahydrated sodium sulphate. The nucleation growth rate kinetics were evaluated by measuring the crystal size distribution (CSD) and using the mass, energy, and population balances. CRYSTALLIZATION KINETICS Industrial crystallization is defined as a tech nique aimed at producing crystals with specific char acteristics of purity and size distribution. Crystalli zation is an extremely complex process which is af fected by a number of variables, such as supersatu ration level, temperature, agitation, impurities, mechanical effects, etc. Important advances related to analytical description and process understanding have been achieved since the 1960s. The populationbalance approach to the descrip tion of crystal size distribution is the most widely accepted approach, and it has proved to be the most fertile in germinating new developments for describ ing and modeling crystallizers. The populationbalance equations were first for malized by Randolph and Larson.11' They allowed us to get the nucleation and crystalline growth kinet ics. Two phenomena are involved in the crystalliza tion process: the formation of new particles by nu cleation processes and crystal growth processes. They both depend on supersaturation, but in different manners. During nucleation, small regions are formed within the homogeneous phase that consist of vari able numbers of ordered atoms or molecules, called clusters or embryos. Some of these are in equilib rium with the mother liquor. This cluster, termed a critical nucleus, is converted during further growth into a macrospecies which forms the new phase. Kinetics data on crystallization processes are of basic importance for the design of industrial crystal lization equipment. These data determine the size of the crystallizer and the crystal size of the product. Tedfilo A. Graber is an associate professor in chemi cal engineering at the University of Antofagasta. He received his BTech (1975) from the Universidad Tcnica del Estado and his MS (1988) from the Univer sidad de Chile. He has presented courses in chemical / reactor engineering and transport phenomena. His re search interests are in chemical processes. Maria E. Taboada is an assistant professor of chemical engineering at the University of An tofagasta. She received her BTech (1980) from the Universidad del Norte and her MS (1989) from the Universidad de Chile. She has presented courses on heat and mass transfer. Her areas of interest are in process crystallization. Chemical Engineering Education Copyright ChE Division, ASEE 1991 POPULATION BALANCE A population balance general relationship valid in a crystal size range Li to L2 (AL) and in the period of time At, is the starting point in the analysis. N of crystals entering the reactor with size AL N of crystals N of crystals + entering range = exiting the AL because reactor with of growth size AL Crystals exiting + the range AL because of growth a) The number of crystal seeds entering the crystal lizer having a size range (L,, Li+AL) during At interval, is given by Q ns AL. At (1) where n. is the population density at the inflow, n AL represents the fraction of crystals with size AL, and Q, is the volumetric inflow. b) The number of crystals entering to AL range in the At interval due to G1 growth is given by VG1n1At (2) where V is the volume of the crystallizer. The growth function of G crystals is represented as a supersaturation and crystal size function. G = G(L, AC) (3) G = Gc (C) .(L) (4) c) The number of crystals having a size range (L1, L,+AL) which are removed from the reactor during At interval are given by Q2 n ALAt (5) where n is the population density at the exit and Q2 is the volumetric exit flow. d) The number of crystals growing outside the size range (L1, L1+AL) at At interval is VG2 n.At (6) Then the population balance [using Eqs. (2) to (5) in the size range (L1, L,+AL)] is VGinlAt+QlnsALAt=VG2nAt+Q2nALAt (7) Carrying out the appropriate arrangements in Eq. (7) and considering that there are no crystals in the feeding, yields d(Gn) Q2  n dL V Defining the halftime residence as V Q The populationbalance equations were first formalized by Randolph and Larson. They allowed us to get the nucleation and crystalline growth kinetics. Two phenomena are involved in the crystallization process: the formation of new particles by nucleation processes and crystal growth processes. and assuming steady state d(Gn) n= dL (10) Integrating Eq. 10, by separation of variables when G # G(L), yields n = no exp(L / Gt) (11) in which no is the nuclei population density. Therefore Eq. (7) represents the crystal size distribution (CSD) of the process, where the dis tribution function n represents the number of particles having a certain size range per unit volume and a characteristic size. Number of particles with size between L and (L + AL) n(L)= (Volume) (AL) (12) This size distribution function can be directly obtained by determining the number of particles associated to each size range, as Mass of crystals retained in a sieve / p, (average size particle volume)(volume) (13) where pc is the crystal density. Using an average size L L1 +L2 L = 2 and defining the particle volume as Vp=kL3 in which kv is the crystal shape factor Also AL = L2 L1 (14) (15) (16) where L, is the lower mesh opening (through which the particles enter) and L2 is the retaining mesh opening of the sieve. Therefore AN n= AL AL n= W pckvL3 ALVs (17) (18) () where Vs is the volume occupied by the solution. Then it is possible to interpret the population Spring 1991 density of zero particle size, or nuclei number den sity, n, as n=B/G (19) resulting in Eq. (11) (n)= tfn L (20) This equation is very important, since by using experimental distribution functions (obtained through screening tests) it is possible to find the adequate system kinetic model. Representing gra phically (n) versus L we obtain a straight line of slope 1/Gt and intercept B/G from which the growth velocity G can be determined at specific values of t. In addition, it is possible to obtain the value of nu cleation velocity B. EXPERIMENT The experimental equipment used in this study (see Figure 1) was a translucent acrylic MSMPR crystallizer, cylindrical in shape and 15.2 cm diame ter by 39 cm height. Inside the tank there were three baffles and a 10 cm diameter by 15.2 cm height concentric tube, located at 6.5 cm distance from the bottom of the tank. The overflow volume is 3.250 ml. The system was provided with agitation similar to a perfect mixed crystallizer proposed by Randolph.13' Due to the significant decrease in solubility exhibited by decahydrated sulphate sodium solution with decreasing temperature, the crystallization was carried out by cooling. The feeding solution was pumped from a storage container provided with a heater (25 0.1 C) to the crystallizer (using a double head peristaltic pump in order to obtain a perfectly regulated flow). The crystallizer was maintained at 18 C inside a 20 1 thermostatic bath, obtaining the supersaturation by cooling. The feeding flow was monitored with a Gilmont rotameter provided with a precision valve. One of the experiments was carried out at 500 rpm for a residence time of 0.62 hours. The solution flow for this experiment was established measuring the solution density in order to reach the steady state. After steady state was reached, the outlet flow was vacuumfiltered and the product was washed with acetone to eliminate residual water and avoid agglomeration of crystals. After the drying stage the crystals were screened in a Rotap provided with standard Tyler sieves with mesh of 16, 18, 20, 30, 40, 50, 70, 100, and 140, by which the crystal size distri bution was obtained. RESULTS Table 1 shows the experimental steadystate data for an experiment at 500 rpm with a residence time of 0.62 hours and the conditions mentioned in the previous section. Equations (13) to (18) were used in order to ob tain the values of the crystal size distribution func tion. The former results were plugged into the popu lation balance from which the experimental results, plotted in Figure 2, were obtained. To determine the crystal shape factor under the conditions used in this work, small samples of known crystal size were counted and weighted, determining the shape factor by the relation k P ( W pc(L)3 AN (21) 1. Constant head reservoir 2. Pump 3. Rotameter. 4. Refrigeration Unit. 5. Cristallizer vessel. 6. Filtration Unit. Figure 1. Experimental equipment TABLE 1 Experimental Data VOLUMETRIC FLOW Q^ (cc/min) 102 CRYSTAL DENSITY r, (g/cc) 1.464 OPERATION TIME top (min) 15 Mesh Sieve Opening Sieve Mass L (mm) (g) 16 18 20 30 40 50 70 100 140 BED 1.180 1.000 0.850 0.600 0.425 0.300 0.212 0.150 0.106 9.12 32.12 39.82 235.42 89.14 54.42 22.02 7.22 1.22 0.50 Sample Mass M,(g) = 490.99 Chemical Engineering Education where AN is the number of crystals in the sample of mass W. An average shape factor of 0.553 was ob tained. From the data plotted in Figure 2, we obtain the slope and interception values by applying a linear regression method to Eq. (20), obtaining 1 1 4.9951 (1/ mm) GI B / G = 2.7154 x 107 (crist./1 mm) with a correlation factor = 0.979. Clearing the equation, we obtain the growth and nucleation velocity G = 0.3216 (mm / h) B = 1.04451 x107 (crist./1h) CONCLUSIONS The laboratory experiment described above al lows a good understanding of the crystallization proc ess. The key factors affecting this process (i.e., agita tion, size distribution, nucleation) are better grasped by the student when theoretical equations are worked out together with reallife processes. Even though this work presented only one set of experimental data, the experiment itself is very flex ible since it is possible to work out various situations under different conditions (temperature, concentra Inten=ptl T G  Slope=Y/Gr T=0622 h N= 500 RPM 11 M= 240 68 9/1 01 02 03 5 06 07 09 t10 1.1 Size T(mm.) Figure 2. Crystal size distribution obtained from a laboratoryscale MSMPR crystallizer tion, spatial time, agitation velocity, etc.). For in stance, the parameters affecting the B and G values can be determined by testing B and G under differ ent operating conditions. Thus the students can find a kinetic equation of the studied system, through B = k(G)b. Furthermore, it also allows the student to understand the influence that each variable has in the crystallization process, i.e., agitation velocity. In industrial processing this has great importance since a homogeneous crystal size distribution is required by connecting processes such as centrifugation, among other things. Due to its simple phase diagram, the Na2SO,  H20 system is a good example for experimental study and teaching purposes. In fact, this system exhibits direct and reverse solubility between 0 and 60 C with formation of different hydrates. For the reason stated below, the experiment allows a good versatil ity in crystallization products when working under different operating conditions. The graphical representation of the equilibrium phases we well as the distribution of crystal size is an effective way to understand the phenomenon from a physical point of view. Also, the solubility diagram allows the student to calculate theoretical output by means of simple material balances. By analyzing the experimental data (presented in Table 1) the crystal mass turned out to be 490.95 g, and the predicted value was expected to be 500 g. This result means a 2% accuracy when the crystal performance is considered. The resulting dif ference may be due to the fact that some of the crystals produced remain attached to the crystal lizer walls and to the losses in the drying and filtra tion processes. Since in the former graph a linear relationship was obtained, it can be stated that the experiment was performed under the basic assumptions of crys tal growth independent of its size and steadystate conditions. ACKNOWLEDGEMENT The authors appreciate the financial support given by FONDECYT to Project 890775. REFERENCES 1. Randolph, A.D., and M.A. Larson, "Transient and Steady State Size Distribution in Continuous Mixed Suspension Crystallizers," AIChE J., 8, 639 (1962) 2. Sehrwin, M.B., R. Skinnan, S. Katz, "Dynamic Behavior of the Well Isothermal Crystallizer," AIChE J., 13, 6, (1967) 3. Randolph, A.D., and M.A. Larson, Theory of Particulate Processes, Academic Press, New York (1971) O Spring 1991 [ classroom PRINCIPLES OF STAGEWISE SEPARATION PROCESS CALCULATIONS A Simple Algebraic Approach Using Solvent Extraction BARRY D. CRITTENDEN University of Bath Bath, BA2 7AY, United Kingdom traditionally, graphical techniques such as the McCabeThiele and PonchonSavarit methods have been used to introduce undergraduate chemi cal engineering students to the design and analysis of multistage separation processes. While the stu dents have quickly grasped the concepts of simulta neously solving the material balances and phase equilibrium relationships, their understanding of transforming such principles into graphical methods has often been slow to develop. A strong emphasis on the use of computers from the beginning of the first year course at Bath has resulted in students who find it increasingly difficult to adapt their minds to solving complex problems by graphical methods. Building on the mathematical expertise of fresh men, a simple liquidliquid equilibrium (LLE) sys tem has been used to demonstrate most of the essen tial features of multistage contacting, whether cross or countercurrent. Solutions to the material bal ances and phase equilibria are all algebraic and simple to derive and only an elementary knowledge of series summation is required to derive the solu tion for minimum solventtofeed ratio. The simple LLE system can then be used to introduce students to the graphical techniques which are necessary for complex equilibria. Barry Crittenden obtained his BSc and PhD de grees in chemical engineering from the University of Birmingham. He is a senior lecturer in the School of Chemical Engineering at the University of Bath. His teaching interests are in separation processes and heat transfer. His research and consultancy interests are in fouling of heat exchangers, novel forms of heat transfer equipment, adsorption, environmental con trol, and hazardous waste management. BACKGROUND At the University of Bath, lecture programs in separation processes are given in each of the three taught years in the BEng Honours degree courses in chemical engineering and chemical and bioprocess engineering. Most students elect to spend their third year on industrial placement, working effectively as graduate engineers with leading process engineer ing companies. Thus it is important that all the core material in separation processes is given in the first two years of the BEng courses. In the first year, students are expected to gain an understanding of the fundamental principles of phase equilibria and their application (with material and energy balances) to the design and operation of com mon separation processes. Examples are drawn es pecially from binary distillation, solvent extraction, batch adsorption, batch crystallization, etc. In the second year, the principles of continuous phase contacting are presented, using examples drawn especially from gas absorption, stripping, dis tillation, and solvent extraction. The selection and sequencing of separation processes, together with the principles and practices of multicomponent sepa rations, adsorption, membrane processes, and other highlyselective separations are reserved for the fi nal year lecture course. Modern textbooks in chemical engineering con tinue to adopt the use of graphical techniques to explain stagewise separation process calculations. The main advantage of using such techniques at the outset is realized by the lecturer, who can easily cre ate visual aids to explain concepts such as cross current multistaging, countercurrent multistaging, minimum solvent flowrate, minimum reflux ratio, total reflux, etc. Copyright ChE Dwiision, ASEE 1991 Chemical Engineering Education However, while some students readily understand that graphical methods are based on the fundamen tal material balances and phase relationships, there are many students who find the use of hypothetical pole points or difference streams to be mysterious techniques. In addition, with the advent of modern, powerful computers and supporting software, the use of graphical methods (with their inherent in accuracies) should be discouraged for all except check calculations or for systems with complex equilibria which are difficult to model thermodynamically. Most freshmen already appreciate the basic con cepts of partitioning a solute between a solvent and a diluent. They are also mathematically competent. With these points in mind, the firstyear course in separation processes now commences with a totally algebraic approach to stagewise contacting, using a simple liquidliquid equilibrium system to illustrate a number of important aspects of stagewise contact ing. For solvent extraction, these are the equilibrium stage model simultaneous solution of singlestage material balances and phase equilibria multistage crosscurrent contacting efficient use of solvent in multistage crosscurrent contacting multistage countercurrent contacting advantage of countercurrent contacting over cross current contacting minimum solventtofeed ratio The use of solvent extraction to explain impor tant facets of stagewise contacting is particularly apt since this process is one of five which have been identified by the UK Science and Engineering Re search Council as requiring special research atten tion under its Separation Processes Initiative. Oth ers include membrane processes, selective adsorp tion, highlyselective separations, and the opportu nities for exploiting centrifugal fields. SIMPLE LIQUIDLIQUID EQUILIBRIUM The algebraic analyses are restricted to the sim plest case of extraction of a solute from a diluent by means of a solvent which is immiscible with the diluent even in the presence of the solute. The distri bution coefficient K for the solute is constant and is given by mass of solute per unit mass K Y of solvent in extract X mass of solute per unit mass of diluent in raffinate In the first year, students are expected to gain an understanding of the fundamental principles of phase equilibria and their application (with material and energy balances) to the design and operation of common separation processes. pure solvent S = mass flow feed F = mass flow of diluent Xf= solute mass/diluent mass rafflnate F= mass flow of diluent X = solute mass / diluent mass Extract S = mass flow of solvent Y1= solute mass I solvent mass FIGURE 1. Single equilibrium stage with pure solvent. The use of mass ratios in place of mass fractions is readily understood by the students. The simple conversions are given later in this article. SINGLE EQUILIBRIUM STAGE Students are encouraged to read about discrete stage solvent extraction equipment such as the mixer settler. A single equilibrium stage is shown sche matically in Figure 1. To keep the problem as simple as possible, a feedstock containing only solute and diluent is contacted with a pure solvent. The per formance of the unit is calculated as a function of the following parameters: S = mass flow of solvent F = mass flow of diluent in feedstock X, = mass of solute per unit mass of diluent in feedstock X, = mass of solute per unit mass of diluent in raffinate The material balances for diluent and solvent are trivial because these two components are immis cible. The solute material balance is XfF = XlF + YlS (1) The assumption that the stage behaves as an equi librium stage means that the phases leaving are in equilibrium, i.e., Y1 = KX1 (2) Hence the performance of the single stage is given Spring 1991 by the simultaneous solution of Eqs. (1) and (2) Xl 1 Xf (r+1) where (3) r=KS/F (4) It is readily seen from Eq. (3) that the amount of solute extracted can be improved by one or a combi nation of the following: increasing the solventtofeed ratio increasing K either by changing the temperature or by using another solvent passing the raffinate as the feedstock to second and further equilibrium stages, i.e., crosscurrent extraction shown schematically in Figure 2. MULTISTAGE CROSSCURRENT EXTRACTION Provided that an equal flowrate of pure solvent S is fed to each stage, the solute balance for the gen eral stage n is Xn_1F = XnF + YnS (5) Applying the equilibrium relationship yields Xn 11 Xn 1 (6) Xn_1 (r +1) Hence for a battery of N equilibrium stages XN 1 (7) Xf (r + 1)N From Eq. (7) it can be seen that X/Xf tends to zero as N tends to infinity. EFFICIENT USE OF SOLVENT Equation (7) can be used to show that a greater extraction of solute can be obtained if the total flow of solvent is split between a number of equilibrium stages rather than all the solvent eed being used in a single equilibrium stage. This general result is most easily demonstrated by the example of splitting the solvent equally be tween two equilibrium stages. For FI FIGURE this case X2 1 1 (8) Xf r}2 I 2+r+l Comparison of Eq. (8) with Eq. (3) confirms the improvement in the extraction of solute, but at the additional expense of providing an extra equilibrium stage. The general result for splitting a total flow of solvent S equally into N stages is XN 1 ( Xf r+N MULTISTAGE COUNTERCURRENT EXTRACTION The countercurrent extraction scheme is shown in Figure 3. A solute balance across stage 1 gives XfF + Y2S = XlF + Y1S (10) Y = KX1 and Y2 = KX2 Hence X1 Xf =r(X2 X1) (11) Applying solute balances across each stage in turn yields. X2 X1 = rX 3 2 ) n n 1 r(Xn1 Xn) XNXN1 r(XN+1 XN) Eliminating X. from Eqs. (11) and (12) gives X2 Xf = r +r2 (X3 X2) (1Z) (13) (14) (15) With further eliminations of intermediate raffinate compositions, it can be shown that solvent solvent s Yn S 2. Multistage crosscurrent extraction with pure solvent. S YI S YV FSY2S Y3 f 1 1 F X F X1 F Xa feed S S + F X,.1 F Xn FIGURE 3. Multistage countercurrent extraction with pure solvent. Chemical Engineering Education Xn Xf = r+r2+r3 +...rn}(Xn+Xn) (16) i.e., n Xn Xf = {Xn+Xn r' (17) and hence i=1 N XN Xf ={XN+ XN} I r' (18) i=1 Since XN, would be nominally in equilibrium with a pure solvent stream S, to infinity as N tends to infinity, and therefore XN/X, tends to zero. Thus complete extraction of the solute is possible with an infinite number of stages. This is clearly shown in Figure 4. Reducing the solvent flowrate reduces the value of KS/F. When KS/F becomes less than unity, rN,1 tends to zero as N tends to infinity, and hence Eq. (21) becomes XN =lr Xf (22) XN+= 0 Hence from Eq. (18) XN 1 1 Xf N N 1 ri 1ri i=1 i=0 The performance of a battery of countercurrent extractors (Eq. 20) is compared with that of a bat tery of crosscurrent extractors in which the solvent is split equally between all N stages (Eq. 9) in Figure 4. It should be noted that for the same total solvent flowrate S and the same number of stages, the per formance of the countercurrent battery is always superior to that of the crosscurrent battery. Figure 4 can be used to demonstrate that the amount of separation that can be achieved on each successive stage decreases as the number of stages increases. MINIMUM SOLVENT FLOWRATE For the countercurrent system, Eq. (20) may be simplified by summation of the series to give XN 1r for r#l (21) Xf 1 rN When KS/F is greater than unity, the term rN** tends 08 cross current   counter current 06  r=05 0.4 01 1= 2 ,r=5 0 1 2 3 4 5 6 7 8 9 10 number of stages. N FIGURE 4. Comparison of multistage cross and countercurrent extraction. (19) It is clear from Eq. (22) that complete extraction of the solute is not possible (even with an infinite number of stages) when KS/F is less than one. The (20) limiting performance is given by Eq. (22), and this result is also clearly shown in Figure 4. The highest flowrate, at which the limiting performance expressed by En. (22) occurs, is given by r=1 ( 23 r=1 (23) i.e., by sF S K (24) Solvent flowrates in excess of this value would allow X,/X, to tend to zero as N tends to infinity. The concept of minimum solventtofeed ratio for a given specification, i.e., to reduce a solute concentration from X, to XN, is thus clearly demonstrated by the simple LLE system. USE OF THE SIMPLE SYSTEM AS AN INTRODUCTION TO GRAPHICAL METHODS The above algebraic analyses enable the princi pal features of multistage contacting to be demonstrated quickly, although the liquidliquid equilibrium system is hypothetical. The equilibria for real systems are more complex, particularly when the solute concentrations are high. The above LLE system can be used to introduce students to the graphical solution methods. For convenience, the solute ratios Y and X should be converted to mass fractions. Thus, since the solvent and all extracts contain no diluent, the mass fraction of solute is given by y Y Y 1+Y (25) Similarly, since the feed and all raffinates contain no solvent, the mass fraction of solute is given by x iX (26) The locus of extracts solutee and solvent only) is clearly the hypotenuse of the rightangled diagram shown in Figure 5, while the locus of raffinates (sol ute and diluent) is clearly the abscissa. Spring 1991 0 solvent mass fraction of solvent 0.4 1 02  0.2 I \oed locus of raffinates ,0, n , ratfinate 0.8 y, fraction of solute in extract 06 0.4 0.2 0.4 0.6 08 mass fraction of solute 0 02 04 0'6 0'8 x, fraction of solute In raffinate FIGURE 5. Single stage extraction with simple LLE system. A single stage calculation of the extraction by a pure solvent of a solute from a mixture with only the diluent is shown in Figure 5. The value of the parti tion coefficient used in this example is K = 1.5. When written in terms of mass fractions rather than solute ratios, the equilibrium relationship is no longer in linear form. Substituting Eqs. (25) and (26) in the equilibrium relationship Y = KX gives the revised form of the equation f 1 y1 y Ixx1 (27) {liy} Klx} (27) Students are encouraged to derive the inverse lever arm rule from the material balances and to apply the rule to the single stage calculation. Analy ses of cross and countercurrent extractions, includ ing minimum solventtofeed ratio, can also be stud ied using the system shown in Figure 5. However, at this point in the firstyear course, students would be expected to be using real chemical systems in which either one pair or two pairs of the three components are partially miscible, and the corresponding graphs 110 would show the extract and raffinate loci not to be the sides of the triangle. CONCLUSION A simple liquidliquid equilibrium system involv ing a constant partition coefficient, which is based on solute ratios, is used to develop an understanding of multistage contacting in the firstyear separation processes course of BEng degrees at Bath. The alge braic solutions are used to demonstrate the advan tage of countercurrent operation over crosscurrent operation, to demonstrate the effectiveness of split ting the solvent in crosscurrent operation, and to demonstrate the problem of minimum solventto feed flow ratio in countercurrent operation. NOTATION F = mass flowrate of diluent in feedstock K = distribution or partition coefficient expressed in mass ratio units N = number of stages in solvent extraction battery r = parameter defined by Eq. (4) S = mass flowrate of pure solvent x = mass fraction of solute (in feed or raffinate) X = mass of solute per unit mass of diluent y = mass fraction of solute (in extract) Y = mass of solute per unit mass of solvent Subscripts f = feed n = phase leaving stage n N = phase leaving stage N 1 = phase leaving stage 1 2 = phase leaving stage 2 O Books received Organic Reactions: Volume 38, edited by Beak et al.; John Wiley & Sons, 1 Wiley Dr., Somerset, NJ 088751272; 805 pages, $89.95 (1990) CAE: Computer Modeling for Polymer Processing, by Charles L. Tucker, III; Oxford University Press, 2001 Evans Road, Cary, NC 27513; 623 pages, $99 (1990) Biotechnology Focus 2, by R. K. Finn and P. Prave; Oxford University Press, 2001 Evans Road, Cary, NC 27513; 543 pages, $79(1990) Fermentation: A Practical Approach, edited by McNeil and Harvey; Oxford University Press, 2001 Evans Road, Cary, NC 27513; 226 pages, $65.00 (1990) Polymer Characterization, by Schr6der, Muller, Arndt; Oxford University Press, 2001 Evans Road, Cary, NC 27513; 344 pages,, $47.50 (1989) Chemical Engineering Education S II I I I I I l I I  I I I with K=1'5 I I n a REVIEW: Viscous Flows Continued from page 97 an appropriate background in fluid dynamics. Since there are those among us who do bring this focus into our undergraduate classes, some thought must be given to the selection of this book for a first undergraduate course. Professor Churchill has laid out the book in a logical and attractive manner. It begins with several chapters on onedimensional laminar flows. These flow fields are physically appealing and mathemati cally tractable for the undergraduate, and they pro vide a foundation for some of the later material. As is the case with most fluids texts, the flows illus trated are almost entirely newtonian (though there is a short chapter on nonnewtonian flow through channels) and flows in which surface tension plays a dominant role are barely mentioned. This is a choice an author must make in order to keep the size of the text manageable, and it is a defensible choice. Ex tensive referencing makes it possible for the intro duction of additional material by the teacher or by the selfmotivated independent student. Following this introductory material there is a presentation of the NavierStokes equations and a discussion of the special cases of creeping flow and inviscid flow. Several subsequent chapters treat boundary layer flows in great detail, with special attention given to a comparison of experimental re sults with the mathematical models for these flows. Similarly, flows over solid cylinders and spheres are discussed with extensive comparison of theory to observations on the structure of the flow (wakes, eddies, etc.) and on drag coefficients for these bodies. A long chapter on bubbles and drops, illustrating the role of the deformable interface (here, of course, sur face tension enters) is presented. There is almost too much material hereI found myself bogged down in the seeming repetitive presentations of data on ter minal velocity of rising bubbles. On the whole, I think this text is a viable option for introduction into the undergraduate curriculum, with the reservations regarding the importance of the instructor that I have indicated above. It would be an excellent choice as the basis for a second course in fluid dynamics. One criticism of this textbook arises first upon reading Chapter 10, which presents a long (seventy pages) description of various flow fields that are exact solutions of the NavierStokes equations. Here the author has an opportunity to introduce a num ber of practical applications of theory (note the sub Spring 1991 title of the book) but this is not done either through worked examples within the chapter or through the introduction of problems at the end of the chapter. Of the 105 problems that follow Chapter 10, most are of the form of "reduce the equations," and "derive an expression." Only four of the problems are stated in a form that implies a clear practical use of the theory presented in the chapter. I am disappointed that in a text with this prominent subtitle there is so little illustration of the practical use of theory. If the feature of the text which I have just cri tized were only a matter of author's choice and style, one could accept the text as it stands since there is so much of it to applaud. Unfortunately, the failure to give more attention to practical applications, in favor of derivations of solutions, leads on occasion to comments that are at least confusing and which are potentially misleading. For example, a derivation is presented on pages 182 and 183 for the radially outward flow field gen erated by pressure within a porous cylindrical reser voir of fluid. This is an extensional flow field, and extensional flows are important and are often ne glected in typical fluid dynamics texts. The solution for the radial distribution of pressure is derived and the statement is made that the pressure is inde pendent of viscosity because there are no shear stresses. To most students this would imply that extensional flows do not exhibit viscous effects, which is clearly at odds with experience and intuition. The introduction of an example at this point, showing how to calculate the pressure required to drive this flow at a specified volumetric flowrate, would serve to clarify this point, with the bonus that the student would be introduced to the concept of balancing the total radial stress (which includes the radial viscous normal stress) at the boundary of the flow. This would permit the student to learn and appreciate the distinction between shear stresses and normal stresses. Practical applications of the theories presented, as well as of the empirical correlations of data de scribed so extensively in many chapters, do appear in several chapters more than in others. For ex ample, in Chapters 19 and 20 the topics of flow through porous media and sedimentation and fluidi zation are covered in considerable detail, and a number of problems at the end of each chapter pro vide an opportunity for the reader to explore the use of the material in several practical contexts. Thus, this text is not devoid of practical applications. I just would have hoped for more of them in view of the implication of the subtitle of the text. O 111 classroom ) COMPUTATION OF MULTIPLE REACTION EQUILIBRIA ALAN L. MYERS University of Pennsylvania Philadelphia, PA 191046393 Chemical equilibrium problems with simultan eous reactions can be solved by direct minimiza tion of the Gibbs free energy or by algebraic meth ods.'11 Direct minimization using optimization tech niques such as steepest descent is slower but has the advantage that the minimization can be carried out adiabatically as well as isothermally.'2' Algebraic cal culations are very fast but require elaborate pro gramming to ensure convergence.'3' Whatever solution method is used, chemical re actions are not required as input data. The input to the program consists of temperature, pressure, and a list of chemical compounds expected to be present at equilibrium with their initial amounts. The Turbo Pascal (MS DOS) program used to solve the examples in this paper by alge braic methods may be obtained by mailing a 3.5inch diskette with a selfaddressed, stamped return envelope to the author, or by Email (myers@cheme.seas.upenn.edu). A minimization program running under Microsoft Windows is avail able from O'Brien.121 The Pascal program uses matrix algebra for the atom balance. The list of chemical compounds is converted to an atomic matrix A (see the Appendix) by a subroutine that parses the chemical formulae of compounds in terms of the number of atoms of each Alan Myers founded the series of International Con ferences on Fundamentals of Adsorption and is the author of several monographs and one hundred pa pers. He is a graduate of the University of Cincinnati (BSc) and the University of California at Berkeley (PhD). His current teaching and research interests are in statistical mechanics and molecular simula tions of adsorption. element. The amount of each compound is expressed as a vector n. The atom balance is m=An (1) where m is determined by the starting concentra tion n . The stoichiometric matrix N for the set of chemi cal reactions is obtained from the atomic matrix A by solving the equation AN =0 (2) for N (see the Appendix). An element of N is v., the stoichiometric coefficient of compound j in reaction i. For C chemical compounds containing E elements, the number of independent chemical reac tions is R = C p, where p is the rank of A. The amount n. of compound j at equilibrium is expressed in the terms of its starting amount n ; n =n + vijni (3) where i. is the extent of the ith reaction. The Newton Raphson method is used to solve the R nonlinear algebraic equations: 0 n. nKivj = iv n( +1v n j (4) for the unknown extent of each reaction 4. Ki is the equilibrium constant of the ith reaction. Possible di vergence of Newton's method is avoided by dividing the compounds into two groups: primary and secon dary. Each secondary compound appears as a prod uct in one and only one reaction (see the Appendix). The algorithm sequentially examines all possible combinations of primary and secondary compounds to find a set of reactions with equilibrium constants less than unity. Then the starting concentration is recalculated from Eq. (1) in terms of the selected set of primary compounds. Convergence is assured be Copyright ChE Division. ASEE 1991 Chemical Engineering Education cause each reaction must proceed to the right to form a finite amount of secondary compound, but not too far to the right because the equilibrium constant K < 1. The search for the convergent set of reactions is accelerated by selecting the most stable compounds as primary, and the least stable (highest values of Gibbs free energy) as secondary compounds. This program is limited to reactions of perfect gases. Condensed phases (liquid or solid) may be present if they are at unit activity. Under these limitations, it is legitimate to view the software as a black box to which the input is thermochemical data, composition of feed, and state variables. The output is the equilibrium composition. The details of the algorithm are less important to the user than the program's speed and the conditions under which it fails, such as high pressure or simul taneous phase and chemical equilibria. Computer output can always be checked by substituting the equilibrium mole fractions into the chemical equilib rium constants. COAL METHANATION We will illustrate the procedure for coal metha nation using steam and hydrogen. Coal is simulated by graphite. Gases present at equilibrium are H2, H20, C CO2, and CH4. In addition to the amount of each compound and its state (solid, liquid, gas), the program calls for the pressure, feed composition, and dimensionless Gibbs free energy (G/RT) at the temperature of interest. The feed is entered as the amount of each compound, but the equilibrium com position depends only upon the atomic composition (C,H,O) of the feed. In this example there are six compounds and three elements, so the number of chemical reactions R = C p = 3. The program prints a set of independent chemical reactions with their associated equilibrium constants to facilitate check ing the results. The thermochemical data may be calculated either by thermodynamics or by statistical mechan ics. The thermodynamic expression for the dimen sionless Gibbs free energy obtained by integrating the GibbsHelmholtz equation is _G f HoI(To)i (T dT (5) RT RTR J R )To T I J RT^ ^ To where G and H are values of the molar Gibbs free energy and molar enthalpy of formation at the refer ence temperature T and reference pressure Po, and I(T) is the indefinite integral of the molar heat ca pacity of the compound at the standard pressure P : I(T)= Cp(T)dT (6) For example, for the commonly used polynomial[41 Cp = A + BT+CT2 +DT3 + ET2 (7) we have I(T)=AT+ T2 +CT3 + 4 E (8) and T Tf (T) dT= AenT + (TTo)+ (T2 T2 RT2 R T 2R 6R To +D 3T3 E1 1 12R( 2R 2 2 (9) Heat capacity data[41 for the compounds under con sideration are listed in Table 1. The dimensionless free energies of formation tabulated in Table 2 were calculated using Eq. (5). The feed contains hydrogen and water in the ratio H/H20 = 2 with excess carbon. Spring 1991 TABLE 1 Free energies (Go) and enthalpies (Ho) of formation at To = 298.15 K; heat capacity coefficients (A,B,C,D,E) for Eq. (7). Cor Go Ho A B C D E pound State kJ/mol kJ/mol J/molK J/molK2 J/molK3 J/molK4 JK/mol CO, (g) 394.65 393.77 19.795 7.344E2 5.602E5 1.715E8 0.0 H20 (g) 228.77 242.00 32.242 1.924E3 1.055E5 3.596E9 0.0 CO (g) 137.37 110.62 30.869 1.285E2 2.789E5 1.272E8 0.0 CH4 (g) 50.87 74.90 19.251 5.212E2 1.197E5 1.132E8 0.0 t (g) 0.0 0.0 27.143 9.274E3 1.381E5 7.645E9 0.0 C (s) 0.0 0.0 16.873 4.773E3 0.0 0.0 8.541E5 TABLE 2 Input to computer program for finding equilibrium of coal methanation reactions at 800K. Com pound State Gi/RT ni, mol CO2 (g) 61.3410 0.0 H20 (g) 32.5318 1.0 CO (g) 28.6855 0.0 CH, (g) 3.4398 0.0 H, (g) 1.2607 2.0 C (s) 0.5925 2.0 Additional data supplied to the program are the pressure (P = 0.5 MPa) and the number of moles of inert gas (zero in this case). Table 3 gives the equi librium state computed for the feed composition in Table 2. Computation time for the equilibrium point in Table 3 is 0.5 second on an 80386/80387 personal computer rated at 0.075 MFLOPS Megaa floating point operations per second). This includes the time for reading and writing to a file. Therefore, enough points for a graph can be generated in less than a minute. For example, Figure 1 shows the effect of the H2/H20 feed ratio upon the equilibrium yield, expressed as moles of methane per mole of carbon consumed. The program's output includes the chemical re actions with their equilibrium constants in Table 4. Results of chemical equilibrium calculations for coal methanation are given by Sandler'51 for the case of no hydrogen in the feed stream. Helfferich161 solved for the amount of hydrogen feed required to produce 0.9 mole of methane per mole of carbon consumed. Ethane can be added to the list of compounds in Table 2 to find out if it is present in detectable amounts at equilibrium (it is not). Or, iron and iron oxide can be added to the list to find out if the process conditions favor oxidation of the reactor ac cording to the reaction Fe + H20 = FeO + H2 (the result is no FeO at equilibrium). COMBUSTION OF HYDRAZINE Chemical equilibrium problems that require Yield ratio, 0.5 CH4/C Feed ratio, H2/H20 Figure 1. Equilibrium yield of CH4 per unit amount of carbon consumed as a function of ratio H/HI0 in feed. T= 80 K, P= 0.5MPa computers for their solution arise in hightempera ture chemistry. For example, combustion of hydra zine (NH2NH2 + 02 2 N2 + 2 H20) generates OH, NH, NO, H2, 02, N, H, and O as well as the principle products N2 and H20. For this problem it is conven ient to use the formulae of statistical mechanics. For TABLE 3 Chemical equilibrium for coal methanation reactions at 800 K, 0.5 MPa. No inert gases; amount in feed, n,; amount at equilibrium, n,; mole fraction in gas phase at equilibrium, y,. Compound ni, mol ni, mol y, CO, 0.0 0.13258 0.05808 H20 1.0 0.70954 0.31080 CO 0.0 0.02530 0.01108 CH, 0.0 0.87494 0.38325 H2 2.0 0.54058 0.23679 C 2.0 0.96718 0.0 Total 5.0 3.25012 1.0 TABLE 4 Chemical equilibrium constants at 800 K Reaction K C(s) + CO2 > 2 CO 0.01043 2 C(s) + 2 H20 => CO, + CH4 0.23041 C(s) + 2 H,0 < CO2 + 2 H, 0.16635 TABLE 5 Molecular constants Molecule MW, g/mol ,, K 0,, K Do/k, K o a H, 2.016 87.55 6332 51,970 2 1 02 31.999 2.07 2274 59,360 2 3 N2 28.013 2.88 3374 113,350 2 1 NO 30.006 2.41 2740 75,390 1 2 NH 15.015 24.03 4722 39,460 1 3 OH 17.007 27.21 5378 50,970 1 2 13.40 2295 H20 18.015 20.90 5254 110,360 2 1 40.10 5404 N 14.007 0 4 H 1.008 0 2 O 15.999 0 5 Chemical Engineering Education a diatomic molecule modeled as a rigid rotor, har monic oscillator in its electronic ground state, the dimensionless Gibbs free energy is G n kT )n (e+n I ex _D n NkT p3 ) r ) kT Translation Rotation TVibration (10) Vibration Electronic where A is the deBroglie wavelength of the molecule A= h (11) V27 mkT and x = J/T = hv/kT. The rotational symmetry num ber is o and the degeneracy of the electronic ground state is e The energy of the molecule in its elec tronic and vibrational ground states relative to the isolated atoms at T = 0 is Do, and the characteristic temperature for rotation is 0, = h2/82Ik. TABLE 6 Chemical equilibrium for combustion of hydrazine at 3500 K, 1 MPa. Input to program, n,; amount at equilibrium, n,; mole fraction, y, Monatomic species (N, H, O) have no rotational or vibrational terms. For nonlinear, polyatomic mole cules (H20), there is a separate term for each vibra tional mode and the rotational term is replaced by 0.5 SG n T3 0 [NkT ]r l 2n i T3 (12) For NO another term must be added to account for excitation from the ground electronic state (1) to the first excited state (2) [NkT]ee n [+ +e2 e r l)/kT (13) NkT eLec 0el I where oe, = oe2 = 2 and (E2 e)/k = 172 K. Constants extracted from Herzberg47' and NBS181 are given in Table 5. Computation time for the equilibrium state re ported in Table 6 was 1.5 seconds on a computer rated at 0.075 MFLOPS. The results are that the equilibrium concentrations of N and NH are low enough to be neglected under these conditions. REFERENCES 1. van Zeggeren, F., and S. H. Storey, The Computation of Chemical Equilibria, Cambridge University, New York, NY (1970) 2. O'Brien, J.A., Department of Chemical Engineering, Yale University; personal communication 3. Myers, A.K., and A.L. Myers, "Numerical Solution of Chemical Equilibria with Simultaneous Reactions," J. Chem. Phys., 84,5787 (1986) 4. Reid, R.C., J.M. Prausnitz, and B.E. Poling, The Proper ties of Gases and Liquids, McGrawHill Book Company, New York, NY (1987) 5. Sandler, S.I., Chemical and Engineering Thermodynam ics, 2nd Ed., p. 531, John Wiley & Sons, New York, NY (1989) 6. Helfferich, F. G., "Multiple Reaction EquilibriaWith Pen cil and Paper," Chem. Eng. Ed., 23, 76 (1989) 7. Herzberg, G., Molecular Spectra and Molecular Structure, 2nd Ed., Vol IIV, Prentice Hall Book Company (1950 1979) 8. NBS Circular 467, Atomic Energy Levels, U.S. Govern ment Printing Office, Washington, DC, Vol 1III (1949) NOTATION atomic matrix number of chemical compounds present heat capacity electronic energy number of elements present Gibbs free energy at Po enthalpy at Po Planck constant function of heat capacity, Eq. (5); rotational moment of inertia Spring 1991 G/NkT ni, mol ni, mol y, Compound H20 61.2859 2.0 1.40718 0.40850 N2 60.9791 1.0 0.96259 0.27944 NO 52.6323 0.0 0.07465 0.02167 02 47.4720 0.0 0.14014 0.04068 OH 41.3420 0.0 0.17333 0.05032 NH 38.4545 0.0 2.95E5 8.57E6 H2 35.8107 0.0 0.39011 0.11325 O 22.5047 0.0 0.06456 0.01874 N 22.0821 0.0 1.29E4 3.76E5 H 17.4415 0.0 0.23205 0.06736 3.0 3.44478 1.00000 Total TABLE 7 Chemical equilibriuum constants at 3500 K and standard pressure Po = 1 atm. Reaction K 0.5 H20 + 0.2502, <= OH 0.31069 0.5 0, = O 0.29191 0.5 H20 = 0.2502 + H 0.26357 0.5 N, + 0.502 4= NO 0.20326 H,0 0.5 H20 + 0.5 N2 < 0.25 0, + NH 2.02E5 k = Bolzmann constant K = chemical equilibrium constant m = element vector N = number of molecules n = compound vector n = amount, mol P = pressure Po = reference pressure R = gas constant T = absolute temperature x = dimensionless frequency of vibration = hv/kT y = mole fraction in gas phase Greek Letters Or = characteristic temperature of rotation 90 = characteristic temperature of vibration A = deBroglie wavelength, Eq. (11) v frequency of vibration S extent of reaction p rank of A o rotational symmetry number (integer) coe degeneracy of electronic ground state (integer) Superscript o refers to feed composition (initial state) Subscript o refers to standard state at 298.15 K, 1 atm. i refers to ith reaction j refers to jth compound APPENDIX Matrix operations are illustrated for a reaction system consisting of nine compounds (C = 9) and four elements (E = 4). The EbyC atomic matrix is: CO SO H O S CO COS CS HS H 2 2 2 2 2 2 2 C 1 0 0 0 1 1 1 0 0 O 2 2 1 0 1 1 0 0 0 A= S 0 1 0 2 0 1 2 1 0 H 0 0 2 0 0 0 0 2 2 The rank of A is p = 4, so there are C p = R = 5 inde pendent chemical reactions. A particular set is found by dividing the C compounds into p primary com pounds and R secondary compounds. The stoichiom etric matrix N is obtained from Eq. (2) as follows: The atomic matrix is written with the p primary compounds in the first p columns of A so that the E byp atomic matrix A for the primary compounds is at the left and the remainder of the A matrix con tains the EbyR matrix for the secondary compounds A=IA,, As For A as written above, the secondary compounds are CO, COS, CS,, H2S, and H2. After selecting the secondary compounds, a unit matrix as large as pos sible is formed in the upper lefthand corner of A using elementary row operations, so that a new matrix A is generated with the following reduced row echelon form I B 0 0 where I is a pbyp identity matrix and B is a pbyR matrix. The number of rows of zeros is E p. Zeros are present when the rank of A is less than the number of elements E. In this example E = p. The stoichiometric matrix N is constructed by appending an RbyR identity matrix Is to the Rbyp negative transpose of B N= BT, Is The result from A as written above is CO SO H 0 S CO COS CS H S H 2 2 2 2 2 2 2 1 0.5 0 0.25 1 0 0 0 0 1 0.5 0 0.75 0 1 0 0 0 N= 1 1 0 1.5 0 0 1 0 0 0 0.5 1 0.75 0 0 0 1 0 0 0.5 1 0.25 0 0 0 0 1 The rows of N are the chemical reactions CO2 +(0.25)S2 = (0.5)SO2 +CO CO2 +(0.75S2)= (0.5)S02 +COS CO2 +(1.5)S2 = SO2 +CS2 H20+(0.75)S2 = (0.5)SO2 +H2S H20+(0.25)S2 = (0.5)SO2 +H2 The secondary compounds (CO, COS, CS2, H2S, H2) appear in one and only one reaction. There are C! R!(CR)! sets of reactions, each containing a different combi nation of R secondary compounds. In this example the number of reaction sets is 9! =126 5! 4! 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