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Front Cover  
Table of Contents  
Larry Duda, of Penn State  
Howard University  
Division activities  
Introduction  
Fundamentals of chemical engin...  
Book reviews  
Mathematics  
Knowledge structure of the stoichiometry...  
Letter to the editor  
Thermodynamics: A structure for...  
The basic concepts in transport...  
Book reviews  
An appetizing structure of chemical...  
Book reviews  
On letting the inmates run the...  
What works: A quick guide to learning...  
Czochralski crystal growth modeling:...  
Speaking of education  
Introducing statistical concepts...  
Purdueindustry computer simulation...  
An inexpensive and quick fluid...  
Helping students communicate technical...  
An interesting and inexpensive...  
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Front Cover 1 Front Cover 2 Table of Contents Page 65 Larry Duda, of Penn State Page 66 Page 67 Page 68 Page 69 Page 70 Page 71 Howard University Page 72 Page 73 Page 74 Page 75 Page 76 Division activities Page 77 Introduction Page 78 Page 79 Fundamentals of chemical engineering Page 80 Page 81 Page 82 Page 83 Page 84 Book reviews Page 85 Mathematics Page 86 Page 87 Page 88 Page 89 Page 90 Page 91 Knowledge structure of the stoichiometry course Page 92 Page 93 Page 94 Letter to the editor Page 95 Thermodynamics: A structure for teaching and learning about much of reality Page 96 Page 97 Page 98 Page 99 Page 100 Page 101 The basic concepts in transport phenomena Page 102 Page 103 Page 104 Page 105 Page 106 Page 107 Page 108 Book reviews Page 109 An appetizing structure of chemical reaction engineering for undergraduates Page 110 Page 111 Page 112 Page 113 Page 114 Page 115 Page 116 Book reviews Page 117 On letting the inmates run the asylum Page 118 Page 119 What works: A quick guide to learning principles Page 120 Page 121 Czochralski crystal growth modeling: A demonstrative energy transport problem Page 122 Page 123 Page 124 Page 125 Page 126 Page 127 Speaking of education Page 128 Page 129 Introducing statistical concepts in the undergraduate laboratory: Linking theory and practice Page 130 Page 131 Page 132 Page 133 Page 134 Page 135 Purdueindustry computer simulation modules: 2. The Eastman chemical reactive distillation process Page 136 Page 137 Page 138 Page 139 An inexpensive and quick fluid mechanics experiment Page 140 Page 141 Page 142 Page 143 Helping students communicate technical material Page 144 Page 145 Page 146 Page 147 Page 148 Page 149 An interesting and inexpensive modeling experiment Page 150 Page 151 Page 152 Back Cover Back Cover 1 Back Cover 2 

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SPCA ISU .. Knowledge Structure^^^^^^^^^^^^^^^ CLISO ...^f ^^>/7~?T~7jy7^^^^^^^^^^^^^^^^ REQUEST FOR FALL ISSUE PAPERS Each year, CHEMICAL ENGINEERING EDUCATION publishes a spe cial fall issue devoted to graduate education. It consists of articles on graduate courses and research, written by profes sors and advertisements describing the graduate programs at various universities. Extra copies of this informative issue are then distributed to the reading rooms and/or AIChE offices of bulksubscribing universities, to be used as a source of information by those students who are interested in going on to graduate school. Anyone interested in contributing to the editorial content of the 1993 fall issue should immediately write to CEE (c/o Chemical Engineering Depart ment, University of Florida, Gainesville, FL 326112022). Please indicate the subject of the contribution and the tentative date it will be submitted. Deadline for submissions is June 15, 1993. L EDITORIAL AND BUSINESS ADDRESS: Chemical Engineering Education Department of Chemical Engineering University of Florida Gainesville, FL 32611 FAX 9043920861 EDITOR Ray W. Fahien (904) 3920857 ASSOCIATE EDITOR T. J. Anderson (904) 3922591 CONSULTING EDITOR Mack Tyner MANAGING EDITOR Carole Yocum (904) 3920861 PROBLEM EDITORS James 0. Wilkes and Mark A. Burns University of Michigan  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 * George Burnet Iowa State University Anthony T. DiBenedetto University of Connecticut Thomas F. Edgar University of Texas at Austin Richard M. Felder North Carolina State University Bruce A. Finlayson University of Washington H. Scott Fogler University of Michigan J. David Hellums Rice University Angelo I. Perna New Jersey Institute of Technology Stanley I Sandler University of Delaware Richard C. Seagrave Iowa State University M. Sami Selim Colorado School of Mines James E. Stice University of Texas at Austin Phillip C. Wankat Purdue University Donald R. Woods McMaster University Chemical Engineering Education Volume 27 Number 2 Spring 1993 EDUCATOR 66 Larry Duda, of Penn State, Written by His Colleagues DEPARTMENT 72 Howard University, Joseph H. Cannon, Ramesh C. Chawla, Dorian Etienne KNOWLEDGE STRUCTURE 78 Introduction, Donald R. Woods 80 Fundamentals of Chemical Engineering, Donald R. Woods, Rebecca J. Sawchuk 86 Mathematics, Stuart W. Churchill 92 Knowledge Structure of the Stoichiometry Course, Richard M. Felder 96 Thermodynamics: A Structure for Teaching and Learning About Much of Reality, John P. O'Connell 102 The Basic Concepts in Transport Phenomena, R. Byron Bird 110 An Appetizing Structure of Chemical Reaction Engineering for Undergraduates, H. Scott Fogler CURRICULUM 118 On Letting the Inmates Run the Asylum, Alva D. Baer CLASSROOM 120 What Works: A Quick Guide to Learning Principles, Phillip C. Wankat 144 Helping Students Communicate Technical Material, William R. Ernst, Gregory G. Colomb CLASS AND HOME PROBLEMS 122 Czochralski Crystal Growth Modeling: A Demonstrative Energy Transport Problem, David C. Venerus RANDOM THOUGHTS 128 Speaking of Education, Richard M. Felder LABORATORY 130 Introducing Statistical Concepts in the Undergraduate Laboratory: Linking Theory and Practice, Annette L. Burke, Aloke Phatak, Park M. Reilly, Robert R. Hudgins 136 PurdueIndustry Computer Simulation Modules: 2. The Eastman Chemical Reactive Distillation Process, S. Jayakumar, R.G. Squires, G. V. Reklaitis, P.K. Andersen, L.R. Partin 140 An Inexpensive and Quick Fluid Mechanics Experiment, J.T. Ryan, R.K. Wood, P.J. Crickmore 150 An Interesting and Inexpensive Modeling Experiment, W.D. Holland, John C. McGee 77 Division Activities 95 Letter to the Editor 85,109,117 Book Reviews CHEMICAL ENGINEERING EDUCATION (ISSN 00092479) is published quarterly by the Chemical Engineering Division, American Societyfor Engineering Education, and is edited at the University of Florida. Correspondence should be sent to CEE, Chemical Engineering Department, University of Florida, Gainesville, FL 326112022. Copyright 1993 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. 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, Chemical Engineering Department., University of Florida, Gainesville, FL 32611. Spring 1993 l =F educator BY HIS COLLEAGUES Pennsylvania State University University Park, PA 168024400 .Larry Duda was born and raised in Donora, Pennsylvania, a small steelmill town twenty miles down the Monongahela River from Pitts burgh. It was considered a good omen when he was delivered by the high school football team physician since his was a family in which most of the sons went to college on football scholarships. In spite of his lack of weight, skill, and interest, when he fi nally got to high school he too fulfilled the family obligation of trying out for the "Donora Dragons," which had given the country not only such great players as "Deacon Dan" Tyler, "Pope" Galiffa, "Bimbo" Ceconi, but also Stan Musial. Although Larry did not make the team, he did hear the first pep talk wherein the coach indicated that there were two paths down from the football field, which tow ered on the hill above the town"One can graduate from high school and go down into the mill, or one can play good football and go to college." Fortu nately, Larry found a third path: a scholarship at Case Institute of Technology. He decided to study chemical engineering because he liked math and chemistry and also because he was fascinated by the old lead chambers which produced sulfuric acid in the zinc works section of U.S. Steel. He started out as a mediocre student at Case, ARRY PUDA of Penn State hampered by a poor high school background and a dyslexia problem which he did not recognize at that time. He was struggling along with Cs and some Bs until he took his first chemical engineering course in stoichiometry and found that his forte was in solving problems. Even in high school, when he had difficulty with formal algebra, he found he could always solve the statement problems through his own devious techniques. As a consequence, he ex celled in stoichiometry and became the top student in the class. Upon graduating, he decided to go to graduate school since he felt he did not yet fully understand chemical engineering and was a little fearful of going out and practicing the subject with his limited knowledge. THE DELAWARE YEARS Larry blossomed as a graduate student at the University of Delaware and was particularly stimu lated by research and interactions with such chemi cal engineering greats as Bob Pigford, Art Metzner, and Kurt Wohl. An outstanding group of graduate students who were at Delaware at the same time also contributed to the exciting intellectual climate. In addition to learning how to do research under the tutelage of Art Metzner, he honed his tennis game, helped integrate restaurants in Delaware, and met his future wife, Margaret Barbalich. He worked in the area of catalysis with ion exchange resins and likes to joke that he did so poorly that neither he nor Art Metzner ever worked in that area again. Larry reminisces that his years at Delaware were the best, blending an intensity of research studies, sports, and personal life. The spe cific subjects studied at Delaware were quite sec Copyright ChE Division ofASEE 1993 Chemical Engineering Education Larry joined the Process Fundamentals Group of the Dow Chemical Company..., and... his long and successful collaboration with Jim Vrentas began... it was [there] that they forged their friendship and created one of the most productive teams in the profession. They represented a contrast in styles and abilities, yet had an abiding respect for each other's points of view and contributions. ondary compared to the enthusiasm he gained for learning and the creation of new knowledge through research. THE DOW DAYS In 1963, Larry joined the Process Funda mentals Group of the Dow Chemical Com pany in Midland, Michigan, and it was there that his long and successful collaboration with Jim Vrentas began. Although the two knew each other in graduate school, it was in the Process Fundamentals Laboratory that they forged their friendship and cre ated one of the most productive teams in the profession. They represented a contrast in styles and abilities, yet had an abiding respect for each other's points of view and contributions. Their differences were demonstrated by an incident one Friday when they had a very difficult problem which they could not solve. Late that afternoon, Larry concluded that they had been pounding on the prob lem too long and had actually begun recy cling potential solutions that they had al ready considered. He felt they were burned out, and he was going to take the evening off, see a play with Marge, have dinner, and hopefully wake up the next morning with fresh insight. In contrast, Jim decided to stay on through the wee hours of the night, continuing to work on the problem. When Larry and Marge returned home later that evening, they found Jim's solution nailed to their front door! He wanted to make it crys tal clear that he had come up with the solu tion first, just in case Larry woke up in the morning with a bright idea of his own. Larry and Marge quickly established a family in Midland, and within less than three years had four children (twins John and David, Paul, and Laura). Larry likes to kid the Dow people that there was nothing else to do in Midland in those days. During the Dow days, Larry and Jim's basic work in the area of diffusion in poly Spring 1993 THE DUDA DISGUISES Cleverly disguised as a young student, circa 1962, at Brown Laboratory, University of Delaware (right) ... and... as jolly old Saint Nick himself (below), with codisguised John Phillips in an interesting impersonation of an elf... as the Shiek of... ah ... University Park as... whatever... with sons Paul, John, wife Marge, son David, and daughter Laura all getting in on the act. mer systems was initiated. To their dismay, how ever, they were not free to continue along the paths of scientific interestinstead, they had to respond to the more direct economic needs of the company. Nevertheless, they were at Dow during the golden days when great advancements were being made in polymer science, led by such individuals as Turner Alfrey and Ray Boyer. It was natural that in this environment they would be drawn into considering problems associated with polymer production and processing. In addition to Jim Vrentas, Turner Alfrey and Art Metzner (as a Dow consultant) also exerted great influence on Larry's professional development. Despite Larry's successful career development at Dow in the late 1960s, he and Jim decided that they should consider academia if they wanted to con ... it became clear to him that he would rather stay at Penn State without research and just teach than to take a position where he could concentrate on his desired research with no opportunityfor teaching. tinue along their main avenues of interest. In his last years with the company, Larry made his most successful contribution through his work on design ing insulation systems for the transAlaskan pipe line that would keep it from melting the permafrost during the short Alaskan summer. Although Larry left Dow for Penn State in 1971, he has maintained strong contacts with Dow. In many ways, Larry has tribal instincts and develops a strong devotion to groups he lives and works with. In addition to his family, he still has vital attach ments to his home town of Donora and to the Dow Chemical Company. He stays in touch with several friends at Dow, including Doug Leng and George Shier. Larry was most recently named a charter member of Dow's Academic Advisory Council. THE PENN STATE YEARS Over the past twenty years, Larry has devoted most of his energies to the development of the De partment of Chemical Engineering at Penn State. The dominant characteristics of Larry's work are in its diversity and its strong emphasis on collabora tion. He has conducted collaborative research work with almost every member of the chemical engi neering faculty as well as with several researchers outside the department. Besides his work with Jim Vrentas in the general area of diffusion in polymer systems, Larry has made contributions in many other fields, most significant of which has been his joint research with Elmer Klaus in the area of tribology. Although Larry was attracted to academia because he sought to define his own research work, he quickly became enthralled by teaching. In fact, within a few years it became clear to him that he would rather stay at Penn State without research and just teach than to take a position where he could concentrate on his desired research with no oppor tunity for teaching. The meetings of his research groups with their inevitable interplay of ideas are the most enjoyable parts of Larry's working schedule, and the most attractive feature of these interactions comes from the general thrill of exploring the natural world. In these group meetings, Larry often makes bets with Elmer Klaus that the results of the new experi ments will turn out a certain way. But Elmer is an expert at oracle statements, and no matter which way the results come out he can be counted on to argue that he had already predicted the results. Second only to chemical engineering is Larry's continued interest in tennis. In fact, it is rumored that Lee Eagleton originally hired him only be cause they were great tennis partners who together could take on opponents from the chemistry depart ment. At present, Jack McWhirter and Larry offer a standing challenge to take on any two students in the department. On the home front, Larry is proud of his belief that the way to educate people is to help them be come themselves. This freedom of spirit is strongly exhibited in his children. None of them has become an engineer, or has even gotten close to engineer ingthey have been students of art, English litera ture, and medicine. Now that the children are grown, Larry and Marge are able to nurture their interest in international travel, and when at all possible they try to couple it with Larry's technical interests and Marge's photographic interests. DUDATHE RESEARCHER Through the years at Dow and at Penn State, Larry's work has exhibited a common thread of re search on polymers and transport phenomena. His wellknown collaboration with Jim Vrentas on mo lecular diffusion in polymer systems has yielded many results which have been presented in over seventy journal publications. At the time Duda and Vrentas initiated their work, the area of diffusion in concentrated polymer solu Chemical Engineering Education tions and melts was in a state of disarray, and no techniques were available to the design engineer for the prediction or even the correlation of diffusivity data. In fact, available experimental data revealed many apparent contradictions. Some experiments showed that the binary mutual diffusion coefficient in polymersolvent systems were strong functions of concentration, while in other studies these coeffi cients were found to be independent of concentra tion. Some investigators found that diffusion in poly mer systems depended strongly on temperature and did not follow an Arrheniustype behavior, while other studies indicated that the data could be corre lated with the Arrhenius equation with relatively low activation energies for diffusion. Superimposed on this perplexing situation were the experimental observations that, in some cases, diffusion in con centrated polymer systems did not even follow Fick's law. Numerous investigations showed that anoma lous effects were present which were not consistent with the classical diffusion theory. In response to this situation, the studies of Duda and Vrentas led to the concept that molecular diffu sion processes involved the coupling of migration and relaxation of molecules. Up to this time it had been implicitly assumed that the molecules partici pating in a diffusion process could relax very quickly to new equilibrium states and that local thermody namic equilibrium was maintained. Duda and Vrentas quantified their theory with the introduc tion of the diffusion Deborah number, which is the ratio of the characteristic relaxation time of the mol ecule to the characteristic time of the diffusion pro cess. This dimensionless group revealed under what conditions classical diffusion theory is appropriate for the description of diffusion in polymeric systems. Probably the most important outcome of the col laborative work of Duda and Vrentas is the develop ment of the free volume theory in which the viscous behavior of polymer melts is coupled to the diffu sional behavior in binary solutions. Their theory allows the prediction of diffusion coefficients as a function of temperature and concentration from vis cosity and thermodynamic data obtained essentially for pure component systems. The free volume theory as developed by Duda and Vrentas has been shown to be applicable up to at least 80 C above the glass transition temperature and for concentrations as high as 70 weight percent solvent. Interestingly, the theory is also capable of predicting anomalous abrupt changes in the diffusivity observed in the vicinity of glass transition temperature. Concurrently, Duda and Vrentas developed experi Spring 1993 mental techniques and associated analyses for the determination of accurate diffusivity data over the wide ranges of temperature and concentration needed for various polymer processes. Their work led to the development of a widely used high temperature sorption apparatus as well as a novel oscillatory sorption experiment. The latter tech Duda and Mary Eagleton presenting the Lee and Mary Eagleton Design Award to Heather Bergman. nique is the only method available to study unam biguously the coupling of diffusional transport and molecular relaxation. Not well known to the academic chemical engi neering community are Larry's contributions to the area of tribology and lubrication. Larry recognized how fundamental principles of chemical engineer ing can be successfully applied to bring order into a traditionally empirical field of research that has remained largely proprietary over the years. This led to his collaborative research with Elmer Klaus, the results of which are summarized in over forty publications. Probably the most important outcome of this re search has been the development of a microreactor technique to study the thermal and oxidative degra dation of lubricants under conditions that simulate automotive engine tests, heavyduty diesel engine performance, electrical power generating equipment, and gas turbine engines. The test has been adapted by over fifteen industrial research groups as a way to minimize costly engine tests and has been suc cessfully used to study the performance of lubricant additives as well as the catalytic effects of metal surfaces on lubricant degradation. Another important result from this research is the development of a novel lubricant delivery system, 69 for applications at elevated temperatures. In this system, a lubricant film is formed on a hot surface from a homogeneous vapor phase. The lubricant forming vapor is adsorbed on the solid surface and reacts to form the lubricant film. This new lubricant system is being evaluated for applicability in di verse areas, including the lubrication of an adia batic ceramic engine and metalforming operations. Duda's work has also led to development of methods for the theological characterization of lubricants under extreme conditions of temperature, pressure, and shear rate. By his work, Duda has taught his colleagues and students how to carry out fundamental research that leads directly and tangibly to industrially signifi cant results. A unique indicator of this success is the fact that virtually all of his research support comes from industry. DUDATHE TEACHER Larry has been a teacher with great impact. Over the years he has developed a unique teaching style and educational philosophy. For example, he starts out each lecture in his graduate course with a quote from a famous engineer, scientist, philosopher, or religious leader. He feels that each lecture should not only present some specific segment of technol ogy, but also should incorporate some thought or philosophy concerning the general aspects of life it self. To illustrate, one of his classroom techniques is role playing. He will introduce himself as an inven tor, while the students play the role of engineers in a company that is considering buying the inventor's latest creation. His "inventor" is usually a super salesman who is very close to playing a con game. The students' roles are to analyze the proposed in vention for its scientific merits and to find its fatal flaws, if any. A quote from Harold McMillan sets the stage for this particular lecture: "Nothing that you will learn in your studies will be of the slight est possible use to you in the afterlife. Save only this: that if you work hard and intelligently, you should be able to detect when a man is talking rot, and that, in my view, is the main, if not the sole purpose of education." Larry's classroom emphasis is on creativity and the ability to solve unique problems, as opposed to the mere accumulation of specific knowledge or so lution of conventional problems. He stays awake at night thinking up problems for homework or exams which at first glance appear to be unrelated to the topic at hand but that can be solved by using the course fundamentals. For example, to illustrate the use of the FloryReiner model for crosslinked poly mers, he considers the case of how the ancient Egyp tians cracked stones in their quarries. They drove a wooden wedge into a crack, poured water on the wedge, and let the swelling wedge crack the rock. By giving properties of polymeric wood, students can develop equations to predict the pressures that such swelling wedges will develop. Larry's success as a teacher stems not only from his classroom lectures, but also from his close work with undergraduate and graduate students in their research. He has advised sixtyone masters' students and thirtytwo doctoral students at Penn State, in cluding the fortysix students who have worked with him and Elmer Klaus in the area of tribology. It is fair to say that almost every industrial tribology researcher with a chemical engineering degree has been trained at Penn State. Duda is a much sought after member of graduate student thesis commit tees. Over the last twenty years, in addition to the students whose work he has supervised he has also served on 100 doctoral committees and 120 masters' committees. The students have been from chemical engineering, chemistry, polymer science, petroleum engineering, mineral processing, agricultural engi neering, fuel science, bioengineering, etc. An impor tant reason for the diverse backgrounds of students seeking Duda's guidance is the active collaboration Duda has developed and maintained with over twenty faculty members in other disciplines. He has also been unusually active in guiding over seventy undergraduate students on their honors research projects. Many of them have gone on to graduate schools, inspired by their research experience. HONORS AND AWARDS Larry has been recognized for his teaching and research through a number of awards. In 1980 he received the Outstanding Research Award from the Pennsylvania State Engineering Society, and in 1981 Larry and Jim Vrentas were corecipients of AIChE's William H. Walker Award in recognition of their work on molecular diffusion in polymers and the analysis of complex transport phenomena. Larry was chosen by Penn State's senior ChE class as the Out standing Professor in 1983, and in 1989, along with Jim Vrentas, he received the Charles M.A. Stine Award in Materials Engineering and Sciences from the AIChE Materials Division in recognition of their development of the free volume theory and the oscil latory sorption technique. Also in 1989, Larry was selected to receive the ASEE Chemical Engineering Lectureship Award. The Pennsylvania State Engi Chemical Engineering Education One oJ Duda's happier duties as Department Head receiving a check for the department! neering Society honored Larry and Jim Vrentas in 1991 with its Premier Research Award, and also in that year Larry was chosen as the Alumni Delegate representing the Class of 1963 at the 1991 Com mencement Ceremony of the University of Delaware. DUDATHE ADMINISTRATOR Larry has been an unusual department head for the past ten years. He has demonstrated that taxing administrative duties need not diminish one's in tense involvement in teaching, research, and guid ing students. Under his stewardship, the depart ment has increased its visibility, with many of the faculty receiving national awards from AIChE, ACS, ASEE, ASME, etc. The department has recruited several outstanding young faculty in John Frangos, Kristen Fichthorn, Lance Collins, Ali Borhan, Wayne Curtis, and Themis Matsoukas. Two of these new faculty, Frangos and Fichthorn, were honored with Presidential Young Investigator Awards. The de partment also added two nationally prominent se nior scientists to its ranks in Art Humphrey and Paul Weisz. Duda's leadership has been responsible for the creation of a strong research program in biotechnology at Penn State, capped by the recruit ment of Art Humphrey as the Director of the Bio technology Institute. PROFESSIONAL INVOLVEMENT Larry has been a spokesperson for academic inter ests to industry. His own experience of having al most all of his research sponsored by industry gives him unusual insights into the mechanisms for and the benefits of universityindustry collaboration. He has been a member of the Council for Chemical Research (CCR) for the past ten years and served on its Governing Board and on the latter's Executive Spring 1993 Committee. He has served on the CCR Committee on Industrial College Relations and as CCR Liaison with the NSF, and has also been active on the Aca demic Advisory Council of Dow Chemical. His ad vice as an educator has been sought after by other departments of chemical engineering: he has served as the external reviewer for Rutger's University; he has served on the Promotion and Tenure Re view Committees of the Illinois Institute of Tech nology and the University of Rochester; he serves on the advisory committees of the chemical engi neering departments at West Virginia University, University of Delaware, and CarnegieMellon University. An example of the esteem in which Duda is held by other department heads is their election of him as the Chair of the Board of Judges for the McGrawHill Kirkpatrick Award in Chemical Engineering. Larry has been active in the AIChE in a number of ways. He has served as a member of the National Program Committee, Public Relations Committee, Polymer Engineering Subcommittee of the Research Committee, Walker Award Committee, Charles M.A. Stine Award Committee, and the National Awards Committee. He is currently a Director of the Materi als Engineering and Sciences Division. He also serves on the Publications Committee of the ASEE. DUDATHE PHILOSOPHER Larry has made unique contributions to his field through his role as a philosopher of graduate educa tion. His three articles in Chemical Engineering Edu cation, "Common Misconceptions Concerning Gradu ate School," "Graduate Studies: The Middle Way," and "Graduation: The Beginning of Your Education" are necessary reading material for all graduate stu dents. They outline a philosophy that has guided Duda's work and offer muchneeded perspective to beginning graduate students. To quote from the con clusion of the second article, Duda says From my presentation, you might conclude that there is a middle way in every aspect of graduate work that is the most appropriate approach. Al though I have attempted to illustrate that this is certainly true in many instances, there is one very important exception. Some students say to them selves, "This is not the best that I can do but it's good enough." Well, it's not good enough. Push yourselftake time and make the effort to perform at the very highest level of which you are capable. There is no middle way when it comes to the pur suit of excellence. Duda's contributions to chemical engineering epito mize the above philosophy in action. I epartmen t HO WARD Frederick Douglass Hall houses Liberal Arts Departments and classrooms JOSEPH N. CANNON, RAMESH C. CHAWLA, DORIAN ETIENNE* Howard University Washington, DC 20059 Howard University is a private, coeducational institution located in Washington, DC. Named for General Oliver Otis Howard, a Civil War hero who helped found the Uni versity, it was incorporated in 1867 by an Act of Congress, and its founding mission was to help educate the four million freed slaves and others to whom education had previously been denied. The University offers degree programs in about two hundred *Graduate Student in chemical engineering. There is strong interaction among faculty members across research areas [that] provide three research focal areas... transport phenomena in environmental engineering, separation processes, and kinetics and reactor modeling. specialties and its four campuses encom pass 241 acres. Most of its schools and facilities, including the radio and televi sion stations, a fullservice hotel, a hos pital, and a number of research centers, are located on its eightynineacre main campus three miles north of the Capitol in the heart of Washington, DC. Howard's more than 1,200 fulltime fac ulty members are a microcosm of the world population of scholars, and its ap proximately 12,000 students come from all over the United States and more than one hundred countries. THE SCHOOL OF ENGINEERING Howard University introduced its en gineering programs in 1911 and they were among the first accredited programs in the United States. Historically, Howard has been the nation's major source of minority engineers, particularly African American engineers. Bachelor's and master's degrees are offered in chemical, civil, electrical, and mechani cal engineering, and in systems and com puter science. The departments of elec trical and mechanical engineering also have PhD programs. Each year about 850 undergraduate and 200 graduate Copyright ChE Division ofASEE 1993 Chemical Engineering Education UNIVERSITY Downing Hall of Engineering: Chemical Engineering Wing on the left. students enroll in the various programs offered. Modern instructional and research laboratories, together with computing facilities, support both student and faculty research pursuits. The Computer Learning and Design Center (CLDC), the school's centralized computing facility, and the Computer Laboratory for Instruction and Design in Engineering (CLIDE), provide a full spectrum of computer resources for faculty and students. These include PCs, HP and DEC VAX minicomputers, Sun Workstations, and access to an Alliant minisupercomputer. These resources are linked via networks to each other, to the university's IBM 3090 mainframe, and to INTERNET. THE CHEMICAL ENGINEERING DEPARTMENT The Chemical Engineering Department was es tablished in 1969 with the appointment of Dr. Herbert Katz as the Chair and with five stu dents at the sophomore level. Between 1970 and 1972 three more faculty joined the department: Pradeep Deshpande (now at the University of Louisville), Joseph Cannon (current Chair of the Spring 1993 ivegnoors of nowara umverslry: ne Lincol Memorial, the Washington Monument, and the U.S. Capitol building. ^lv t~lAi Graduate students reviewing laws of motion. department), and Franklin King (now Chair at NCA&T State University). In June 1972, the five original stu dents successfully completed the curriculum and were awarded the first BS degrees granted by the depart ment. Presently, there are six fulltime faculty posi tions (one vacant), one parttime faculty, approximately 73 one hundred undergraduate students, and twelve MS students. In 1975 a modern chemical engineering wing was added to the L.K. Downing Hall of Engineer ing. This facility contains a number of research laboratories, each equipped with stateoftheart equipment to meet the experimental research needs of the faculty. The Fluid and Thermal Engineering Laboratory houses equipment and instrumentation for the measurement of flow and heat transfer. A Laser Anemometry System, a rotational vis cometer, along with other instruments enable researchers to measure velocities, map shear stress patterns, and conduct routine measure ments of shear viscosity. The undergraduate program is structured to provide a broad background in the fundamental areas of chemical engineering, with special attention given to the development of analysis and problemsolving skills. The Biochemical Engineering Laboratory is equipped to conduct research in microbial fermen tation, protein purification, bioremediation, and protein adsorption. Specialized equipment in cludes an inverted phase contrast photocapable microscope, automated highpressure and low pressure liquid chromatography systems with vari able wavelength detection capabilities, fullspec trum scanning spectrophotometry instrumentation, and a microtome. The Microelectronics Materials Processing Labo ratory features two chemical vapor deposition re actors (horizontal and vertical) and a sublimation reactor, all for the growth of silicon carbide and related materials. This laboratory is a part of the NSFfunded Materials Science Research Center of Excellence (MSRCE) located in Downing Hall of Engineering where faculty and students from elec trical and chemical engineering, physics, and chem istry carry out interdisciplinary research. The environmental engineering laboratories have facilities dedicated to analytical instrumentation, microbiology, incineration, water pollution, and air pollution. Jointly shared by the environmental en gineering faculty in civil engineering, these labo ratories are the focus of several interdisciplinary research projects. All the necessary equipment for the growth, isolation, and analysis of microorgan 74 Undergraduate unit operations laboratory Undergraduate unit operations laboratory. isms is located in the microbiology laboratory. Equip ment for studying the kinetics, chemistry, and heat and mass transfer characteristics of hightemperature reactions are available in the Incineration Laboratory. This includes a Shirco infrared incinerator, a liquid/ gas combustion unit, and a fluidized bed hightem perature reactor. Howard is one of a handful of aca demic institutions possessing the incineration facili ties capable of studying thermal degradation of waste in all phasessolid, liquid, and gas. The EPAfunded Great Lakes and MidAtlantic Hazardous Substances Research Center (a con sortium of the University of Michigan, Michigan State University, and Howard University) supports coop erative research efforts among chemical engineering and other university faculty. These environmental research programs are in the areas of bioremedia tion and composting. UNDERGRADUATE PROGRAM The undergraduate program is structured to provide a broad background in the fundamental areas of chemi cal engineering, with special attention given to the development of analysis and problemsolving skills. The breadth of the undergraduate program is intended to prepare students to either enter the chemical engi neering profession upon graduation or to successfully continue their education at the graduate level. The curriculum is particularly strong in providing comprehensive design experience, basic engineering technology in separation processes, and the fundamen tals of transport processes. Computer use is integrated throughout the curriculum, with special emphasis on digital simulation and software for analysis and de sign. Laboratories support undergraduate instruction in momentum, heat, and mass transfer, reaction kinet ics, process control, and process design. Electives of Chemical Engineering Education The EPAfunded Great Lakes and MidAtlantic Hazardous Substances Research Center [is] a consortium of the University of Michigan, Michigan State University, and Howard University [which] supports cooperative research efforts among chemical engineering and other university faculty. feared by the department include: polymer engineering, bio medical engineering fundamentals, bioprocess engineering, processing of electronic materials, transport phenomena, energy systems, and environmental engineering. Most of the BS graduates have found employment in in dustry, while about onethird of them have gone on to pur sue advanced degrees in chemical engineering, environmen tal engineering, business, or other professional areas such as medicine, law, and dentistry. GRADUATE PROGRAM The goal of our Master's program is to provide the neces sary academic experiences to prepare students for challeng ing and responsible careers as practitioners and adminis trators in the chemical engineering profession and for the numerous other opportunities associated with this level of achievement. The program is intended to extend the student's training in the mainstream areas of chemical engineering at an advanced level, with sufficient indepth study of a n, selected area and involving both formal course work and a osep thesis research project. The instructional program is based on core courses in TABLE 1 thermodynamics, transport phenomena, reaction kinetics, Faculty and Research Areas advanced engineering mathematics, and elective courses re Joseph N. Cannon, P.E., Professor and Chair; lated to the student's area of specialization. Graduate the PhD, University of Colorado ses are generally based on faculty research. Transport phenomena in environmental systems, computational fluid mechanics, heat transfer FACULTY AND RESEARCH FOCUS Ramesh C. Chawla, Professor; PhD, Wayne State University Since ours is a small department, there is a great oppor Chemical kinetics, separation processes, bioremedia tunity for interaction among students and faculty. Stu tion, incineration, environmental engineering dents feel comfortable visiting faculty at any time to seek M. Gopala Rao, Professor; advice or assistance on matters related to their courses, PhD, University of Washington, Seattle their research, or personal wellbeing. There is also strong Separation processes, energy systems, radioactive waste management interaction among faculty members across research areas. Mobolaji E. Aluko, Associate Professor; These interactions provide three research focal areas for PhD., University of California, Santa Barbara the department: transport phenomena in environmental Process control, mathematical methods, reactor engineering, separation processes, and kinetics and modeling, crystallization, microelectronic materials reactor modeling. Table 1 lists the research interests of processing * processing each faculty member. John P. Tharakan, Assistant Professor; PhD., University of California, San Diego Mobolaji Aluko's research is in three specific areas: Reactor design and bioprocess engineering, protein experimental analyses and numerical modeling of gas separations, protein adsorption, biological hazardous phase deposition reactors for semiconductor materials; solu waste treatment Robert J. Lutz, Visiting Professor; tion crystallization of ceramic materials; and control of non PhD., University of Pennsylvania linear chemical systems. Recent MS theses projects have Hemodynamics, intraarterial drug delivery focused on the analysis of mixedsuspension mixedproduct Herbert M. Katz, Professor Emeritus; removal (MSMPR) crystallizers and on the design of hetero PhD., University of Cincinnati generous catalytic reactors. Environmental engineering In addition, he directs the Engineering Coalition of Schools Spring 1993 75 for Excellence in Education and Leadership (ECSEL) program at Howard. This coalition consists of seven universities funded by NSF to seek fundamental changes in engineering education through active stu dent involvement in learning and by incorporating interactive, openended teaching approaches. Dur ing the 199293 academic year he is spending a sabbatical leave at two coalition schoolsthe Uni versity of Washington, Seattle, and the University of Maryland, College Park. In his spare time, he plays tennis, pingpong, and chess, and he is onehalf of the 199192 Howard University Tennis Doubles' Championship team. He is always ready to argue politics and religion. Joseph Cannon's research focuses on transport phenomena with applications in environmental en gineering. He is currently studying the movement of hazardous organic in soil and has both experimen tal and numerical work underway. He is also inter ested in the cooling of electronic equipment contain ing printed circuit boards. One of his students has just completed a thesis on the numerical analysis of conjugate heat transfer in electronic packages. For over twenty years, Joe has been known to frequently challenge a student to a oneonone bas ketball game. It appears as though "Father Time" has caught up with him, however, and he has re cently started taking tennis lessons. He also enjoys pocket billiards and chess. Ramesh C. Chawla's research combines the ap plication of the principles of mass transfer and ki netics to environmental systems. He has been in volved in an ongoing EPAfunded research program in hazardous waste treatment using physical and chemical techniques such as soil washing, adsorp tion, acid protonation, and biodegradation of haz ardous wastes using indigenous microorganisms cul tured from the contaminated sites. He has also been studying the combined technique of surfactantas sisted biodegradation of hazardous wastes. His projects on thermal treatment of hazardous wastes deal with the assessment of organic emission and heat and mass transfer limitations in incineration. Ramesh loves to discuss politics and sports with his colleagues and students. He is the faculty advi sor for the AIChE Student Chapter and frequently conducts some of the chapter meetings with stu dents while bowling at the University Center. Gopala Rao has been very active in the areas of adsorption and ion exchange separation processes, radioactive waste management, and alternative pro cess energy systems. His current research, funded 76 by the Office of Civilian Radioactive Management (DOE), concentrates on sorption equilibrium mea surements of binary and ternary ionic systems of radionuclides (such as cobalt, nickel, strontium, ce sium, and lead) in aqueous phases and on single and mixtures of minerals such as clinoptilolite, mont morillonite, and goethite. These efforts are in sup port of the Yucca Mountain Site Characterization Project being conducted at the Los Alamos National Laboratory and the Sandia National Laboratory. Gopala is an avid swimmer and jogger. When ever he is out of town for a meeting or a conference, he can be found after hours on the jogging trails around his hotel. John Tharakan's protein separation research fo cuses on the effects of such parameters as ligand distribution, resin structure, and flow configuration on process efficiency. He has carried out cell culture research to investigate the fundamental physico chemical parameters at the microenvironmental level that affect cell viability and productivity in novel bioreactor configurations for largescale cell culture. His bioremediation research focuses on the syner gistic effects of pathways and cofactors utilized by individual and consortia of microbes in the biodeg radation of toxic wastes. John enjoys discussing politics and is especially interested in the interactions of science, technology, and culture. He is a member of the local Chapter of Science for the People. When not involved with class or lab work, he can usually be found cooking in the kitchen. Robert Lutz has been studying methods of intra arterial drug delivery to achieve high concentrations of an anticancer drug at the tumor site while main taining subtoxic levels at other sensitive sites in the remainder of the body. He is investigating catheter design and infusion methods that minimize nonuniform drug distribution. Bob has been teaching and participating in re search at Howard for the past twelve years. When not working at NIH or Howard, he. can be found playing basketball or golfing or participating in any other sport for which the weather is suitable. Howard University has come a long way since its inception in 1867 with the mission of educating freed slaves. Today it successfully conducts the daily busi ness of educating young people anxious to and ca pable of making significant contributions in many ways and in many areas. We are proud of our gradu ates and look forward to the educational and soci etal challenges of the future. O Chemical Engineering Education lhE Division Activities ASEE Annual Conference WhenJune 2024, 1993 WhereUniversity of Illinois campus in UrbanaChampaign, Illinois Since this is ASEE's centennial year, the overall topic of this year's meeting will be the history of engineering. With that theme in mind, the ChE di vision has organized three sessions pertaining to our history: a lecture on the history of chemical engineering education; a display of textbooks used throughout our history; and a poster session on his tories of chemical engineering departments at the various universities. Other sessions will deal with new developments in education and research, such as new environmental courses and curricula, high performance computing, new courses not tradition ally taught in chemical engineering, new chemical engineering research areas, and new partnerships with industry in chemical engineering The program promises to be interesting and entertaining. SCHEDULE 1213 1413 Monday 8:3010:15 Monday 12:302:00 1613 Monday 4:306:00 2213 Tuesday 8:3010:15 2413 Tuesday 12:302:00 2513 Tuesday 2:304:15 2613 Tuesday 4:306:00 2713 Tuesday 6:30? 3213 Wednesday 8:3010:15 3413 Wednesday 12:302:00 3513 Wednesday 2:304:15 3613 Wednesday 4:306:00 4213 Thursday 8:3010:15 Lecture Lunch Tutorial Papers Lunch Poster Papers Dinner Papers Lunch Poster Papers Tour The History of Chemical Engineering Education Donald Dahlstrom, University of Utah Moderator: James E. Stice, University of TexasAustin Chemical Engineering Chairpersons' Luncheon Moderator: Richard Alkire, University of Illinois Environmental Engineering Courses and Curricula Moderator: Gary K. Patterson, University of MissouriRolla High Performance Computing in Chemical Engineering Moderator: Mark A. Stadtherr, University of Illinois Chemical Engineering Executive Committee Meeting Moderator: John Friedly, University of Rochester Histories of Chemical Engineering Departments Moderators: Ron Larsen, Montana State University Susan Montgomery, University of Michigan New Courses not Traditionally Taught in Chemical Engineering Moderators: J. L. Zakin, The Ohio State University L. S. Fan, The Ohio State University Chemical Engineering Division Banquet and Division Lecture Moderator: John Friedly, University of Rochester New Chemical Engineering Research Areas Moderator: Thomas Marrero, University of MissouriColumbia Chemical Engineering Division Luncheon, General Business Meeting Moderator: John Friedly, University of Rochester Textbooks in the History of Chemical Engineering Moderators: Melanie McNeil, San Jose State University Polly R. Piergiovanni, Lafayette College New Partnerships with Industry in Chemical Engineering Research Moderator: Neil Book, University of MissouriRolla Tour of Research Facilities Leader: To be announced Spring 1993 7; KNOWLEDGE STRUCTURE mnowo courtesy of ictoria nau, unwersaiy oT Uairornia, aong neacn Participants in the AIChE session on Knowledge Structure in Chemical Engineering, held in Los Angeles, November, 1991. Pictured, left to right: Scott Fogler, Stuart Churchill, R. Byron Bird, Richard M. Felder, and John P. O'Connell (not pictured, Donald R. Woods). Chemical Engineering Education F> Knowledge has structure; structure to facilitate learning and structure to facilitate problem solving. Research by cognitive psychologists has revealed the characteristics of those different structures. The Undergraduate Education Committee of the AIChE spon sored a session on knowledge structure at the Los Angeles meeting in 1991. At that session (which I cochaired with Bill Kroesser), Stu Churchill, Rich Felder, John O'Connell, Bob Bird, and Scott Fogler shared their views of the fundamentals and the structure of knowledge in the areas of mathematics, mass and energy balances, thermodynamics, transport phenomena, and reaction kinetics/reactor design. The results were exciting and diverse. Some of the presenta tions focused on the importance of the subject and the process of using the knowledge effectively, some on structure related to learning, some on problem solving, and some on a combination of these factors. We are pleased to present those papers on the following pages. Don Woods, McMaster University Guest Editor Spring 1993 KNOWLEDGE STRUCTURE FUNDAMENTALS OF CHEMICAL ENGINEERING DONALD R. WOODS, REBECCA J. SAWCHUK McMaster University Hamilton, Ontario, Canada L8S 4L7 he subject "Chemical Engineering" has struc ture. It is not an unrelated collection of about three thousand equations that we somehow put together to solve problems. The subject is built upon fundamental laws, concepts that allow us to use those laws, models, theories, semiempirical cor relations, and data. English and mathematics are the languages we use to work within the subject. Unfortunately, some surveys of our graduating seniors reveal that many see the discipline as a "collection of isolated equations to be memorized and 'cooked' to solve problems." They see no rela tionship between such courses as thermodynamics and heat transferthe topics are seen simply as different courses taught in different semesters by different instructors. Students fail to recognize links between the courses and the concepts in chemical engineering, and consequently they see little struc ture to the subject. There are two vital types of structure: we use a structure of the knowledge to facilitate learn ing, and we use a structure of the knowledge to solve problems. Structures to Facilitate Learning To facilitate learning, Ausubelm emphasized the importance of providing students with "advanced organizers." Such advanced organizers help students see the structure of the subject and provide a "big picture" of the route ahead. The structure, selected to facilitate learning, provides a framework that we can hang new knowledge on as we learn it. One considers which concepts are easier to learn first and notes a certain sequence of topics. Most texts attempt to provide such structure, and most of us in the field of teaching attempt to provide such struc ture to facilitate learning. The structures and relationships are created to facilitate learning. The structures may pertain only 80 Don Woods is a professor of chemical engi neering at McMaster University. He is a gradu ate of Queen's University and the University of Wisconsin. His teaching and research inter ests are in surface phenomena, plant design, cost estimation, and developing problemsolv ing skills. Rebecca Sawchuk is a senior in McMaster University's chemical engineering undergraduate program. The goal of her senior thesis project is to link the fundamentals of chemical engineering to form an organized "structure" of the knowl edge. She plans to work at Dow Chemical Canada Inc. after graduation. to the course and the subject we are teaching. Rarely does the structure interlink with other courses. Novak and Gowin[21 suggest "concept map ping" as a useful way of displaying the structure. Our work with seniors shows that they can create reasonable concept maps that reflect the structure used to help them learn. However, they provide separate and unconnected maps for each course. Furthermore, the maps are very detailed and tend to classify the information on the basis of the se quence in which it was taught. As they develop the maps they say, "First we had this, and then this,..." Thus, what we and the textbooks are providing seems to help their recall. On the other hand, they rarely have thought previously about connecting the maps to see the bigger picture of all the under graduate subject matter. Structures to Facilitate Problem Solving A crucial finding about problem solving is that the problem a person solves is their own internal, men tal image, or representation of the problem. We do not simply solve "problem 6.3 at the end of Chapter 6." Although one reads the problem statement, the mental task is one of reformulating the words and images into some mental image of what "we think the problem is all about." The creation of that inter nal representation is dictated by the problem solver's Copyright ChE Division ofASEE 1993 Chemical Engineering Education KNOWLEDGE STRUCTURE internal structure of the subject knowledge. For example, a student's internal representation of chemical engineering for the purposes of problem solving may be a "collection of unrelated equations." Unsuccessful problem solvers tend to use a trial anderror tactic of using equations that will "use up" the information they are given. For example, a problem statement in Chapter 3 of a fluid mechan ics textbook included extraneous viscosity data. One of the A+ students searched through the text until he found, in Chapter 5, an equation that included viscosity and all of the other information in the problem statement! This behaviour might be interpreted as being re lated to people whose grasp of the subject discipline is only an unstructured collection of unrelated equa tions. Clement'31 and Larkin"'4 provide evidence in the context of physics. Clement suggests that we use four interconnected and hierarchical modes of thinking with our internal knowledge: observations Design of a solution Write relations involving known and desired Combine and solve information S1014 Figure 1. Unsuccessful problemsolver's script (From Larkin;151 reproduced with permission) POINTER Rotating object. Motion of various points on that object. METHODS PRINCIPLES SDescription Immediate Analytic s Diagram showing object's rotation, Visualize separately motion of path of center of mass center of mass and motion relative to center of mass  Motion of center of v R mass is just like motion of a particle. POINTER to another area of physics Particle Lotion mx=F F Relate by integration SFgrav=mg Beloci Figure 2. Successful problemsolver's script. (From Larkin;ts5 reproduced with permission) Spring 1993 POINTERS Resistors in series i R=R1+R2 C C1C CC=1 C2 ap: i tors in neres KNOWLEDGE STRUCTURE and practical knowledgeleading to qualitative physical modelsleading to concrete mathematical modelsleading to written symbol manipulation. Successful problem solvers tend to start solving prob lems by checking the observations, qualitatively un derstanding what is going on, invoking mathemati cal models, and then manipulating symbols to ob tain a quantitative result. Thus, they start with observations and a qualitative understanding of what is going on. Unsuccessful problem solvers depend solely on symbol manipulation. Larkin's research uncovered key differences between unsuccessful and successful problem solvers: the unsuccessful prob lem solver, as illustrated in Figure 1, selects "point ers" in a problem in DC circuits that lead to a broad set of relationships that then had to be played around TABLE 1 Comparison Between Unsuccessful and Successful Problem Solvers' Use of Knowledge UNSUCCESSFUL SUCCESSFUL Problem Solvers' Use of Subject Knowledge Problem Solvers' Use of Subject Knowledge cannot quickly and accurately identify the pertinent subject knowledge; tend rapid and correct identification of the pertinent subject (usually within to play around with many equations;[4,5] tend to manipulate symbols and seconds of completing the reading of the problem statement)[51 combine what they select as being a relevant relationshipI3'4] misinterpret and misuse "pointers"l51 identify and use "pointers" to zero in rapidly on key principles and fundamentals[51 redescription and creation of mental image is limited, formal, and often not redescription is rich, accurate, and uses assumptions and approximations helpfull51 rapidly to identify key features;[5] use qualitative analysis to point to crucial concepts[61 a particular relationship is recalled independently of any general relationship strong structure connecting concepts, principles and laws[51 apply upon which it is based;15] no restructuring and chunkingg" of knowledge; related "chunks" of subject knowledge[6] work with independently applied individual principles(61 do very little qualitative analysis[61 do extensive qualitative analysis of the situation16] unwilling to guess, to make approximations, and have no memorized, order have memorized "tacit" or orderofmagnitude experience factors that ofmagnitude values to assist them in doing a qualitative analysis110'11,121 allows them to do rapid and extensive qualitative analysisl0',l1,12] have incomplete and imprecise knowledge about knowledge[8] have a complete set of knowledge181 lack an organized, hierarchical and abstract knowledge structure that is based possess an organized, hierarchical, and abstract knowledge structure that on fundamentals and tied to the real world by pointers[9'10] is based on fundamentals and tied to the real world by pointers19'101 do not know when to apply general theory and when to apply specific subsets of the general theory that seem to apply[6,81 confuse specific and special cases with generally applicable relationshipsl81 have difficulty recalling/identifying conditions under which special case equations apply and hence try to apply these when they are inapplicable[7,8] have difficulty identifying and formulating the specific information to which the general principles applyl81 have difficulty reasoning from basic principles; instead rely on "beginning" and "end" events without reflecting on the chain of events between the two; depend on redescriptive activities which merely rephrase the problem situation without advancing one's understanding of it; depend on inappropri ate arguments by analogy181 cannot distinguish between additive and nonadditive quantities;[81 have difficulty working with "intensive" properties[81 place more emphasis on collecting sample solutions and working examples than on understanding the fundamentals when "learning" a subjectll'0 replace precise technical definitions with imprecise, everyday usage, e.g., "velocity"l81 fail to realize that once certain physical parameters are set, other measurable quantities cannot be varied independently181 have conceptual difficulty applying calculus in physics[81 82 Chemical Engineering Education KNOWLEDGE STRUCTURE with and "cooked" to see which one might apply. The successful problem solver, illustrated in Figure 2, selects "pointers" in a problem on a falling disk that show a direct and rapid connection with funda mental principles and methods. A summary of the research on unsuccessful and successful problem solver's use of subject knowledge is summarized in Table 1. '313 More specifically, research has shown that suc cessful problem solvers have a structure to their subject knowledge thatinstead of being a collec tion of unrelated concepts and equationsis charac terized as follows: 1. The knowledge is structured hierarchically (with fundamental laws and principles at the higher levels and surface structure and pointers at the lower levels. [6,9,14.15,16] 2. The highest levels in the hierarchyor the under pinningsare the fundamental laws, the abstrac tions.56.9.'141] 3. Related to the fundamentals are concepts and "chunks" of information that allow us to apply the fundamentals effectively. The knowledge is encoded to include conditions and constraints when the knowledge is applicable.t4'7'1,6 4. The lower levels are the surface structure (key words in a problem statement that trigger one to use certain approximations or concepts or descriptions of the everyday events that work because of the fundamentals) and "pointers" that link the surface structure to the fundamentals.5'"'7''16171 5. Encoded with the subject knowledge is "tacit" or memorized, orderofmagnitude numerical values that allow qualitative application of the knowl edge. 10121 6. Subject knowledge is organized in block or "chunks" convenient for mental processing.6'7'121 Concerning the types of knowledge, there are * the fundamentals * concepts or defined terms to allow us to use the fundamentals the procedural knowledge about how to work with the information the pointers or links a rich set of episodic knowledge that gives us a qualitative understanding of what is going on, as opposed to a series of symbolic equations that one manipulates. This includes memorized, numerical, and orderofmagnitude knowledge. Glaser114' suggests that the knowledge structure is not static; rather, as new knowledge comes in it should be embedded in the hierarchy, attached to the fundamentals, and related to the episodic knowl Spring 1993 KNOWLEDGE STRUCTURE edge so that it relates to our past experience. This embedding modifies the original structure. IDEAS ABOUT THE FUNDAMENTALS Identifying the fundamentals is not easy. Some times the things we call "laws" are "wishes," not laws; sometimes "principles" are really laws, etc. Some terminology might be: Law A universally applicable explanation of how things behave; e.g., the conservation of mass. Constrained Law An explanation that is applicable over a defined set of circumstances; e.g., the ideal gas law. Balance An equation applied to a conserved entitythus one would have a "mass balance," but not a "mole balance" or a "volume balance." Model A representation of a situation for the purpose of explaining how it behaves. Theory A mathematical relationship between the dependent and independent variables that is almost completely based on fundamental laws and constrained laws. There may be a few constants that have to be used to tune the theory to the specific situation. There may be many different theories for one particular behaviour. Empirical Correlation A mathematical relationship between the dependent and independent variables. No theory or fundamentals were used in creating the relationship. It considers the system to be a "black box." SemiEmpirical Correlation A mathematical relation ship between the dependent and independent variables that is based on some fundamental laws and constrained laws. Concept A general term for an entity or idea that is useful in applying a law; e.g., the concept of "force." Convention An agreedupon set of rules; e.g., Gibbs convention for the dividing surface in surface phenomena. Postulate A simplifying set of agreedupon conditions. Examples of "laws" and "postulates" pertinent to chemical engineers include1'18191 LAWS 1. Law: Mass is neither created nor destroyed; it is conserved; the total mass is conserved; the mass of an element is conserved (unless nuclear reactions occur or E=mc2 occurs, in which case, mass and energy will exchange). 2. Law: Electrical charge is neither created nor de stroyed; it is conserved. 3. Law: Energy is neither created nor destroyed; it is conserved (unless nuclear reactions occur or E=mc2 occurs, in which case mass and energy will ex change). 4. Law: Momentum is conserved. 5. Law: The law of definite proportions is related to compounds and their formation. 6. Law: The second law of thermodynamicssystems of processes occur so as to minimize the total free energy in the system. Concept: free energy. KNOWLEDGE STRUCTURE 7. Law: If a process proceeds spontaneously, the reverse process can never proceed spontaneously. 8. Law: If a system is left alone, it will go to a state of dynamic equilibrium that has equal forward and reverse rates and no available free energy. Extensive details are needed for each law or corre lation.'4'12' The details include a statement of the fundamental principle law of equation an identification of the meanings of all the concepts used in the law identification of the dependent and independent variables numerical units of measurement listing of the region of application, identification of the limitations and assumptions hints to prevent errors in the application utility hints (tacit information) about when a particular principle is most useful In addition, we must have a qualitative under standing bf what is going on as predicted by the law. POSTULATES To simplify our ways of thinking about nature and how it behaves, we often define simplifying postu lates. Rase"1' provides the following examples of pos tulates: 1. Postulate: Isothermal (constant temperature) 2. Postulate: Isobaric (constant pressure) 3. Postulate: Isochoric (constant volume) 4. Postulate: Isentropic (constant entropy); simplifica tion for a compressor or turbine 5. Postulate: Isenthalpic (constant enthalpy); simplifica tion for flow through a valve 6. Postulate: Adiabatic (no exchange of energy between the inside and the outside of the system); simplifica tion for perfect insulation 7. Postulate: Equilibrium exists (assume an infinitely fast rate) 8. Postulate: Reversibility (neglect friction) 9. Postulate: Ideality (this has many subcomponents); ideal gas when the ideal gas law applies; ideal liquid (could be zero viscosity or Newtonian depending on how ideal is defined); ideal Hookean solid, ideal isotropic solid, ideal solution, ideal mixture, ideal crystal, ideal catalyst 10. Postulate: Models for mixing; plug flow or complete mixing 11. Postulate:Incompressible flow (Vv) = 0 12. Postulate: Unidirectional flow 13. Postulate: Black body radiation and grey body radiation 14. Postulate for shape and configurations: infinite shape, semiinfinite shape, perfectly smooth surface, zero thickness surface region, point source, constant total crosssectional area, and perfect geometrical shapes (flat, cylindrical, spherical) 15. Postulate for time: steady state, pseudo steady state, zero time, infinite time 16. Postulates about limiting cases As we move from laws to models, through con cepts and through to postulates and conventions, we move down the structure. Indeed, the pointers that connect the real world to the structure are usually connected to "postulates." SUMMARY Knowledge has structure. Having the appropriate structure facilitates learning and problem solving. Key characteristics of the knowledge structure to aid in problem solving are that knowledge is hierar chically organized with the fundamentals at the higher levels and pointers at the lower levels. Knowl edge is "chunked" to include the bases, assumptions, conditions of application, and tacit or experience knowledge. Some example "laws" and "postulates" have been given in this paper. REFERENCES 1. Ausubel, D.P., Educational Psychology: A Cognitive View," Holt, Rinehart, and Winston, New York (1968) 2. Novak, J.D., and D. Bob Gowin, Learning How to Learn," Cambridge University Press, Cambridge (1984) 3. Clement, J., "Some Types of Knowledge Used in Under standing Physics," unpublished manuscript, Dept. of Phys ics and Astronomy, University of Massachusetts (1977) 4. Larkin, J.H., "Developing Useful Instruction in General Thinking Skills," Paper JL010276, Group in Science and Mathematics Education, University of California, Berkeley (1975) 5. Larkin, J.H., "Cognitive Structures and Problem Solving Ability," Paper JL060176, Group in Science and Mathemat ics Education, University of California, Berkeley (1976) 6. Larkin, J.H., "Processing Information for Effective Problem Solving," unpublished paper, Group in Science and Math ematics Education, University of California; presented at the Amer. Asso. of Physics Teachers, Chicago (1977) 7. Larkin, J.H., "Understanding Problem Representations and Skill in Physics," Internal Report, Carnegie Mellon Univer sity (1980): Larkin, J.H., et al., "Expert versus Novice Per formance in Solving Physics Problems," Science, 208, 1335 1342 (1980): Larkin, J.H., "Cognition in Learning Physics," Am. J. of Physics, 49(6), 534541 (1980) 8. Lin, H.S., "Problem Solving in Introductory Physics: De mons and Difficulties," PhD Thesis, Department of Physics, MIT, Cambridge, MA (1979) 9. Voss, J., "Problem Solving and the Educational Process," in Handbook of Psychology and Education, R.Glaser and A. Lesgold, eds., Lawrence Erlbaum Publishers, Hillsdale, NJ 10. Woods, D.R., et al., "56 Challenges to Teaching Problem Solving," CHEM 13 News, 155, (1985); "Major Challenges Chemical Engineering Education KNO WLEDGE STRUCTURE to Teaching Problem Solving," Annals of Engr. Ed., 70(3), 277284 11. Mettes, C.T.C.W., A. Pilot, H.J. Roossink, and H. Kramers Pals, "Teaching and Learning Problem Solving in Science," J. Chem. Ed., 57(12), 882885 (1980) and 58(1), 51, 55 (1981); B. van Hout Wolters, P. Jongepier, and A. Pilot, "Studiemethoden," AULA, Uitgeverij Het Spectrum, Utrecht (in Dutch), and K. Mettes and J. Gerritsma, "Probleem Oplossen," AULA, Uitgeverij Het Spectrum, Utrecht (in Dutch) (1985) 12. Reif, F., and J.I. Heller, "Making Scientific Concepts and Principles Effectively Usable: Requisite Knowledge and Teaching Implications," Paper ES13; "Cognitive Mecha nisms for Facilitating Human Problem Solving in Physics: Empirical Validation of Prescriptive Model," Paper ES14b; and "Knowledge Structure and Problem Solving in Phys ics," Paper ES18; Physics Department, University of Cali Sbook review FLUIDIZATION ENGINEERING (Second Edition) by D. Kunii, O. Levenspiel Butterworth /Heinemann, Stoneham, MA 02180; 491 pages, $145 (1991) Reviewed by Roy Jackson Princeton University The first edition of this book, which appeared over twenty years ago, enjoyed considerable success in drawing together the research results available at that time and synthesizing from them a con nected account of direct value to engineers involved in the design of fluidized beds. It is, therefore, a hard act to followbut this second edition succeeds in preserving (and even enhancing) the virtues of its predecessor, while at the same time weaving many newer ideas into the fabric of the text. Though some passages from the earlier work are retained, the present book is essentially a completely rewritten text. Even where the material is similar to the earlier presentation, it has been reorganized, expanded, and supplemented with more worked ex amples. There is much more attention paid to mat ters such as the influence of the properties of the particulate material on fluidization behavior, rest ing on concepts (such as the Geldart classification) which have appeared since publication of the first edition. Variants on the classical dense fluidized bed are also treated; for example, a whole chapter (entitled "High Velocity Fluidization") is devoted to turbulent beds and fast fluidized beds, configura tions that have become increasingly important. On the other hand, the many students and practitio Spring 1993 fornia, Berkeley (1982); 13. Woods, D.R., "Summary of Novice versus Experts Research Results," PS News, 55, 552 to 5521 (1988) 14. Glaser, R., "Education and Thinking: The Role of Knowl edge," Amer. Psychologist, 39(2), 93104 (1984) 15. Boreham, N., "A Model of Efficiency in Diagnostic Problem Solving: Implications for the Education of Diagnosticians," Instructional Sci., 15, 119121 (1986) 16. Bransford, J., et al., "Teaching Thinking and Problem Solv ing," Amer. Psychologist, 41, 10781089 (1986) 17. Bhasker, R., and H. Simon, "Problem Solving in Semanti cally Rich Domains: An Example from Engineering Ther modynamics," Cognitive Sci., 1, 195215 (1977) 18. Porter, S.K., "Ordinary Atoms Made in Stars," J. of Col. Sci. Teach., Dec 1985/Jan 1986, p. 168 (1986) 19. Rase, H.F., Philosophy and Logic of Chemical Engineering, Gulf Publishing Company, Houston, TX (1961) J ners who have benefited from the information in Chapter 3 of the first edition (which provided ex plicit instruction on how to estimate such elemen tary, but vital, properties as the terminal velocity of fall and the minimum fluidization velocity) will be happy to know that the same chapter of the second edition provides the same help, but in an updated and improved form. My only criticism of the first edition was that the very success of the authors in presenting the mate rial in such simple, clear exposition tended to give a false impression that the material was well estab lished, reliable, and beyond controversy. In fact, this was far from the truth. Many of the correlations presented were extrapolations from limited data, while the models, though reasonable and the best available at the time, were gross simplifications which had been subjected to only the most superfi cial testing. In short, the story was told so well that it made the stateoftheart seem much more firmly based than it really was. I have some of the same feeling about the second edition. The unwary designer might easily be se duced into following the path so clearly marked out, only to receive a rude awakening further down the road. The subject remains today a very messy one, in a state of continuing flux, with both the physical principles and the tools available to apply them changing very quickly. But this is only a minor reservation about a book which is likely to be as well received as was its predecessor. We might even hope that the rapid changes in the field will encourage the authors to venture a third edition at some time in the future. KNOWLEDGE STRUCTURE KNOWLEDGE STRUCTURE MATHEMATICS STUART W. CHURCHILL The University of Pennsylvania Philadelphia, PA 191046393 he assigned objective for the presentation that led to this paper was a discussion of the struc ture of knowledge in applied mathematics which is appropriate to the undergraduate chemical engineering curriculum. That presentation was, and this paper is, actually focused on a limited aspect of the assigned topicnamely, the form of exposition of applied mathematics in the curriculum and its reception and retention by students. The state and consequences of current undergraduate preparation in applied mathematics will be examined first, and then proposals for improvement will be presented. THE CHALLENGE Doctoral students in chemical engineering have sufficient time and a sufficiently narrow focus so that they can master and utilize those aspects of applied mathematics that are directly useful in their research. On the other hand, undergraduate stu dents are currently exposed to a great amount of material, including applied mathematics, in a form and at a rate that precludes its mastery. The need for such mastery as contrasted with exposure is first considered, and then the degree to which it is cur rently accomplished. The superior preparation in mathematics of students from Europe and Japan is evident to all who encounter them in graduate courses. Their preparation provides a measure of what we might aspire to achieve. Stuart W. Churchill is the Carl V.S. Patterson Professor Emeritus at the University of Penn sylvania, where he has been since 1967. His BSE degrees (in ChE and Math), MSE, and PhD were all obtained at the University of Michi gan where he also taught from 19501967. Since his formal retirement in 1990 he has continued to teach and carry out research on heat transfer and combustion. He is also currently complet ing a book on turbulent flow. Copyright ChE Division ofASEE 1993 THE ESSENTIAL ROLE OF MATHEMATICS IN ENGINEERING "It's staggering to consider how much one's social acceptance depends upon being quadrati cally integrable." Snoopy Most of those in the academic community do not need to be convinced that innovative applications of mathematics have made great contributions to the advancement of the practice of chemical engineer ing in recent decades. Unfortunately this contribu tion is largely ignored and grossly underestimated by its principal beneficiarythe chemical and process industries (CPI). The leaders of the CPI take for granted the improvements in process de sign, process control, process analysis, and process safety that are a direct consequence of better modeling and better understanding. They do not see the link between those improvements and the articles in mathematical language which have appeared in the literature of engineering science, such as the AIChE Journal. Faculty members who read this article (and in particular, the authors of the associated papers of this symposium) owe their academic and professional achievements at least in part to a superior grasp of, and facility with, applied mathematics. A good un derstanding of applied mathematics and a willing ness to extend that understanding, as stimulated by new topics in research or teaching, is a necessary condition for successful academic practice today. We owe our students an appropriate preparation in mathematics, not only for the problems that are current or foreseeable, but also as a foundation for the acquisition of those mathematical skills that will become important during their lifetime. If we are successful, our students will have sufficient con fidence in their mathematical background and a suf ficient vision of its value to exercise, maintain, and extend this competence throughout their career, or at least as long as that career is focused on technol Chemical Engineering Education KNOWLEDGE STRUCTURE One of [my graduate students] devised a general method for deriving similarity transformations, and he and others were among the first in engineering to use digital computers. They produced the first numerical solutions of the partial differential equations governing laminar, transient, and multidimensional natural convection, and subsequently they were among the first to model the turbulent regime multidimensionally. ogy as contrasted with management. I assert that we now fail almost totally in this respectat least with those who do not pursue graduate work in chemical engineering. The math ematical knowledge of those who enter industrial practice with a bachelor's degree fades rapidly after graduation owing to its disuse. An ancient but nev ertheless instructive study is reexamined below as evidence thereof. THE GOALS OF ENGINEERING EDUCATION STUDY The 1968 Goals of Engineering Study,'" sponsored by the American Society for Engineering Education, is still instructive despite its date. Although it floun dered for several reasons, the findings and recom mendations with respect to mathematics will be ex humed here. As a first step of the study, a survey was conducted to determine the retroactive selfas sessment of their education by engineers in indus try who had been practicing five, ten, and twenty years since receiving their baccalaureate degree. The participants were asked to identify those aspects of their undergraduate studies which had proved the most and the least useful. An increasing majority at each level of experience asserted that they had never used mathematics (and in particular, calculus) in their professional career. The only cited deficiency in their mathematical preparation was in statistics. This response was totally misleading; most, if not all, of the participants had used mathematics in the first few years of practice, but at the current stage of their career the ambitions of many had become more focused on skills and credentials required by management. The technical and mathematical skills they had used to reach the point of consideration for management had been forgotten. The authors of the Goals report used the results of the survey as justification for recommending more courses in managerialrelated topics at the expense of courses in engineering science and math ematics. This survey is an example of obtaining the wrong answer by virtue of asking the wrong ques tion. Fortunately, a number of recommendations of the Goals report, including those related to math ematics, were eventually rejected by the AIChE and Spring 1993 other professional societies as unacceptable criteria for accreditation. My informal conversations with undergraduate stu dents at the University of Pennsylvania over the past twentyfive years suggest that when they gradu ate they still lack confidence in their working knowl edge of engineering science and, to an even greater extent, advanced mathematics. This is undoubtedly a factor in the choice by many of positions in mar keting, sales, etc., that will not expose this pre sumed deficiency. Similar conversations with our graduate students from other schools (consisting pre dominantly of students who performed exception ally well in engineering science and mathematics) indicates that this insecurity is not unique to any one school or group of students. If the Goals survey were reconducted with industrial practitioners to day, a quarter of a century later, I suspect the same general response would be obtained. TEXTBOOKS The standard textbooks in chemical engineering provide additional insight into the role of applied mathematics in the undergraduate curriculum. In Elements of Chemical Engineering, by Badger and McCabe,[2' (out of which I studied as an under graduate) the models were almost wholly algebraic. Even Unit Operations, by Brown and Associates, 31 a generation later in 1950, utilized very few differ ential models and then only elementary ones. Two outstanding books on applied mathematics in chemi cal engineering appeared in the interimApplied Mathematics in Chemical Engineering, by Sherwood and Reed in 1939,[4] and Application of Differential Equations to Chemical Engineering Problems, by Marshall and Pigford in 194751but the material therein was not required to solve any of the prob lems considered in the undergraduate curriculum and had no direct impact thereon. Indeed, to this day material of the level of mathematical sophisti cation of these latter two books is hardly recognized in industrial practice, at least outside research de partments or their equivalent. As an aside, it may be significant to note that no mention was made of the former pioneering book in the citation for the recent award of the National Medal of Science to Charles E. Reed. KNOWLEDGE STRUCTURE Subsequent undergraduate texts, beginning in 1960 with Transport Phenomena by Bird, Stewart, and Lightfoot,"6' have used more advanced notation, models, and solutions, but otherwise have not greatly extended the mathematical demands on students. COMPREHENDING THE LITERATURE OF CHANGE Several years ago, on the occasion of the 75th Anniversary Meeting of the AIChE, I was asked to review the role of mathematics in the history of our profession and particularly in its publications.[7' One of my conclusions was that our graduates were no longer sufficiently prepared in mathematics to read much of the AIChE Journal. That situation has not changed significantly in the intervening nine years. The mathematical sophistication of our published research is certainly advancing more rapidly than the preparation of our undergraduates in this respect. This inaccessibility of the articles in our archival journals to our bachelor's graduates in terms of com prehension has at least two serious consequences: 1) the advances in knowledge, as described in the journals, are a wellkept secret insofar as most of our profession is concerned, and 2) the cultural gap and the difficulty of technical communication be tween those with graduate education and those with out becomes ever greater. How can we expect the results of analysis to be implemented in industry if they are effectively hidden from the practitioners and managers by their expression in an unknown language? How can we maintain professional continuity across the division of degrees without a common language? This is a relatively new phenomenon, and hence it is not widely recognized. A Personal Digression * At this point I will take the liberty of citing some of my own experiences as evidence of the impact on chemical engineering practice of even modest skills in applied mathematics. Such a personal digression is perhaps tolerable since these experiences form the basis for my commitment to, and proposals for, improved instruction in this field. As an undergraduate I majored in applied math ematics as well as in chemical engineering, and I received a bachelor of science degree in each. The decision to do this was one of the more felicitous ones in my career since it set me somewhat apart from my classmates in chemical engineering and greatly enhanced my selfconfidence. The added 88 Faculty members who read this article (and in particular, the authors of the associated papers of this symposium) owe their academic and professional achievements at least in part to a superior grasp of, and facility with, applied mathematics. mathematics was not very sophisticated by current standards, and the topics themselves did not differ greatly from those we now offer our undergraduates in an elective or required course in "advanced math ematics for engineers." My courses were, however, taught by mathematicians, and the classes included students majoring in mathematics as well as in en gineering. Accordingly, the instruction included a stronger focus on structure and rigor. That focus has proven to be a longterm benefit one which is often denied our current students when such courses are taught by engineers. For the short term, including my first years of practice after gradu ation, the primary benefit of the added mathematics was a capability to solve problems that my peers in chemical engineering could not. Upon returning to graduate school five years later, I was able to main tain this competitive edge by taking as many elec tives as possible in that lowly branch of mathemat ics known as analysis, and this had the unexpected but happy collateral consequence of allowing me to take advanced courses in physics. In each phase of my subsequent academic career I have been able to take advantage of this marginal preparation in mathematics by my choice of and approach to problems of research. My graduate students have also been encouraged to undertake problems involving advanced applications of ap plied mathematics. One of them devised a general method for deriving similarity transformations, and he and others were among the first in engineering to use digital computers. They produced the first numerical solutions of the partial differential equa tions governing laminar, transient, and multidimen sional natural convection, and subsequently they were among the first to model the turbulent regime multidimensionally. In the course of solving nu merically the integrodifferential equations govern ing radiative transfer through dispersed media, we were privileged to interact personally with Peter J. W. Debye, John von Neumann, George Uhlenbeck, and Subrahmanyan Chandrasekhar. My later stu dents solved models for radiatively stabilized com bustion that involved integrodifferential equations and complete freeradical kinetic models. My most Chemical Engineering Education KNOWLEDGE STRUCTURE recent students devised the first numerical solu tions for flow and heat transfer with secondary mo tion in doublespiral heat exchangers and for thermoacoustic convection. These exciting and productive experiences have all been a consequence of undertaking problems for which no method of solution was yet known. We did not necessarily even know in advance what forms of mathematics would prove helpful; we simply were confident (or foolhardy) enough to believe in our ability to identify, master, and apply the necessary techniques, whatever they might be. This is not a unique story; it could be told with slight differences by a number of others in our pro fession.[8' The only excuse for reviewing my own ex periences is that they illustrate the advantages that accrue from a working knowledge of advanced math ematics and the confidence to use that knowledge. This confidence, particularly when it extends be yond classical solutions, leads to boldness in tack ling problems of unpredictable difficulty and in de vising new techniques for their solution. Our objec tive as teachers should be to prepare and encourage students to undertake such challenges rather than to avoid them. Although the above experiences were generally in the framework of doctoral research, in most instances one or more undergraduates also participated and they often made significant intellectual contribu tions. Insofar as it is possible, such an experience should be provided for our undergraduates as a supplement to their regular course work. (As an asidewithinadigression, there appears to be a strong correlation between undergraduate partici pation in exciting research and a positive decision to attend graduate school.) THE ROLE OF COMPUTERS The principal technological event of our genera tion has been the rapid development of computers and their software. This development has shifted the emphasis on mathematics rather than replacing it. Students are more receptive to computer use than to mathematics, but some analogous problems have arisen. Symbolic manipulators and canned numeri cal algorithms are often a convenience, but they isolate the user from the mathematics and technol ogy of the process itself. Most computer scientists show the same disdain as do pure mathematicians for engineeringhence, we should anticipate some of the same difficulties in instruction in numerical methods that have been endemic in mathematics. Spring 1993 TOPICS Said the Mock Turtle with a sigh, "I only took the regular course." "What was that?" inquired Alice. "Reeling and Writhing, of course, to begin with," the Mock Turtle replied; "and then different branches ofArithmeticAmbition, Distraction, Uglification, and Derision." Alice's Adventures in Wonderland The choice of appropriate topics in applied math ematics is difficult, but perhaps less important than the methodology used in the classroom. I have re cently attained the position in academic life desig nated as "emeritus." This title apparently means that you are welcome to assist, but not to advise or to expect compensation. From that perspective, it would be unseemly for me to make recommenda tions concerning specific topics in applied mathemat ics to be included in the curriculum of the future. In any event, I do not have a crystal ball with which to predict those topics of engineering science that will either fade, continue, grow in importance, or newly appear in the decades ahead. Recently, in this same journal, Ramkrishna91 mentioned some aspects of mathematics which may become important to chemi cal engineers, but his focus was presumably on re search rather than on undergraduate education. I will limit myself to a single guideline. The topics of chemical engineering science that were included in the knowledge structure sympo sium (physical chemistry and stoichiometry, ther modynamics, transport phenomena, and reaction engineering) constitute one obvious criterion for the choice of topics of mathematics to be included in the curriculumthat is, the essential elements are those needed to describe the laws and relationships of these and other engineering sciences in the form of algebraic, differential, integral, or stochastic mod els, as well as to derive solutions for these models for general or specific cases. The elements and pro cedures of mathematics that are common to more than one of the engineering sciences are of particu lar importance. It is, after all, the latter commonal ity that gives mathematics an allencompassing role and importance in the curriculum. AN ANALYSIS OF MODELS One technique which I have found to be successful in the classroom and in homework for providing an overview of applied mathematics is to emphasize the analysis of models rather than the process of solution. (This is not to say that instruction in meth ods and solutions should be neglected.) The models 89 KNOWLEDGE STRUCTURE KNOWLEDGE STRUCTURE which serve as a starting point for such analyses should ordinarily be the general partial differential equations of conservation, together with equations of state, kinetic mechanisms for chemical reactions, etc. If these equations are not familiar to the stu dents from their previous courses in engineering science, they must be derived at this point as a preliminary step. A list of questions which can then be posed is presented in Table 1. In some complex processes, for example in turbu lent flow1131 and in the motion of a rising bubble,[141 considerable information can be attained, even if a simple list of variables rather than a set of partial differential equations is used as the model. Conven tional dimensional analysis is then applied to deter mine a minimal set of linearly independent dimen sionless groups incorporating all of these variables. One or more procedures for identifying these group ings are described in most standard textbooks. They generally fail, however, to indicate the possibility of error owing to omissions or improper inclusions in the list of variables. They also often neglect to indi cate the consequences of alternative choices of vari ablesfor example, the shear stress on the wall rather than the pressure gradient, and the mass rate of flow rather than the mean velocity. They frequently fail to stress the significance of alterna tive groupings and of the speculative deletion of variables.[11"12141 These procedures often produce asymptotic solutions whose only deficiency relative to a complete analytical solution is a numerical value for the leading coefficient. As a consequence, this methodology may prove to be more useful to a stu dent and a practicing engineer than some particular TABLE 1 Illustrative Questions to Stimulate the Critical Analyses of Models 1. Which terms can be dropped in general? Why? 2. Which terms can be dropped for particular cases on mathematical grounds? Which ones can be dropped on physical grounds? 3. Which terms must be dropped and which must be retained to obtain the appropriate model for classical limiting cases? For example, for fluid motion the following limiting cases might be considered: inviscid flow incompressible flow developing flow openchannel flow purely viscous flow onedimensional flow boundarylayer flow buoyant motion purely inertial flow rectilinear flow steady flow freestreamline flow slightly inertial flow fully developed flow unconfined flow turbulent flow 4. Which of the reduced models are linear? 5. What is the form of the reduced models from a mathematical point of view (parabolic, elliptic, hyperbolic)? What is the significance of this division by form? 6. What are the relative advantages of the Eulerian and Lagrangian forms? (This question provides an opportunity to contrast the approaches in engineering and in pure science.) 7. How can the model be dimensionalized? (This provides an opportunity to introduce the method of Hellums and Churchill'"" or the equivalent.) 8. What are the advantages and disadvantages, if any, of dedimensionalization? 9. Is a similarity transformation possible? (Exposition of the method of Hellums and Churchill"0' is again suggested.) 10. Can the model be simplified by a transformation of variables other than a similarity transformation? (Examples are the stream function, the vector potential, and the vorticity.) 11. What is the physical significance of each of the boundary conditions? Are they physically realistic? 12. What is the physical significance of each term in the model? What are the criteria for dropping a term? 13. Will different methods of solution, such as 1) separation of variables and expansion in Fourier series, 2) conformal mapping, and 3) the Laplace transform, lead to different solutions? 14. How can the Laplace transform be used to derive asymptotic solutions? 15. Try to conceive as many types of asymptotic behavior as possible. What reductions in the model are appropriate for these limiting cases? (See Churchill" .121) 16. To what extent can the behavior of interest be circumscribed by asymptotic solutions? 17. What are the consequences of timeaveraging an equation for conservation? 18. Is dimensional analysis of the equations of conservation applicable for turbulent flow in both timedependent and timeaveraged forms? 19. Does a numerical method of solution yield exact results as the subdivisions are increased? 20. What are the relative advantages of finitedifference, finiteelement, and Monte Carlo methods? 21. What are the advantages of generalized computer programs as compared to special purpose ones? 22. What is the significance of a pseudosteady state? Suggest possible applications. 23. What is stiffness with respect to numerical solution of a differential equation? 24. What are the advantages and consequences of developing a solution for the "phaseplane"? 25. What is the consequence of simplifications in a model which reduce the required number of boundary conditions? 26. What is the consequence of a transformation such as the introduction of the stream function which raises the order of the derivatives? 27. How can the required number of boundary conditions be identified? 28. What is the significance and consequence of an integral approximation such as for a boundary layer? ) Chemical Engineering Education KNOWLEDGE STRUCTURE analytical method such as conformal mapping. The development of correlating equations that in corporate asymptotic solutions as components also helps to provide an overview. The derivation of as ymptotic solutions may then be recognized as an essential part of this process. The derivation of ei ther complete analytical or numerical solutions may similarly be recognized as a means of generating precise data with which the coefficients in the corre lating equation can be evaluated. In this context, Shinnar~'15 has recently mentioned the need to base correlations on the advances of engineering science, and Churchill"161 has asserted that one of the princi pal roles of analysis is to support the construction of correlating equations. What are the advantages of the above approach? It focuses on the model rather than on a particular solution. It focuses on the process and significance of reducing the model rather than on the solu tion for some reduced model of unknown applicability. It emphasizes the possibility of more than one method of solution and suggests an objective basis for comparison of competitive solutions. It integrates the physics and chemistry with the mathematics. It stresses a method of pure reasoning which will be applicable to new problems. It reveals the asymptotic character and significance ofparticular solutions. (Most solutions in closed form actually fall in this category.) It avoids excesses by focusing on possible simplifications and their significance rather than on general solutions. It helps to alleviate one of the principal sources of frustration for students, namely the evocation of simplified models by the teacher without explanation or justification in ad vance. How and where can we incorporate the above ap proach in the curriculum? The simplest procedure is to incorporate it in each of our present courses in engineering science as applicable, rather than add ing or replacing a course. Arthur E. Humphrey, my previous departmental chairman and dean, has asserted that I teach the same material and methodology in whichever course I am assigned. In regard to this approach to analy sis, I am willing to confess to the crime, if it be one. Spring 1993 SUMMARY We are failing to prepare our undergraduates to use mathematics in their professional work. This failure has serious consequences relative to our profession and to the recognition of new devel opments when they are expressed in the language of advanced mathematics. The superior preparation in mathematics of students from Europe and Japan is a benchmark in this respect. Focusing on the structure of models rather than only on detailed analytical solutions is proposed as a partial correc tive. The increasing role of computers in the prac tice of chemical engineering can be expected to in fluence the choice of topics in applied mathematics but not to eliminate the importance of proficiency therein. The wellknown problems of instruction in mathematics can be expected to reappear in courses in computer science. REFERENCES 1. "Goals of Engineering Education," Amer. Soc. Eng. Ed., Washington, DC (1968) 2. Badger, W.L., and W.L. McCabe, Elements of Chemical En gineering, McGrawHill, New York (1931) 3. Brown, G.G., and Associates, Unit Operations, John Wiley & Sons, New York (1950) 4. Sherwood, T.K., and C.E. Reed, Applied Mathematics in Chemical Engineering, McGrawHill, New York (1939) 5. Marshall, Jr., W.R., and R.L. Pigford, The Application of Differential Equations to Chemical Engineering Problems, University of Delaware, Newark, DE (1947) 6. Bird, R.B., W.E. Stewart, and E.N. Lightfoot, Transport Phenomena, John Wiley & Sons, New York (1960) 7. Churchill, S.W., "The Changing Role of Applied Mathemat ics in Chemical Engineering," AIChE Symp. Ser. No 235, 79,142 (1948) 8. Aris, R., and A. Varma, Eds., The Mathematical Under standing of Chemical Engineering Systems: Selected Papers ofNeal R. Amundson, Pergamon Press, Oxford (1980) 9. Ramkrishna, D., "Applied Mathematics: Opportunities for Chemical Engineers," Chem. Eng. Ed., 24, 198 (1990) 10. Hellums, J.D., and S.W. Churchill, "Simplification of the Mathematical Description of Boundary and Initial Value Problems," AIChE J., 10, 110 (1964) 11. Churchill, S.W., "The Use of Speculation and Analysis in the Development of Correlations," Chem. Eng. Commun., 9, 19 (1981) 12. Churchill, S.W., "Derivation, Selection, Evaluation and Use of Asymptotics," Chem. Eng. Technol., 11, 63 (1988) 13. Churchill, S.W., "New and Overlooked Relationships for Turbulent Flow in Channels," Chem. Eng. Technol., 13, 264 (1990); 14, 73 (1991) 14. Churchill, S.W., "A Theoretical Structure and Correlating Equation for the Motion of Single Bubbles," Chem. Eng. Proc., 26, 269 (1989); 27, 66 (1990); also see Viscous Flows: The Practical Use of Theory, Chap 17, Butterworths, Bos ton, MA (1988) 15. Shinnar, R., "The Future of Chemical Engineering," Chem. Eng. Prog., 87, No. 9, 80 (1991) 16. Churchill, S.W., "The Role of Analysis in the Rate Pro cesses," Ind. Eng. Chem. Res., 31, 643 (1992) 0 KNOWLEDGE STRUCTURE KNOWLEDGE STRUCTURE OF THE STOICHIOMETRY COURSE RICHARD M. FIELDER North Carolina State University Raleigh, NC 276957905 Most chemical engineering curricula in North America begin with the stoichiometry course. The content of this course is fairly standard: definitions, measurement, and estimation of various process variables and physical properties of process materials; descriptions and flow charts of unit operations and integrated processes; gas laws and phase equilibrium relations; laws of conserva tion of mass and energy; and the incorporation of all of the above into material and energy balance calcu lations on individual chemical process units and multiunit processes. The material is not intrinsi cally difficult, especially compared to the content of later courses in transport processes and thermody namics, but the approach required to set up and solve course problems takes most students consider able time to grasp.[1 The course may conveniently be divided into two parts for the purposes of defining a knowledge struc turematerial balances and energy balances. Pos sible structures for each part are shown in Figures 1 and 2. The following paragraphs comment on those structures. Knowledge Structure Material Balances (Figure 1) E The concept of conservation is essential to the course and is generally accepted implicitly. The prin Richard M. Felder is Hoechst Celanese Pro fessor of Chemical Engineering at North Caro lina State University. He received his BChE from City College of CUNY and his PhD from Princeton. He has presented courses on chemi cal engineering principles, reactor design, pro cess optimization, and effective teaching to vari ous American and foreign industries and insti tutions. He is coauthor of the text Elementary Principles of Chemical Processes (Wiley, 1986). Copyright ChE Division ofASEE 1993 92 cipal concepts that all students must bring with them from their prior education come from math ematics (basic algebraic and graphical manipula tions, solving sets of linear equations and word prob lems), physics (phases of matter, conservation of mass), and chemistry (atoms and molecules, stoi chiometric equations, molecular weight, and molar quantities). O The building blocks of the course are properties of process systems and materials including mass, volume, pressure, temperature, and (later) en ergy. These properties are conceptually taken for granted in the course, although both professors and students might be hard pressed to define most of them. Fortunately, they are familiar enough for us to be comfortable with them, which is all we need to be able to build on them successfully. E Other broad concepts that may be presented in firstyear courses but are more likely introduced in this one include (a) multistep chemical processing and graphical representation of chemical processes flowchartss); (b) the idea that a system has a state, defined as the collection of all its physical properties and determined by the values of a subset of those properties; (c) various physical laws and relations among system variables that allow some variable values to be determined from specified values of others; (d) the notions of equilibrium, dynamic equi librium, phase equilibrium, reaction equilibrium, and steadystate and transient operation of a system; (e) the idea that variables must sometimes be estimated approximately rather than calculated to six signifi cant figures; (f) the idea that problems must some times be solved by trialanderror; (g) the idea that there's nothing illegal or shameful about (e) and (f). E Most of the content of this part of the course consists of definitions of and relations among the variables that characterize chemical process sys temstemperature, pressure, volume, density, flow rate, mass fractions and concentrations, frac tional conversion, compressibility factor, vapor Chemical Engineering Education KNOWLEDGE STRUCTURE pressure, relative humidity, etc.and procedural and computational algorithms for calculating values of some of these variables from known values of others. The sequence of the information flow is sug gested in Figure 1. Knowledge Structure Energy Balances (Figure 2, next page) All of the material listed in the previous section is prerequisite to that which follows. O Energy now takes its place as a basic course concept that few involved with the course either understand or question. Again, the fact that we think we know what it is and feel comfortable about it keeps us from hopelessly bogging down at this point. D The integral of a function now joins the list of prerequisite mathematical concepts and the prin ciple of conservation of energy joins the required physical concepts. ED Once energy and temperature are admitted as working concepts, the three forms of energy (kinetic, potential, and internal) and modes of energy trans fer (heat and work) can be introduced, setting the stage for the first law of thermodynamics. D A concept that arises in the context of the first Figure 1. Knowledge structurematerial balances Spring 1993 KNO WLEDGE STRUCTURE law is enthalpy, defined for convenience as a fre quently occurring combination of other system vari ables (H = U + PV). Perhaps because of its strange sounding name, students never get fully comfortable with enthalpythey eventually learn to work with it (as in Q = AH), but they always have the feeling that there is something fundamental and mysteri ous about it that puts it beyond their intellectual reach. Trying to convince them that enthalpy is re ally a simple concept and things like mass and en ergy are concepts much more worth worrying about is generally futile. (Later they will get into thermo dynamics, which will finish the job of overwhelming them with variables defined for convenience and given strange names.) 0 The previously introduced notions of the state of a system and state properties now reappear, lead ing to the concepts of reference states and process paths for calculating AU and AH. All the necessary ingredients for energy balance calculations are now in place. Figure 2. Knowledge structureenergy balances. Chemical Engineering Education KNOWLEDGE STRUCTURE KNOWLEDGE STRUCTURE E Most of the content of this part of the course consists of (a) definitions of and procedures for measuring and estimating the energyrelated vari ables that characterize chemical process systems heat capacities, latent heats of phase change, solution, and mixing, and heats of reaction, forma tion, and combustion; (b) procedural and computa tional algorithms for calculating internal energy and enthalpy changes associated with transitions from one system state to another; and (c) procedures for solving the first law equation for unknown en ergy flows or changes in state in various unit pro cesses. The sequence of the information flow is sug gested in Figure 2. TRANSIENT BALANCES Most stoichiometry textbooks contain a chapter on transient system balances. A key concept here is that of a derivative. While students in the course can differentiate functions on demand, they have no physical or intuitive understanding of derivatives, in part because most mathematics professors seem to fear that they would harm their reputations by putting applications in the elementary calculus se quence. Covering transient balances in the stoichi ometry course could help the students make signifi cant progress toward this understanding; unfortu nately, the course almost never gets to transient balances and most introductory transport courses take the underlying knowledge structure of this topic for granted. AFTERWORD Once a knowledge structure has been defined, the next logical step is to consider how it can best be transferred into students' brains. I believe that for stoichiometry there are two keys: 1. Provide explicit instruction and lots of drill in basic problemsolving procedures, especially the systematic use of the flow chart coupled with informal degreeoffreedom analy sis to organize the solutions of material and en ergy balance problems. 2. Establish an active, cooperative learning environ ment. Have students work in teams on problems in class and on the homework, identifying concep tual and procedural sticking points and finding out how to get past them, teaching and learning from one another. For specific ideas about how to accomplish these tasks, see Reference 1. REFERENCES 1. Felder, R.M., "Stoichiometry Without Tears," Chem Engr. Ed., 24(4), 188 (1990) 0 RJR% letter to the editor Dear Editor: Due to an unfortunate oversight, the article on the Mark ovian approach to chemical kinetics (CEE, 27, 4243) does not discuss the importance of choosing properly the duration of a stage for the sake of acceptable numerical accuracy. In any discrete approximation to a contin uous phenomenon, the time increment in the former must be sufficiently small, and Markov chains are no exception. In the numerical example of the article, the stage width of 0.001 minutes is one appropriate choice, when 75% of species A at a given time decompose to B and 5% of species B at a given time decompose to species A in one minute. With this choice, the Markov formulation A(n+ 1) (0.99925 5.0e5)(A(n)) B(n+ 1)) (7.5e4 0.99995)(B(n)) and the integral rate equations A(t) =0.075 +0.925 exp(8.0 e 4t) B(t)= 1.1250.925 exp(8.0 e 4 t) Spring 1993 agree to at least a fourdecimal accuracy when t=n=stage number, as shown in the tabulation. Steady state condi tions are reached essentially at n = 10000. The author regrets the omission of this material, and wishes to thank Dr. Alan M. Lane at the University of Alabama, Tuscaloosa, for drawing it to his attention. n A(n) B(n) Markov Rate Eq. Markov Rate Eq. 1 0.9993 0.9993 0.2007 0.2007 10 0.9926 0.9926 0.2074 0.2074 1000 0.4905 0.4906 0.7095 0.7094 5000 0.0919 0.0919 1.1081 1.1081 10000 0.0753 0.0753 1.1247 1.1247 inf. 0.075 0.075 1.125 1.125 Thomas Z. Fahidy University of Waterloo KNn)WLFf Qn= STRUCTURE THERMODYNAMICS A Structure for Teaching and Learning About Much of Reality JOHN P. O'CONNELL University of Virginia Charlottesville, VA 22903 Thermodynamics is an amazing discipline. Its two brief laws contain the complete basis for establishing the states of pure and mixed sys tems and their tendencies for change. The founda tion for scientific investigations into all forms of matter lie in its rigor. Constraints on engineers to interconvert heat and work, separate components from solutions, and obtain ultimate yields from chemical reaction arise with its symbolic manipula tion. Reliable screening for feasibility and optimiza tion of nearly every type of process can be guided by its procedures. Thermodynamics is fundamental and applicable to all technical endeavors. Though thermodynamics focuses on natural phe nomena, it is really just a deductive structure devel oped by creative and systematic human minds. Na ture has carried out her diverse processes for eons without being explicit about energy, entropy, and fugacity. We find these mental constructs useful be cause they give us a chance to assimilate extensive amounts of real behavior, rather than being over whelmed by its totality or misguided by less general alternatives. Further, we can use "always true" ther modynamics with appropriate information and ap proximation to effectively describe and predict mul titudes of reality. Modern thermodynamic ideas originated over 150 years ago, but the subject still evolves. Although some scholars claim that "there is nothing new in thermodynamics," a few still find challenges in its John O'Connell is H.D. Forsyth Professor of Chemical Engineering at the University of Vir ginia. He received his BA from Pomona College, his BS and MS from MIT, and his PhD from the University of California (Berkeley). He taught thermodynamics and statistical mechanics as well as materials science for chemical engineers at the University of Florida from 196688. His research on varieties of fluids involves theory, molecular simulation, and experiment. Copyright ChE Division ofASEE 1993 Though thermodynamics focuses on natural phenomena, it is really just a deductive structure developed by creative and systematic human minds. Nature has carried out her diverse processes for eons without being explicit about energy, entropy, andfugacity. abstractness, rigor, and universality as well as in debating the "best" way to phrase the principles and their limits of application. But most current engi neering work deals with the practical uses of thermodynamicspredominantly with models of reality. Modern computers enable testing of quantitative expressions for phenomena at every level of complexity. As a result, we find thermody namics being used to an unprecedented extent to mimic and predict Nature's behavior more easily (and often more reliably) than experimentespe cially for mixtures. Unfortunately, the word "thermodynamics" pro vokes uneasiness or frustration in many welledu cated people, especially in alumni of engineering thermodynamics courses. This often arises from an incomplete or insecure classroom experience com bined with insufficient background in assimilating all the basics. Becoming really comfortable with ther modynamic concepts and proficient in their use re quires a comprehensive appreciation of the subject in addition to care, maturity, and intelligence. Thus, major objectives of thermodynamics education should include overcoming confusion and antipathy while fully integrating the concepts, knowledge, and pro cedures. The process, though quite demanding, must guide students to appreciate the structure and rel evance of thermodynamics and to become effective in its use. It should also enrich their vision of Nature's unity and diversity. What follows is one teacher's view of fundamental thermodynamic structure and how it leads to ap plications that could foster a useful and satisfying learning experience for chemical engineering stu dents. While integration and connection require Chemical Engineering Education KNOWLEDGE STRUCTURE terms of study and often years of practice, the ideas presented here may be valuable for others in en hancing learning.* STRUCTURE Because thermodynamics is a logical construct, there are many ways that the subject can be devel * Jim Haile (Clemson) contributed much to these beginning thoughts. A Pedagogical Structure of Thermodynam Category Elements Observations PrimitjveConcepts ral Phenomer S ns Mathema Generalizations Measu les & Variables & Constraints as kles & Vanables onstraMaterial Conservation ( Initially For Energy Conservatio~ Nonequivlnce \Fixed Composition I Degradation_ st& 2Tfaw Equatio # ii eeident arables of Sti Articulation & St te Prdperties & Boundaries' Conce pa Quantification / fConnections Among Partial Deri Pro rties........ ...Principles .of Multicomponent Fluids :: Compoiion Variables Partial M Equilibrium & Change Extrema of Conceptuals Pro Phase Stability Diffe Phases and Reactions Phas ilibum Phase Reaction SRelations ia ams Relatio ods Organization of Information Models Data Tabulations Simulations ............................................................ ... ............ ...... ....... ........ .. ". 'Mixing & Separation Chemic Applications , Transport Tendencie Heat & "* Volumes and Heats Direct Connection  Indirect Connec Figure 1. A structure of chemical engineering thermod PRIMITIVE CONCEPTS NATURAL PHEN MEASURABLES HAPPENING Things Properties & State Changes Thermal and Material System Force Input mechanical transfer of Surroundings Length Output effects on substances Boundaries Pressure Accumulation fluids via various Volume Generation and solids mechanisms Consumption Table 1. Observations Definitions Mathemat Identity Chemical species Algebraic equations a Systemsurrounding interactions Functions of several Quality Extensive and intensive Independent and depe Reversible and irreversible Calculus derivatives Quantities Mass Differential equations Temperature Exact and inexact Work Balance equations Kinetic energy Path dependence of ii Potential energy Table 2a. Generalizations I Spring 1993 oped. That is why there are so many textbooks. One extreme approach is to begin with axiomatics and mathematics, which then lead through formalisms to applications (the most elegant and difficult trea tise on this is by Truesdellt11). The other extreme is to note common observations, followed by generali zations and applications (Fenn has cleverly shown this technique with a cartoon character called "Charlie the Caveman"[21). Presentday students tend to be ics inexperienced in "the way things work," so I find that discussing ob servations first can be motiva na .. ................. tional, informative, and organiza tional. The flow diagram I gener f Work & Heat ally follow is shown in Figure 1. nns & Inequality te ............. The way basics are initiated is a Properties j through primitive concepts and ves as Properties natural phenomena, as listed in ....... Table 1. The key to the concepts is lar Properties a high level of precision that will ead easily to later mathematical erty Differences . rental Finite descriptions of the phenomena. ................These initial elements should ns / be phrased and illustrated in what .... ever terms that will make the Equation Solving properties Flow group of learners relate to them. alReactions Years ago, references to cars and Work Machine farming worked. Nowadays it needs to be connected to tele tion vision, sports, music, environ ment, and the materials and goods dynamics. of affluence. IOMENA The next step is generalizations s and constraints, beginning with Reactive definitions related to physics and conversion chemistry as well as to mathemat with regular ics. Table 2a shows the kinds of changes in things I define in familiar terms, form and amount in addition to the mathematical tools that must be used with facil ity in the study and implementa ics tion of thermodynamics. One point that I usually make is that we do nd variables not know what temperature (hot 1 variables indent variables ness) really iswe only know it ad integrals can make a difference to a system, although not always. This uncer differentials tainty of what a property "really integration is" often makes the later concep tual quantities of energy, entropy, and fugacity less threatening since KNOWLEDGE STRUCTURE something as familiar as temperature is really unknown yet easily utilized with experience. Another device I have used to deal with the unfamiliar prop erties is to read the story of 37 sugar cubes, a small boy, and his mother.[31 (Some students, however, find that these challenges make the whole pro cess even less appealing!) Table 2b lists a set of "convenient" observations, definitions and equations which encompasses the conservation of mass, the number of variables needed to completely describe a sys tem, the definition and conservation of energy, and the definition and gen eration of entropy. These particular choices are made because they lead di rectly to the most widely used state ments of the laws and open system results, even though at this stage only systems of fixed composition are dis cussed. The level and amount of time on this part depends on the students' prior exposureobviously, less is done with graduate students. Because the fundamentals given to this point are often alien and abstract, they are articulated further, as shown in Table 3. The objectives are under standings, procedures, and recognition that users must assimilate. It is es sential that learners understand at this point that people invented state prop erties and conceptuals for their gener ality and directness, even if they were not measurable like the things we pre fer to (and ultimately must) deal with. The next step separates chemical en gineers from the rest because the de velopment is extended to multicompo nent systems (see Tables 4a,b). This leads to a morass of definitions and complexities as the dimensionality of the system grows, and I know of no way to simplify this. By this time I have begun to insist that students have a notebook of definitions and I give the first part of each exam as a closed book set of definitions, asking both word and equation answers for the quantities previously defined. I also al ways use the symbol for the definitions to distinguish them from mere qualities. Particularly troublesome is fugacity. Students must recognize it is not a "corrected partial pressure"; it is a practical substitute for the chemical potential. Also, fugacity must be connected to temperature, pressure, and composition. The "Four Famous Fugacity Formulae" (FFFF) of Mike Abbott'41 (I use Five FFF) assures students that there are only a few options for every problem of phase and reaction equi libria. Also, they should be aware that it is now routine, though complicated, to connect complex composition behavior of activity co Convenient Observations Definitions Mass conserved (except in nuclear changes) # independent variables is # interactions Work depends on path except if no thermal interactions (Joule) Work and heat are not equivalent even in reversible changes Work can be degraded to heat, but not vice versa Objective Proper # variables for describing system Replace boundarycrossing quantities with changes of system state properties Conceptual properties and their "natural" variables Connections among properties via partial derivatives Partial derivatives as properties Property evaluation from integration of partial derivatives Atomic and molecular "weights" Heat, work, and material interactions Closed system AE WAdiabatic Q = AE W U = E EK EP Closed system dS 8QRev / T T is integrating factor (Born and Caratheodory) dSGen a dS 0 T Equations Mass balance MIn MOut = MAccumulated (#Ind) = (#Work) + (# Species) + 1 P = P(T,V,x) V' = V(T,P,N') = N'V(T,P,x) Energy balance Ein(Work,Heat,Material) EOut(Work,Heat,Material) = EAccumulated Closed system dE= TdS + WRev Entropy balance Sin(Heat,Material) SOut (Heat,Material)= SAccumulated Example Mechanisms and Equations Determine total # variables; Count # equations Difference is # independent variables = # dependent (solvedfor) variables is # equations dUSys = 8Surroundings + WSurroundings =dQRev +dWRev = TSysdSSys PSysdVSys HU+PV G=HTS dH=TdS+VdP dG= SdT+VdP Maxwell relations (S / ap), = (av / aT)p GibbsHelmholtz relations (G /T)/a(l/T)p= H T =_(aU / aS)V P = (au / aV)S Cp(T,P)=( QRev / dT)p = T(aS / aT)p = (aH / aT)p AH = f(aH/aT)pdT + f(aH/aP)TdP Path independent Path dependent Path dependent Table 3. Articulation Chemical Engineering Education Table 2b. Generalizations II KNOWLEDGE STRUCTURE Composition Variations Amounts or fractions of species affect system Nt =[N]t xi [x]i n variables n 1 variables Independent variables Extensive = n + 2 Intensive = n + I Mass fractions, volume fractions, molarity, molality, etc. Chemical potential gi(S,V,X) =aut /aNt St ,V t,Nj J*i Fluid Mixtures Gases Compressibility factor Residual properties Fugacity and fugacity coefficient dGi = RTd In fi (Fixed T) Condensed Phase Solutions Excess properties Reference fugacities and activity coefficients LewisRandall (LR) reference Henry's Law (HL) reference Famous Fugacity Formulae (FFF) Have P in various terms Use Poynting correction Connections of residual to excess properties Partial Molar Properties Fi F / N P F Ft/ T,P,Nt Fi= YxiFi GibbsDuhem equation shows how n+2 intensive variables (Fi,T, P) are related by one equation (aF /aT)p,x dT + (aF / aP)T, dP = xidFi to give n+l independent variables Partial Molar Gibbs Energy GiaGtc'/aNI =gi(T,P,x) TPNji Nonidealities and Idealities PV = zNtRT lim z= IG FR F FIG fi xiiP lim G i = 1 IG Real z, i from EOS F(T,P,x) xiFio(T,P)+FE (T,P,x) Ideal Solution FE = 0 fi (T,P,x) = xiifo Ideal Solution Yi =1 fio pure i lim yil xi*l fi=Hi lim i=l1 xi>0 #2 fi(T,P,x)=xiYi(T,P,x)fi(T,P) #3fi(T,P,x)=xiYi(T,P,x)fio(T)exp[J( Vo/ RT)dP] #4i(T,P,x)= i(Txxii(Tx)fi(T)exp[(Vi /RT)dP] #5 fi(T,P,x)=xiYi(T,P,x)f(T) FFF#2 f(T,P)= ?(T,P)P Yi (T,P,x) = i (T,P,x) / (T, P) Table 4b. Multicomponent systems II efficient to parameter mixing rules for PVTx equations of state (e.g., Heidemann and Kokals51). By this point in the course, there has been a tremendous amount of abstractness and it is time to get to applications which can be addressed via change and equilibrium, as shown in Tables 5a and 5b. This is where the generalizations can be made real with characterizations of driving forces and entropy genera tion in interesting systems under going change as well as in equilib rium (and metastable!) cases. A key is to make sure students overcome the myth about entropy always be ing maximized. The next section (Table 6) shows the sets of relations that apply to phase and reaction equilibria as well as some of the physics of what Na ture can do when it settles down. I use many plots of different variables for different kinds of substances and mixtures. The message is that "Na ture does all things easily; ain't Na ture grand!" I also insist that stu dents recognize that "for every equa tion there is a graph, and for every graph there is an equation." If they are not sure of what an equation re ally means, they should draw its graph and vice versa. At this point, the fundamentals are done. It's time to use thermodynam ics. Table 7 shows the elemental methodology. The ultimate goal is a quantitative result that is reliable Change Driving forces for change Heat flows from high to low temperature Work flows from high to low "force" (e.g., PV work from high to low P) Material diffuses from high to low chemical potential fugacityy) Reversible changes Equilibrium changes (S,. =_ 0) Only differential differences in T, P, Gi Spontaneous changes Real changes (Se. > 0) Finite differences in T, P, Gi SG. increases with property difference Greatest for heat flow with T difference Table 5a. Change Spring 1993 Criteria for StabilityWhat is Observed Systems Only in isolated systems is entropy maximized All othersminimization of an energy function e.g., Minimum G if T,P fixed while varying x, phase, reaction (Entropy not minimized for ambient 2liquid oil/water!) Phases Differential criteria Pure fluidsProposed phase unstable if (aP / aV)T > 0 MixturesProposed phase unstable if stability matrix of aGi /IN T,,N t not positive definite J * SMetastability satisfies differential but not global criteria Can occur in solids, microstructured fluids (polymer, bio, surfactant, colloid) Table 5b. Equilibrium Table 4a. Multicomponent systems I I KAlflWI FflIE RTRIJCTURE and appropriately accurate for the case at hand. This requires organization of thermodynamic knowledge and introduc tion of models at the proper stage. Since with models "where there's a way, there's a will," the latter requires decisions. While students feel unprepared and/or unmotivated to choose among the myriad of options, "life's like that," so the practice is good. Modeling consists of a math ematical relation used to connect certain properties to measurables that will allow calculation of values for unknown measureables. Generalized thermo dynamic models contain parameters that depend on the substances) of interest. The kinds of choices are suggested in Table 7. Teachers must make sure that students are given the tools to make these deci sions, including the common choices and the usual rules of thumb. The final requirement is to solve a set of nonlinear algebraic equations. With cur rent computers and model software, stu dents can now solve numerically more "re alistic" problems, though the "black box syndrome" can arise if the only student input consists of numbers and "run." PEDAGOGY This process can be formalized in differ ent ways; I prefer the concept of problem solving.[6' Table 8 shows a method devel oped with Jim Haile (Clemson University) called "PSALMS". It is a stepbystep tech nique that works well for typical chemical engineering thermodynamic problems. The two initial steps of "Problem" and "Sys tem" are the same as in essentially all "PS" methodologies. The next uses the power of thermodynamics that declares cer tain relations to be "ALways true" so us ers can initiate something valid and rel evant rather than stare at a blank piece of paper or make an assumption too early. The fourth step of "Model" is an essential part of contemporary thermodynamics (the table suggests some of the choices to be made). The final step is "Solve and check," which is again a part of all PS methods. By now this article has either lulled you to sleep because all of this seems so straightforward, or made you extremely 100 Phase Equilibrium Relations Chemical Potentials gi(T,P,x)=ii (T,P,x")=... Fugacities fi (T, P,x')= fi(T,P,x")... Reaction Equilibrium Relations Minimum Gibbs Energy SvikGi =0 (Independent Reactions k) Equilibrium Constant and Standard State (o) Kk(T)= exp vikG? / RT = exp vikAGO /RT = [xiii(T,P,x)P] k (FFF#1) Ref.()is pure IG at P=1 = I[fi(T,P,x)/fo(T) ik (FFF#35) Ref.(o) is pure real (LR) or hypothetical (HL) substance Phase Diagrams Pure P T 2phase boundaries (S/V, L/V, S/L, S/S) Fixed points (V/L, L/L critical; triple points) Mixed multiphase systems PTxy (multidimensional and projections) Azeotropes, critical, 3 and 4phases Enthalpies ("Heats") of Vaporizing, Melting, Subliming Related to P T 2phase lines by Clapeyron equation d i(PS) (H"H') d(/T) R  d T) 2phase R z ' Clausius approximation for gases (") and liquids/solids (') z =l>>z Table 6. Phases and reactions Organization of Information Models and Data Mathematical relations for PROPERTIES (z, C GE, ) in terms of MEASURABLES (T, P, x, V) for manipulation to get ALL properties (e.g., conceptuals) (H, S, fi, etc.) needed for SOLVING EQUATIONS for dependents (x, P, T, V, W, Q, etc) containing PARAMETERS depending on molecular constitution COMMON EXPRESSIONS requiring decisions PVTx equations of state GE = activity coefficients Reference fugacities, f9 Mixing rules for pseudopure parameters of mixtures Combining rules for unlike parameters from likes (often via kij) Solve Nonlinear Algebraic Equations for Intensive variables (T, P, x, etc.) in phases Material flows (flash, etc.) Phase existence and amounts Table 7. Methods Chemical Engineering Education I\ I Q I EDGE STRUCTURE   KNOWLEDGE STRUCTURE agitated because of how unrealistic it might seem to be. Cer tainly, it's not easybut much of it is possible to achieve. PSALMS Problem Desired quantity, other variables System Physical and chemical situation Contents and constraints Boundaries, work modes, species Total variables, specified variables ALways True Relevant generalized relations for specified system Balances on mass, energy, entropy Property differences Fugacity, reaction equilibrium constant equations Model Approximations to generalized relations Choice of Famous Fugacity Formula If FFF #1, EOS Type Ideal, Virial, CSP, "Full"; P or V Independent If FFF #25, Reference State, Pressure Effect Specific choices, e.g., CSP parameterization; Cubic EOS; fo values; GE correlation, group contribution method Data (new or literature) Solve and check Analytic, graphical, tabular, numerical Table 8. A thermodynamics problemsolving strategy. The Dilemmas of Beginners There's a lot of material! I've never done deduction before! It's mostly abstract. It's incredibly detailed! It's a long way before real applications appear! If I get started wrong, it takes a lot of work to get to the answer! Table 9. How students respond to thermodynamics. Suggestions to Keep Students Focussed Stress procedure more than results, particularly in the beginning. "Any fool, even a computer, can do a calculation." Articulate that the goal is to quantitatively describe the richness of nature. "Nature does all things and without any difficulty." Emphasize exponential pattern of learning the subject. "Hang in there. When things begin to click, you take off The question is whether the end of the term happens first." Connect equations to observable phenomena and pictures (graphs). Student inexperience with natural behavior is pervasive and growing. Insist upon precision of expression and thought, especially definitions. "You gotta know what you're talking about!" Minimize "understanding" and maximize "doing." "I don't know what entropy andfugacity are, but I can tell you when to use them and how they go." Give practice problems involving only the setup steps (PSAL) of problem solving. Assist students to develop their own PS style. Have students read and report on the literature of physical properties. "Hey guys! They actually use fugacity out there!" Have students code a VLE program for real substances: Forces decisionmaking and precision. "Computers are unforgiving; they do all and only what they're told." Undergraduates hard to teach fundamentals to; are not used to deduction, precision. They want to "do" something immediately. Hard to get graduates to unlearn old errors; they are reluctant to change old ways. "They got me a B+!" Table 10. Suggestions to keep students focused. Spring 1993 Table 9 shows how I think the beginner in this subject reacts. Of course, selfrecogni tion is vital to making progress, so I confront students with this soon after I begin to get the "glazedeyes syndrome" somewhere in the multicomponent section. I also tell them that I only became fully comfortable with thermo dynamics after the third time I taught it. But that does not mean they can cop outit merely declares that progress is tough. Finally, I have given in Table 10 a list of some suggestions that seem to help keep us on track. They are phrased as admonitions, followed by salient quotes from instructors and students. My success as a teacher has fluctuated with the class, my own distractions, the ions in the air, and who knows what else. But it has been tremendously satisfying when things have clicked with students (the number in class ranging from one to nearly all). Inter estingly, I think there is less a correlation with intelligence than with commitment, at tentiveness, and willingness to move ahead without being completely satisfied. ACKNOWLEDGMENTS In addition to those already mentioned, many other stimulating individuals have in fluenced my pedagogy in thermodynamics. They principally include Martin Fuller (Pomona College), Bob Reid (MIT), John Prausnitz (CalBerkeley), Tim Reed (Florida), Grant Wilson (Wiltec), Aage Fredenslund and Peter Rasmussen (DTH, Lyngby, Denmark), Anneke Sengers (NIST), Ed Glandt (Penn), and Herb Cabezas (Arizona). Also, Warren K. Lewis (MIT), John Biery (Florida), and Verna O'Connell (wherever I am) have been tremendous inspirations. REFERENCES 1. Truesdell, C., Rational Thermodynamics: A Course of Lectures on Selected Topics, McGrawHill, New York (1969) 2. Fenn, J.B., Engines, Energy and Entropy, W. H. Freeman, New York (1982) 3. Van Ness, H.C., Understanding Thermodynamics, Chap. 1, McGrawHill, New York (1969) 4. Abbott, M.M., personal communication, Rensselaer Polytechnic Institute, Troy, New York (1978) 5. Heidemann, R.A., and S.L. Kokal, "Combined Ex cess Free Energy Models and Equations of State," Fluid Phase Equil., 56, 17 (1990) 6. Woods, D.R., ed., P.S. News, McMaster Univer sity, Hamilton, Ontario, Canada I KNOWLEDGE STRUCTURE THE BASIC CONCEPTS IN TRANSPORT PHENOMENA R. BYRON BIRD University of WisconsinMadison Madison, WI537061691 he transport phenomena can be described at three scales: the molecular, the microscopic (continuum), and the macroscopic. At each scale the conservation laws for mass, momentum, angular momentum, and energy play a key role. Also, at each scale empiricisms have to be intro duced to complete the description of the systems: an intermolecular potential expression at the molecu lar scale, the flux expressions (constitutive equa tions) at the microscopic scale, and the transfer co efficient correlations at the macroscopic scale. The three scales are intimately connected, with the re sults for each scale contributing to the understand TABLE 1 The Equations of Change Based on Conservation Laws (A) pa = (V pav)(V ja)+ra a = 1,2,3... (B) pv = [V pvv] [V ]+ paga aat (C) p p[rx v] + )= V pv([rx v]+ [V ] V. rx w'} + [rx pga] +XPata T a a (D) tp (1v2 + =(V.v[v2 + ) (V q) (V [. v]) ((pav +ja) ga) a p. = mass concentration of species a p = density of fluid mixture v = massaverage velocity j = mass flux of a with respect to v r = mass rate of production of a by chemical reaction zT = (total) stress tensor g. = external force per unit mass acting on a r = position vector L = internal angular momentum per unit mass X = couple stress tensor t = external torque per unit mass acting on a U = internal energy per unit mass q = heat flux vector ing of the next larger scale. At the microscopic scale, some information about the constitutive equations can be obtained from the thermodynamics of irreversible processes. This ap proach is particularly important in understanding multicomponent diffusion and the "crosseffects" in energy and mass transport. For the most part, the notation and sign conven tions here will be those used in references 1, 2, 3, 4, and 5, hereinafter referred to as TrPh, DPL1, DPL2, STTP, and MTGL, respectively. The Equations of Change The basic equations of transport phenomena are the equations of change for the conserved quantities as shown in Table 1: (A) Conservation of mass for each species TrPh Eq. 18.34; MTGL 11.11 (B) Conservation of momentum TrPh Eq. 18.32; MTGL 11.13; DPL1, 1.18 (C) Conservation of angular momentum MTGL, p. 831, Problem 6 (D) Conservation of energy TrPh Eq. 18.36; MTGL 11.14;DPL1, 1.112 These equations can be obtained by writing conser vation statements over (a) a region fixed in space through which the fluid is moving (DPL1, Chapter 1) (b) a material element of fluid (i.e., a "dyed" blob of fluid) moving through space.[61 "Bob" Bird retired in 1992 after forty years of teachingone year at Cornell and thirtynine years at Wisconsin. The book Transport Phe nomena, which he wrote with colleagues Warren Stewart and Ed Lightfoot, was the first textbook on the subject specifically prepared for under graduate chemical engineering students. He also coauthored Dynamics of Polymeric Liquids, with Bob Armstrong (MIT), Ole Hassager (DTH), and Chuck Curtiss (UW). Chemical Engineering Education KNO WLEDGE STRUCTURE The equations of change have been written in Table 1 in terms of the total stress tensor t which is conventionally split into two parts: i = p5 + T (where 8 is the unit tensor); p is the "thermody namic pressure"; and T is the "(extra) stress tensor" which vanishes in the absence of velocity gradients. No assumption has been made here that the stress tensor be symmetric. Equations (A) through (D) have to be supplemented with the thermal equa tion of state p = p(p,T,o,) and the caloric equation of state U = U(p,T,o,)), where o. stands for the mass fractions of all but one of the chemical species a in the mixture. By adding the equations in Eq. (A) over all spe cies, one gets the equation of continuity for the fluid mixture (TrPh, Eq. 3.14]. By forming the cross prod uct of the position vector r with the equation of motion, Eq. (B), one obtains Eq. (E); when the latter is subtracted from Eq. (C) (the equation of conserva tion of total angular momentum), the equation for internal angular momentum, Eq. (F), is obtained. 71 Similarly, by forming the dot product of the fluid velocity v with the equation of motion, Eq. (B), one obtains Eq. (G), the equation of change for the ki netic energy; when the latter is subtracted from Eq. (D), the equation of change for the internal energy, Eq. (H), is obtained. These various derived equa tions are tabulated in Table 2. As pointed out in TrPh (page 314), the term (nT:Vv) appears in Eq. (G) with a plus sign and in Eq. (H) with a minus sign; it describes the interconversion of mechanical and thermal energy. Similarly, the term [e:'T] appears with a plus sign in Eq. (E) and with a minus sign in Eq. (F), thus TABLE 2 Equations of Change for Nonconserved Quantities (E) p[rxv]=[V.pv[rxv]] V. rxnrTT] + [rxpag ]+ [e:rrT] a (F) pL= VpvLp[Vk]] [ pt _e:,] (G) 2 v(2)) ) a +(,T:v)((V.paga) (H) apt=(v pvt)(Vq) ( T:vv)+^(v.pag a) a NOTE: On page 831 of MTGL, Eq. (E) is given for a symmetric stress tensor, but [r x p] should be re placed by [r x p]T. Spring 1993 describing the interconversion of external and inter nal angular momentum. In fluid dynamics textbooks, it is usually assumed that the stress tensor is sym metric (i = eT), so that the external and internal angular momentum are conserved separately, since [E:'T] is then identically equal to zero. The socalled "proofs" that the stress tensor is symmetric (such as in Problem 3.L in TrPh, pages 114115) tacitly as sume that there is no interconversion of external and internal angular momentum, and that the ex ternal angular momentum is conserved in the fluid. The kinetic theory of dilute monatomic gases yields a symmetric stress tensor, as does the kinetic theory for dilute solutions of flexible and rodlike polymers. So far there is no experimental evidence that a nonsymmetric stress tensor is needed. When all species are subjected to the same exter nal forces (so that all gn equal g), and when it is assumed that the stress tensor is symmetric, Eqs. (B) and (D) simplify to Eqs. 3.28 and 10.19 in TrPh. If all species are subjected to the same exter nal torques so that all t, are equal to t, a similar simplification occurs in Eq. (C). We emphasize that the equations in Table 1 are to be considered the fundamental equations at the mi croscopic scale, whereas those in Table 2 are de rived from those in Table 1. As explained in TrPh, the equations of change may be put into many alter native forms; for example, they may equally well be written in terms of the "substantial" (or "material") derivative operator D/Dt (TrPh Eq. 3.02). The en ergy equation has always been a special problem because it can be written in so many different ways (see TrPh, pages 322323, 582, for useful tabular summaries). The Flux Expressions (Also Called "Constitutive Equations") In order to get solutions to the equations of change, we need to have expressions for the fluxes j, T, and q. The standard expressions for these are the "lin ear laws," in which the fluxes are proportional to gradients, as shown in Table 3. Equation (I) for the massflux vector is shown only for the binary system AB, and the thermal diffu sion, pressure diffusion, and forced diffusion terms have been omitted (see Eq. (Z) for the complete ex pression). Equation (K) shows the conductive and diffusive contributions to the heatflux vector, but the diffusionthermo (Dufour) effect has been omit ted. In Eq. (J) we have included the two viscosity coefficients I and K, although the latter is omitted in most fluid dynamics texts since it is zero for mona 103 KNOWLEDGE STRUCTURE KIfTJL4I FflIF STRIIC~TIJRE tomic gases (we know this from kinetic theorysee MTGL, Chapter 7) and since for liquids incompress ibility is often assumed, so that div v = 0 and the term containing K is zero anyway. The flux expressions do not have the exalted sta tus accorded to the conservation laws in Table 1. They are empirical statements, proposed as the sim plest possible linear forms; they also emerge from the kinetic theory of gases when one works to the lowest orders in the gradients of concentration, ve locity, and temperature (see MTGL, Chapter 7). It is well known that Eq. (J) does not describe the me chanical responses of polymeric liquids (see DPL1, Chapter 2); various nonlinear expressions, and in deed timedependent expressions, arise from the ki netic theory of polymeric liquids (see DPL2, Chap ters 1316, 1920). Furthermore, for some complex materials it is found that the thermal conductivity and diffusivity are tensors rather than scalars, so that the fluxes and forces are not collinear. In order to use Eqs. (I,J,K), one needs numerical values for the diffusivity, viscosity, and thermal conductivity; these are preferably obtained from experiments, but in the absence of experimental values kinetic theory results can be used. Once the flux expressions have been substituted into the equations of change, we then have a set of equations which, when solved, will give the concen tration, velocity, and temperature distributions as functions of time. There are many ways in which these important equations can be used: Analytical solutions can be found (for simple, ideal ized problems, in which transport properties are assumed to be constant)[''10 Approximate solutions can be found with perturba tion theories1'l Numerical solutions can be foundl12"15 Boundarylayer solutions can be found116 Time smoothing can yield the turbulent transport equations"17"9] Volume smoothing leads to the equations for po rous media'20' Flows with chemical reactions can be analyzedt211 Approximate solutions can be used for lubrication flows['1 Mixing and chaos can be studied1221 Particulate motion, suspensions, and emulsions can be described121 Interfacial transport equations can be established123' Polymer fluid dynamics and transport phenomena can be studied[DPL"1 This partial list of topics gives some idea as to the breadth of the field of transport phenomena and the extremely great importance of the equations of change. All these topics are active research fields in which chemical engineers are obligated to play an important role. The Macroscopic Balances The statements of the laws of conservation of mass, momentum, angular momentum, and energy can be written down for a typical macroscopic engineering system, with one entry port ("1") and one exit port ("2"); heat can be added to the system at the rate Q, and the system can do work on the surroundings at a rate Wm by means of moving parts (such as pistons or rotatory devices). These conservation statements are given in Eqs. (LO) in Table 4. It is assumed there that the fluid velocities at the inlet and outlet planes are parallel to the directions of flow n, and n2. It is also assumed that the extra stress tensor does not contribute to the work done on the system at the entry and exit planes. It is further assumed that there are no masstransfer surfaces in the mac roscopic system; such surfaces are considered in TrPh, Chapter 22, and in STTP, Chapter 1. Of course, Eqs. (LO) can also be obtained by inte grating the equations of change in Eqs. (A,B,E,D) over the entire volume of the flow system; in doing this we must take into account the fact that the shape of the volume is changing with time because of the moving parts.[24,25] The macroscopic mechani cal energy balance (also called the engineering Ber noulli equation) cannot be written down directly since there is no conservation law for mechanical energy. It can be derived by integrating Eq. (G) over the macroscopic system as outlined in Table 5. For the sake of simplicity, we take the external forces go to be all the same (g = 6, where D is the potential TABLE 3 The Flux Equations (or "Constitutive Equations") (I) JA =PDABVoA (binary system of A and B) (J) T = VV+(VV)T) + V)a (K) q=kVT +(H, /Ma)ja DA = binary diffusivity oA = pA/p = mass fraction of a p = viscosity K = dilatational viscosity 8 = unit tensor (with components 5.) k = thermal conductivity Ha = partial molar enthalpy of a Chemical Engineering Education KA1W1 )Df STRCTUR KNOWLEDGE STRUCTURE TABLE 4 Macroscopic Balances Assumptions: no masstransfer surfaces; all species subject to same external forces and external torques; 7r contributions neglected at "1" and "2" (L) mtot =walWa2 +ra,tot (M) Ptot 2 wi+PiSij wni ( 2 2+P2S2 2 F+mtotg (M) tPtot= I f2 (N) Mtot= )1 w+plS1 [rlxni] w2+P2S2 [r2xn2]T+[rcxmtotg] dt (vl M2 ()3 1 ____3) P (0) (Ktot+ tot+Uto 2t) (V +il+1 W 2 +2 W2 2+QWm (Q v3) 1 1 3 2 M2 (P) d(Ktot + _tot)= +1+ wl 21 v 2 + 2 EcEv Wm ()2 (v)d 1w 2 M P2 (Q) dUtot=UilwlU2W2+Q+Ec+Ev dt mt = total mass in flow system Pt = total momentum in flow system Mt = total angular momentum in flow system Ktot= total kinetic energy in flow system tot = total potential energy in flow system Utt = total internal energy in flow system () = averages over tube cross section at entry and exit n,n2 = unit vector in flow direction at entry and exit w l,w = mass rate of flow of a at entry and exit w,, w2 = mass rate of flow at entry and exit pl, p2 = thermodynamic pressure at entry and exit S,, S2 = crosssectional areas of entry and exit conduits Q = heat added to system through container walls Wm = work done on surroundings E,, Ev = quantities defined in Eq. (S) rl,r2,r = location of the centers of the entry and exit planes and the center of mass of the fluid in the system energy per unit mass, which is considered to be independent of time). In doing the integration, we need to use the Gauss di vergence theorem (TrPh, A.51) and the 3dimen sional Leibniz formula (TrPh, A.55). This leads to Eq. (R), in which S, and S2 are the crosssectional areas at "1" and "2", Sf stands for the fixed surfaces of the system, and Sm stands for the moving surfaces, by means of which work can be done on the surround ings. Since the velocity v of the fluid equals the sur face velocity vs on the fixed and moving sur faces, these surface inte grals contribute nothing to the first term on the right side. Also, since the fluid velocity v is zero on all fixed surfaces, the fixedsurface contribution to the second term on the right side is zero; the in tegral over the moving surfaces gives the work transmitted via these sur faces, Wm, (sometimes called the "shaft work"). The integrals of the extra TABLE 5 Intermediate Steps in Deriving the Macroscopic Mechanical Energy Balance (R) A J (lpv2+p )dV=_J(n.(pv2+p()(v vs))dSJ(n.[(p6 +T)v])dSEcEv V(t) S=S,+S,+s+S,(t) S=S,+S,+S,+S,(t) (S) inwhich Ec= fp(V.v)dV and E = J(Tr:Vv)dV V(t) V(t) (T) t (Ktot+(Dtot)= P 3l(v13S1lp2 v3 2S2+Pl(vl(1SI p2(v)2 2S2+Pl(V)lS1p2(v)2S2EcEvWm V(t) = volume of engineering flow system S, = fixed surfaces of flow system Sm = moving surfaces of flow system v. = velocity of surface (equals zero on S,,S,,S,) 6 = potential energy per unit mass n = outwardly directed unit normal on surface S 7 = (extra) stress tensor Spring 1993 10O KNOWLEDGE STRUCTURE stress tensor T over S, and S2 are presumed small and have been omitted here; they are identically zero for laminar, Newtonian flow when the fluid velocity vectors are parallel to the walls of the entry and exit tubes. The inte grals labeled E, and E, are not evaluated; the latter gives the rate at which mechanical en ergy is degraded into thermal energy. From Eqs. (R) and (S) we get Eq. (T), which is easily rearranged to give the mechanical energy bal ance in Eq. (P); the latter includes the two special cases given in TrPh Eqs. 15.21 and 2. Equation (P) is particularly convenient for in compressible fluids for which E, is exactly zero. Equations (L)(P) are easily generalized to sys tems with multiple inlet and outlet ports. NOTE: In some textbooks it is stated that the mechanical energy balance (Eq. P) is an "alternative form" of the total energy balance (Eq. O). Such a comment seems inappropriate since Eq. (P) comes from the equation of con servation of momentum, whereas Eq. (0) has its origins in the equation of conservation of energy. In other textbooks some thermody namic "incantations" are offered to get from Eq. (0) to Eq. (P). The arguments must essen tially involve Eq. (Q), obtained by subtracting Eq. (P) from Eq. (0); of course, Eq. (Q) can also be obtained from integrating Eq. (H)which is a consequence of the equations of energy and motionover the macroscopic flow sys tem. Certainly Eq. (Q) cannot be written down directly, since there is no conservation law for the internal energy in an open system with dissipative processes. Furthermore, the ther modynamic arguments cannot yield the expres sions in Eq. (S), showing how E, and E, are related to the velocities and stresses in the system. Comments from textbook authors (and others) on this point would be welcome; before commenting, however, it would be advisable to read Whitaker's historical essay.[6, pp 90931 The Transfer Coefficients Although the macroscopic balances can be used, as shown in Table 4, it is often useful to estimate some of the terms in them by using dimensionless correlations: F can be estimated by using friction factor correlations E, can be estimated by using friction loss factor correlations Q can be estimated by using heattransfer coefficient correlations wa m can be estimated by using masstransfer coefficient correlations These quantities are given in the form of dimensionless correlations based on large amounts of experimental data; they contain the transport properties and the density and the heat capacity, as well as quantities describing the char acteristic length, velocity, temperature, etc. For steadystate systems, the macroscopic balances form a set of algebraic relations; for unsteadysystems they become a set of differential equations, with time as the independent variable. The macroscopic balances are the starting point for calculations involving heat exchangers, separations equip ment, chemical reactors, and fluidshandling systems. The Three Levels of Transport Phenomena For many engineering applications, one starts with the macroscopic balances in order to understand the overall behavior of the system. One can often estimate some of the quantities in the balances by using transfer coefficient correlations, photographic or other visualization methods, direct pressure, temperature, and density measurements on the system, etc. Other quantities may be assigned by crude methods. In other problems, one needs to know more about the de tails of the pressure, velocity, temperature, and concentra tion distributions within the system. This calls for "moving down" one level (see Table 6) and solving the equations of change. Many analytical solutions are available, but there are also modern computing techniques if numerical solu tions are needed (usually the case if pressure, temperature, TABLE 6 The Three "Levels" of Transport Phenomena Basic Empirical Equations Expressions Results Macroscopic Dimensionless Solve to get Balances over correlations relations among b engineering f, h, k,, inlet, outlet, and system and e, transfer quantities S J T dimensional analysis S Equations of Flux Solve to get 8' change for + expressions concentration, o 0 conserved for pressure, velocity, S quantities j,, T, q and temperature a Equation for Intermolecular Solve to get dg time evolution + force D^, Ki, and S of phasespace expression kT in the flux distribution function expressions Chemical Engineering Education KNOWLEDGE STRUCTURE and concentration dependence of the physical prop erties have to be taken into account). Dimensional analysis of the equations of change suggests the form that the transportcoefficient correlations should take, these being needed for the macroscopic balances. It should be recognized that there is still one scale smaller than the macroscopic and microscopic scales, namely the molecular scale. Although this part of the subject normally lies in the domain of the theo retical physicist or the theoretical chemist, engineers occasionally need some familiarity with the molecu lar aspects of transport phenomena. The basic equa tion at the molecular level is an equation for the time evolution of a phasespace distribution func tion. One example of this is the Boltzmann equation for dilute gases (MTGL, Chapter 7), and additional examples may be found for dilute polymer solutions and polymer melts in DPL2, Chapters 1719. From the differential equation for the phasespace distribution function, one can obtain a "general equa tion of change," special cases of which are the usual equations of change in Table 1; in developing these equations, one makes use of the fundamental con r Spring 1993 servation laws as applied to molecular collisions. As a byproduct of this derivation, formal expressions are obtained for the fluxes in terms of the distribu tion function. In this way expressions are obtained for the transport properties in terms of molecular models. Recently there has been an interesting develop ment in connection with the kinetic theory of dilute gases and the Boltzmann equation. This famous equation, although over one hundred years old, has been found to be in error in that it cannot be ob tained by starting with the quantum Boltzmann equation and letting Planck's constant vanish.26" The new "BoltzmannCurtiss equation" does not suffer from this defect since it accounts properly for the contributions associated with bound pairs of mol ecules; the added terms in the equation are appar ently important at low temperatures; as a result the table in TrPh, page 746, will have to be modified. It is seen in Table 5 that at each of the three scales, use is made of the basic conservation laws. Also, at each scale some kind of empiricism is intro duced. Each scale can be better understood by going to the next smaller scale in order better to appreci ate the origins of the equations Thermodynamics of Irrevers ible Processes If into Eq. (H), the equation of change for the internal en ergy, we insert the thermody namic relation Eq. (U) (see Table 7) for a binary mixture, we get (after using the equa tion of continuity) the result in Eq. (V)an equation of change for the entropy. In this equation we can identify an entropy flux s as the sum of two contributions, one associ ated with heat conduction and one with diffusion; we can also identify a rate of entropy pro duction o, which is given as a sum of terms, each of which is the product of a flux and a force. Then, according to the ther modynamics of irreversible processes, every flux will de pend linearly on each of the 107 TABLE 7 Thermodynamics of Irreversible Processes (Binary Systems) (U) dJU=TdSpd(1/p)+ AdOA (V) pS=(v.pvS)(V.s)+o at in which s=l(qIjA) c =((q jA) 1VT)'(jA (V + (gB gA))) rAr (T: Vv) ( ) JA =11 vA+(BgA)) a12 V (X) qRJA=a21(Va +(gBgA))a22VT 2 T2 (Y) q= a12 A 22 1 VT=HA HB kVT (Z) jA =PAB(VOA +kTVinT+kpVenp)+kF(gBgA) S = entropy per unit mass A = (GA/MA)(GB/MB) s = entropy flux a = rate of entropy production a. = phenomenological coefficients q = Dufour effect contribution to heat flux kT = thermal diffusion coefficient k = pressure diffusion coefficient kl = forced diffusion coefficient and their limitat s. KNOWLEDGE STRUCTURE forces, with the restriction that fluxes must depend on forces of the same tensorial order, or with order differing by 2 (Curie's law). There is also the restric tion that the matrix of coefficients in the fluxforce relations be symmetric (OnsagerCasimir reciprocal relations). This leads us to Eqs. (W) and (X), in which a12 = a21. Then combination of Eqs. (W) and (X) gives Eq. (Y) for the heat flux vector. In this equation, the coefficient of VT can be identified as the thermal conductivity for the mixture. The other term in Eq. (Y) leads to the second term on the right side of Eq. (K), the diffusion term, plus one addi tional very small term associated with the Dufour effect. The term involving Vj in Eq. (W) can be expanded by using the chain rule of partial differentiation V= = (D / 3COA)Vw(A + ( 1/ T)VT + (/ / ap)Vp The term in VT combines with the other VT term in Eq. (W), and the final result is Eq. (Z); in this equa tion the coefficients kp and kF are completely deter mined from the thermodynamic properties of the mixture, whereas the diffusivity DA and kw are two phenomenological coefficients that have to be deter mined experimentally for each gas pair or estimated by kinetic theory. As a result of the Onsager rela tions, the four phenomenological coefficients in Eqs. (W) and (X) have been reduced to the three trans port properties: diffusivity, thermal diffusion ratio, and thermal conductivity. Equation (Z) shows clearly that a mass flux of species "A" can result from a concentration gradient (ordinary diffusion), a temperature gradient (ther mal diffusion), a pressure gradient (pressure diffu sion), and a difference of external forces (forced dif fusion) (TrPh, Chapter 18 and MTGL, Chapter 11). A concise introduction to the thermodynamics of ir reversible processes has been given by Landau and Lifshitz;'27' a more thorough discussion can be found in the classic text by de Groot and Mazur.1281 The thermodynamics of irreversible processes has been found to be particularly useful in the systematiza tion of the flux expressions for multicomponent dif fusion as well as in linear viscoelasticity.[291 Although this topic is not essential for undergraduate stu dents, perhaps graduate students can benefit from the extra insight provided by the thermodynamic approach. CONCLUDING COMMENTS It is essential that students of transport phenom ena recognize the central position occupied by the conservation statements. The conservation laws for 108 mass, momentum, and energy applied to a large engineering system through which a fluid is flowing lead to the macroscopic balances; the two additional balances for angular momentum and mechanical en ergy can be obtained from the integration of mo ments of the equation of motion. The utility of the balances is enhanced by the use of empirical corre lations for the transfer coefficients. The five macro scopic balances are the starting point for many analy ses of unit operations and chemical reactors. They are invaluable for making orderofmagnitude esti mates for engineering systems. The conservation laws, when applied to a small region of space through which a fluid is flowing, lead to the equations of continuity, motion, and en ergy; the assumption of the symmetry of the stress tensor is usually made, and this assumption makes it unnecessary to deal with the interconversion of external and internal angular momentum. The flux expressions usually used in the equations of change are the simplest possible relations that are linear in the gradients. The vast literature dealing with solu tions of the equations of change should be familiar to engineers, even though these solutions are for idealized systems; they are, however, very useful for making orderofmagnitude estimates and for check ing the computer programs used for obtaining nu merical solutions. The conservation laws applied at the molecular scale are used in kinetic theory developments. Ki netic theory provides expressions for the transport properties in terms of intermolecular forces; these expressions are highly developed for dilute mona tomic gases. In the last several decades the kinetic theory of polymers has developed rapidly, so that much more is now known about the transport prop erties of polymeric liquids.'301 The subject of transport phenomena can be useful in many fields, including micrometeorology, zool ogy, analytical chemistry, nuclear engineering, tri bology, metallurgy, biomedical engineering, phar macology, and space science. Chemical engineering departments are in a good position to provide gen eral service courses in transport phenomena for other department on campus. ACKNOWLEDGMENTS The author wishes to thank Professors W.E. Stewart and T. W. Root, and Mr. Peyman Pakdel of the Department of Chemical Engineering at the Uni versity of Wisconsin, and Professor J.D. Schieber at the University of Houston for valuable suggestions. Chemical Engineering Education KNOWLEDGE STRUCTURE ~~` REFERENCES 1. Bird, R.B., W.E. Stewart, and E.N. Lightfoot, Transport Phenomena, Wiley, New York (1960) 2. Bird, R.B., R.C. Armstrong, and 0. Hassager, Dynamics of Polymeric Liquids. Vol. 1: Fluid Mechanics, 2nd ed., Wiley, New York (1987) 3. Bird, R.B., C.F. Curtiss, R.C. Armstrong, and 0. Hassager, Dynamics of Polymeric Liquids. Vol. 2: Kinetic Theory, 2nd ed., Wiley, New York (1987) 4. Bird, R.B., W.E. Stewart, and E.N. Lightfoot, Selected Top ics in Transport Phenomena, Chem. Eng. Prog. Symp. Se ries No. 58, Vol. 61, AIChE (1965) 5. Hirschfelder, J.O., C.F. Curtiss, and R.B. Bird, Molecular Theory of Gases and Liquids, Corrected Printing with Added Notes, Wiley, New York (1964) 6. Whitaker, S., in One Hundred Years of Chemical Engineer ing, ed. N.A. Peppas, Kluwer Academic Publ., Dordrecht, pp. 47109 (1989) 7. Dahler, J.S., and L.E. Scriven, Nature, 192,3637 (1961) 8. Berker, R., "Integration des equations du movement d'un fluide visqueux incompressible," in Enyclopedia of Physics, ed. S. Fliigge, Springer, Berlin, pp. 1384 (1968) 9. Carslaw, H.S., and J.C. Jaeger, Heat Conduction in Solids, 2nd ed., Oxford University Press (1959) 10. Crank, J., The Mathematics of Diffusion, Oxford University Press (1956) 11. Leal, L.G., Laminar Flow and Convective Transport Pro cesses: Scaling Principles and Asymptotic Analysis, ButterworthHeinemann, Boston (1992) 12. Kim. S., and S.J. Karrila, Microhydrodynamics: Principles and Selected Applications, ButterworthHeinemann, Bos ton (1991) KNOWLEDGE STRUCTURE 13. Finlayson, B.A., The Method of Weighted Residuals and Variational Principles, Academic Press, New York (1972) 14. Finlayson, B.A., Nonlinear Analysis in Chemical Engineer ing, McGrawHill, New York (1980) 15. Finlayson, B.A., Numerical Methods for Problems with Mov ing Fronts, Ravenna Park, Seattle, WA (1992) 16. Schlichting, H., Boundary Layer Theory, 4th ed., McGraw Hill, New York (1960) 17. Hinze, J.O., Turbulence, 2nd ed., McGrawHill, New York (1975) 18. Tennekes, H., and J.L. Lumley, A First Course in Turbu lence, MIT Press, Cambridge, MA (1972) 19. Speziale, C.G., in Ann. Rev. Fluid Mech., 23, 107157 (1991) 20. Adler, P.M., Porous Media, ButterworthHeinemann, Bos ton (1992) 21. Rosner, D.E., Transport Processes in Chemically Reacting Flow Systems, ButterworthHeinemann, Boston (1986) 22. Ottino, J.M., The Kinematics of Mixing: Stretching, Chaos, and Transport, Cambridge University Press (1989) 23. Slattery, J.C., Interfacial Transport Phenomena, Springer, Berlin (1990) 24. Bird, R.B., Chem. Engr. Sci., 6, 123 (1957) 25. Slattery, J.C., and R.A. Gaggioli, Chem. Engr. Sci., 17,893 (1962) 26. Curtiss, C.F., J. Chem. Phys., 97, 1416, 1420, 7679 (1992) 27. Landau, L., and E.M. Lifshitz, Fluid Mechanics, Chap. VI, AddisonWesley, Reading, PA (1959) 28. de Groot, S.R., and P. Mazur, NonEquilibrium Thermody namics, NorthHolland, Amsterdam (1962) 29. Kuiken, G.D.C., Thermodynamica van de Irreversibele Processen, T.U. Delft, Netherlands (1992) 30. Bird, R.B., and H.C. Ottinger, in Ann. Rev. Phys. Chem., 43, 371 (1992) 0 r M book review NATURAL GAS ENGINEERING: PRODUCTION AND STORAGE by Donald L. Katz, Robert L. Lee McGraw Hill, New York, NY 10020; 760 pages, $54.95 (1989) Reviewed by R. A. Greenkorn Purdue University This book covers most aspects of natural gas engi neering. It is a survey suitable for a short course to introduce practicing engineers to the topic. The book is descriptive and as such is much too broad to be used as a textbook. The later half of the book is essentially a monograph recording the senior author's extensive experience in this area. Chapters 17 de scribe the material properties of the system, chap ters 813 contain the core of the material concerned with the production and storage of natural gas, chap ters 1415 mainly discuss operations, and chapters 1617 contain miscellaneous topics. Chapter 1 Natural Gas Technology and Earth Spring 1993 Sciences. This chapter is a concise review of natural gas engineering production and underground stor age of natural gas. Several subjects are covered, e.g., the branches of petroleum industry, sources of information for natural gas engineering, a brief dis cussion of geology and earth sciences, and earth temperatures and pressures. Chapter 2 Properties of Rocks. This chapter con tains some descriptions of the properties of rocks or porous media, including a description of how these properties are measured. The discussion is under standable and relatively clearbut very terse. Chapter 3 Thermodynamics: Flow Equation, Fluid Properties, Combustion. This chapter is basi cally descriptive. It is terse, explaining how the equa tions are derived and giving some limited informa tion on how to calculate combustion of natural gas. Chapter 4 Physical Behavior of Natural Gas Systems: Physical and Thermal Properties, Phase Behavior, Analyses. The initial part of this chapter is a review of pressure, volume, and temperature relationships of pure fluids. The phase rule and the behavior of complex mixtures are briefly discussed. Continued on page 116. KNOWLEDGE STRUCTURE AN APPETIZING STRUCTURE OF CHEMICAL REACTION ENGINEERING FOR UNDERGRADUATES H. SCOTT FOGLER The University of Michigan Ann Arbor, MI 48109 Chemical reaction engineering (CRE) is fun to teach, not only because it has extremely in teresting subject matter and is one of the few courses that sets chemical engineering apart from other engineering disciplines, but also because it has a very logical structure. The six basic pillars that hold up what could be called the "Temple of Chemical Reaction Engineering" are shown in Fig ure 1.11] The four on the left are usually covered in the majority of undergraduate reaction engineering courses.[2' But diffusion effects, which include mass transfer limited reactions, effectiveness factors, and the shrinking core model, are covered in only a small number of courses. Contacting, which includes reac tor characterization (e.g., residence time distribu tion) and modeling nonideal reactors, is normally left to graduatelevel courses. The pillar structure shown in the figure allows one to develop a few basic concepts and then to arrange the parameters (equations) associated with each concept in a variety of ways. Without such a structure, one is faced with the possi bility of choosing, or perhaps memorizing, the correct equation from a multitude of equations that can arise for a variety of different reactions, reactors, and sets of conditions. We draw a loose analogy with dining at a Swedish smorgasbord where it is difficult to choose H. Scott Fogler is the Ame and Catherine Vennema distinguished professor of chemical engineering at the University of Michigan. His teaching interests are in the areas of reaction engineering and problem solving. His research interests are in the areas of colloid stability and flow and reaction in porous media, in which he has over one hundred research publications. from a multitude of dishes in order to end up with a satisfying, wellbalanced meal that fits together. In CRE, consider the number of equations that arise in calculating the conversion in CSTRs, batch, plug flow, and semibatch reactorfor zero, first, second, and third order reactionsfor both liquid and gas phase systemswith and without pressure drop. The number of equations (dishes) from all the above pos sible combinations which we must choose (memo rize) is then 4 x 4 x 3 = 48. If we also consider catalyst decay with either first, second, or third or der decay laws, the number of dishes increases to 192. IfLangmuirHinshelwood kinetics are included, the number of equations, or dishes (i.e., equations in isothermal reactor design) increases to well over 1,000. Finally, if we add nonisothermal effects, the MULTIPLE REACTIONS MASS TRANSFER OPERATIONS INONISOTHERMAL OPERATION, MULTIPLE STEADY STATES MODELING REAL REACTORS, RTD, DISPERSION. SEGREGATION ANALYSIS OF RATE DATA, LABORATORY REACTORS, LEASTSQUARES ANALYSIS DESIGN OF CHEMICAL REACTORS, PFR, CSTR, BATCH, SEMIBATCH, PACKED BEDS) M R E I B L A A L W A S C S S E D T e I I R F C G U H Y S O B 0 M A N E L T A R N Y C C 10 N T A C T N G number of dishes in creases to such an ex tent that choosing the right dish, or dishes, becomes a task of un believable gastronomi cal proportions. The challenge is to put ev erything in an orderly and logical fashion so that we can proceed to arrive at the correct equation (dishes that fit together) for a given situation. Copyright ChE Division ofASEE 1993 Chemical Engineering Education Figure 1. Pillars of the Temple of Chemical Reaction Engineering. KNOWLEDGESTRUCTUR KNOWLEDGE STRUCTURE Fortunately, by structuring CRE using an algorithm analogous to a fixedprice menu in a fine French restaurant, we can eliminate virtually all memorization (see Figures 2 and 4) and proceed in a logical manner to de velop the reaction engineering equation nec essary to describe the given situation. The lower price (220 FF) menu corresponds to isothermal reactor design, while the higher price menu (280 FF) corresponds to noniso thermal design. Here we start by choosing one dish from the appetizers listed. The analog is to choose the mole balance from one of four reactor types shown. Next, we choose our main course from one of four entries: the main course analog in CRE is to choose the appropriate rate law. Continuing with our meal, we choose cheese or dessert; the analogy in CRE is stating whether the reaction is liquid or gas phase in order to use the appropriate equation for concentration. The main difference between CRE and ordering and eating a fine French meal as we have just done is that in CRE we com bine everything together at the end; such a mixing of the courses on a single plate before eating a wonderful French meal would be a disaster! The application of this struc ture to a first order gas phase reaction car Le Cataliste Flambi 344 Champs Elysees AMenu 4 220TT appetizer fatd de Canard (supplement 15F7) Coquifessaint5acques Potage Crime de Cresson Escargots & La Bouguine (supplment 1577F) Entrie Cassoutet Ragnons de Veau Coq au 1in 'Boeufd a provenpale (Tous nos plats sontgarnis) Dessert Brie on Crime Anglais 1/2 bouteilfe e vin b6anc ou vin rouge Mole Balance sBatch Pactor CMzIR Semibatcht actor Rate Law Power Law (e.g.) Ist Order 2nd Order N9nInteger Order Stoichiometry Gas orLiquid Combine Mix together and digest with 1/2 bouteiife of PoLyMr'1 Service Compris Figure 2. French Menu I: Isothermal reactor design Spring 1993 ried out in a PFR (with a change in the total number of moles) is shown in Figure 3. As an example, we will follow the dark lines as we proceed through our algorithm. The dashed lines represent possible pathways for other situa tions. Here we choose 1. the mole balance on species A for PFR, 2. the rate law for an irreversible first order reaction, 3. the equation for the concentration of A in the gas phase, and then 4. combine to evaluate the volume necessary to achieve a given conversion or the conversion that can be achieved in a specified reaction volume. For the case of isothermal operation with no pressure drop, we were able to obtain an analytical solution. In the majority of situations, however, analytical solutions of the resulting ordinary differential equations appearing in the combine step are not possible. Consequently, we include POLYMATH131 in our menu. POLYMATH is analogous to vin blanc ou rouge in that it makes obtaining solutions to the differential equa tions much more palatable. 1. MOLE BALANCES PFR CSTR BATCH dX V FAnX X =rAV dV FA A dt NAO 2. RATE LAWS rA= kCA rA CA 1+KA A A CA 3. STOICHIOMETRY FLOW BATCH CA FA = FAO(1X) NA =NAO(X) A LIQUID GAS GAS LIQUID OR GAS constant flowrate variable flow rate variable volume constant volume PT. P T S= o = ol( +sX)V' = Vo(l +X) V=Vo CA=CAO(IX) CA= C(lXPL C C"n(lX)P], CCAo(1X) S(+X) P T (1+X) T 4. COMBINE (1st order Gas Phase Reaction in a PFR) From mole balance Ifrom rate law from stoichiometry dX rA kC k C dV FFA FA = AO (+eX)P. T = where y = (A) Integrating for the case of constant temperature and pressure Vi 3 li +EX)nISrea rsX Figure 3. Algorithm for ISOTHERMAL reactors KNOWLEDGE STRUCTURE HEAT EFFECTS Studying nonisothermal reactor design is analo gous to ordering from a more expensive (280 FF) French menu (see Figure 4) in which we have an extra category from which to make a selection. In CRE this corresponds to choosing which form of the energy balance to use (e.g., PFR, CSTR) and which terms to eliminate (e.g., Q=0 for adiabatic opera tion). The structure introduced to study these reac tors builds on the isothermal algorithm by introduc ing the Arrhenius Equation, k = A eE/RT in the rate law step, which results in one equation with two unknowns, X and T, when we finish with the com bine step. The students realize the necessity of per forming an energy balance on the reactor to obtain a second equation relating X and T. For example, us ing again the PFR mole balance and conditions in Figure 3 (Eq. A), we have, for constant pressure dX AeE/RT (X)(T) A) dV vo (1+ X) () An energy balance on a PFR with heat exchange yields the second equation we need relating our in dependent variables X and T dT [UA (T T) + (rA)(AHR)] ( dV FAOCPA Le Cataliste Flamb6 344 Champs Elyses Menu tt28OrP appetizer Pati de Canard CoquiffesSaintacques Pouge Crime de Crsson 'Ecargots A La Bourguine Entrie Bouifabaisse I hroutruue qanmi oufsBourauat ona Tous nospfatssontgarnis) Assiette de Fromge Dessert Emvaroi a range souffia u Cuoto at fdtuaua eL Crps a [a "inarmi Petit Tour _ revenz so me, Mole Balance Batch Semibathd RatLa w ktsAe Power Law Langmuvir.nshduwood MidichaeMenten Stoichiometry qas or Liquid LEnerqg Bafancxfm Adiabatic Combine 5u(# Steadyj tats Service Compris Figure 4. French Menu II: Nonisothermal reactor design With the emergence of extremely userfriendly software packages, we can now allow students to explore the problem much more effectively, to develop an intuitive feeling for the reactor/reaction behavior,... 1111111111Ei: l Figure 5. Paradigm shifts in chemical engineering education. These simultaneous differential equations can be readily solved with an ODE solver, as discussed below. A PARADIGM SHIFT With the emergence of extremely userfriendly soft ware packages (see Figure 5), we can now allow students to explore the problem much more effec tively, to develop an intuitive feeling for the reac tor/reaction behavior, and to obtain more practice in creative problem solving. To illustrate this point, consider an exothermic reaction carried out in a plug flow reactor with heat exchange. Obtaining the temperature and concen tration profiles requires the solution of two coupled nonlinear differential equations such as those given by Eqs. (A) and (B). In the past, it would have been necessary to spend a significant amount of time choosing an integration scheme and then writing and developing a computer program before any re sults could be obtained. Now, with the available software programs (especially POLYMATH), it rarely takes more than ten minutes to type in the equa tions and obtain a solution."31 As a result, the major ity of the time on the exercise can be spent explor ing the problem through parameter variation and analysis of the corresponding observations. For ex ample, in the above exothermic reaction in a PFR with heat exchange, the students can vary such pa rameters as the ambient and entering temperatures, the flow rates, and the heat transfer coefficient, and look for conditions where the reaction will "ignite" and conditions for which it will "run away." By try ing their own different combinations and schemes, the students are able to carry out openended exer cises which allow them to practice their creativity and better understand the physical characteristics of the system. Chemical Engineering Education KNOWLEDGE STRUCTURE VARIATIONS ON A THEME As a result of the paradigm shift in the ease of computation using ODE solvers, the study of a wide variety of chemical reaction engineering sys tems just becomes a variation on our main theme (menu?). Once the concepts of the four leftmost pil lars are mastered, many important extensions can be viewed as minor variations on the four basic steps in our isothermal reaction design algorithm. Table 1 shows the basic algorithm for solving CRE problems (including the energy balance), along with the steps that need to be examined to handle the individual variation. To reinforce how many different CRE problems are minor extensions of the basic algorithm, we shall discuss three in greater detail below. Pressure Drop If pressure drop is not accounted for in gas phase reactions, significant underdesign of the reactor size can result. This variation is handled in the stoichi ometry step, where concentration is expressed as a function of conversion, temperature, and total pres sure. The change in total pressure is given by the Ergun equation'" I Variations MOLE BALANCE Reactive Distillation Membrane Reactors ." RATE LAW STOICHIOMETRY   Catalyst Decay Catalysis/CVD Pressure Drop Multiple Reactions Membrane Reactors COMBINE ENERGY BALANCE ADIABATIC NON ADIABATIC Multiple Steady States PARAMETER EVALUATION ODE SOLVER What if...?? I ' Table 1. Variations on the basic algorithm Spring 1993 dP_ G(10) 150(10)p .75G (C) dL pgcDp3 Dp This equation can be rearranged by lumping the constant parameters to arrive at the following equa tion, giving the variation of the pressure ratio (y=P/ Po) with either reactor volume dy al(l+eX) (D) dV 2y or catalyst weight dy_ 2 (1+eX) (E) dW 2y Either of these equations can be coupled with the combined mole balance, rate law, and stoichiometry and solved numerically (e.g., with an ODE Solver). For example, for isothermal conditions, Eq. (E) would be coupled with Eq. (A) adopted to an isothermal PBR dX k(1X) dW vo(l+eX)y (F) Catalyst Decay For the case of separable kinetics, we simply in clude a catalyst decay law in the rate law step of our algorithm. For example, for a straight through trans port reactor (STTR), the rate law might be given by kCA rA =a(t) ACA (G) 1+KACA where the catalyst activity, a(t), is a(t)= 1 (H) The algorithm for studying a catalytic reaction in a straight through transport reactor is shown in Fig ure 6. STRAIGHT THROUGH TRANSPORT REACTOR MOLE BALANCE dX =  dV FAO RATE LAW rA a(t)CA 1+KACA 1 DECAY LAW a(t)= 1+ STOICHIOMETRY CA = CA(1 X) COMBINE dX k (1X) 1 dV u(1+KACAo(1X)) (1+3t1/2 O.D.E. SOLVER Figure 6. Variations on a theme: Catalyst decay in a STTR KNOWLEDGE STRUCTURE Membrane Reactors The only trick in studying membrane reactors is to make sure to write the equations in terms of molar flow rates rather than conversion, and to ac count for the products that are leaving the reactor through the sides of the membrane reactor in our mole balance step. Consider the reaction A>B+C taking place in a membrane reactor $C A ) A, B, C For the product that exits through the side of the membrane reactor, C, the mole balance and stoichi ometry steps are =rAkcCc dV c _Fi V=v~o=V FAO+FB Fo ( FTO After writing a mole balance on A and B, tl ing set of nonlinear ODEs is solved numer sample POLYMATH solution is shown in Figure 7. MULTIPLE REACTIONS The steps that are varied when multiple reactions occur are rate law and stoichiometry. As with membrane reactors, we work in terms of the number of moles or molar flow rates of each species rather than concentration or con version. Figure 8 shows the appli cation of the algorithm to a sample reaction problem. MECHANISMS / RATE LIMITING STEPS One of the primary pedagogical advantages of developing mecha nisms and rate limiting steps in heterogeneous catalysis is that it provides insight into how to ana lyze and plot the data in order to evaluate the rate law parameters. Most schools spend oneandahalf to two weeks on heterogeneous ca talysis. Once the basic concepts of 114 ie result rically. A adsorption, surface reaction, and desorption are in troduced in conjunction with the idea of a rate limit ing step, one can derive many possible rate laws by varying the mechanism and rate limiting step. For example, consider the following dual site isomeriza tion mechanism A+ S= A*S A.S+So BS+S BSo B+S One can write the rate laws for each step in this mechanism and then show that if the catalytic reac tion (A B) in this example is surface reaction 19 *99 B * 6.9 4 *9 0.00 2.00 4.90 6.00 8.90 I19B. r (Vi/o) Figure 7. Composition profiles in a membrane reaction MULTIPLE REACTIONS STOICHIOMETRY A4B rAl= kAICA AC+D rA2=kA2CA Ci= V B+D4E rB3 = kB3CBCD RATE LAWS rA =A1 +rA2 =kA1CA kA2C rB = rB1 +rB3 = kACA kB3CBCD rc = rc2 = kA2C rD = rD2 +D3 = kA2C kB3CBCD E = rE3 = kB3CBCD MOLE BALANCES dNAA =kA NAkA2 V2 =Adt V=2 V dNE NBND dNE = rE = kB3 V USE O.D.E. SOLVER IT'S ONLY A MATTER OF BOOKKEEPING! Figure 8. Variation on a theme: Multiple reactions Chemical Engineering Education KNO WL EDfF STRUC~TIIRF limited, a plot of the initial rate data in the form of 'o HrAo versus PAo should yield a straight line, as shown in Figure 9. By formulating different mechanisms and rate limiting steps, a variety of rate laws can be developed which provide a number of options on how to interpret the data and evaluate the rate law parameters. Currently, there is an added incentive to study mechanisms in heterogeneous catalysis because of the emergence of chemical vapor deposition (CVD). CVD is widely used in the microelectronics indus try, and the mechanisms for CVD are very similar to the mechanisms analyzed in heterogeneous ca talysis. By developing fundamental laws and principles such as those in heterogeneous catalysis, the students will be prepared to analyze chemical reaction engineering problems in engineering tech nologies, e.g., CVD. Other mechanisms and rate laws that can be eas ily incorporated into the original algorithm include: * Enzyme kinetics (e.g., the MichaelisMenten equations) pCs rs = 1+KCs PAO Figure 9. Gaining insight into how to analyze the data. Bioreactors (e.g., the Monod equation for bacteria growth; see Figure 10) r ^C ^ T+KCs.CB g = B Pseudo SteadyStateHypothesis Reaction A>B Mechanism A+A<>A* +A A* B r =0 Anet klCA rA j A 1+k2CA Polymerization (long chain approximation) In studying these topics, rules are put forth to guide the student in the development of the under lying mechanism and of the rate law. Once the rate law(s) is formulated by analyzing the particular re action mechanism, one can then use it (them) in step 2 of the algorithm (menu) to study the particu lar system of interest. THINGS TO COME Discussion of future directions in CRE with col leagues at Michigan and elsewhere is the same as discussion on other academic issues. Where n fac ulty members are gathered to express an opinion on an issue, there will be 1.5 n opinions. But my feeling is that in the immediate future we will continue to focus on developing problems that exploit software packages such as POLYMATH, Maple, and Mathematica. We will see materials processing, en vironmental reaction modeling, reaction pathways and more applications on safety, batch processing, mixing, ecology (see Figure 11), and novel reactors (membrane batch reactors?) along with stochastic approaches for analyzing reacting systems. Finally, in the nottoodistant future I see a greater emphasis on predicting the reactivity of different species, first perhaps by using empirical means but u Time Figure 10. Phases of bacteria cell growth Spring 1993 0 z Figure 11. Using wetlands to degrade toxic wastesil4 I KNOWLEDGE STRUCTURE Vm mI KNOWLEDGE STRUCTURE later on from first principles. This direction will lead us into what I would call molecular chemical reaction engineering. These and other topics not men tioned here may first be covered (and in some cases are currently covered) at the graduate level, but they will filter down to the undergraduate level. This filtering will occur much more rapidly than have analogous topics in the past. SUMMARY By arranging the teaching of chemical reaction engineering in a structure analogous to a French menu, we can study a multitude of reaction systems with very little effort. This structure is extremely compatible with a number of userfriendly ordinary differential equation (ODE) solvers. Using ODE solv ers such as POLYMATH, the student is able to fo cus on exploring reaction engineering problems rather than on crunching numbers. Thus, one is able to assign problems that are more openended and to give students practice at developing their own creativity. Practicing creativity is extremely important, not only in CRE but also in every course in the curriculum, if our students are to compete in the world arena and succeed in solving the relevant problems that they will be faced with in the future. REFERENCES 1. Fogler, H.S., The Elements of Chemical Reaction Engineer ing, 2nd ed., Prentice Hall, Englewood Cliffs, NJ (1992) 2. Eisen, E.O., "The Teaching of Undergraduate Kinetics/Re actor Design," paper presented at the AIChE Annual Meet ing, Los Angeles, CA, November 14 (1991) 3. Shacham, M., and M.B. Cutlip, "Applications of a Micro computer Computation Package in Chemical Engineering," Chem. Eng. Ed., 121), 18 (1988) 4. Kadlec, R.H., "Hydrologic Factors in Wetland Treatment," Proc. Int. Conf. on Constructed Wetlands, Chattanooga, TN, Lewis Pub., Chelsea, MI (1989) NOMENCLATURE a catalyst activity A frequency factor, appropriate units Ac cross sectional area, m2 Ci concentration of species i (i = A,B,C,D), mol/dm3 C heat capacity of species i, J/g/K D, particle diameter, m E activation energy, J/mol F. entering molar flow rate of species i, mol/s G superficial gas velocity g/m2/s ge conversion factor k specific reaction rate (constant), appropriate units Ke equilibrium constant, appropriate units L length down the reactor, m N. number of moles of species i, mol P pressure, kPa ri rate of formation of species i per unit volume, mol/s/dm3 r' rate of formation of species i per unit mass of catalyst, mol/s/g t time, s T temperature, K U overall heat transfer coefficient, J/dm3.sK V volume, dm3 W catalyst weight, g X conversion y pressure drop parameter, (P/Po) yA mole fraction of A Subscripts A refers to species A 0 entering or initial condition Greek a AHR CL V V pressure drop parameter, g'1 catalyst decay parameter, s12 heat of reaction, J/mole A change in the total number of moles per mole of A reacted volume change parameter = yA08 porosity viscosity, cp density, g/dm3 volumetric flow rate, dm3/s REVIEW: Natural Gas Engineering Continued from page 109 There is a discussion of the compressibility of natu ral gases with an explanation of the various correla tions that have been used, including the effects of nitrogen, carbon dioxide, and hydrogen sulfide. There are a few examples that show how to use these particular charts. Chapter 5 Gas Hydrates and Their Prevention. The formation of hydrates is an important issue associated with the production of natural gas, espe cially in colder circumstances. The discussion is quite complete. 116 Chapter 6 Applications of Flow Equations: Pres sure Drop, Compression, Metering. The material in this chapter is relatively standard on fluid flow. However, the emphasis is on problems of natural gas flow and twophase flow. The problems associ ated with calculating vertical and horizontal flow are usefulespecially the hints on how to calculate flow in such systems. Chapter 7 Drilling and Completion of Wells. Chapter 7 is an overview containing relatively con cise descriptions of gas fracturing and acidizing op erations. The discussion of well logging is a review of most of the various kinds of logs that are used. Chemical Engineering Education Chapter 8 Flow in Reservoir and Adjacent Aqui fer. This is a strong chapter. It presents a discussion of the flow of gas in reservoirs. The pressure, (pres sure)2, and pseudopressure methods of general flow are discussed. The unsteady state solution for the constant terminal rate case and for the steadystate drainage radius case are discussed. In addition, there is a good discussion of the skin effect, the effect of highvelocity flow, and the well storage effects. Chapter 9 Gas WellTesting. Another strong chap ter, it begins with a good discussion of deliverability tests. The second part discusses tests for determin ing reservoir parameters. Examples are given of how to calculate the actual pressures. Tests for deter mining reservoir parameters include drawdown tests, multirate tests, tworate tests, and build up tests. The discussion, though concise, is complete, and there are several examples that show how to use these particular tests to determine reservoir properties. Chapter 10 Reservoir Engineering Applied to Gas, Gas / Condensate, and Gas / Oil Fields. This sur vey chapter discusses determining initial estimates of oil and gas reserves using either volumetric cal culations or early production history. The mecha nisms of oil recovery are discussed in very general terms. The solution of the material balance equa tion for a reservoir is shown. Chapter 11 Simulation: Field and Reservoir Per formance. This chapter and its first three sections discuss the implicit, explicit, and CrankNicolson numerical methods for solving the partial differen tial equations that approximate the flow in a reser voir. The discussion is concise and includes an ex ample of the onedimensional situation. There is also a brief discussion of the inverse problem. Chapter 12 Conversion of Depleted Gas, Gas/ Condensate Fields to Gas Storage Reservoirs. The gas storage problem is discussed at a survey level in this chapter. There is a good description of why storage is needed and how gas is stored. A detailed case study is presented. Chapter 13 Gas Storage in Aquifers. This is an excellent chapterthe strongest in the book. It be gins with procedural steps in locating and develop ing an aquifer storage reservoir. The discussion of locating such a reservoir is detailed, and there is a series of discussions of the measurements that are required. Predictions on the rate of bubble develop ment or water pushback are discussed. There is a general discussion of the various studies of aquifers. Chapter 14 Monitoring, Inventory Verification, Deliverability Assurance, and Safety in Storage Op erations. This chapter surveys what must be done to Spring 1993 run a gas storage operation and represents the tre mendous experience of the senior author. This chap ter and the previous one are condensed from Under ground Storage of Fluids, by Katz and Coats (1968). Chapter 15 Natural Gas Liquid Recovery and Gas for the Fuel Market. Natural gas liquids (ethane, propane, butanes, and pentanes) are recovered by refrigeration adsorption stripping or cryogenic ex pansion/compression. Chapter 16 Storage in Salt Cavities and Mined Caverns. The description in this chapter is narra tive, explaining the attributes of such caverns and how one develops caverns. Also, there is a discus sion of creating cavities by dissolving materials or leaching out the materials. Chapter 17 Miscellaneous Topics. This chapter opens with a narrative of compressed air energy storage for electric power peaking cycles. Much of the chapter discusses the design of a storage facil ity. It also contains calculations associated with transcontinental pipelines, geochemical identifica tion of natural gas, superheat limit vapor explosion, and the phase behavior associated with it. Six appendices contain data on computer programs for calculating flow, derivations of gas flow equa tions in reservoirs, a detailed discussion of the Peng Robinson equation of state, equilibrium constants, and nomenclature. n book review MASS TRANSFER by J. A. Wesselingh, R. Krishna Ellis Horwood Ltd., Market Cross House, Cooper St., Chichester, West Sussex, P019 1EB England; 243 pages, $69.95 (1991) Reviewed by Phillip C. Wankat Purdue University This is an extremely interesting (but in many ways frustrating) short book on the use of the Maxwell Stefan (MS) approach for solving complicated mass transfer problems. Since the authors assume con siderable familiarity with Fickian diffusion and with various separation methods, this book is appropri ate for graduate students. A finite difference ap proximation to the differential equations is used throughout the book, and the calculations required are well within the capabilities of graduate students. After an introductory chapter, Chapter 2 explores Continued on page 126. re, curriculum  . ON LETTING THE INMATES RUN THE ASYLUM ALVA D. BAER University of Utah Salt Lake City, UT 84112 Please accept my apology for the deceptiveness of the title of this paper. It should read "What About Telling Students How and Why We Run Engineering Colleges the Way We Do," or some thing like thatbut that would really be too long to be useful. The deception was designed to attract your attention. (Besides, we professors do let the inmates run the asylum by permitting anonymous students' comments to affect RPT deci sions in the universities!) Many engineering students consider an engineer ing college to be simply a super high school which has as its main purpose subjecting them to a cur riculum of difficult and unrelated courses, or worse. Such a belief is, of course, incorrectbut it is sel dom that anyone attempts to change the perception. James Wei wrote a paper entitled "The Reju venation of Chemical Engineering" (first presented in 1979 as a Phillips Petroleum Lecture at Okla homa State University and later given wider distri bution in CHEMTECIH1) that included an excellent discussion of the rationale for most chemical engi neering curricula. This discussion was, and is, an effective means of explaining to students the nature of their progress toward an engineering degree. I have given a onepage synopsis of the lecture to undergraduate students for some time now, and the perceptive students greatly appreciate Professor Wei's observations. One thing that is not obvious to students (or even Copyright ChE Division ofASEE 1993 to some young faculty!) is the manner in which prob lem solving pervades the whole of engineering study and practice. Although the list of successive courses in the curricula bears titles of chemical engineering topics, the nature of the problems treated in each course is more complex than those that were en countered in the prerequisite classes. Table 1 at tempts to outline how problems change throughout the education and career of an engineer. This table is, for the most part, selfexplanatory. The word "paths" was used as a shortened term to indicate strategies or approaches, and "practitio ner" is used in a broad sense to include students at all levels. Also, the term "technician" implies the semiprofessional or industrial technicianoperator. The number of levels corresponds to about the nor mal yearly educational breaks in engineering edu cation and was selected to avoid any religious or political implications. The fact that such a progression is deliberate and proceeds in an ordered fashion is something that students need to know and to appreciate. When this table is given to serious students who then take the time to ponder its information, their acceptance and understanding of the engineering approach to problem solving becomes easier. Perhaps the faculty is no longer seen as just being "difficult" when they require more demanding and complex assignments. Note also that it is here implied that the introduction of truly "openended" problems is later in the course of study than is normally sug gested by ABET requirements. However, it appears that the undergraduate's later encounter with such difficult problems corresponds to current engineer ing education practice. Table 1 is not an outline for a problemsolving algorithm. The manner in which complexity is in troduced into the problem solving process of very quantitative disciplines is illustrated. The method for introducing complexity into more qualitative fields would be much different than the process shown in the table. This is just one of the more obvious differences between problem solving in en Chemical Engineering Education Alva Baer has taught chemical engineering at the University of Utah since earning his PhD from that school in 1969. His academic and industrial research efforts have been in support of the areas of propulsion and combustion. He has now reached the age where it is easier to write short papers than it is to read long ones. TABLE 1 Possible Levels of EngineeringType ProblemSolution Methods NOTE: Each level is based on the lowerlevel method Level Number of Steps and Concepts 'Information Source Characteristics of Solution Method 1 1 or 2 Given only the data needed 2 2 or 3 May change units of data 3 4 or 5 May be given extraneous data 4 several Must find some needed data 5 many Must decide on and find needed data in published sources 6 many Must evaluate conflicting data, the data are incomplete, and needed accuracy depends on how the data enter the problem. 7 many Measurement of data paths by standard methods may be required 8 most paths Measurement of fail needed data may require new techniques or be impossible. Numbers are inserted into a given equation Numbers are inserted into given, combined, or rearranged equations Final relationships must be developed; the problem has an exact answer; and one may work toward a given solution The problem has one unique solution and one may work toward a known answer. At this point, trial anderror and iterative methods may be introduced. Computer solution methods become practical. The problem has a unique solution, but the answer is not given. A method is required to verify the solution. Progress is now based on personal efforts mainly by learning from one's own mistakes. The problem may have several possible solutions, but there may be an optimum answer. Usually approximations must be made. Timecritical answers are required. Economic factors are important. The type of problem may never have been solved before. Economics must be considered at all stages. Safety and environmental considerations maybe important. The starting and ending points are not obvious. The problem selection is critical, but the selection is usually by the practitioner. Often, the final answer may not be recognized. Likely, an acceptable solution is not possible. High school students and technicians Firstyear science and engineering students; technicians Secondyear science and engineering students; advanced technicians Second and thirdyear engineering students Thirdyear engineering students Fourthyear engineering students; graduate students; design engineers Graduate students; design engineers; research engineers Researchers; creative engineers gineering and activities in less mathematical fields. A result of this difference is that it is not likely that a general problemsolving algorithm exists for the range of human endeavors, and this fact is too often missed by engineers. People with quantita tive training too often get into difficulties by attempting to attach numbers to truly quali tative activities such as in the arts and humani ties, or for supervision and evaluation of other people, etc. Engineering students should be made aware of the limitations of their quantitative edu cation. Anyone who disagrees with this suggestion should consider attaching a number to indicate the affection of their dog. Spring 1993 Finally, it should be noted that the details in Table 1 represent my observations and biases. Others might organize the information in a different order or with different emphasis. The important point, however, is that there is a continuous progression in complexity leading to the goal of efficiently solving realworld problems. The table represents an origi nal effort, but if this notion or the information ap pears elsewhere the omission of a reference is the result of ignorance, not perfidy. REFERENCES 1. Wei, James, "The Rejuvenation of Chemical Engineering," CHEMTECH, 15, 655, November (1985) 0 Practitioners O classroom ~l~sssmomJ WHAT WORKS A Quick Guide to Learning Principles PHILLIP C. WANKAT Purdue University West Lafayette, IN 47907 Great teachers may be born that way, but the vast majority of professors have to work to improve their teaching. Fortunately, a re search base now exists that shows which teaching methods work in a variety of situations. In this pa per, ten of the procedures which are known to work will be briefly presented and applied to chemical engineering education. More details and a variety of earlier references are given by Wankat and Oreovicz.[11 TEN LEARNING PRINCIPLES 1. Develop a structured hierarchy of content and guide the learner. Content is king (or queen). The professor should be sure that the content of his subject is both impor tant and uptodate. Some structure should be evi dent to the students, and they should be guided in their learning. Tell the students where they are go ing and why it is worth their effort to get there. For example, thermodynamics is both beautiful and ex tremely useful, but many professors act as if the beauty of thermodynamics alone should be suffi cient to hold their students' attention, and they ne glect to tell the students what they will be able to do once they have mastered the subject. Be sure that the students know what the objectives of the course are. Actually developing some of the structure of knowledge themselves helps students learn the ma terial; thus, an overly rigid structure should be avoided. A good homework assignment is requiring the students to prepare a "key relations chart" which lists everything the student wants to know to solve problems or for a test. Obviously, firstyear students ...thermodynamics is both beautiful and extremely useful, but many professors act as if the beauty of thermodynamics alone should be sufficient to hold their students' attention ... Copyright ChE Division ofASEE 1993 need considerably more structure than graduate stu dents, and courses should be designed accordingly. Since problem solving is a major part of chemical engineering, both the structure and the method of problem solving should be part of the course.1'"21 Much of the structuring of content and guiding the stu dent can be done in lectures, although other teach ing methods work just as well if not better. 2. Develop images and use visual modes of learning. Most people prefer visual learning and remember visual images much longer than words, but most college instruction is auditory (e.g., see Felder and Silverman[31). The McCabeThiele diagram has been a successful teaching method for decades simply be cause it provides the student with a visual image. Modern computer graphics and plotting calculators can also be used to provide visual imagesthey are particularly useful for threedimensional plots and for showing motion. Most students better under stand equations when they are plotted for a variety of circumstances rather than simply looking at the symbolic form. The professor should require that the students develop their own visual images. 3. Make the students actively learn. People learn best by actively grappling with infor mation; thus, some sort of classroom activity is re quired.[4] This activity can be external (such as dis cussing a question, solving a problem, developing a structured flowsheet of knowledge, brainstorming, or working in a group) or internal (such as reading, questioning by oneself, pondering, etc.). Lecturing without student interaction is active only for the Chemical Engineering Education Phil Wankat received his BSChE from Purdue and his PhD from Princeton. He is currently a professor of chemical engineering at Purdue Uni versity. He is interested in teaching and counsel ing, has won several teaching awards at Purdue, and is Head of Freshman Engineering. His re search interests are in the area of separation processes with particular emphasis on cyclic sepa rations, adsorption, preparative chromatography, simultaneous fermentation and separation. professorwhich is one reason why professors often feel they have learned more than anyone else in the class. Most students will initially resist active in volvement in the classroom since it is not safe and they have been trained to passively take notes. But once the students become familiar with classroom activity, they usually grow to like itand most stu dents certainly benefit from it. 4. Practice and feedback. The professor should provide the students with an opportunity to practice what they learn while they are still in a supportive environment. A variety of different problems and questions should be tackled, and it is important to have some (but not excessive) repetition to increase both speed and accuracy. A series of regular assignments with frequent feed back will elicit more work and higher levels of com mitment to the class than will one long assignment.151 Following this principle, a long design project can be broken into several smaller parts with various assigned due dates. Students should have feedback during, or shortly after, their first practice so that they do not keep practicing incorrect methods.12' Feed back a month later is not useful. The students should have the opportunity to practice againafter they have received the feedback. For instance, after a laboratory or design report has been returned to the student with the usual excessive amount of red ink, it is most effective to require the student to produce a final, corrected, clean copy. With the aid of word processors, preparing a clean copy is much less work than it used to be. Computeraided in struction can provide very useful practice, particu larly if it is interactive. 5. Positive expectations and student success. Studies have shown that when a teacher expects students to do well, they usually respond by doing well."41 When someone important believes in the student, his or her expectations can be a major in fluence in the student's success. A very interesting and accessible report on this topic, pertaining to families, is given by Caplan, et al.16' Success is a strong motivation in itself, and it leads to additional success. When a student does not have the proper educational background, he or she will be probably be unsuccessful; so one useful activity is to pro vide background material for those students, and then to make sure that they use it. For instance, a lack of skill in algebraic manipulation will cer tainly sink a student in a mass and energy balance courseextra help in algebra can be much more effective in advancing that student than tutoring in mass and energy balances. Many capable students Spring 1993 The professor should provide the students with an opportunity to practice what they learn while they are still in a supportive environment. A variety of different problems and questions should be tackled... leave engineering due to a lack of encouragement or a lack of success."71 6. Develop a cooperative class with students teaching each other. Most students learn better in a cooperative envi ronment where a significant amount of the work is done in groups.l41 Since modern engineering practice usually involves groups of engineers, group classwork can be good training for the students' professional careers. Many students who leave engineering cite the overly competitive atmosphere as a major rea son for leaving."' A number of successful programs involving group work with engineering students have been reported.1'2] A recent study at Harvard Univer sity found that the students who grow most aca demically and who are happiest structure their time to include intense interpersonal interactions with faculty or other students."5' In large classes the pro fessor may not have time to meet individually with every student, but he or she can and should encour age group work both in and out of class. Study groups should be set up with the understanding that each group member must do the reading or problem as signments before coming to the study group. Opti mum group size appears to be from four to six stu dents. Competitive grading procedures using "the curve" do not encourage cooperation; other proce dures, such as grading against an absolute standard or mastery testing, will encourage more cooperation with the professor and between the students them selves."11 One advantage of working in groups is that students have an opportunity to informally teach other students (which helps both of the students learn better). Formal approaches to encouraging stu dents to teach other students (such as tutoring or serving as the expert on a laboratory experiment) also increase student learning. It is important to note that teaching others should not be reserved for only the best students. 7. Be enthusiasticcare about teaching. Students respond to enthusiasm. It is important that the professor cares about what he or she is teaching. Those professors who put teaching on "au tomatic" cannot possibly do a good job. There is no excuse for reading a book to the students in lec Continued on page 127. jg 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 O. Wilkes and Mark A. Burns, Chemical Engineering Department, Univer sity of Michigan, Ann Arbor, MI 481092136. CZOCHRALSKI CRYSTAL GROWTH MODELING A Demonstrative Energy Transport Problem DAVID C. VENERUS Illinois Institute of Technology Chicago, IL 60616 he development of new and interesting trans port phenomena examples and problems that can be solved using relatively simple math ematical tools can be a challenge. This is especially true when teaching an undergraduate course in transport phenomena where the students have little or no experience solving partial differential equa tions. There are, unfortunately, a finite number of physically meaningful problems one can formulate that lead to linear, ordinary differential equations (even with three coordinate systems and several types of boundary conditions to choose from). This paper presents an energy transport problem that is both instructive and interesting; it can be used to demonstrate the use of dimensional analysis the quasisteady state approximation the fin approximation As the example progresses, students see an "intimi David C. Venerus is an assistant professor of chemical engineering at Illinois Institute of Tech nology. He received his BS degree from the Uni versity of Rhode Island and his MS and PhD degrees from Penn State University He has been at IIT since 1989 and conducts research in the areas of polymer theology and processing. He has taught courses in material and energy bal ances, unit operation, transport phenomena, and polymer processing, and is faculty advisor to the AIChE student chapter. Copyright ChE Division ofASEE 1993 dating" PDE transformed into an innocent ODE through the introduction of several physically rea sonable assumptions. The novelty of the example arises from the fact that it applies to a technology not traditionally associated with chemical engineers, although it is one that virtually all engineers use. INTRODUCTION The example arises from an energy transport analysis of a process widely used in the semiconduc tor device industry. The process, known as Czochralski Crystal Growth (CZCG), is used to produce singlecrystal, defectfree ingots of Si (and similar materials) which are subsequently sliced into thin disks (or "wafers"), polished, and used as substrates in the fabrication of microelectronic devices, or "computer chips." The example or prob lem might be introduced by giving a short descrip tion of the process. CZCG is a batch process initiated when a seed crystal is dipped into a melt of the same material so that the liquid wets the seed crystal. As solidifica tion occurs, the seed is slowly withdrawn from the melt so that a neck and shoulder are grown. Once the desired radius is achieved, a nearly cylindrical crystal is grown by manipulation of the pull rate and/or melt temperature. It should be noted that even for the simplified description of CZCG given above, a high level of complexity is required to develop detailed transport models. The presence of a number of free bound Chemical Engineering Education aries (at the crystalmelt, crystalambient, and melt ambient interfaces), radiative heat transfer, and tem peraturedependent physical properties all make the problem highly nonlinear. Detailed transport mod els which account for these phenomena require nu merical solution on large computers. An excellent review of the CZCG and other crystal growth pro cesses along with discussions on the importance of various transport processes can be found elsewhere.11 PROBLEM FORMULATION AND ANALYSIS Before they are presented with this example, stu dents should have been exposed to the appropriate energy transport phenomena fundamentals: conser vation laws (either by the shell balance[2] or Reynolds Transport Theorem"" approach), constitutive equa tions, and boundary conditions. For the example, we will consider a relatively simple model of the CZCG process that describes energy transport within the cylindrical crystal. A schematic diagram of the process in shown in Fig ure 1, which indicates the position of the coordinate system. Results from this analysis could be used to estimate thermoelastic stresses (due to temperature gradients), which can lead to crystal defects, or used to find relationships between crystal length, growth rate, and melt temperature. The assumptions to be used in the development of the model are 1. Axial symmetry in the crystal. 2. All physical properties are isotropic and indepen dent of temperature. 3. Heat transfer between the crystal and the ambient V Crystal TR Ta L T Ambient z Tm Melt Figure 1. Schematic diagram of Czochralski Crystal Growth (CZCG) process. Spring 1993 can be described by a convective heat transfer law to an ambient temperature that is independent of time and position. 4. Heat transfer between the crystal and the melt can be described by a convective heat transfer law to a melt temperature that is independent of position. 5. The velocity of the crystal (pull rate) is constant. 6. The crystalmelt interface is planar and fixed at the origin of the coordinate system. Assumptions 1 to 6 lead to the following for the thermal energy equation and boundary conditions: _T 1T 1 aT a2 T] at +Vz =ar ar =i (1) T(r,z,0)= Tf 0 kzT(r,L(t),t) =ha[T(r,L(t),t)Ta] 0 r az k (R,z,t)=ha [T(R,z,t)Ta ] 0 where a = k / pCp. The (jump) energy balance at the crystalmelt interface gives k ( (r,0,t))= hm[Tm (t) Tf ]+ pVAHf t>0 (6) where ( ) indicates a radially averaged quantity. A list of the dimensional variables that appear in this set of equations can be found at the end of this paper. Equations (1) to (5) define the linear boundary value problem (BVP) for T(r,z,t). The boundary con ditions given by Eqs. (4) and (5) simply relate the conductive and convective energy fluxes at the crys talambient interfaces according to assumption 3. Equation (6) is an energy balance for the crystal melt interface that must be satisfied so that a con stant radius crystal is grown by manipulation of the melt temperature, Tm(t). If Tm is made constant, then the crystal velocity V, rather than the melt temperature, is manipulated to maintain a con stant radius crystal. In this case, Eq. (6) would be solved for the crystal velocity which would be a func tion of the temperature gradient at z = 0 rather than a constant. Hence, Eqs. (1) to (6) would consti tute a nonlinear BVP since Eq. (1) would be non linear (due to the convective term) and because the moving boundary L(t) would be a function of the dependent variable rather than some external influ ence. In this case, assumptions 4 and 5 would, of course, be modified. Although the problem defined by Eqs. (1) through (6) can be solved analytically, we will try to find 123 ways to simplify it using several additional assump tions. To begin, we first put the equations in dimen sionless form using Sr z t TTa R =R R2 TfTa Substitution of the above definitions into Eq. (1) gives ao ao i a + 8 ao2 T+ ePe 1 (7) where Pe is a dimensionless group VR Pe = VR Peclet No. The problem at hand would be much simpler if it were a steadystate problem, but unfortunately no steadystate exists because the length of the crystal is a function of time: V = dL(t)/dt. Suppose, how ever, that we could neglect the unsteady term in Eq. (7) but still allow the length of the crystal to change. Under what conditions would this be a good as sumption? To answer, let us consider the time scale for energy transfer (tE) and the time scale associated with a change in the length of the crystal (tL). If t << tL, i.e., conduction along the length of the crys tal is instantaneous compared to the time required for the length to change, then neglecting the un steady term in Eq. (7) would seem reasonable. Of course, what we are saying is that the quasisteady state approximation (QSSA) would be valid. If we let tE = L2/a and tL = L/V, then we have tE = VL tL Oa L For CZCG growth of Si, a ~ 101 cm2/sec and V ~ 103 cm/sec, so that the QSSA will be valid if L < 100 cm. We will later see the QSSA will also be valid for much greater crystal lengths. Thus we will add the following assumption to our list: 7. The quasisteady state approximation is valid. The complete problem in dimensionless form is now given by P e +_ 1 a ( 2 (8) (4, 0) =1 0 <1 (9) o (,A)+Bia (I,A)=0 050 <1 (10) (1,)+Bia(1,)=0 0 (, ))+ Bi[l1]= PeSt (12) which includes the following dimensionless groups: A = L Aspect Ratio R Bii = Biot No. for ambient (i=a) or melt (i=m) St = CpAHf Stefan No. Tf Ta The solution to Eqs. (8) through (11) can now be found by the separation of variables method for #((,0), and Eq. (12) can be evaluated for the dimen sionless melt temperature, m,. For the case when Pe  0, one might have the students find the solu tion in the literature.[41 Let us see if there are other physical arguments that will further simplify our CZCG model. For stages of the process when the crystal is long (A > > 1), it would seem reasonable to expect the temperature variation in the zdirection to be much greater than in the rdirection. Does this mean that neglecting the radial conduction term in Eq. (8) would be a good assumption? While this seems like a good idea at first glance, we remind the students that in doing so we are in effect saying that the cylindrical sur face of the crystal is insulated and no energy is transferred across it. For large A, this surface is much larger (2A times) than the surface of the top of the crystal and neglecting the heat transfer from it would be a poor assumption. Our original argument, however, still seems valid, and it would be nice if we could find some way of simplifying the radial conduction term. Since the variation of T in the rdirection is probably small, suppose we use an average radial temperature to represent it? This approach is, of course, the "fin approximation" which is frequently used to describe finned heated transfer surfaces. In terms of dimen sional variables, the definition for average tempera ture we use is 2n R fJ T(r,z)rdrd6 R (T(z))= 0 0 =2 J T(r,z)rdr 21c R R2 (0 J Jrdrd6 0o o0 or, in dimensionless form 1 <((())= 2\ $(,0))d (13) 0 Since A can be large (102) in a typical CZCG process, we will pursue this approach and add the following assumption: 8. The fin approximation is valid. Of course, the fin approximation can also be incor porated into the governing equations by the shell Chemical Engineering Education balance approach.2' Integration of Eq. (8) according to Eq. (13) gives Pe =2 (1, ) + 2 (14) ao a4 ao and substitution of the boundary condition given by Eq. (11) in Eq. (14) leads to a(4) a2() Pe =2 Bia(,o)+ a2 which, since (1,ao) =< 0(o) >, can be written as d2(o) d(e) dG2 Pe d 2 Bia() = 0 (15) Equations (9), (10), and (12), in terms of the radially 1.00 0.80 0.60 0.40 0.20 0.2o 0.00 0.00 0.20 0.40 0.60 0.80 1.00 a/A Figure 2. Dimensionless axial temperature distribution from Eq. (19) for the indicated values of Bio. Solid lines: Pe = 0; dashed lines: Pe = 0.1. 1 Bi.*0.2 0.05 / ^____ 0.1 06.02 0.01 0 1 2 3 4 5 6 7 8 9 10 A Figure 3. Dimensionless temperature gradient at the crys talmelt interface from Eq. (20) versus crystal length for the indicated values of Bi.. Solid lines: Pe = 0; dashed lines: Pe = 0.1. Spring 1993 averaged temperature, < (oc) >, can be written as ()(0) = 1 (16) do (A)+ Bia()(A) = 0 (17) d(~) d (O) + Bi [m 1] = Pe St (18) Hence, utilization of the quasisteady state and fin approximations has transformed the original problem (Eqs. 16) to the problem given by Eqs. (15) through (18), which the typical junior or senior chemical engineering student can solve. SOLUTION AND APPLICATIONS For the sake of space, we present only the solution to the last model, Eqs. (15) through (17), which is given by cosh[X(A)]+ + 2 sinh (Aa ) (0(Y)) = exp[ (Y] P2. 2 ((I)) exp[] cosh [A]+ +2 Bia sinh A] (19) where X= Pe2 + Bia. The gradient at the crystal melt interface is given by d(o) J0 (0) Bia cosh[ A]+ Bia(Pe4) sinh[ A] cosh[A]+ Pe+2 Bi sinh[A] 2 X 2 which can be used in Eq. (18) to find 0. This solution can be used to demonstrate various aspects of the heat transfer processes in CZCG. Stu dents can see how the temperature distribution and pull rate depend on the dimensionless groups that arise in the model, which always provides physical insight into their meaning. The temperature distri bution predicted by Eq. (19) is shown in Figure 2 for typical values of Bia and Pe. One might also point out that a crystal length A, can be found beyond which the crystal has an effectively infinite length. For A > A&, we can infer that tL  so that the QSSA will be valid for long crystals as was men tioned earlier. A, can be estimated by plotting the interfacial temperature gradient 3 from Eq. (20) as a function of crystal length A, as shown in Figure 3. Another interesting exercise is to have students find the range of Bia for which the fin approximation is valid (this turns out to be Bia 0.2). This can be done by comparing P from Eq. (20) to the radial average of the crystalmelt temperature gradient determined from the twodimensional model, which 125 can be given in class or derived from results found in the literature.[41 The simple model and its solution that have been presented in this paper are most appropriate for an undergraduatelevel transport phenomena course. When used in a lecture, it is a compact example that demonstrates the use of two important engineering approximations. At the graduate level, the twodi mensional models (both unsteady and steady) could provide the basis for a good homework or exam prob lem. The validity of the QSSA can be determined by comparing results from the transient and quasi steady models. A more realistic transient model could be developed by allowing the crystalmelt interface to move according to a mass balance on a melt of finite volume. In this case, the crystal pull rate and crystal velocity will not be the same. This type of problem can also be useful to demon strate techniques for boundary immobilization. There are, of course, many other ways to look at or use this example; they are left for the reader to ponder. ACKNOWLEDGMENT The author is grateful to Daniel White, Jr., for bringing the CZCG modeling problem to his atten tion during an excellent course Dr. White taught at Penn State University in the fall of 1986. NOMENCLATURE C specific heat capacity of crystal h convective heat transfer coefficient to ambient h convective heat transfer coefficient to melt AHf specific enthalpy of fusion k thermal conductivity of crystal L crystal length r radial position R crystal radius t time T crystal temperature distribution Ta ambient temperature T, melting temperature of crystal Tm melt temperature V crystal velocity or pull rate z axial position a thermal diffusivity of crystal p density of crystal REFERENCES 1. Brown, R.A., "Theory of Transport Processes in Single Crys tal Growth from the Melt," AIChE J., 34, 881 (1988) 2. Bird, R.B., W.E. Stewart, and E.N. Lightfoot, Transport Phenomena, John Wiley and Sons, Chap. 9 (1960) 3. Slattery, J.C., Momentum, Energy and Mass Transfer in Continue, McGraw Hill, New York, Chap 5 (1972) 4. Carslaw, H.S., and J.C. Jaeger, Conduction of Heat in Sol ids, 2nd ed., Oxford University Press, Chap. 8 (1959) O REVIEW: Mass Transfer Continued from page 117 some problems in using Fickian theories of diffusion when more than two species are present. Chapters 3 and 4 start formulating the MS theory, but with little mention of it by name. Chapter 3 discusses driving forces for mass transfer, while Chapter 4 considers friction effects. The idea of a "bootstrap" relationship to provide an absolute level of velocity in the MS equations is introduced in Chapter 4 and is explained with examples in Chapters 5 and 6. Chapter 5 shows several binary ideal solution ex amples and notes that the MS theory gives the same results as Fickian diffusion and is no more difficult to use. Ternary examples are the subject of Chapter 6. The example for distillation is a particu larly clear explanation of how the Murphree effi ciency can be infinite or negative. Chapter 7, on combined mass and heat balances, suffers from the need for a more complete descrip tion of the energy balance. Chapter 8, on nonidealities, has an interesting example on etha nol water distillation, but the reasons for lack of agreement with the exact solution are not spelled out. This chapter also contains the first detailed comparison between the MS and Fickian ap proaches. Moving parts of this comparison to a place much earlier in the book would help many readers. Chapter 9 briefly presents theories for determin ing the MS diffusivities. Driving forces other than activity gradients are the topic of Chapter 10. These include pressure gradients, centrifugal force, sup port forces (from solid matrices), and electrical forces. With these additional forces, Chapter 11 can look at the diffusion of ions in electrolytes. The end of Chap ter 11 is a natural break in the book since the fun damental ideas have all been presented. The second part of the book briefly covers a vari ety of separation processes. Chapter 12 is an over view of various membrane separation processes, while individual processes are covered in detail in the following chapters: gas permeation (13), dialysis and pervaporation (14), electrodialysis (15), and re verse osmosis and ultrafiltration (16). There is very little detail on the nature of the membrane itself, and statements such as "We shall treat the mem brane as homogeneous," (p. 125, referring to reverse osmosis) could easily be misinterpreted. Supplemen tation of these sections with a book such as R.E. Kesting, Synthetic Polymeric Membranes: A Struc tural Perspective (2nd ed., Wiley, New York, 1985) is Continued on page 149 Chemical Engineering Education Guide to Learning Principles Continued from page 121 tureit is boring and shows a tremendous lack of respect for both the students and the material. En thusiasm and caring (both for the students and for the material) are so important that they are suffi cient to help cover a variety of other teaching sins. One advantage of professors teaching courses in their research areas is that most of them are naturally enthusiastic and caring about their subject. Of course, someone still has to teach the beginning courses, and it is vitally important to also show a love of learning in them. Small classes can be a big advantage since it is easier for professors to show enthusiasm and caring when there are fewer students. Small classes almost force personal inter action between students and faculty. It has been shown that students who took small classes early in their careers were much more likely to become en gaged in academics."5 8. Challenge the students ask thoughtprovoking questions. Many students leave engineering because they see it as boring!"7 To offset this, the professor should find ways to provide some measure of challenge to each of the students. One method is to ask ques tions which "stretch" the students, requiring that they use their fundamental knowledge in new ways to answer questions about real phenomena. For example, ask what the temperature will be in a car sitting on the street if the wind chill is 10C but the ambient temperature is 200Cthen ask the stu dent to explain what "wind chill" is. It is often a good idea to leave a question unanswered during class and to challenge the students to obtain an answer within their study groups. The challenges should be arranged so that each student can shine once in a while. 9. Individualize the learning environment. Since students have very different learning styles,"['3 it is useful to employ a variety of teaching styles throughout the course. In that way each stu dent will be able to use his or her favorite style at some time during the course. The professor should use both inductive and deductive approaches to teach the material, although an inductive approach is usu ally more effective the first time through the mate rial. Use a variety of different exerciseswhen brain storming is one exercise and analysis is a second exercise, you will often be able to observe that dif ferent students shine in the different exercises. Rich Spring 1993 Felder's column, "Random Thoughts" in CEE, has contained many examples of individual learning styles and methods to individualize instruction in chemical engineering. 10. Ifpossible, separate teaching and evaluation. Evaluation gets in the way of teaching since the evaluator tends to be seen as the "enemy," particu larly if grading is done on the curve. The professor who separates teaching and evaluation can then be come a coach who is there with the sole purpose of helping the students learn. Someone else should do the evaluation, or a mastery style course where ev ery student can succeed should be used. For ex ample, in a large multisection course with several professors, one of the professors could write and be in charge of scoring all tests and quizzes while the other professors do the teaching. In a design course, an industrial evaluation of the designs may well be appropriateit is certainly realistic. CONCLUDING REMARKS These learning principles are certainly not inclu sive, but they do present a good start for improving teaching and avoiding disastrous classes. Note that most of the focus of these principles is on the stu dents. It is the students, not the professor, who have to learn in order for the course to be a success. ACKNOWLEDGMENT This article was written while the author was en joying the hospitality of the Department of Chemi cal Engineering at the University of Florida while on sabbatical there. The work was partially sup ported by NSF grant USE8953587. REFERENCES 1. Wankat, P.C., and F.S. Oreovicz, Teaching Engineering, McGrawHill, New York; (1993) 2. Hewitt, G.G., "Chemical Engineering in the British Isles: The Academic Sector," Chem. Eng. Res. Des., 69 (Al), 79, Jan. (1991) 3. Felder, R.M., and L.K. Silverman, "Learning and Teaching Styles in Engineering Education," Eng. Ed., 78 (7), 674 (1988) 4. Chickering, A.W., and Z.F. Gamson, "Seven Principles for Good Practice in Undergraduate Education," American As sociation for Higher Education Bulletin, 3, March (1987) 5. Light, R.J., "The Harvard Assessment Seminars", Second Report, Harvard University, Cambridge, MA (1992) [Free copies of this report can be obtained by writing to: School of Education Office, Harvard Graduate School of Education, Larsen Hall, Cambridge, MA 02138] 6. Caplan, N., M.H. Choy, and J.K. Whitmore, "Indochinese Refugee Families and Academic Achievement," Sci. Amer., 266 (2), 36, Feb. (1992) 7. Hewitt, N.M., and E. Seymour, "A Long Discouraging Climb," ASEE Prism, 1(6), 24, Feb. (1992) O 127 Random Thoughts... SPEAKING OF EDUCATION RICHARD M. FIELDER North Carolina State University Raleigh, NC 27695 What all great teachers appear to have in common is love of their subject, an obvious satisfaction in arousing this love in their students, and an ability to convince them that what they are being taught is deadly serious. (Joseph Epstein) The only rational way of educating is to be an exampleif one can't help it, a warning example. (Albert Einstein) Teaching is not a lost art, but the regard for it is a lost tradition. (Jacques Barzun) A good education is not so much one which prepares a man to succeed in the world, as one which enables him to sustain failure. (Bernard Iddings Bell) If we desire to form individuals capable of inventive thought and of helping the society of tomorrow to achieve progress, then it is clear that an education which is an active dis covery of reality is superior to one that consists merely in providing the young with readymade truths. (Jean Piaget) The Romans taught their children nothing that was to be learned sitting. (Seneca) There is nothing on earth intended for innocent people so horrible as a school. To begin with, it is a prison. But it is in some respects more cruel than a prison. In a prison, for instance, you are not forced to read books written by the wardens and the governor. (George Bernard Shaw) + "We must remember," said a Harvard Classics professor at a meeting, "that professors are the ones nobody wanted to dance with in high school." (Patricia Nelson Limerick) I try not to let my schooling interfere with my education. (Mark Twain) I learned three important things in collegeto use a library, to memorize quickly and visually, and to drop asleep at any time given a horizontal surface and fifteen minutes. (Agnes de Mille) It can be said unequivocally that good teaching is far more complex, difficult, and de manding than mediocre research, which may explain why professors try so hard to avoid it. (Page Smith) 128 Chemical Engineering Education + Do not try to make the brilliant pupil a replica of yourself (Gilbert Highet) At present the universities are as uncongenial to teaching as the Mojave Desert to a clutch of Druid priests. If you want to restore a Druid priesthood you cannot do it by offering prizes for Druidoftheyear. If you want Druids, you must grow forests. (William Arrowsmith) Examinations are formidable even to the bestprepared; for the greatest fool may ask more than the wisest man can answer. (Charles Colton) If you are given an openbook exam you will forget your book. If you are given a takehome exam you will forget where you live. (Variant of Murphy's Law) One of the great marvels of creation is the infinite capacity of the human brain to with stand the introduction of knowledge. (Theodore Roosevelt) + Universities are full of knowledge; the freshmen bring a little in and the seniors take none away, and knowledge accumulates. (Abbott Lowell) Ifyou want a track team to win the high jump, you find one person who can jump seven feet, not seven people who can jump one foot. (Anonymous) The best way to get a good idea is to get a lot of ideas. (Linus Pauling) A first principle not formally recognized by scientific methodologistswhen you run onto something interesting, drop everything else and study it. (B. F. Skinner) If you hear the word "Impossible!" spoken as an expletive, followed by laughter, you will know that someone's orderly research plan is coming along nicely. (Lewis Thomas) Four to six weeks in the lab can save you an hour in the library. (G. C. Quarderer) Experience is not what happens to you; it is what you do with what happens to you. (Aldous Huxley) Believe those who are seeking the truth; doubt those who find it. (Andr6 Gide) I arise in the morning torn between a desire to improve the world and a desire to enjoy the world. This makes it hard to plan the day. (E. B. White) We know that the most advanced computer in the world does not have a brain as sophisti cated as that of an ant. True, we could say that of many of our relatives but we only have to put up with them at weddings or special occasions. (Woody Allen) + The only thing God didn't do to Job was give him a computer. (I. F. Stone) Why, a fouryearold child could understand this. Someone get me a fouryearold child. (Groucho Marx) C Spring 1993 laboratory INTRODUCING STATISTICAL CONCEPTS IN THE UNDERGRADUATE LABORATORY Linking Theory and Practice ANNETTE L. BURKE, ALOKE PHATAK, PARK M. REILLY, ROBERT R. HUDGINS University of Waterloo Waterloo, Ontario, Canada N2L 3G1 Laboratory experiments are an integral part of the chemical engineering curriculum because they serve several purposes. Their primary purpose is to reinforce key chemical engineering concepts, but they are also supposed to teach stu dents about model development and how to obtain reliable data in the presence of experimental error. With the presentday emphasis on quality control in chemical industries and manufacturing, these skills are needed by every chemical engineer who will collect and analyze data, and they are espe cially important for engineers involved in process modeling and development. Unfortunately, with the exception of one course in statistics, we do very little to teach under graduates about data collection and analysis. At Wa terloo, an introductory course in statistics is given in the second year, and topics include an introduc tion to probability distributions, properties of means and variances, estimation, confidence intervals, sig nificance tests, and linear regression. These tools provide a background in collecting and analyzing databut students forget most of the material be cause they never get a chance to apply it. As a result, they complete their undergraduate training without really grasping the connection between sta tistics and experimentation. In the students' defense, most laboratory experi ments are not designed using the same principles that we teach in class. For example, in a statistics course we might emphasize the importance of re porting confidence intervals for a parameter that we have estimated, but laboratory experiments are rarely designed to allow students to do just that. Copyright ChE Division ofASEE 1993 Annette Burke obtained her BASc in chemical engineering from the University of Waterloo in 1990. She is working on the development of improved methods for designing sequential model discrimination experi ments. Her research interests include a variety of issues related to process modeling and experimental design. Aloke Phatak obtained his BASc and MASc in chemical engineering from the University of Waterloo. After working as a research scientist in the field of rocket propellants for three years, he returned to UW for his doctorate. He is currently working on applications of multivariate statistics in ChE. Bob Hudgins holds degrees from the University of Toronto and Princeton University. He teaches reaction engineering, staged operations and labo ratories that go with them. His research interests lie in periodic operation of catalytic reactors and in the improvement of gravity clarifiers. Park Reilly graduated from the University of Toronto in 1943 and worked in industry until 1967 when he joined the faculty at the University of Waterloo. He studied statistics at the University of London and received a PhD in Statistics in 1962. His research and publications are in the area of applied statistics. Consequently, they are left wondering about the practical "realworld" value of statistical techniques. To bring statistics down from the blackboard and onto the lab bench, therefore, we must include sta tistical concepts in undergraduate laboratory experi ments. If we do not reinforce this link between the theory and the practice of statistics, we will be do ing a disservice to our students who, as practicing engineers, will have to deal with measurement error on a daily basis. OBJECTIVES The purpose of this paper is to show that it is possible to incorporate statistical ideas within exist ing experiments, while still respecting the need to illustrate chemical engineering concepts. We have made changes in two secondyear physical chemis try experiments. These experiments are particularly appropriate, not only because they are a part of physical chemistry courses in many departments, but also because here at Waterloo they are carried out in the term following the introductory statistics course. Thus, students begin applying statistical tools very early in the curriculum. We hope that through this early exposure they will come to view sound Chemical Engineering Education statistical analysis as a necessary part of all experi mentation. Our longterm objective is to incorporate more advanced concepts, such as design of experi ments and response surface methodology, into all laboratory coursesespecially into the unit opera tions laboratories in the third and fourth years. In the following paragraphs we outline the old procedures, the changes we have made, and the sta tistical concepts that have been introduced. We be lieve that the new procedures are better, but we also suggest additional modifications which could be made to further improve the didactic value of the experiments. Complete laboratory procedures, which include laboratory questions and supplementary ma terial, can be obtained from the authors. EXPERIMENT 1 Determination of the Molecular Weight of Polystyrene by Viscometry In this experiment, students determine the viscos ityaverage molecular weight (My) of a sample of polystyrene by dilute solution viscometry. Some of the concepts introduced in this experiment (the rheo logy of suspensions, for example) are also discussed in the physical chemistry course and in a fluid me chanics course. In addition, the students learn a little bit about polymers and polymersolvent inter actions. The standard experimental procedure for determining My is described by Smith and Stires."' It is quite commonly used in both industrial and research laboratories. In dilute solution viscometry, the idea is to relate My to the viscosity of a very dilute solution of poly mer and solvent. The viscosity of a polymer solution increases with both the concentration and the mo lecular weight of the polymer. By measuring the viscosity of a polymer solution at several concentra tions, however, and then extrapolating to zero con centration, the effect of molecular weight can be isolated, thereby allowing us to estimate My. The viscosityaverage molecular weight of a poly mer is related to the intrinsic viscosity of a polymer by the MarkHouwinkSakurada (MHS) equation[21 [ ]= KMa (1) Here, [il] is the intrinsic viscosity, and K and a are constants which depend upon the polymer, solvent, and solution temperature. The intrinsic viscosity, sometimes known as the limiting viscosity number, is defined in terms of the Newtonian viscosity of a polymersolvent solution of concentration, c, as the concentration approaches zero, e.g., [TI] = lim (T( / 11o 1) (2) [J= im (2) Spring 1993 Spring 1993 where Tr is the viscosity of the polymersolvent solution of concentration c, and io is the viscosity of the solvent alone. Once we know the intrinsic viscosity of a polymer in a given solvent and the MHS constants K and a, we can calculate its viscos ity average molecular weight by solving Eq. (1) for My. But how can we determine the intrinsic vis cosity in the first place? The Newtonian viscosity of a polymersolvent so lution depends on the concentration of the polymer. For very dilute solutions this concentration depen dence can be described by the Huggins equation," which is written as ( /i 1) [l] + kH [l]2c (3) where the constant kH is known as the Huggins constant. Thus, to determine the intrinsic viscosity, we first measure the viscosity of the solvent as well as the viscosities of at least two polymer solutions of known concentration. Then, assuming that the Huggins equation is correct, we can use linear re gression to estimate [il] in Eq. (3). In the experiment, however, 1" and rn are never actually measured. In the viscometer used, the time required for the polymer solution to flow through a marked length of glass tubing is measured. It turns out that in such a viscometer, the flow time is pro portional to the viscosity of the solution and in versely proportional to its density. However, because the different polymer solutions used are very dilute, their density is roughly the same, and flow time depends on the viscosity of the solution only. Thus, we can write i/To = t/to, where t is the flow time for a polymer solution and to is the flow time for the pure solvent. As a result, Eq. (3) can be written in terms of flow times instead of viscosities, e.g., (t/t 1) = []+kH[n]2c (4) and we can carry out a linear regression as outlined above to estimate [i]. Old Procedure: A 50ml solution consisting of 0.5 g of polymer in solvent (toluene, for example) is prepared and left for a day to allow the polymer to dissolve. A 10ml aliquot of pure solvent is then placed in a CannonUbbelohde viscometer, and the flow time is measured three times. These measure ments are then averaged. All flow times are deter mined in this way since uncertainty in these mea surements is the major source of error in this ex periment. The solvent is removed and the viscom eter cleaned. Next, 10 ml of polymer solution is placed in the viscometer and the flow time is measured. The solution is diluted by the successive addition of 131 2, 5, 5, 10, and finally 20 ml of solvent. After each addition the solution is mixed and the flow time measured. Then, the data are plotted using the Huggins equation, and by using linear regression, [1i] is estimated. Figure 1 is a plot of typical data. Once [il] has been determined, Mv can be calcu lated using the MarkHouwinkSakurada equation. Students are supplied with appropriate values of the constants K and a from the Polymer Handbook. 4 0.__ Why is such a design inherently 0.48 flawed? Reilly, et 6 al.,[51 pointed out that as more and 0.44 more solvent is o added to the ini 0.42 tial polymer so 0.40 lution, the error in measuring flow 0.38 times increases, o.36 as does the un 0.0 0.2 0.4 0.6 0.8 1.0 certainty in the c (g/mL) concentration. As Figure 1. Huggins plot of viscosity a result, the error data generated using the old ex in the quantity perimental procedure. The polymer (q/Tio 1)/c in system is polystyrene in toluene at creases as con 300C. centration de creases, and making a large number of measure ments at low concentrations decreases the precision with which we can determine [Tn]. Our objective in modifying this experiment, therefore, was to imple ment an improved procedure suggested by Reilly, et al.,one which yields more precise estimates of [qr] and My and which, more importantly, allows students to construct confidence intervals for these two quantities. New Procedure: How many polymersolvent so lutions should we run through the viscometer to estimate the intrinsic viscosity with the greatest precision? The answer, according to Reilly, et al.,51 is only two! The first solution has a concentration given by c1, and the second a concentration of c1/2, which we denote by c,2. Once the flow times of these solutions and of the pure solvent have been mea sured, the problem of estimating [r] by regressing (t/to 1)/c on c reduces to fitting a straight line between two points. After a little bit of algebra, it is easy to show that the intercept of this line, the intrinsic viscosity, is given by t +4 tl/2 3 t (5) cito Here, to denotes the average flow time of pure sol 132 vent, while t, and t/2 are the average flow times of the solutions of concentration cl and c,2, respectively. In the modified procedure, c, corresponds to an ini tial solution of 0.35 g polymer in 50ml solvent. Two solvents are used: toluene and 80/20 by volume mix ture of toluene and methanol. Thus, in all, students measure the average flow times of six solutions, where each average has been calculated from three measurements. This allows them to estimate the variance of the flow measurements as S2 = 1 n[ ki)] (6) n(k 1) i=1 (6) where ti is the jth replicate measurement of the ith solution, ii is the average of k(= 3) replicate mea surements of solution i, and n(= 6) is the total num ber of solutions. Our practice is to combine the data from two groups of students to get a more reliable estimate of the variance based on n = 12 solutions. Having determined s2, it is relatively straightfor ward to estimate the variance of [T1] by applying standard formulas for the variance of the quotient of random variables to Eq. (5). If we do so, it turns out that 2 s2V var [] tll 2 (7) where V is a factor that depends on the number of replicates of flow time measurements, el, and the estimate of [rl] obtained by using Eq. (5). Then, con fidence intervals for [in] and Mv can be constructed in the usual way. Discussion; The new procedure is better in two important respects: 1) the estimate of [i], and hence of Mv, is more reliable, and 2) the students can now construct confidence intervals based on an estimate of the variance that is independent of the regression that is carried out to estimate [rn]. In addition, we also briefly discuss the old procedure so that the students can understand why its design is flawed and why the new procedure yields a more precise estimate of intrinsic viscosity. How could we further improve the didactic value of the experiment? One way would be to explain to the students why a design in which only two concen trations are used is optimal. In addition, we could also make them derive Eq. (7), including the exact value of the factor V. However, we have to strike the right balance between illustrating statistical con cepts and illustrating physical principles. Although we are convinced of the value of introducing statisti cal ideas into these experiments, we do not want to Chemical Engineering Education do so at the expense of the chemical engineering concepts being illustrated. Thus, we leave it up to the instructor to decide whether or not to incorpo rate the additions mentioned above. EXPERIMENT 2 Adsorption of Acetic Acid on Charcoal This experiment illustrates the discussion of adsorption from solution that is presented in the secondyear physical chemistry course. Like dis tillation, adsorption can also be thought of as a chemical engineering unit operation.'61 Two expres sionsthe Freundlich isotherm and the Langmuir isothermare used to describe the adsorption of acetic acid onto activated charcoal. Each isotherm is based on different assumptions about the nature of adsorption, and they apply under different condi tions. The Freundlich isotherm"7' is a purely em pirical model which works well at low solute con centration. It relates the mass of solute adsorbed (x) on the adsorbent to the equilibrium concentration of solute (C), e.g., _x = kC" (8) m where m is the mass of adsorbent, and k and n are empirical constants. The Langmuir isotherm,'71 how ever, was derived assuming an explicit adsorption mechanism. It may be written as x (x / m)o KC m 1+KC (9) where K is the equilibrium constant, and (x/m)O is the mass ratio required for monolayer coverage of the surface of the adsorbent. Equations (8) and (9) are nonlinear, and they are usually used in their linearized form, e.g., n = in k + n nC (10) m for the Freundlich isotherm, and 1 1 1 1 (11) x/m K(x/m)0 C (x/m)0 for the Langmuir isotherm. After measuring x/m for several different concen trations of acetic acid, the students are asked to comment on the fit of Eqs. (10) and (11) to the data. The procedure used in the past is based on the ex periment described by Ellis and Mills;1"' it is not well designed to allow the students to quantitatively assess which of the two isotherms better describes adsorption of acetic acid onto charcoal. Furthermore, note that the linearized forms of the equations are used. Also, as we will see from the procedure below, x and C are not statistically independent. Old Procedure: Two grams of activated charcoal Spring 1993 are placed in each of six flasks. Starting with 0.5 M acetic acid, six 100ml lots of acetic acid with con centrations ranging from 0.5 to 0.025 M are pre pared. The acetic acid solutions are added to the charcoal, mixed, and left to stand overnight to reach equilibrium. The solutions are then suction filtered. Filtrate samples are titrated with 0.2 M NaOH to determine the equilibrium concentrations. Finally, the amount of acetic acid adsorbed onto the charcoal is calculated. Students then plot the data using Eqs. (10) and (11). The correlation coefficient for the Freundlich isotherm is typically 0.99, and for the Langmuir isotherm it is typically 0.70. Figures 2(a) and 2(b) show plots of representative data. Students notice the curvature in the plot of the Langmuir isotherm and then conclude that it is not due to chance alone, but to systematic departure from the fitted model. Unfortunately, 3.0 they rarely real 2.8 ize that the ob 2.6 served curvature 2.4 provides informa 22 tion which is dif \2. ferent from that 12. provided by a low 1.8 correlation coeffi 1.6 cient. As a result, 1.4 they often pro 1.2 ceed in later 1.0 .5 years to rely 0.0 0.5 1.0 1.5 2.0 2.5 C30 3.5 4.0 4.5 5.0 heavily on the 1n (C) Figure 2(a). Acetic acid adsorption correlation coeffi data generated using the old pro cient as a mea cedure and plotted according to sure of modelfit Freundlich isotherm. and sometimes even neglect to 20 plot data. Our s1 purpose in modi 16 fying this experi 14 i ment, therefore, is to emphasize 12 the limitations of 10 the correlation co 8 o efficient and to 6D give the students 4 experience in us 2 ing other mea 0 sures of model fit. 0 20 40 60 80 100 120 140 160 New Proce 1/cdure: The proce Figure 2(b). Acetic acid adsorption dure: The proce data generated using the old proce dure is un dure and plotted according to changed except Langmuir isotherm, for the number of 133 solutions used. Instead of preparing six solutions of different concentration, three independent replicates of four different concentrations are prepared. The concentrations used are between 0.5 and 0.025 M. For each replicate, charcoal is weighed out and ace tic acid solution is prepared separately to ensure independence. The twelve samples are left overnight to reach equilibrium and are then suction filtered; the filtrate from each is again titrated using 0.2 M NaOH. It is tempting here to titrate a set of three replicates sequentially, but this would invalidate the estimate of the error variance. Filtrate samples must be titrated in random order so that the corre lation between any two measurements is constant, and the data may be treated as independent. Fi nally, students perform leastsquares regression to fit Eqs. (10) and (11) to the data, calculate the corre lation coefficients, plot the residuals, and perform the lackoffit test described below. Figures 3(a) and 3(b) show typical results using Eqs. (10) and (11). The lackoffit test is an extension of analysis of variance in linear regression, which students learn in their introductory statistics course. It is described in standard texts such as Draper and Smith."19 If a model is a good representation of the data, the re siduals, or prediction error, should reflect only ran dom error. If a model is a poor representation of the data there is additional variation caused by lackof fit, which manifests itself as a systematic departure from the fitted line. This is evident when the data from this experiment are plotted using the Langmuir isotherm, but in the original experiment there is no way to estimate random error independently of the model or to confirm lackoffit quantitatively. The introduction of replication allows us to esti mate the random error, or pure error, independently 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 In(C) Figure 3(a). Acetic acid adsorption data generated using the new proce dure and plotted according to Freundlich isotherm. 134 20 18 14 12 m 10 6 2 of the model that is postulated. The model predic tion errors can then be divided into random error and lackoffit error. Comparison of the lackoffit sum of squares to the pure error sum of squares using an Ftest serves as a quantitative measure of the fit of the model. The calculations for the lackoffit test are straight forward. Let yij, i = 1,2,...,k, j = 1,2,...,n, be the jth measurement on the 'dependent' variable at the ith concentration. In the modified procedure outlined above, three replicates (ni = 3, Vi) are performed at each of four (k = 4) different concentrations. Recall that because we are using the linearized forms of the Freundlich and Langmuir isotherms, y = ln(x/m) for Eq. (10) and y = 1/(x/m) for Eq. (11). The random, or pure, error can be estimated by k ni 2 I I (YijY) 2 i=l j=l nk k n= Yni i=l where yi is the average of the ni measurements at the ith concentration. In much the same way, the lackoffit sum of squares (LFSS) is estimated as LFSS= ni(yii)2 (13) i=1 where yi is the value predicted by the model (Eqs. 10 or 11) at the ith concentration. Once we have fitted the Freundlich and Langmuir isotherms and calculated the corresponding values of s2 and LFSS, we can construct an Fstatistic and compare it to the critical Fvalue at the desired confidence level, e.g., SLFSS/(k 2) 2 Fk_2,nk (14) If the calculated value is larger than the critical F value, then lackoffit error is signifi cant at the chosen confidence level, and o the model does not describe the data adequately. Using such an Ftest, stu dents find significant lackoffit for the Langmuir isotherm, which provides quantitative reinforcement of the con clusions they draw by simply observ ing the curvature in Figure 3(b). DISCUSSION The changes we have made to the experimental procedure are minor; the benefits reaped by the students, how ever, will be substantial. First, the stu dents will be introduced to replication, which is essential in estimating ran Chemical Engineering Education A4 0 20 40 60 80 100 120 140 160 1/C Figure 3(b). Acetic acid adsorption data generated using the new proce dure and plotted according to Langm uir isotherm. dom error and in identifying problems such as non constant variance. More important, we hope that students will realize just what experimental error really is when they carry out repeat measurements which do not yield the same results. Second, the introduction of the lackoffit test and the analysis of residual plots encourages students to use tools other than the correlation coefficient in discriminat ing between competing models. Finally, students are forced to review leastsquares regression and analy sis of variance in order to understand the lackoffit test and to interpret the residual plots. We recognize, however, that some flaws which are present in the old procedure remain in the modified one. First, linearized forms of the original expres sions are still fitted, which may change the error structure. Second, the amount of solute adsorbed is determined from the change in solution concentra tion, which causes the variables x and C to be statis tically dependent. Finally, we can see in Figure 3(a) that the variance of the data, plotted according to the Freundlich isotherm, increases as the con centration, C, increases. This violates one of the assumptions of leastsquares regressionthat of constant variance. How can we remedy these deficiencies? One way of doing so is to express the models in terms of the actual quantities measured: the initial acetic acid concentration, the equilibrium concentration, and the mass of charcoal. Since the resulting model will be nonlinear with error in all the variables, an analysis using the errorinvariables method""l would be most appropriate. It would be unrealistic, how ever, to expect secondyear students to carry out such an analysis. Here, we face a question that we will no doubt encounter when trying to incorporate statistical concepts into other experiments: how can we adopt the best, "statistically correct" analysis of a poorly designed experiment without burdening our secondyear students with statistical methodol ogy that would tax even a competent researcher? Our solution here is a compromisewe have incor porated changes that we think are better, but we also recognize the remaining deficiencies and en courage the students to think about and discuss other ways of analyzing the data and why they might be more appropriate. In this way we hope that they will be able to recognize how the design of an experiment can affect the statistical analysis of data derived from it. CLOSING REMARKS Our objective in modifying these two experiments was to introduce statistical concepts into the under Spring 1993 graduate laboratory. The changes to the procedures themselves are minor, but by modifying the analy sis of the data it is possible to include a wealth of ideas which reinforce the connection between statis tics and experimentation. By introducing replica tion, we force the students to confront experimental errorthey see that measurement uncertainty is an unavoidable fact of life. By showing them the means to quantify this error, we show them a rational ba sis for dealing with it. In the long term, our objective is not only to make notions like replication and interval estimates an essential element of all undergraduate laboratories but also to include advanced concepts such as facto rial designs, especially in upperyear unit opera tions laboratories. As we saw with the analysis of Experiment 2, however, it is sometimes difficult to incorporate statistical concepts into existing proce dures that are poorly designed to begin with. Short of redesigning all undergraduate experiments or in troducing students to advanced statistical techniques which they may not be able to appreciate, our solu tion has been to incorporate statistical techniques, but at the same time point out deficiencies where they exist and encourage the students to discuss alternative methods of data analysis. However we choose to do it, it is clear that we must incorporate statistical concepts into the undergraduate labora tory. By doing so as early as possible in the chemical engineering curriculum, we hope to remove the mis taken notion of statistics as something complex and mysterious when it is really fundamental to the engineer's craft. REFERENCES 1. Smith, J.L., and A. Stires (Eds.), Experimental Physical Chemistry, 7th Ed., McGrawHill, New York (1970) 2. Rudin, A., The Elements of Polymer Science and Engineer ing, Academic Press, New York (1982) 3. Huggins, M.L., "The Viscosity of Dilute Solutions of Long Chain Molecules. IV. Dependence on Concentration," J. Am. Chem. Soc., 64, 2716 (1942) 4. Brandrup, J., and E.H. Immergut (Eds.), Polymer Hand book, WileyInterscience, New York (1975) 5. Reilly, P.M., B.M.E. Van der Hoff, and M. Ziogas, "Statisti cal Study of the Application of the Huggins Equation to Measure Intrinsic Viscosity," J. Appl. Polym. Sci., 24, 2087 (1979) 6. Mantell, C.L., Adsorption, 2nd Ed., McGrawHill, New York (1951) 7. Castellan, G.W., Physical Chemistry, 3rd Ed., Addison Wesley, Reading, MA (1983) 8. Ellis, R.B., and A.P. Mills, Laboratory Manual in Physical Chemistry, McGrawHill, New York (1953) 9. Draper, N.R., and H. Smith, Applied Regression Analysis, 2nd Ed., John Wiley & Sons, New York (1981) 10. Reilly, P.M., and H. PatinoLeal, "A Bayesian Study of the ErrorsinVariables Model," Technometrics, 23, 221 (1981) 0 1 laboratory PURDUEINDUSTRY COMPUTER SIMULATION MODULES 2. The Eastman Chemical Reactive Distillation Process* S. JAYAKUMAR, R.G. SQUIRES, G.V. REKLAITIS, P.K. ANDERSEN, L.R. PARTIN Purdue University West Lafayette, IN 47907 As described in previous papers,"1'21 a series of computer modules for use in the chemical en gineering senior laboratory is being devel oped at Purdue University. The modules are meant to supplement, not to replace, traditional laboratory experiments. In our laboratory, for example, only one of three monthlong experiments may be the use of a computer module. Computer simulated ex periments have a number of advantages over tradi tional experiments: Processes that are too large, complex, or hazardous for the university laboratory can be simulated with ease on the computer. Realistic time and budget constraints can be built into the simulation, giving the students a taste of "real world" engi neering problems. The emphasis of the laboratory can be shifted from the details of operating a particular piece of laboratory equip ment to more general considerations of proper experimental design and data analysis. Computer simulation is relatively inexpensive compared to the cost of building and maintaining complex 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. EASTMAN CHEMICAL REACTIVE DISTILLATION PROCESS The Eastman Chemical Reactive Distillation Pro cess is part of a series of steps for obtaining acetic anhydride from coal. Acetic anhydride is an impor tant chemical intermediate used in the production of cellulose acetate, which itself is used in the manu * The first paper in this series, "PurdueIndustry Computer Simulation Modules: The Amoco Resid Hydrotreater Process," appeared in CEE, 25, 98 (1991). S. Jayakumar is a postdoctoral research fellow in the School of Chemi cal Engineering at Purdue University. He received a B.Tech from Indian Institute of Technology (1985), and his MS and PhD from Purdue Univer sity (1988, 1992). His research interests include process design, simula tion, optimization, and plant layout R. G. Squires is a professor of chemical engineering at Purdue Univer sity. He received his BS from Rensselaer Polytechnic Institute (1957), and his MS and PhD from the University of Michigan (1958, 1963). His current research interests center on the educational applications of com puter simulation. G. V. Reklaitis is Head of the School of Chemical Engineering at Purdue University. He earned his BS from Illinois Institute of Technology (1965), and his MS and PhD from Stanford University (1969). His research interests include process systems engineering, process scheduling meth odology, and the design and analysis of batch 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 (1981) and his PhD from UC Berkeley (1987), both in chemical engineering. His research has dealt with transport in multiphase flows and the educational applications of computer simulation. L. R. Partin is a Research Associate with Eastman Chemical Company in Kingsport, Tennessee. He received his BS in chemical engineering from the University of Kentucky in 1976 and his MS in chemical engineering from Purdue University in 1977. facture of photographic film base, fibers, plastics, and other products. Each day the plant converts 900 tons of coal to acetic anhydride. Using conventional methodology, the chemicals produced would require the annual equivalent of one million barrels of oil. A brief de scription of the process is: synthesis gas produced from coal is used for methanol production; methanol (MeOH) is reacted with recycled acetic acid (HOAc) to produce methyl acetate (MeOAc) and then acetic anhydride; and finally, acetic anhydride is reacted with cellulose to form cellulose acetate. The process for formation of MeOAc was developed at the Eastman Chemical Company3' and patented. The reader is also referred to a paper by Agreda, Pond, and Zoeller[41 for more details. The formation of MeOAc is the focus of this project. In this process, methanol reacts with recycled acetic Copyright ChE Division ofASEE 1993 Chemical Engineering Education This part of the project involves analyzing trays of the column. Students do not run a tray to "obtain data," unlike the batch reactor or the equilibrium cell. Instead, they input the kinetic and phase equilibrium parameters to observe tray performance and use the results of the simulation to calculate the tray efficiency. In addition, for the same feed (vapor and liquid), they are asked to predict the conversion that will be obtained in a CSTR. acid in the presence of sulfuric acid catalyst to form methyl acetate and water: CH3COOH + CH3OH => CH3COOCH3 + H20 (1) The reaction rate is given by rMeOAc = koA exp(E / RT){ CHOAcCMeOH where ko = preexponential factor CMeOAcCH20 () K1 (2) A = catalyst acidity function (0 < A < 1) T = temperature E = activation energy and the equilibrium constant is K = MeOAcCH20 (3) e CHOAc MeOH Clearly, the maximum conversion of the reactants is equilibrium limited. This Reactive Distillation Process relies on the fact that MeOAc is more volatile than water or the reactants. Thus, if the reaction mixture is distilled simultaneously, a significant amount of MeOAc prod uct will vaporize, forcing the reaction to shift to the right and thereby allowing a much higher conver sion than would be possible in the absence of dis tillation (conventional process). An additional con sequence and advantage is that high purity MeOAc (> 99.5 wt%) is produced as the overhead product. THE COMPUTER PROGRAM The program is written entirely in the C language and uses some IMSL routines for solving systems of linear, nonlinear, and ordinary differential equa tions. It can simulate A batch reactor An equilibrium cell A tray in the distillation column The program can run on any machine that sup ports the X Window System. At Purdue, it runs on Sun Sparc workstations with 12 MB of memory. Each module uses less than 10 MB of disk space. An important feature of the program is its menu Spring 1993 TABLE 1 Expenses* BATCH REACTOR Cleanup $700 Sample analysis $50 / sample EQUILIBRIUM CELL Cleanup $500 CONSULTATION $500 All expenses are to be multiplied by 1.5 and 2 for Saturday and Sunday runs respectively. driven graphical user interface. This enables any one to use it, regardless of his or her knowledge of computers. An online help facility is provided to further assist the user in navigating through the program. The user can exit the program at any time. STUDENT ASSIGNMENTS Budget and Experiments In the first part of the Eastman project, the stu dents are required to determine the following: 1. Activation energy 2. Preexponential factor 3. Catalyst activity function 4. Wilson parameters for liquid activity coefficients To determine these quantities, the students simu late a batch reactor and an equilibrium pressure cell, both described below. Also, a requirement that the students work within a budget of $30,000 con tributes a sense of realism to the module. Table 1 shows costs associated with operating the reactor and cell. Laboratory Batch Reactor A batch reactor is available for the students to study reaction kinetics for the determination of items 13 above: activation energy, preexponential factor, and the catalyst ac tivity function. As seen in Eq. (2), the reaction is first order in the concentrations of each of the reac tants and products. Preliminary data obtained us ing laboratory batch apparatus suggest that in the range of conditions used in the Eastman column, the equilibrium constant is independent of tempera ture and catalyst concentration. The catalyst acidity 137 function, A, depends on the sulfuric acid concentra tion, as shown in Figure 1. The students are to design experiments to deter mine the activation energy E, the preexponential factor ko, and establish the functional dependence of A on the catalyst concentration. The equilibrium constant, Ke is known. Equilibrium Cell The purpose of this appara tus is to determine liquid phase activity coefficients in twocomponent systems. The cell is simply a closed vessel with a pressure gauge and a temperature sensor. Temperature control is provided, so isother mal runs can be made. The user can charge it with two components and record the equilibrium pres sure. For all practical purposes, equilibrium can be assumed to have been established in four hours. There is no facility to measure or monitor the vapor or liquid phase mole fractions. However, since the vapor volume is very small compared to the volume of the liquid, it can be assumed that the concentra tions of the components in the liquid phase at equi librium are equal to the corresponding concentra tions of the liquid charged into the cell. Note that there are five components of interest: the reactants, the products, and the catalyst, H2SO4. When the critical region is not approached (as in this case), we can assume that the liquid phase activity coefficients and standard fugacities are in dependent of pressure. If the standard fugacity is taken in the sense of the LewisRandall rule, we have for each component i y where for component i, y = liquid phase activity coefficient PO = vapor pressure P = equilibrium pressure of the system x = liquid phase mole fraction yi = vapor phase mole fraction 0i, 0o = fugacity coefficients ofi, the latter calculated at the saturation vapor pressure. Quite often, however, 4, and 4o are nearly equal, and Eq. (4) simplifies to Yi P = xi y, P (5) Since the total pressure equals the sum of the partial pressures of the components, adding Eq. (5) for each component results in P = x,1P +X22 P (6) The vapor pressures, Pi, of the pure components 138 Catalyst Acidity Function Figure 1. The catalyst activity function Figure 1. The catalyst activity function may be calculated from the Antoine equation: nP=A iB (7) fn po = Ai (7) i T+C( where the Antoine constants, A,, Bi, C, are known from the literature, and T is the temperature. At low to moderate pressures, the Wilson equa tion[5'6' may be used to predict the activity coeffi cients as a function of temperature and composition for a variety of liquid solutions comprising diverse chemical species. The Wilson equation for compo nent i is nT = 1'n (xGij) G(8) The summations are over all components present in the mixture. For an ij pair, there are two tem peraturedependent parameters, Gij and Gji. For i = j, Gj = 1. Over the narrow temperature range of interest, the temperature dependence of the param eters is weak enough to be ignored. The Wilson pa rameters for all of the component pairs except MeOH MeOAc have been previously estimated and are known. The assignment given to students is to design a series of runs in the equilibrium cell to determine the two Wilson parameters for the MeOH MeOAc pair. It should be noted that acetic acid was not chosen as a component in the binary pair since it exhibits vapor phase association and the simplification for Eq. (5) does not apply. Application ProblemTray Simulation This part of the project involves analyzing trays of Chemical Engineering Education [~7~17~17 ~~7rT1TT~~1Tr7 i i I i ~ j the column. Students do not run a tray to "obtain data," unlike the batch reactor or the equilibrium cell. Instead, they input the kinetic and phase equi librium parameters to observe tray performance and use the results of the simulation to calculate the tray efficiency. In addition, for the same feed (vapor and liquid), they are asked to predict the conversion that will be obtained in a CSTR. It is to be observed that the tray is actually a CSTR with an additional operation, e.g., distillation. It is instructive to see that the conversion obtained in a tray is much higher (for the current process) than in a simple CSTR. This is an important observation since the basic idea in carrying out the methyl acetate process in a distillation column was to increase the conversion. Two representative trays, one in the upper portion of the column and the other in the lower portion, are simulated. The students must run both. For the purpose of the current simulation, the tray is assumed to operate isothermally at a known temperature. Thus, material balance and equilib rium relationships are used to model the tray. A tray efficiency is incorporated in the model. Given the input flow rates of the vapor (from the bottom tray), the liquid (from the upper tray), the composi tion of the input streams, the pressure, tempera ture, tray efficiency, and the kinetic and phase equi librium parameters, the model predicts the flow rates and compositions of the output liquid and vapor streams of the tray. The tray model does not explicitly account for the dependence of the acidity function on the acid con centration. For the steady state, it suffices to pro vide the simulator with the acidity value corre sponding to the steadystate acid concentration in the liquid phase (output). This value, however, is not known since the output acid concentration in the liquid phase is not known. The student must therefore resort to an iterative procedure. He must guess a value of the acid composition in the output liquid stream, calculate the value of A from his catalyst acidity function, and input this value to the simulator. The model solves the problem using this value of A and predicts the output liquidphase acid concentration. This procedure must be repeated until the entered acidity function value agrees with the predicted acid concentration according to the student's function. In the event that students are unable to evaluate the kinetic and phase equilibrium parameters within the assigned time, or that they come up with im practical values or cannot establish the acidity func tion curve, they have the option of using the Spring 1993 instructor's data (with the permission of the instruc tor, of course). In this case, the students do not have to input the kinetic and phase equilibrium param eters; furthermore, the acidity function dependence is implicitly taken into account in the model, so that iteration is not required. CONCLUSION Our experience with the Eastman module has been very positive. The module presents a challenging problem that helps prepare students for the kinds of problems they are likely to encounter in industry. The simulated budget is especially effective in mak ing the project more truetolife than conventional lab experiments. Although the Eastman problem is challenging, students report that the software itself is very userfriendly. One advantage of computer simulations is their flexibility. The Eastman module was originally de veloped for the chemical engineering laboratory; how ever, it would also be useful in courses in thermody namics, chemical kinetics, and separations. AVAILABILITY OF THE MODULES The PurdueIndustry ChE Simulation Modules are being made available for educational use by the CACHE Corporation. Anyone interested in obtain ing more information should contact Professor Squires. ACKNOWLEDGMENTS This work has been supported by the National Science Foundation (Grant No. USE888554614), the Eastman Chemical Company, and the CACHE Cor poration. REFERENCES 1. Squires, R.G., G.V. Reklaitis, N.C. Yeh, J.F. Mosby, I.A. Karimi, and P.K. Andersen, "PurdueIndustry Computer Simulation Modules: The Amoco Resid Hydrotreater Pro cess," Chem. Eng. Ed., 25(2), 98 (1991) 2. Squires, R.G., P.K. Andersen, G.V. Reklaitis, S. Jayakumar, and D.S. Carmichael, "MultiMedia Based Educational Applications of Computer Simulations of Chemical Engineering Processes," Comp. Appns. Engr. Ed., 1(1), 25 (1992) 3. Agreda, V.H., and L.R. Partin, U.S. Patent 4,435,595, March 1984 (Assigned to Eastman Kodak Co.) 4. Agreda, V.H., D.M. Pond, and J.R. Zoeller, "From Coal to Acetic Anhydride," Chemtech, 172 (1992) 5. Sander, S.I., Chemical and Engineering Thermodynam ics, John Wiley & Sons, New York, NY (1989) 6. Wilson, G.M., "Vapor Liquid Equilibrium. XI: A New Expression for the Excess Free Energy of Mixing," J. Am. Chem. Soc., 86, 127 (1964) 0 laboratory AN INEXPENSIVE AND QUICK FLUID MECHANICS EXPERIMENT J.T. RYAN, R.K. WOOD, P.J. CRICKMORE University ofAlberta Edmonton, Alberta, Canada T6G 2G6 he first laboratory course in chemical engi neering at the University of Alberta is taught to about seventy students in the first term of their junior year, and its primary objective is to improve and develop the students' writing skills. They are required to write three reports. The first two reports are each about ten pages in length and deal with technical material which is familiar to the student. Each of the first two experiments is per formed and the reports written within a period of two weeks, and the corrected reports are returned to the students within another two weeks. The En glish construction and the presentation of the re ports are brutally criticized by the academic staff responsible for the course. The students then do a standard engineering experiment and write their third (hopefully readable) report. The key to this approach is to present simple and short experiments. Typically, the first two experi ments should each take less than ten minutes to complete. Quick experiments have the advantage of conveying to the students that even though the tech nical aspects are easy, describing them in clear, un derstandable English is often very difficult. For the last six years the first experiment we have used has been a computer simulation of a simple concept that the students should be able to under stand. Usually, the simulated experiment is based on a fundamental principle that was taught to the students in the previous semester, i.e., the vapor pressure of water as a function of temperature. The students run the program, specifying the tempera ture, with the simulator returning a slightly inaccu rate value of the vapor pressure. The students are asked to compare the simulated vapor pressures with those in the steam tables and those calculated Copyright ChE Division ofASEE 1993 from a published correlation of vapor pressure and temperature. They then write a report about the simulated experiment. Experience has taught us that both of the short experiments should not be simulations since, if they are, the students will write a simulated second re port. Their attitude seems to be, "If you don't take the experiment seriously, why should we take the report seriously?" Clearly, this is not the objective of the course. So, we make the second experiment a real experimentbut still quick. One experiment that is simple and fast is the filling and blowdown of a tank of air. In spite of its simplicity, this experiment is surprisingly rich in its technical content, involving ideal gas ther modynamics, unsteady state material balances, and simple fluid mechanics. All of these subjects have been covered in the preceding term or are being taken concurrently with this course. A further advantage is that the complexity of the data analy sis can be adjusted to accommodate the technical skills of the students. EXPERIMENTAL EQUIPMENT AND PROCEDURE The experiment consists of two stages: 1) filling the tank with air at about 90 psig and 70'F, and 2) emptying the tank by venting the compressed air to the atmosphere. The equipment (shown in Figure 1) J.T. Ryan is a professor and registered engineer. He has taught thermo dynamics, fluid mechanics, and process design for more than twentyfive years. R. K. Wood is professor of chemical engineering at the University of Alberta. His recent teaching responsibilities, in addition to the introduc tory laboratory course, have involved process analysis, optimization, dynamic modeling, and simulation. His research is concerned with digital simulation of the dynamic and control behavior of process systems and the computer control of distillation columns. P. J. Crickmore is an associate professor of chemical engineering at the University of Alberta. He received his BSc (Chemical Engineering), MSc (Mathematics), and PhD (Chemical Engineering) degrees from Queen's University, Kingston. Research areas include oil sands, coal and envi ronmental sampling, and remediation. Chemical Engineering Education I ChE consists of a modified 30pound propane bottle and a manifold mounted at the top of the bottle. The manifold has four nozzles, each of which is isolated with a quickacting ball valve. Standard 1/2inch copper tube and fittings are used for the manifold. The nozzles are brass plugs which have holes drilled to diameters ranging from 1/16 to 7/64 inch. These plugs are soldered into the outlet of 1/2inch unions which are located above each of the ball valves. While it is not required because of the limited air supply pressure, a relief valve is installed on the tank for educational purposes. A cheaper alterna tive would be to incorporate the relief valve in the manifold. Highpressure air is supplied from the building service air through a flexible hose. Another quickacting ball valve is installed on the tank at the hose connection. The instrumentation consists of a fast response thermocouple, a pressure transducer, and associ ated signal conditioning equipment. The thermo couple is installed through the tank wall. Since one of the objectives of the experiment is to finish the experiment quickly, the datalogging was done with a microcomputer using an OPTO 22 interface. The experimental procedure is straightforward: With the pressure in the tank at atmospheric, close valves (VI V4). Start logging the pressure and tem perature using a onesecond sampling time. Open V5. r* Figure 1. Spring 1993 The tank will reach the supply pressure in about ten seconds. Close V5 and open one or more valves in the manifold. The pressure in the tank will reduce to near atmospheric in about one minute, depending on which valves) is opened. At this time the datalog ging can be stopped or the experiment repeated. The cost of the equipment is small (less than $100, not counting the instrumentation and microcom puter), and the total shop time required for machin ing and welding is less than two hours. Our advice is to purchase a new propane bottle and have the propane relief valve removed upon purchase since this valve is extremely difficult to remove. An entire class can perform the experiment in about two days by using scheduled 15minute time slots, so the in strumentation and datalogging computer can usu ally be borrowed. FILLING THE TANK This part of the experiment focuses primarily on thermodynamics. As it is usually presented in ther modynamics texts, the theory for filling a tank with an ideal gas is correctbut the major assumption is wrong. The standard assumption is that the process is adiabatic. When the experiment is actually per formed, however, the dominant influence is the heat transfer, not the thermodynamics. But, the students believe the textbooks and their professorswho also believe the textbooks! Van Wylen and Sonntag"1 give the following equa tion as the appropriate form of the first law of ther modynamics over a control volume for a uniform state, uniform flow process: Qcv + mi{hi +( )v2+gZi =me{he +( )v2 +gZe+Wcv +m2{h2 +() +gZ2 S m 2 h 1+( +)gZ1 (1) When we apply this equation to the filling of a tank, neglecting the heat transfer, work, potential energy changes, and all kinetic energy terms except for the input, we get mi hi+ ()v2Jm2u2miul (2) When it is combined with the definitions ofh and u for an ideal gas, this equation can be used to solve all the cases appropriate to this experiment. The simplest case occurs if the incoming kinetic energy and the initial mass of the system is neglected. Then hi = u2 (3) If we assume constant heat capacities, then T2 kTi (4) where k Cp / Cv. A better approximation of the final temperature can be made, a priori, by correcting for the initial mass of air in the tank. A further refinement can be made, after the experiment, by including an esti mate of the incoming kinetic energy. Supposedly, the theory can be expanded or refinedhowever, our objective is to introduce the students to a simple laboratory experiment and to the difficulty of writ ing a technical report on such a simple experiment. Table 1 shows a comparison of the measured final temperature and those calculated from Eq. (2), corrected for both the initial mass and kinetic en ergy of the incoming air but still assuming no heat transfer. The point to be made from this table is that all of the calculations are simply wrong and differ from the measurement by a minimum of ap proximately 200F. As soon as the students see the difference between the theory taught in thermodynamics lectures and the results of the experiment, they question the ex periment. There is sufficient time to do multiple runs, but they find that the repeated experiments produce virtually the same results. The students are faced with an experiment which has precision but, in their minds, is of dubious accuracy. To ex plain the difference between the experiment and the temperature calculated from Eq. (4), many stu dents do all the corrections indicated in Table 1. They work hard to prove that the theory is right and the experiment is wrong. Ultimately, they realize Eqs. (2) and (4) are simply not true and are based on a bad assumption, and finally they conclude that the process is not adiabatic and that the heat trans fer is the dominant effect. A typical value of the heat transfer is 14 18 Btu/cycle. VENTING THE TANK At this point the students are convinced that ex periments are worthwhile, but they are somewhat skeptical of theory. Venting of the tank is designed to resolve this conflict for them. The venting of air illustrates the polytropic decompression of an ideal gas and an unsteady state material balance. The relationship between the temperature and the pressure of air in the tank, as it empties, must be established before the material balance is attempted. Analysis of the data is relatively simple and is cov ered in most introductory courses in engineering thermodynamics. The decompression of the air in the tank is taken to be a polytropic process. The appropriate equation in terms of the measured vari ables is TABLE 1 Comparison of Experimental and Calculated Adiabatic, Final Air Temperatures Method of Approximate Final Determination Air Temperature Experiment 100F Equation 4 315F Equation 2 (corrected for initial mass) 305F Equation 2 355F T (n1)/n (5) T0 P0 If the decompression is isothermal, n is equal to one. The process is isentropic when n = k. The value of n is found from the slope of the line through the measured pressure and temperature data when plot ted on loglog paper. Many students use a regres sion program to estimate n from their data; how ever, we require the T versus P plot for educational reasons. Using the equipment and procedure de scribed earlier, the typical experimental value of n was 1.04 0.005. Even though the temperature of the air in the tank drops by approximately 850F, the students conclude that the decompression process is better approximated by an isothermal process than by an isentropic one. This conclusion simplifies the mathematics of the material balance. A more accu rate analysis is possible but is not worthwhile given the intent of the course. After the students have established that the de compression process is approximately isothermal, the unsteady state material balance equation fol lows easily dm = (6) dt mN Since the volume of the system is constant and the temperature is nearly constant, the material equa tion for the air in the tank is dm Vv dP 7 dt RT dt The mass flow rate of air through the nozzle(s) is rN = PN AN VN (8) Provided that the air pressure in the tank is above the critical pressure required for sonic velocity, the velocity of the air through the nozzle is equal to VN =(kRTN)12 (9) The differential equation for the unsteady state ma terial balance reduces to V dP (kRT)112 T dt PN A (RTN)I (10) The trick is to convert, in a simple way, the ther modynamic variables evaluated at nozzle conditions Chemical Engineering Education to those measured in the tank. The theory required for this transformation is fully developed in most mechanical engineering thermodynamics texts, though not in many chemical engineering texts. Our students do not deal with compressible flow in lec ture courses until after the experiment. This prob lem is solved by simply stating that the thermody namic variables at the nozzle can be evaluated at tank conditions by applying a correction factor. Stu dents seem to like correction factors. The two rela tionships, shown below, are derived by Holman.[21 T=T 2 (11) I k I PN=P( 2k l (12)\ k+ (12) When the change in mass inventory is equated to the mass flow rate out of the nozzle(s), the differen tial equation for the pressure in the tank is A k k+1 l dP AN (kRT) /2( 2 2(ki)p (13) dt V\v Ik+)I k )) Since the students previously established that the absolute temperature in the tank is approximately a constant, they can now write this differential equa tion in a short form as dPt dKlP (14) where K, is the constant term in Eq. (13). The solu 1.0 0.9 0.8 Theory K1 = 0.027 0.7  Empirical K2 = 0.028 0.6 *\ P Po 0 10 20 30 40 50 60 70 Time (sec) Figure 2. Spring 1993 tion, shown below, is simple; however, it is valid only until the critical pressure ratio is reached. in a Kt (15) Another tack would be to regard this equation merely as the basis of a correlating equation. The equation would be the same as Eq. (15) but have a leading coefficient of K2, as In( =K2t (16) The students are required to plot the ratio of the measured pressure to the maximum pressure ver sus time on semilogarithmic paper. They then com pare the slope of the line determined by the data and Eq. (14) and that predicted by Eq. (13). A typical set of data taken by the staff, a regres sion line based on Eq. (16), and the theoretical pre diction from the solution of Eq. (15) are shown in Figure 2. A nozzle with an internal diameter of 3/ 32inch was used. The empirical value of K2 was found to be 0.028 based on ten runs with a total of 462 data points. The value of K, predicted by theory, at the average temperature, was 0.027. About 90% of the students find that the difference in the slope of the lines between theory and data is 5% or less. This difference is not statistically signifi cant given the inaccuracies in measurement of the nozzle diameters and the volume of the tank and manifold. Surprisingly, the other 10% of students, who predict differences of up to 200%, make the mistake of using the wrong nozzle(s) or recording the nozzle diameter(s) incorrectly. None of the stu dents have difficulty with the mathematics, though some think that Eqs. (14) and (16) apply even when the velocity in the nozzle is subsonic. CONCLUSION The experiment described in this paper is ideal when the experiment requirements are a quick turn around time, inexpensive equipment, and flexible technical content. NOMENCLATURE A = Area; ft2 h = enthalpy; Btu/lb Ki = constant; defined by Eq. (14) KI = constant; defined by Eq. (16) ke = kinetic energy; Btu/lb m = mass flow rate; lb/s m = mass of system; lb n = polytropic exponent P = pressure; psia Q = rate of heat transfer; BTU/cycle Continued on page 149. classroom HELPING STUDENTS COMMUNICATE TECHNICAL MATERIAL WILLIAM R. ERNST Georgia Institute of Technology Atlanta, GA 303320100 GREGORY G. COLOMB University of Illinois at UrbanaChampaign Urbana, IL 61801 Communication skills are important to engi neers and to their employers, but the commu nication skills of graduates in engineering are seldom as good as their technical skills.l1"3 In most engineering curricula, laboratory and design reports provide an opportunity to help students learn how to communicate technical material.[48 We miss that chance, however, if we evaluate the tech nical merit of students' reports but ignore how well they are written. The least we can do is to identify those places where the reports communicate poorly, require that the students rewrite them, and hope for improve ment. The best we can do is to show students why their reports communicate poorly and how to make the required improvements. This article will outline a method of showing students how to write clearly and will explain the principles behind that method. BAD WRITING, GOOD ADVICE Some writing problems are easy to spot and easy to fix: errors in spelling, grammer, and punctuation; problems in literature references; tables and figures that lack legends or are not discussed in the text; etc. Though important, these problems alone may not determine how well a report communicates. By focusing only on them, we do not help students to master a skill crucial to employers and working en gineersthe ability to communicate technical infor mation in words as well as in numbers. One key to effective communication is stylethe sentence forms in which students express technical information. But when it comes to problems of style, William R. Ernst is Professor of Chemical Engi neering at Georgia Institute of Technology and has taught technical economics and the capstone design course to seniors for the past twenty years. His principal technical interests are kinetics and reaction engineering. He is also interested in pipe line issues and has developed science and engi neering modules for precollege education. Gregory G. Colomb is Associate Professor of English and Director of Business and Technical Writing at the University of Illinois. With others, he created the "Writing Across the Curriculum" (WAC) program at the University of Chicago and has conducted WAC faculty workshops at more than fifty institutions. He has published on writing theory, WAC pedagogy, and the relation ship between writing and critical thinking. some of us have little to say. We might tell students that their writing is unclear, indirect, abstract, convoluted, flowery, awkward, etc., and advise them to be "clear and direct" or to "write as you speak." While such comments may be accurate, they are far too general to be of much use. In order to improve as writers, students need to know both what causes their writing to be unclear or convoluted and what they must change in order to make it clear and direct. Writing researchers have recently developed bet ter and more useful methods of responding to stu dents' writingmethods based on research on how people process and understand what they read. Much of that work can be found in the book Style, [9 which presents a simple, but powerful, method of teaching style. The research base of the book can be found in Colomb and Williams,[o10 and the methodology de veloped by those authors is summarized and ap plied to scientific writing by Gopen and Swan."] In this paper we will describe its most useful tools and show how they can be used by teachers to help stu dents improve their communication skills. Copyright ChE Division ofASEE 1993 Chemical Engineering Education The First Principle of Readable Writing Express important actions as verbs, and the characters associated with those actions as the subjects of those verbs. Consider the following "Conclusions and Recom mendations" section of a senior design report that is technically sound but poorly written in typical ways. From the study done regarding this process a fairly firm conclusion may be stated affirming the feasibility of Case 1 in which only the nbutane rail imports are replaced. Be cause no modifications are made to the gas concentration unit itself the specifications predicted may be obtained with very little error.... For Case 2, in which all of the butane rail imports are to be replaced, a feasible plan, which involves the purification of the excess nbutane entering with the required amount of isobutane in the NGL, has been developed. The introduction of the NGL stream was made into the feed to the butane splitter. The desired quantity of isobutane from the top of the column was achieved by this method. The bottoms from the butane splitter would then be sent to a packed column which has been designed to separate pure nbutane which meets industry specs. The bottoms from the new column would then be returned to the blending butane product stream which would then be producing an extra 10,000 Bbl/yr. The style of this passage is typified by the sen tence la. The introduction of the NGL stream was made into the feed to the butane splitter. In order to see the distinctive features of the sen tence la, compare the following three variations on a theme: 2a. The heating of the reaction mixture occurred after the introduction of the catalyst. 2b. The reaction mixture was heated after the cata lyst was introduced. 2c. She heated the reaction mixture after she intro duced the catalyst. Sentences 2ac tell roughly the same story, but most readers find 2a less clear and readable than either 2b or 2c. Between 2b and 2c, most readers find 2c slightly more readable, but readers with tech nical backgrounds are perfectly comfortable with 2b. Note that 2a is most similar in feel to la. These reactions are uniform among readers be cause these examples demonstrate key features of the way we understand sentences. Sentences, even the most technical ones, tell stories. With rare ex ceptions, sentences have two necessary elements: subjects and verbs. Similarly, stories have two nec essary elements: characters and actions. Readers Spring 1993 Writing researchers have recently developed better and more useful methods of responding to students' writingmethods based on research on how people process and understand what they read. find that sentences are clearer, more direct, less abstract, less complexin short, more readable when the story elements line up with the sentence elements: characters as subjects and actions as verbs. In 2b and 2c, key actions are expressed as verbs: was heated . was introduced and heated . . introduced. Subjects are characters: reaction mix ture ... catalyst and She ... she. In 2c the character is a person, while 2b treats the experimental mate rials reaction mixture and catalyst as characters. Although sentences are usually clearer when the subject/character is a person (preferably the agent or "doer" of the action) readers with technical back grounds are accustomed to stories about such things as reaction mixtures and catalysts, and they gener ally prefer not to have their stories focus on the persons who do the heating and introducing. In both la and 2a, however, the actions are ex pressed not as verbs, but as nouns. As a result, readers must struggle through the grammar in or der to unpack the story. The la and 2a sentences are built around nouns made from verbs (often by adding a suffix: tion, ness, ence, ity, or ing). These nouns, called nominalizations, are usually a prob lem because they steal important action from the verb, forcing writers to use a weak or empty verb. Students tend to overuse nominalizations, and they need our feedback in order to distinguish between those that are necessary technical terms and those that steal action from the verb. So now, for sentences la and 2a we can locate the problem explain to the writer what caused the sen tences to seem to us unclear, indirect, and difficult tell the writer how to make them more read able: "Sentences la and 2a are unclear because the ac tions in the sentences are expressed as nouns rather than verbs. As a result, the key sentence elements subject and verbdo not correspond to the key story elementscharacter and action. You can make the sentences more readable if you change the nouns expressing actions into verbs (e.g., introduction into introduce) so that the subjects express characters and the verbs express actions." The Second Principle of Readable Writing Keep subjects as short as possible so that sentences move quickly from a short, specific subject to an action verb. Once again, we begin with sentences that tell roughly the same story: 3a. The mixture, because it was vigorously stirred and the temperature was maintained above 200 Deg. C, reacted rapidly. 3b. The mixture reacted rapidly because it was vig orously stirred and the temperature was main tained above 200 Deg. C. While neither sentence is unreadable, most read ers find 3b more readable than 3a, and all readers begin to struggle in passages with lots of sentences like 3a. In this case, the story elements (character and action) do line up with the sentence elements (subject and verb). But in 3a the story in the main clause, The mixture . reacted rapidly, is inter rupted by all the rest of the sentence. Readers must process all of the intervening information before they achieve the subjectverb closure that holds the story together. In 3b, the subjectverb/characteraction pairs are all joined, so that we are able to process the story in three discrete chunks connected by logi cal markers (because and and). Technical writers are particularly prone to write sentences with long, complex subjects or with infor mation intervening between subject and verb. Since they so often use passive verbs in order not to focus on the persons who perform the actions, technical writers often push the verb toward the end of the sentence. Here is an instance from our long example: 4a. For case 2, in which all of the butane rail imports are to be replaced, a feasible plan which involves the purification of the excess nbutane entering with the required amount of isobutane in the NGL, has been developed. In this sentence, readers are forced to process quite a lot of information before they attain subjectverb closure. Here too, the method allows us to locate the prob lem, explain to the writer what caused the sentences to seem to us unclear, indirect, and difficult, and tell the writer how to make them more readable: "Sentence 4a is unclear because its subject is long and complex. As a result, readers have to process too much information before they can connect the key sentence elements, subject and verb. You can make the sentence more readable if you move quickly from a short, specific subject to an action verb." 146 The Third Principle of Readable Writing Sentences should begin with old information and end with new information. It is not enough that our students write sen tences that are individually clear. The sentences also have to "flow" together into a story that is coherent as a whole. Sentences flow together be cause readers use the information they have al ready read and remembered to look forward to the next sentence. If the next sentence surprises them by beginning with something they did not expect, they feel a little jolt of disorientation. If the sen tences in a passage consistently surprise readers, their feeling of disorientation builds until it be comes hard to follow the story. In order not to surprise readers, sentences should begin with something that places them in the context of the discussion: they should begin with information that readers will already have read and remembered. This familiar infor mation can be something in the immediately previous sentence or any information that is as sumable or expectable, given what has come be fore. In short, sentences should begin with old information. Once again, we find an instance in our long ex ample: 5a. The introduction of the NGL stream was made into the feed to the butane splitter. The desired quantity of isobutane from the top of the column was achieved by this method. These sentences do not "flow." They feel dis jointed, even after we eliminate the nominalization from the first sentence and connect the subject and verb in the second sentence: 5a'. The NGL stream was introduced into the feed to the butane splitter. The desired quantity of isobutane was achieved from the top of the col umn by this method. Few readers of the first sentence in 5a or 5a' would expect the second sentence to begin with "The desired quantity ofisobutane." Isobutane had been mentioned earlier, but not in a way that readers would expect it to return. In the second sentence, the phrase that most strongly refers backward is "this method." Although "method" has not occurred before, it is nevertheless old informa tion, because the whole passage has been describ ing the method. The oldbeforenew principle has even greater Chemical Engineering Education effect in longer passages, as in these examples: 6a. We should consider employing multiple reactors in parallel before we finalize our design. If one reactor shuts down, the other reactors can operate. For this reason, the parallel arrangement is flexible. Identical controllers can be used on all the reactors, thus mak ing the parallel arrangement easier to control than a series arrangement. Plant operators have more diffi culty in understanding series operation than parallel operation. 6b. Before we finalize our design, we should consider employing multiple reactors in parallel. The parallel arrangement is highly flexible; if one reactor shuts down, the others can continue to operate. Parallel re actors are easier to control than reactors in series be cause all of the parallel reactors utilize identical con trollers. Parallel operation can be understood by the plant operators more easily than series operation. 7a. We should consider employing multiple reactors in series before we finalize our design. More control equipment but less volume at a given conversion are required for a series of reactors as compared to a single reactor. Three reactors in series would save us about $1,000,000 in fixed capital, at our required con version of 90 percent. Higher quality separators could be purchased with the saved capital. 7b. Before we finalize our design, we should consider employing multiple reactors in series. A series re quires more control equipment than a single reactor but requires less volume for the same conversion. At our required conversion of 90 percent, three reactors in series would save us about $1,000,000 in fixed capital. These savings could be invested in higher qual ity separators. In both pairs, the second passage feels "tighter" and more organized because each new sentence be gins in a way we expect. In 6b, each sentence re turns to the same idea ("parallel"). In 7b, the sen tences begin differently, but with an idea from the immediately previous sentence. Both arrangements create an organized flow through the passage. RESPONDING TO STUDENTS' WRITINGS Thus far, we have described the methodology in terms of an interrelated set of principles. Once teach ers understand the principles, the methodology can be implemented through a series of simple decision procedures. These procedures focus on the first five or six words of the sentence, because the three prin ciples work together to put the key elements there. If the first several words of a sentence include a subject that names a character, a verb that expresses a key action, and some old information, then that sentence is likely to be in a readable style. Spring 1993 What follows is a method of responding to the style of student writing before you require a revi sion. (It is equally useful as a way to edit our own work.) At first the method might feel counter intuitiveespecially if you usually start reading, red pen in hand, marking as you go. In the long run, however, the method allows us to mark those problems that matter most and to give students useful feedback. * Read once, very quickly, for an overview. If the report is long, skim just the major sections. The goal of this step is to determine the overall story line and to run a first check on the technical merit of the report. Do this quickly, without mak ing any marks on the page. * Check that the report has the right sections and the right results in the right places. If data tables or figures are especially important to the results, check them now. Comment on any problems. * Read through the report. Let the "feel" of the prose, more than your understanding, be your guide. (Because you know the material so well, you can often understand even poorly written pas sages, supplying from your knowledge the infor mation and connections that students leave out or misstate.) Whenever you feel that you are be ginning to work too hard to read a passage, slow down and give it the sixword test. * The sixword test: Check the first four to six words of each sentence (ignore short introductory phrases). The first several words should include a short, specific subject naming a character a verb expressing a key action old information that sets a context for the rest of the sentence If a sentence fails the test, especially if it begins with a nominalization that is not used as a term of art, the sentence is very likely to violate the principles. * Comment on passages or sentences that violate the principles. Don't mark up the page too much; if there are many problems, comment only on the most important ones. Your comments can take any form that makes you comfortable, but it is generally best to give the student something to do: 1) analyze a portion of a problem passage on the page, and then direct the student to use the sixword test to check the rest for him or herself; or 2) pick out the problem element in a sentence or passage and suggest a specific kind of change (e.g., "Make this word a verb" or "Make sure your sentences begin with old information"). If you don't 147 trust the student to be able to make the change and you have the time, you can edit the sentence or passage and comment on the change you made (e.g., "This is clearer with X as a verb"). If you have the time and energy to spare and you have not already made many comments, you can check grammar, punctuation, spelling, etc. Un less students have very serious problems, these comments will be less important in helping them to communicate effectively. Yet correctness does count, and some teachers believe that students ought to be held to industry standards. It is gen erally better to pick out a problem and require the student to fix it rather than to fix it yourself. HOW STUDENTS RESPOND One of the authors (Ernst) introduces the above principles and report writing in general in a techni cal economics course, a prerequisite to the senior capstone design course. The students are required to submit a one to threepage report every other week, usually in the form of a letter discussing in detail an assigned homework problemits solution and the implications of the solution. Each report is graded on how well the student communicates the information. If the report is poorly written, the writ ing style is checked and appropriate comments are written in the margin as described above. Students are given a chance to revise unsuccessful reports. We have been pleased with the results of this process for two reasons: 1) when it is applied to reports assigned early in a quarter, most students who initially submit poor reports produce wellwrit ten reports after only one revision, and 2) toward the end of the quarter, most students routinely sub mit reports that do not need revising. For one assignment, students were asked to revise a report previously written by another studentin this case the "Conclusions and Recommendations" section which we discussed earlier. Here is one of the best revisions: In Case 1, only the nbutane rail imports are to be replaced by NGL. We have developed a feasible plan, under which NGL would be transferred directly to the blending butane product stream, yielding a com bined product which meets specification .... In Case 2, all of the butane rail imports are to be replaced by NGL. We have developed a feasible plan, under which the NGL would be fed to the butane splitter, where isobutane would be removed as over head at the desired rate. The splitter bottoms would be fed to a new packed column, designed to produce 148 a pure nbutane overhead stream which meets in dustry specs. The column bottoms would be returned to the blending butane product stream at a rate that would increase production by 10,000 Bbl lyr. Often, students find it necessary to add informa tion as they revise the original work, which illus trates an additional feature of these principles: they serve as a mental discipline that improves the qual ity of students' thinking. While any welldesigned writing assignment can help students consolidate and improve their knowledge, students get an addi tional boost by writing and revising in accord with these principles. Because the principles focus stu dents on the key elements of the story they have to tell, they help students to think through those sto ries and discover missing information or gaps in their logic. When students adhere to the principles, they are encouraged to be complete, precise, and logical. When teachers adhere to the principles and follow three easy steps (locate the problem, explain what caused it, explain how students can fix it), the students' gain is threefold: they understand their own research and its results more fully, they com municate their results to us more effectively, and most of all, they learn how to do better next time. REFERENCES 1. Cranch, E.T., and G.M. Nordby, "Engineering Education: At the Crossroads Without a Compass," Eng. Ed., 76(8), 742 (1986) 2. Bennett, A.,W., and D. McAuliff, "Integrating Communica tions Skills into the Engineering Curriculum," ASEEIEEE Frontiers in Ed. Conf. Proc., Vol 2, 693, November (1987) 3. Friday, C., "An Evaluation of Graduating Engineers' Writ ing Proficiency," Eng. Ed., 77(2), 114 (1986) 4. Frank, C.W., G.M. Homsy, and C.R. Robertson, "The Devel opment of Communications Skills Through a Laboratory Course, Chem. Eng. Ed., 16(3), 122 (1982) 5. Bakos, Jr., J.D., "A Departmental Policy for Developing Communication Skills of Undergraduate Engineers," Eng. Ed., 77(2), 101 (1986) 6. Sullivan, R.M., "Teaching Technical Communication to Un dergraduates: A Matter of Chemical Engineering," Chem. Eng. Ed., 20(1), 32 (1986) 7. Hudgins, R.R., "Tips on Teaching Report Writing," Chem. Eng. Ed., 21(3), 130 (1987) 8. Hanzevack, E.L., and R.A. McKean, "Teaching Effective Oral Presentations as Part of the Senior Design Course," Chem. Eng. Ed., 25(1), 28 (1991) 9. Williams, J.M., and G.G. Colomb, Style: Toward Clarity and Grace, University of Chicago, Chicago (1990). Also pre vious editions of this book: Williams, J.M., Style: Ten Les sons in Clarity and Grace, 1st and 3rd eds., Scott Foresman, Glenview, IL (1981) 10. Colomb, G.G., and J.M. Williams, "Perceiving Structure in Professional Prose: A Multiply Determined Experience," in Writing in Academic Settings, edited by L. Odell and D. Goswami, Guilford, NY (1986) 11. Gopen, G.D., and J.A. Swan, "The Science of Scientific Writ ing," Amer. Sci., 78, 550, NovDec (1990) C Chemical Engineering Education Fluid Mechanics Experiment Continued from page 143. R = gas constant; Btu/lb(R) t = time; s u = internal energy; Btu/lb v = velocity; ft/s V = volume; ft3 W = power input; BTU/cycle p = density; lb/ft3 Subscripts cv = control volume e = exiting air i = incoming air N = nozzle 0 = time zero valve opening 1 = initial state 2 = final state REFERENCES 1. Van Wylen and Sonntag, Fundamentals of Classical Ther modynamics, 3rd ed., SI Version, John Wiley, New York (1985) 2. Holman, J.P., Thermodynamics, 4th ed., McGrawHill, New York (1988) 0 REVIEW: Mass Transfer Continued from page 126 strongly recommended. Chapter 17, on sorption processes, discusses fixed bed adsorption and ion exchange. The presentation on why loading and elution in ion exchange are not symmetrical is particularly clear and easy to under stand. In general, the authors assume that the reader is familiar with these separation processes. Readers who are not (particularly electrodialysis) will find these chapters difficult, but readers familiar with the processes will gain deeper insight. A third part of the book starts with Chapter 18, which compares the MS, Fickian, and irreversible thermodynamics approaches to mass transfer. This is a very enlightening chapter, and sophisticated readers should read it following Chapter 2 or 3. Chapter 19 cites references. A rather complete list of symbols starts on page 160. I found myself refer ring to this list often and wish it were in a more prominent location. The fourth part of the book consists of thirtysix worked exercises (pages 163 to 238) which consider some very interesting and challenging problems. Al though the solutions are not polished, they are cer tainly sufficient to show how to attack the problems. A major problem with this book is highlighted in the Guidelines to the Reader on page 11: "This text was written to accompany overhead transparencies Spring 1993 The 1993 (maroon) revised printing of the CHEMICAL REACTOR OMNIBOOK is now out, and it still costs $24. Order at your bookstore, or FAX your order and card number to OSU Bookstores, Corvallis, OR at 5037373398 in a course on multicomponent mass transfer. So the Figures are quite important." Unfortunately, many readers will not pay enough attention to this section and will find reading the book difficult until they have learned the proper way to read it. Also, since the figures are hand drawn, the reader needs to learn how to decipher the authors' script. The inclusion of equation numbers would be useful. Some of the examples are confusing since the problem statements are not clear (e.g., Figure 6.2) and data or formulas are slipped into the solutions with little explanation (e.g., Figures 3.7 and 5.5). Statements such as "Qualitatively the reasoning should be clear," (page 91) will unintentionally demotivate readers who are struggling, and they should be removed. The basic ideas of the MS approach are not sum marized until pages 64 and 65. A much earlier expo sition of this would help many readers. Also, since the authors assume considerable familiarity with mass transfer, Chapter 18 could appear earlier in the text. If a second edition is planned, the authors could aid readers by correcting these problems. One hopes that the authors will make this effort since the book presents a very important topic in a way which will be accessible to most readers. Where can this book be used in the curriculum? The book is a curious mix of sophistication (MS theory and challenging problems) and of approxima tions (difference solutions and overly simplified ther modynamics). Because of the subject matter and the assumed high degree of knowledge in mass transfer and separations, this text is appropriate at the gradu ate level. However, the approximations and some lack of rigor may cause difficulties. It book would be a very useful supplement in a graduatelevel course, particularly if journal articles are used in most of the course. It is also a very good source of problems and examples for a graduatelevel course. Finally, for practicing professionals who missed the MS theory in their formal education, this book would be very useful for self study. Wesselingh and Krishna will stimulate and frustrate, but the reader will never be bored. ) re. laboratory AN INTERESTING AND INEXPENSIVE MODELING EXPERIMENT W.D. HOLLAND, JOHN C. MCGEE Tennessee Technological University Cookeville, TN 38505 In the search for new laboratory experiments, a simple experiment that works well is always welcome. In this paper we describe an inexpen sive apparatus, using simple and widely available components, that will help student understanding of process modeling. The equipment can be arranged in a variety of configurations to allow study of dif ferent models. Many chemical engineering depart ments carry out mixedtank experiments, some with computer interfaces for data collection, that can be rearranged and modified to include the models sug gested in this article. THEORY In a text by Levenspiel1' several models are pre sented for long time scale behavior of real stirred tanks. The models examined here are Levenspiel's model L (which is described in more detail by Bischoff and Dedrick121) and a modification of that model. In these models, shown in Figure 1, flow enters a perfectly mixed tank of volume aV, is interchanged at a rate by with a second perfectly mixed tank of William D. Holland is a professor of chemical engineering at Tennessee Technological Univer sity. He has taught chemical engineering for twentyfive years and has served as a consultant at Oak Ridge National Laboratory in nuclear fuel reprocessing. John C. McGee is a professor of chemical engi neering at Tennessee Technological University, where he served as the first chairman of the department for twenty years. He holds BS and MS degrees from West Virginia University and a PhD from North Carolina State University. He has had industrial experience with Dupont. @ Copyright ChE Division ofASEE 1993 Syphon tubes tubes PumpLL L Notched weir overflow Rotameter Tank 2 Tank 1 Water supply Figure 1. Stirred tank model (Levenspiel's Model L) volume (1a)V, and is discharged from the first tank. Nomenclature used here is consistent, where pos sible, with that used by Levenspiel. The total vol ume of the system is V. In Levenspiel's model L, a unit impulse is imposed in the feed to tank 1. If the concentration in tank 1 is C1 and the concentration in tank 2 is C2, the material balances on the two tanks, assuming per fect mixing, yield for tank 1 v6(t)+ bvC2 bvC1 ClV1 = (1) and for tank 2 d[(1 a)VC2] Cbv C2bv = dt 2) Initial conditions for each tank reflect no tracer in either tank with the initial condition in tank 1 a formal property assigned to the Dirac delta function as indicated by Churchill13" C(0)= 0 and C2(0)= 0 (3) These equations yield to rather simple Laplace trans form solution. The transformed equations are 1+bC2(s) (4) 1C( as +(1+b) bCl(s) C2 (s) =E e Ed) (5) (1 a)lts +b Chemical Engineering Education where t=V/v. Inverse transformation of these equations yields the solutions in dimensionless time, 0, given by Levenspiel for the two tanks Ee=C1 1 [miam +b]em(mam2 +b)em20 (6) a(1a)(m1 m2) and O2 b [emle (7m2) a(1a)(mim2) where = 1a+b 1 4ab(1a) ml,m2 = a 1+ 1 2a(1a) ( (1a+b)2 The discussion in Levenspiel is necessarily brief, and stud need to be sure they understand the equations describing model, Eqs. (6) and (7) above, and the procedures to reduce data to a similar form (or to change the equation for the m to the data form). Fogler[41 also shows the development ol equations for Levenspiel's model L. Most of the long time scale models presented by Leveni could be examined in the experimental apparatus with a ] equipment rearrangement. A variation which has been trie students in our laboratories is a modification of Levensy model L in which the tracer or unit impulse is imposed in "stagnant" compartment. The solution to this model as wo out with Jones15' gives the following expressions: Ee =Co a(1a)(mlm2)1emem2 ] C2 am2)[(am +b+ 1)eml (am2 +b+ 1)em2] EQUIPMENT The stirred tanks for this experiment were one 5gE aquarium and one 10gallon aquarium placed endtoen, schematic diagram of the apparatus is shown in Figure 2 a photograph of the apparatus is shown in Figure 3. Water fed to the larger aquarium through a small rotameter, water was discharged from the larger tank via four syp tubes into a small notchedweir overflow tank and then tc drain. Flow from the larger tank to the smaller tank was enabled by using four syphon tubes. Return flow from the sm; tank to the larger tank was accomplished by using a sii aquarium pump/filter device without the filter.* The fil intake was positioned in the smaller tank and the dischE which was adjustable with an integral valve, was made to larger tank. The filter used in this case included a one holdup tank which was filled with inert materials to elimi: a possible third mixed tank in the apparatus. Tracer selec could be dye, salt, or any tracer with detection capabil available. In this work, the tracer selected for the quantity work was sodium chloride because a YSI Scientific Mode * In this case a Model 2 Secondnature Whisper Power Filter: catalog No. 6( Willinger Bros., Inc., Wright Way, Oakland, NJ (2013370001). Spring 1993 C1, aV 2, (1a)V Figure 2. Schematic diagram of apparatus rked  Figure 3. The experimental apparatus (9) conductance meter was available. This meter allowed for either a continuous record (10) of conductance when used with a millivolt potentiometric recorder or an instantaneous reading. Total equipment cost excluding the conductance meter, rotameter, and stirrers illon was $85.00. d. A nd a PROCEDURE was Both tanks were initially filled with wa and ter. Then water flow at a rate of 3.1 liters/ )hon minute was initiated through the rotame the ter into the larger tank, and flow from the also larger tank through the two syphon sys aller teams was started. Flow rates are typical mple and, of course, may be set at any reason ter's able level. Stirrers, placed in both tanks, Large, were activated. Flow through the pump/ the filter was started and measured using the liter bucketandwatch method on the outflow nate of the power filter after a period of time to .tion allow steadystate flow. A return water flow cities rate to the larger tank of 4.8 liters/minute Live was measured. At steadystate the volume S35 of liquid in tank 1 was 36.2 liters, and the )02, volume in tank 2 was 16.5 liters. The above tank volumes and flow rates gave model 151 parameters of 0.678 for a and 1.55 for b. A one molar solution of sodium chloride was prepared for use as tracer, and a calibration curve for the con ductivity meter was prepared. Before an experimen tal run was made using the salt tracer, a run was made using dye as the tracerthis demonstrated the flow patterns in the system and gave some in sight into the perfectly mixed tank assumptions. Dye, instead of salt, has also been used in separate experiments to monitor the tracer concentration. When flows were properly established and steady state conditions were obtained, one liter of the 1 M salt tracer was rapidly poured into the center of the larger tank over a short period of time to approximately replace the regular water flow in a pulseshaped input. The concentration of the mate rial in each tank was monitored alternately with the single conductivity probe, with the probe rein serted into the tanks in approximately the same location each time. Sampling was halted after ap proximately 37 minutes. RESULTS AND DISCUSSION OF RESULTS The experimental results are shown in Figure 4. The response of Model L to a unit impulse input was also determined by solving the equations numeri cally; these results are compared to the experimen tal results in Figure 4. The expected characteristic shapes were obtained and agreement between the experimental results and'the model were within seven percent for tank 1 and within eleven percent for tank 2. The maximum concentration in tank 2 was eleven percent below the model and about two minutes late. No attempt was made to adjust model parameters. Many variations of the experiment demonstrated here could be studied including other models, effect of tracer injection method, effect of adjusting the model parameters, and effect of mixing. Because of the flexibility derived from the ease of rearranging the system, individual laboratory participants or groups could study a number of different models or a few models in depth. SUMMARY AND CONCLUSIONS An interesting and inexpensive processmodeling experiment was demonstrated with qualitative and quantitative results. Other models could be exam ined by simple modifications to the experimental apparatus. The work integrates studies in chemical reaction engineering courses with process modeling and control courses and provides the students with some insight into problems in modeling systems. 152 0 5 10 15 20 25 30 35 40 Time, minutes Figure 4. Comparison of model with experiment ACKNOWLEDGMENTS The authors gratefully acknowledge helpful criti cism by the referees of this paper. NOMENCLATURE a = model parameter, fraction of total volume in feed tank b = model parameter, fraction of feed volume flowing to "stagnant" region C, = tracer concentration in tank 1 C2 = tracer concentration in tank 2 Ce1 = Ccurve for tank 1 based on 6, C1 = Eg = tC1 C02 = Ccurve for tank 2 based on 9, C02 = tC2 E, = exit age distribution for tank 1 in dimensionless time t = mean residence time, V/v V = total system volume v = volumetric feed rate 8(t) = Dirac delta function for unit impulse 8 = dimensionless time t / REFERENCES 1. Levenspiel, Octave, Chemical Reaction Engineering, 2nd ed., Wiley, New York (1972) 2. Bischoff, KB., and R.L. Dedrick, J. Theor. Biol., 29, 63 (1970) 3. Churchill, Ruel V., Operations Mathematics, 2nd ed., McGrawHill, New York (1958) 4. Fogler, H. Scott, Elements of Chemical Reaction Engineer ing, 2nd ed., Prentice Hall, Englewood Cliffs, NJ (1992) 5. Jones, S., private communication (1990) 01 Chemical Engineering Education AUTHOR GUIDELINES This guide is offered to aid authors in preparing manuscripts for Chemical Engineering Education (CEE), a quarterly journal published by the Chemical Engineering Division of the Ameri can Society for Engineering Education (ASEE). CEE publishes papers in the broad field of chemical engineering education. Papers generally describe a course, a laboratory, a ChE department, a ChE educator, a ChE curriculum, research program, machine computation, special instructional programs, or give views and opinions on various topics of interest to the profession. Specific suggestions on preparing papers * TITLE Use specific and informative titles. They should be as brief as possible, consistent with the need for defining the subject area covered by the paper. AUTHORSHIP Be consistent in authorship designation. Use first name, second initial, and surname. Give complete mailing address of place where work was conducted. If current address is different, include it in a footnote on title page. TEXT We request that manuscripts not exceed twelve doublespaced typewritten pages in length. Longer manuscripts may be returned to the authors) for revision/shortening before being reviewed. Assume your reader is not a novice in the field. Include only as much history as is needed to provide background for the particular material covered in your paper. Sectionalize the article and insert brief appropriate headings. TABLES Avoid tables and graphs which involve duplication or superfluous data. If you can use a graph, do not include a table. If the reader needs the table, omit the graph. Substitute a few typical results for lengthy tables when practical. Avoid computer printouts. NOMENCLATURE Follow nomenclature style of Chemical Abstracts; avoid trivial names. If trade names are used, define at point of first use. Trade names should carry an initial capital only, with no accompanying footnote. Use consistent units of measurement and give dimensions for all terms. Write all equations and formulas clearly, and number important equations consecutively. ACKNOWLEDGMENT Include in acknowledgment only such credits as are essential. LITERATURE CITED References should be numbered and listed on a separate sheet in the order occurring in the text. COPY REQUIREMENTS Send two legible copies of the typed (doublespaced) manuscript on standard lettersize paper. Submit original drawings (or clear prints) of graphs and diagrams on separate sheets of paper, and include clear glossy prints of any photographs that will be used. Choose graph papers with blue crosssectional lines; other colors interfere with good reproduction. Label ordinates and abscissas of graphs along the axes and outside the graph proper. Figure captions and legends will be set in type and need not be lettered on the drawings. Number all illustrations consecutively. Supply all captions and legends typed on a separate page. State in cover letter if drawings or photographs are to be returned. Authors should also include brief biographical sketches and recent photographs with the manuscript. ACKNOWLEDGEMENT DEPARTMENTAL SPONSORS The following 154 departments contribute to the support of CEE with bulk subscriptions. 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