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Don Paul, of the University of Texas at Austin ( PDF )
Efficient, effective teaching ( PDF ) A supercritical extraction experiment for the unit operations laboratory ( PDF ) FAQS. III: Groupwork in distance learning ( PDF ) The business meeting: An alternative to the classic design presentation ( PDF ) Thermodynamic properties involving derivatives: Using the PengRobinson equation of state ( PDF ) Computer modeling in the undergraduate unit operations laboratory: Demonstrating the quantitative accuracy of the Bernoulli equation ( PDF ) Using inbed temperature profiles for visualizing the concentrationfront movement ( PDF ) Studentperformance enhancement by crosscourse project assignments: A case study in bioengineering and process modeling ( PDF ) Developing the best correlation for estimating the transfer of oxygen from air to water ( PDF ) A projectbased spiral curriculum for introductory courses in ChE: Part 3. Evaluation ( PDF ) Undergraduate process control: Clarification of some concepts ( PDF ) The interface between ChE and mathematics: What do students really need? ( PDF ) Book reviews ( PDF ) ( XML ) 
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;J1 EDITORIAL AND BUSINESS ADDRESS: Chemical Engineering Education Department of Chemical Engineering University of Florida Gainesville, FL 32611 PHONE and FAX: 3523920861 email: cee@che.ufl.edu EDITOR Tim Anderson ASSOCIATE EDITOR Phillip C. Wankat MANAGING EDITOR Carole Yocum PROBLEM EDITOR James O. Wilkes, U. Michigan LEARNING IN INDUSTRY EDITOR William J. Koros, University of Texas, Austin PUBLICATIONS BOARD CHAIRMAN * E. Dendy Sloan, Jr. Colorado School of Mines MEMBERS Pablo Debenedetti Princeton University Dianne Dorland University of Minnesota, Duluth Thomas F. Edgar University' of Texas at Austin Richard M. Felder North Carolina State Universiot Bruce A. Finlayson University of Washington H. Scott Fogler University of Michigan William J. Koros University of Texas at Austin David F. Ollis North Carolina State University Ronald W. Rousseau Georgia Institute of Technology Stanley I Sandler University of Delaware Richard C. Seagrave Iowa State University Stewart Slater Rowan University James E. Slice University of Texas at Austin Donald R. Woods McMaster University Chemical Engineering Education Volume 35 Number 2 Spring 2001 > EDUCATOR 86 Don Paul, of the University of Texas at Austin, William J. Koros > CLASSROOM 92 Efficient, Effective Teaching, Phillip C. Wankat 104 The Business Meeting: An Alternative to the Classic Design Presenta tion, James A. Newell 128 StudentPerformance Enhancement by CrossCourse Project Assign ments: A Case Study in Bioengineering and Process Modeling, Giilnur Birol, Inane Birol, Ali (inar 148 Undergraduate Process Control: Clarification of Some Concepts, R. Ravi > LABORATORY 96 A Supercritical Extraction Experiment for the Unit Operations Laboratory, Ronald G. Gabbard, Dana E. Knox 116 Computer Modeling in the Undergraduate Unit Operations Laboratory: Demonstrating the Quantitative Accuracy of the Bernoulli Equation, David J. Keffer 122 Using InBed Temperture Profiles for Visualizing the Concentration Front Movement, Paulo Cruz, Addlio Mendes, Ferndo D. Magalhdes 134 Developing the Best Correlation for Estimating the Transfer of Oxygen from Air to Water, Wayne A. Brown > RANDOM THOUGHTS 102 FAQS. III: Groupwork in Distance Learning, Richard M. Felder, Rebecca Brent > CLASS AND HOME PROBLEMS 112 Thermodynamic Properties Involving Derivatives: Using the Peng Robinson Equation of State, R.M. Pratt > CURRICULUM 140 A ProjectBased Spiral Curriculum for Introductory Courses in ChE: Part 3. Evaluation, David DiBiasio, Lisa Comparini, Anthony G. Dixon, William M. Clark 152 The Interface Between ChE and Mathematics: What do Students Really Need? Michael D. Graham, Susan L. Ganter 91, 95, 110 Book Reviews 107, 109 Letters to the Editor 111 Call for Papers 120 ASEE, Chemical Engineering Division Program CHEMICAL ENGINEERING EDUCATION (ISSN 00092479) is published quarterly by the Chemical Engineering Division, American Society for Engineering Education, and is edited at the University of Florida. Correspondence regarding editorial matter, circulation, and changes of address should be sent to CEE, Chemical Engineering Department, University of Florida, Gainesville, FL 326116005. Copyright 0 2001 by the Chemical Engineering Division, American Society for Engineering Education. The statements and opinions expressed in this periodical are those of the writers and not necessarily those of the ChE Division, ASEE, which body assumes no responsibility for them. Defective copies replaced if notified within 120 days of publication. Write for information on subscription costs andfor back copy costs and availability. POSTMASTER: Send address changes to Chemical Engineering Education, Chemical Engineering Department., University of Florida, Gainesville, FL 326116005. Periodicals Postage Paid at Gainesville, Florida and additional post offices. Spring 2001 ] educator DON PAUL ... of The University of Texas at Austin WILLIAM J. KOROS The University of Texas at Austin Austin, TX 78712 I recently conducted an experiment by asking several colleagues at the University of Texas at Austin what words came to mind when they thought of Don Paul. For those who know him well, it is not surprising that the common descriptors included "smart," "organized," "hon est," "practical," and "tough." While those five words undoubtedly capture his core per sonality, the word "productive" also pops to mind when I think of Don. By any standard, Don's prodigious contribu tions to the chemicalengineering and materialsscience lit erature place him almost in a class by himself. In addition to coauthoring over 450 archival journal articles and editing eight books, Don has also mentored 52 PhD students, 47 MS students, and 46 postdoctoral fellows during his career at Texas. Serving as the EditorinChief of Industrial and En gineering Chemistry Research for fifteen years and being on the editorial boards of eight other journals has made his impact on the field of chemical engineering truly enormous. Don's research interests include the broad areas of poly mer science and engineering and chemical engineering. His eight edited books cover a broad range of topics, but they have a common thread as a result of his interest in polymers. Don's current research involves polymer blends, mem branes for separations, drug delivery, packaging, and poly mer processing. The blend research deals with the thermo dynamics of polymerpolymer miscibility, phase diagrams and interfaces, reactive compatibilization of multiphase mix tures, rubber toughening, the control of phase morphology during processing by both chemical and physical means, and polymeric nanocomposites. His research on diffusion in poly mers involves investigation of structureproperty relation ships to design better membranes for separation processes, improved barrier materials, physical aging of thin films, and "thermal switch" membranes. Don has also contributed significantly to theories and models for describing sorption and permeation of small molecule penetrants in polymers. A broad range of materi als, including rubbery, glassy, semicrystalline and liquid crystalline states of these materials, has been considered. Synthesis and characterization of novel materials is a key aspect of his work in all of the above subareas. A BROAD ARRAY OF CONTRIBUTIONS One of our departmental colleagues once joked that he held a stillunproven hypothesis that there are really identi Copyright ChE Division ofASEE 2001 Chemical Engineering Education cal twins with the initials DRP wh office. While highly valuing product dards for quality are also apparent, a a creative and insightful investigate pect of his nature. Beginning with the 1973 ACS Arti steady stream of honors bestowed underlines the respect in which his chemistry and chemical engineer ing communities. In addition to the Doolittle Award, the ACS has rec ognized his contributions through the Phillips Award in Applied Polymer Science and the E.V. Murphree Award for Contributions to Industrial and Engineering Chemistry. The AIChE has recog nized him with the Stine Materials En Award and the William H. Walker Av to the Chemical Engineering Literatu tion as a Fellow. He was elected to the National Ac in 1988 for "outstanding research c meric materials and for leadership in education." Don's Council of Chemi Pruitt Award and the Plastic Institute Award also emphasize not only hi: publication and research arenas, but the interface between industry, goven Don has presented numerous invite the Warren McCabe lecture at North sity, the R.L. Pigford Memorial Lecti Delaware, the Ashton Hall Cary Lec tute of Technology, and the Donald University of Michigan. He has als engineering community through his mittees and organizations throughout the Education Projects Committee of 77 and served as the editor for the Faculties Directory from 196777. accreditation visitor from 197483. to both the chemistry and the chemi munities is reflected by his active ACS and the AIChE. Don served on the Executive Comn sion of Polymeric Materials Sciences 198085 and in many capacities relate well beyond his work as Editor in Ch His work on I&EC Research has seen of archival journal pages published un collaborative assistance of many edit 1986. His editorial contributions hav on editorial boards for The Journal Spring 2001 o operate from Don's vity, Don's high stan nd his recognition as or documents this as hur Doolittle Award, a )n Don by colleagues work is held by the Polymer Engineering and Science, Journal of Applied Poly mer Science, Chemical Engineering Education, Polymer, Journal of Polymer Science, Polymer Physics, Polymer Con tents, and the Imperial College Press Series on Chemical Engineering. Beyond the AIChE and ACS, Don has also been involved in activities of the Council of Chemical Research, serving on its Governing Board (198184) and its Executive Committee [Don] published a classic paper regarding the mechanism of hydraulic permeability through membranes [that] helped call attention to the new program in polymers at UT and launched the membrane activities that have been a strong and continuous component of UT's graduatestudies area for over three decades. gineering and Science (198384). He was a member of the Founding Committee of ward for Contributions the North American Membrane Society. His work with the ire as well as by elec National Academy of Engineering has included service on the NAE Peer Committee in 198992 and 1994 as well as the ademy of Engineering Membership Committee from 199497. The National Re ontributions on poly search Council benefited from his input on its National chemical engineering Materials Advisory Board from 198894, its Committee on cal Research Malcom Polymer Science and Engineering from 199294, its U.S. 's Educational Service National Committee on the International Union of Pure and s impact in scholarly Applied Chemistry from 199396, and its Solid State Sci also his leadership at ence Committee from 199497. He also served on panels for nment, and academia. Materials Science and Engineering at NIST and on the panel ed le i g for International Benchmarking of U.S. Materials Science ted lectures, including Carolina State Univ and Engineering Research. Carolina State Univer ire at the University of Don's story begins in North Carolina where he grew up on tures at Georgia Insti a small farm near Washington, NC. He freely acknowledges L. Katz Lecture at the the strong effect that this background has had on his lifestyle o served the chemical and motivation. An anecdote regarding this point is useful contributions to com here. Don once told me that he recalls going out to hoe his career. He was on weeds out of a large field one hot North Carolina day. the AIChE from 1968 Looking at the very large and intimidating field, he decided Chemical Engineering not to think in terms of its size. Instead, he looked down the le also was an ABET first row and thought, "I can get to the end of this one." Don's ability to speak Hoeing his way to the end of the row, he straightened up and cal engineering com looked down the next row, deciding "I can get to the end of work with both the this one, too," You can guess the rest128 rows later he looked back on the entire field with a sense of accomplish nittee of the ACS Divi ment and an insight that has remained with him throughout and Engineering from the years. Whether it is writing papers or books, or educating ed to ACS publications nearly 150 graduate students and post docs, it is best to take ief of I&EC Research. it "one row at a time" and to just keep on working. close to 50,000 pages Don's contributions to teaching have also been widely ider his watch, with the recognized. He received the General Dynamics Teaching orial colleagues, since Award in 1977, which is the highest teaching recognition in e also included service the College of Engineering, and it focuses on contributions of Membrane Science, to undergraduate education. In 1994, our department nomi PhD Students D.R. Kemp (1972) C.E. Locke (1972) O.M. EbraLima (1973) W.J. Koros (1977) A.H. Chan (1978) C.A. Cruz Ramos (1978) J.E. Harris (1981) R.S. Barnum (1981) E. Woo (1984) J.S. Chiou (1985) Y. Maeda (1985) A.C. Fernandes (1986) M.J. ElHibri (1986) T.A. Barbari (1986) M.E. Fowler (1987) N. Muruganandam (1987) M.C. Schwarz (1987) C.H. Lai (1988) P.S. Tucker (1988) A.C. Puleo (1988) J.H. Kim (1989) P.C. Raymond (1989) J.M. Mohr (1990) J.S. McHattie (1990) H. Kim (1990) G.R. Brannock (1990) T.W.Cheng (1991) I. Park (1991) D.H. Weinkauf (1991) Y. Takeda (1992) C.L. Aitken (1992) C.K. Kim (1992) T.A. Callaghan (1992) M. AguilarVega (1993) J.D. Le Roux (1993) M. Nishimoto (1994) P.P. Gan (1994) B. Majumdar (1994) A.G. Gonzalez (1995) M.R. Pixton (1995) M. Lu (1995) A.J. Oshinski (1995) S. Ziaee (1995) K.A. Schult (1996) C.T. Wright (1997) F.A. RuizTrevino (1997) G.S. Wildes (1998) W.R. Hale (1998) M.S. McCaig (1998) G.D. Merfeld (1998) R.A. Kudva (1999) J. H.C. Chu (1999) Z. Mogri (2001) MS Students D.R. Kemp (1969) J.H. Troell (1969) O.M. EbraLima (1970) J. St. Lawrence (1970) V. Mavichak (1970) C.E. Vinson (1971) D.H. Carranza(1972) A.E. Mann (1972) R.E. Robertson (1972) M. Garcin (1973) J.O. Altamirano (1974) J.R. Stell (1974) J.D. Paciotti (1974) A.A. Rocha (1974) W.E. Garmon (1975) R.L. Imken (1975) S. McSpadden (1975) A.J. Meyer (1975) D. Wahrmund (1975) T.R. Nassar (1976) R.N. Mohn (1977) R.E. Bernstein (1977) J.C. Tiffany (1978) G. Wonders (1978) E. Nolley (1978) A.J. Erb (1979) D.W. Bartlett (1979) C.R. Lindsey (1979) P.T. Chang (1980) M.D. Lorenz (1980) J.J. Ziska (1980) P. Masi (1980) E.A. Joseph (1981) W.A. Smith (1981) E.Y. Adham (1982) T.D. Traugott (1982) W.E. Preston (1982) S.R. Murff (1983) J.D. Keitz (1983) C. McCutcheon (1983) J.L. G. Pfennig (1984) V.J. Triacca (1989) G.P. Shaver (1989) J. Oshinski (1990) A.B. Lombardo (1994) S. Gupta (1995) A. Kelkar (2000) TABLE 1 Don Paul's Former Graduate Students nated Don for the Universitywide Graduate Teaching Award. We con tacted his former graduate students for possible letters of support. The response was overwhelming. Letters poured in from all over, since by that time Don's former students had achieved distinguished positions in many parts of the world. The recurring theme of these letters was an expression of the writer's feelings of deep appreciation for Don's help in their educational development by his tough, but ultimately compassion ate, mentorship. As one of these former students, I was more than pleased that Don received this highly competitive award in recognition of his educational efforts. Don's BS in chemical engineering was.earned at North Carolina State University (1961) and his graduate work was carried out at the University of Wisconsin, Madison (1965). He has been recognized by both of his alma maters with distinguished graduate awards. In addition to summer work at DuPont in the nonwoven fabric area in 196061, Don was a Research Chemical Engineer at Chemstrand Re search Center in North Carolina's Research Triangle Park from 1965 to 1967. LIFE AND LEADERSHIP IN THE DEPARTMENT Don joined the University of Texas faculty in 1967 and has been here now for 34 years. Progressing through the ranks to Associate Professor in 1970 and to Full Professor in 1973, he took an early role as a departmen tal leader. He served as the department's Associate Chairman from 1973 77 and as its Chairman from 197785. During his Chairmanship, Don recognized the need for a forwardlooking approach. He assembled a committee comprised of distinguished leaders in the chemical and petro chemical industries as well as from the academic community to evaluate the curriculum. The committee also analyzed the future needs of the department and the larger chemical engineering community. Many of the elements of this visionary plan are still used as the guiding principles for our department. One of Don's favorite statements is that "chemical engineering is defined by what chemical engineers do." That attitude helped position the department as an early player in the polymer, materials science, microelectronic, and biotechnology opportunities that have helped main tain the vitality of our discipline. Don was also quick to see the need for better bricks, mortar, and laboratory facilities to allow the department's movement toward the new technological areas, while still maintaining connections to its petro chemical roots. He was a key person in acquiring the needed resources to construct our current modem facility, which was occupied in 1986 at the end of his term as Chairman. Strong connections with our alumni and industrial friends also led to the establishment of a large number of endowed positions in the department and college during this period. Don himself was selected as the T. Brockett Hudson Professor in 1978 and as the Melvin H. Gertz Regents Chair in Chemical Engineering in 1985. Following his term as Chairman, Don returned to his active research and teaching duties in the department and served as a mentor for several faculty who were at the time making the transition to academia from industry. During the time he served as Chairman, he managed to maintain an energetic research program, but when he stepped down from that Chemical Engineering Education position, a literal explosion of activity became apparent through his PhD supervision and his publications. MAJOR TECHNICAL CONTRIBUTIONS Don's interests and contributions in polymer engineering and science have included work in both polymer blends and membranes. Not surprisingly, he has managed to also com bine his insights in these two separate areas to provide im portant contributions in advanced blend membrane systems for gas separation membranes. Don's work in polymer blends has led to an important route to new commercial polymer products. His work has integrated thermodynamics, interfacial phenomena, rheol ogy, process, morphology, and properties of these novel materials to provide a solid scientific foundation for this field. Since the late 1940s, numerous papers have suggested that polymerpolymer mixtures were unlikely to be miscible. This belief discouraged and delayed the development of any widespread interest in blends. Indeed, the favorable entropy of mixing for two polymers was known to be very small, if not entirely negligible. Moreover, the premise at the time was that enthalpic effects were positive and unfavorable for mixing. Don was a pioneer in focusing attention on polymerpoly mer interactions as the key to developing miscible blends. He and his colleague, Joel Barlow, published an important paper showing that intramolecular repulsive interactions in random copolymers can provide the basis for exothermic mixing, thereby promoting miscibility with other polymers. This effect meant that such random copolymers could form miscible blends, even when the corresponding homopoly mers could not. This nonintuitive concept was simulta neously recognized by two other groups and is now a corner stone of polymerblend technology. In 1992, Don and his students initiated a series of papers that combined this copolymer model with a modern equa tionofstate theory of mixing. Their work allowed a matrix of interaction energies to be constructed to predict the misci bility of multiple polymers and to design copolymers for controlled phase behavior in blends. This work is also useful for understanding and designing UT's chemical engineering faculty at the time of Don's Chairmanship in 1984. Top row: Keith P. Johnston, E.T. Beynon, James R. Brock, Hugo Steinfink, Douglas R. Lloyd, Joel W. Barlow. Middle row: James R. Fair, Thomas F. Edgar, Gary T. Rochelle, John G. Ekerdt, James E. Stice, Herbert Grove. Seated; John J. McKetta, Eugene H. Wissler, William A. Cunningham, Donald R. Paul, Howard F. Rase, Joel Hougen. (Missing: David M. Himmelblau, W.J. Koros, R.P. Popovich, and R.S. Schechter) Spring 2001 phaseseparated immisciblee) blends in which polymerpolymer interac tions are manifested in the nature of the interface between the phases. Don's work in this area has been com mercialized through longstanding col laborations with various companies. In addition to the enormous amount of work in polymer blends, Don has pioneered the development of mem branes. Within his first year as an As sistant Professor at Texas, he pub lished a classic paper regarding the mechanism of hydraulic permeability '" through membranes. This paper helped call attention to the new program in polymers at UT and launched the membrane activities that have been a strong and continuous component of UT's graduatestudies area for over three decades. Soon after completing this paper on liquid permeation, he pub lished a second classic analysis of mem branesthis one related to gas trans port in glassy polymers. Don cooper ated with the group at Monsanto that Don and Sallj developed the first truly commercially successful gas separation membrane system, called "Prism." Over the intervening years, Don and his coworkers have systematically studied the relationship between polymer struc ture and the gas permeation properties of novel materials synthesized in their labs. Important principles of molecular design have emerged from his work. These insights have been codified into a group contribution scheme for predict ing membrane performance. Several new materials of sig nificant commercial interest have been identified. Moreover, novel processing schemes involving flourination, crosslinking (and of course, blending) of polymers and lowmolecular weight compounds have been studied. FAMILY The only commitment that exceeds in length Don's asso ciation with the UT department is the one with his extraordi nary wife, Sally. Don and Sally met while in graduate school at Wisconsin in 1963. Her disposition and nature caused her to take an interest in children with special needs. Completing her Masters in Speech Therapy meshed well with the timing of Don's completion of his PhD, and they celebrated by getting married in 1964. After locating in Austin, they raised a family that includes Mark, a master pastry chef trained at the James Beard School in New York City, and Ann, who is currently an auditor with the State of Texas. Over the years, Don and Sally shared another favorite yon activityhiking. In addition to hik ing, boating, and other outdoor pur suits, Don has a great love of cooking and a passion for music, especially jazz and blues. His music collection is of H such a size that only someone with his organization skill could maintain it in functional form. In 1995, the saddest event in Don's life removed Sally from him and his children. Her death led to a period of . deep mourning that eventually yielded to the tough nature that, as noted in the introduction, is one of Don's sig nature qualities. THE RECENT PAST AND THE FUTURE I recall having lunch with Don eigh , teen months after Sally's death. He S had his old spark back and told me J that he wanted to do something sig ,. nificant for the institution that had helped him so much. He said he had been thinking about the lack of a for a hiking trip. mal Materials Science Department at UT and how this was often cited as a problem that needed to be dealt with. He said, "I now see this as a possible advantage, rather than a disadvantage, if it is handled properly." He unveiled an idea for a materials institute that would cut across college as well as departmental boundaries. Don visualized a network of individuals linked together by their common interest in materials and with a core of instru ments and facilities in a central institute. His vision quickly spread beyond lunchtime conversation to the offices of deans and the vice president of research. With the valuable support of the administration, Don's concept moved toward reality. At this point, Don's "takeonerowatatime" approach resurfaced. He made the rounds from the physics department to the chemistry department to the aerospace, chemical, elec trical, and mechanical engineering departments, recruiting support at the grassroots level to match the upperadminis tration support. In 1998, the Texas Materials Institute be came a reality, and Don was inducted as its first director. Under his leadership, materials work is now prospering at UT. New facilities, new positions in various departments, and colleagueships that would probably not have occurred have begunone row at a time. Our colleagues in the department, in the college, and across the university appreciate and value Don's catalytic contribution in fostering this unusual and valu able addition to our university. We are all indebted to Don for his uniquely broad and deep contributions. 7 Chemical Engineering Education MM book review Elementary Principles of Chemical Processes 3rd Edition By Richard M. Felder and Ronald W. Rousseau John Wiley & Sons, 605 Third Avenue, New York, NY 10158 0012; 675' pages; $111.95 (cloth); (2000) Reviewed by D. Hunkeler Swiss Federal Institute of Technology The third edition of this classic introductory chemical engineering text is intended to compliment a first course in stoichiometry, material and energy balances, and introduc tory thermodynamics. As such, it is aimed at engineering and chemistry students who have completed their first year of general university education. Freshman physics and chem istry are valid prerequisites, although if the course is taught with the complimentary teaching modules, one could con sider offering it earlier. The third edition follows the same format as the previous two editions, with a preliminary set of three chapters discussing the units and dimensioning of pro cess variables and their associated calculations. This section is (in some curricula) omitted, due to its coverage in other courses, but it is a valuable asset since many student difficul ties in balances occur due to sloppy "accounting." The body of the text discusses material balances, first for nonreactive singlephase processes and then adding multiphase systems, recycling, and bypass. One of the strengths of the book is the ease with which the authors' introduce thermodynamics into the subject matter. Equa tions of state for nonideal gases, compressibility, multicom ponent equilibrium, and twophase partitioning and solid liquidvapor phase diagrams are presented in a comprehen sible manner that permits students to begin solving problems on the day of the lecture. This is something Felder has long advocated in his interactive teaching approaches, and the third edition certainly shows the value of the NSF's sponsor ing of the concepts which brought it to fruition. The text also integrates graphical presentations of correla tions with computerbased programming challenges. The students will not realize until subsequent courses, to what extent they have been introduced to (and to a large extent mastered) elementary chemical and engineering thermody namics. The problems at the end of the chapter do an excel lent job of integrating the concepts presented, along with statistics, into the estimation of thermodynamic data. Practical problems, related to a series of important unit operations including various separation methods such as absorption, adsorption, condensation, crystallization, distil lation, and extraction are presented throughout the first eleven chapters. The authors' also discuss batch, semibatch, and Spring 2001 continuous reactors operating under adiabatic and isother mal conditions, both at steady state and dynamically. Com bustion is treated separately. Liquidgas processes including evaporationcompression, humidification, dehumidification, and scrubbing are also integrated into material and energy bal ances. Overall, the new problems are challenging, yet doable. The third section of the book discusses energy and energy balances. There is minimal overlap with the discussion of forms of energy typically presented in freshman physics. Energy balances on nonreactive processes challenge stu dents to organize their solutions. The text pulls itself to gether in Chapter 9 when the enthalpy of reaction is used, and estimated, principally to permit the calculation of a reactor's energy loss, temperature, or pressure. The balances are also extended to complete processes. Discussions of alternative fuels, which may appear oldfashioned, is a take home deliverable from this text, as are its extensive data base (tables, graphs, and CDs) that may convince sopho mores they never have to set foot in an engineering library. The text concludes with a chapter on computeraided calculations, which many schools cover in a separate course (as they do the material on transient processes). But if Chap ters 10 and 11 are omitted, Chapters 12 through 14 cannot be. The authors' offer three case studies (one in the area of materials and two in commodity chemistry) that need to be presented at the end of the twosemester sequence to con vince students they can, indeed, design plants. It is a motiva tion which will drive many of them to integrate kinetics, reactor design, transport phenomena, and separations into their working knowledge and become chemical engineers. As the only chemical engineering course taught to chemists, in my experience, it provides an excellent sensitization to the challenges facing industrial organic and polymer chemists when they develop new (macro) molecules. The text comes with a CD that includes an animated encyclopedia of chemical process equipment, the EZ solve software for balances along with tutorials, and an index of learning styles. As fantastic as these are, the real value is that the physical property database demystifies the coupling be tween thermodynamics and engineering, which confuses so many students. With the database provided, carrying out material balances is no longer a cumbersome task akin to financial accounting, but is fun. Felder and Rousseau have made chemical engineering enjoyable. My students make significantly less calculation errors on their balances thanks to the third edition of this book, and they are motivated and listen better to the concepts their predecessors had ignored. Overall, the authors' present a way for introductory stu dents to respect complexity and understand the need for engineering approximations. Take the authors' advice to let the students enjoy problembased learningthey will better understand themselves, their career, and their choices. The book is a service to our profession. 0 rMe classroom EFFICIENT, EFFECTIVE TEACHING PHILLIP C. WANKAT Purdue University West Lafayette, IN 479071283 Good teaching requires that students must learn the right content, have a good attitude, and learn how tolearn. Teaching is efficient for students when there is a high ratio of (student learing)/(student time on the course). Because they are so busy, professors also benefit from courses that are reasonably efficient. A course is effi cient for professors when there is a high ratio of (student learing)/(professor's time on the course). Although there are times when effective teaching and efficient teaching conflict, most of the time effective teaching can also be efficient. As a professor, you can apply the techniques of time management and efficiency by becoming familiar with con cepts such as missions, goals, priorities, todo lists, calen dars, and prime time.''21 These methods should be applied,r3] paying special attention to efficient teaching.1361 EFFICIENT TEACHING OF LECTURE COURSES[3] Course Development Designing a course is basically an engineering design problem. What is the purpose of the course? The purpose of a required undergraduate course is obviously very different than the purpose of an elective. You should obtain several old outlines and syllabi. Talk both to professors who have Phil Wankat received his BSChE from Purdue and his PhD from Princeton. He is currently a Professor of Chemical Engineer ing at Purdue University. He is interested in teaching and counseling, has won several teaching awards at Purdue, and is Head of Interdisciplinary Engineering. His research in terests are in the area of separation pro cesses, with particular emphasis on cyclic separations, adsorption, and preparative chromatography. taught the course and to those who teach prerequisite courses to see what you can expect the students to know. Talk to professors who teach followup courses to determine what students must learn in your course. The syllabus is a contract with the students. Find a good one and adapt it with appropriate modifications for your course. Be explicit about rules and regulations. The students will not know what you expect of them until you tell them (even then some students will claim ignorance). Start with firm, and perhaps even tough, rulesthen relax later on. As part of the syllabus, you should develop a tentative course outline. Plan to spend one or two periods at the beginning of the semester reviewing material the students are supposed to know, and plan one period before every major test for catch up and review. Cover less, but cover it in more depth than was previously done. Many students only work when there are assignments or tests, so there should be something for the students to do outside of class at least every other week, preferably more often. Shortly after the first test, ask for feedback from the stu dents, using a "oneminute quiz." Pass out index cards and ask students what you (and the TAs) can do to help them learn more. Using the responses you receive, make appropri ate changes to improve the course. Midcourse corrections based on this feedback can rescue a course headed for disas ter. Allowing students to have input into test dates and due dates of projects also indicates your willingness to listen and will be greatly appreciated by your students. Finally, arrange to teach the same course three or four times in succession. This allows you to reuse much of your preparation and results in a better course in less time. At the end of the semester reflectively analyze what worked and what didn't, then plan changes for the next offering while the details of the course are still fresh in your mind. Copyright ChE Division of ASEE 2001 Chemical Engineering Education Lectures Lecturing is the most efficient teaching method the first time a course is taught. Since lectures can be prepared im mediately before class, it is easy to adjust the course as you proceed through the semester. Lectures must actively en gage the students in order to be effective. In subsequent offerings of the course, try modifying the lecture approach or try other teaching approaches such as cooperative group techniques. When you know the material, you can prepare a new fifty minute lecture in two hours or less. Repeat lectures can be prepared in onehalf hour. Trying to prepare a lecture in less time is obviously dangerous. Unfortunately, many new fac ulty spend significantly more time than this without becom ing good teachers.15'61 Spend the two hours of preparation time in several short bursts, starting at least a day before the lecture will be delivered. The first fifteen minutes of prepa ration should be used to develop a title and a brief concep tual outline. Fill in some of the details later, but do not write out your notes wordforword. Since a student's maximum attention span is 15 to 20 minutes, the standard fiftyminute lecture hour should have one or two lecture breaks to make it effective. For example, a good scheduling might be U Introduction and short review U Minilecture C Lecture break C Minilecture C Summary and transition to homework for next class Good lecture breaks include active learning exercises such as smallgroup discussion, smallgroup problem solving, brainstorming, and student reflection. Since the audience's limited attention span forces you to use breaks, you will naturally cover less material; but the breaks serve to refresh the students so they pay more attention to the minilectures, and the indepth processing that occurs during breaks in creases student learning. With a little practice it is possible to be comfortable lec turing and to actually enjoy it. If you are uncomfortable the students will be uncomfortable, regardless of how well prepared you are. Quickly prepared, brief lecture notes are effective since they control content tyranny. By focusing on the most important points and leaving details to examples, you don't have to race through every second of the lecture. Remember that from the students' viewpoint, it is more important to end on time than to cover everything. The second time you teach the course, try making partial lecture transparencies. Include most of the material needed for the transparency, but skip some of the key points. Give copies of these notes to the students. This procedure will eliminate many of the errors inherent in note taking and will give the students time to thinkbut it will still require them to pay attention so they can fill in the key missing items. You can thus cover more material without sacrificing stu dent understanding. Tests Write new tests every term. As you teach, create a file of possible test problems. They can be variants of homework problems, or problems sparked by student misunderstand ings, and so forth. The purpose of the file is to provide potential problems that can be considered when you write the test. Avoid disasters by solving the test completely be fore using it, and record how long it takes you to solve the test. Freshmen and sophomores will need about five times as long, juniors about four times as long, and seniors about three times as long. Discussing procedures in class thoroughly before the first test will help reduce the students' anxiety. A good practice is to use old tests as ungraded practice tests that the students can do on their own, posting the solution on a bulletin board or on the web. This access to old tests helps greatly in reducing student test anxiety. Be present for the test since you are the best one to fix any lastminute errors or prob lems. There is also less cheating when the professor is present. If at least half the class is unable to finish the test on time, the test is too long. Try to make grading as fair as possible, keeping in mind that students consider unfair grading to be unethical. For reasons of consistency, prepare a solution key to allocate partial credit when appropriate. Fair grading requires a re grade procedure. Reduce the hassle of regrades by requiring written regrade requests. Attention to Students Students want and deserve individual attention. They are very tolerant of fumbling in the lecture if they believe you care about them. Although the average engineering under graduate may not be as smart as your peers in graduate school were, remember that he or she counts among the best undergraduates at your school. And sheer technical compe tence is less important for success in industry than motiva tion, hard work, timing (or luck), communication skills, and the ability to work well with a diverse assortment of people. Look for the best in your students, and you will probably find itprofessors with a good attitude usually end up with students with good attitudes. If you don't learn the students' names, they will feel like just numbers on a list and will be much more likely to skip class, be disruptive, not do the work, and/or cheat. Admit tedly, learning a lot of new names each semester is difficult, but the effort is repaid by smoother course operation. Any Spring 2001 thing you know beyond their names, such as hometowns or career goals, will greatly help you gain rapport with them. Since personal attention to the students' needs requires a significant expenditure of time, efficiency and effectiveness can get lost in the competition for their share of time. A reasonable compromise is to hold scheduled group help ses sions (particularly before tests) and a modest number of scheduled office hours during the week. Be available to the students during your office hours. Also, asking your teach ing assistants to hold office hours provides another opportu nity for the students to learn. Come to class five minutes early and stay five minutes after class. In addition to giving you a chance to prepare the classroom, coming early sends the message to the students that you are looking forward to this class. Staying late offers a good time to answer questions. The combination of com ing early and staying late provides an opportunity for indi vidual attention, particularly for those students who will not use office hours. When students ask for special arrangements to take tests or to turn in homework, be flexible, but require them to be responsible and to inform you in advance if possible. Occa sionally students will abuse your generosity. It will usually be clear when this has happened, however, and you should make sure it does not happen a second time. If you treat students as adults, most of them will act accordingly. A NEW TEACHINGLEARNING PARADIGM Standard courses use a teachercentered paradigm. Even when such courses are well taught, using advanced strate gies such as cooperative groups, they suffer from some deficiencies that appear to be inherent to the basic paradigm. Students seldom learn howtolearn on their own and there is a clear limit to the professor's efficiency in teaching the course. Relatively mature students can take more responsi bility for their learning and be taught with a problem or projectcentered paradigm. Engineering students will focus on learning when there is a task that must be completed. Problembased learning171 (PBL) is a method for using problems or short projects to focus student attention on learning. While PBL does help students learn howtolearn, it does not increase the professor's efficiency since preparation and grading of the projects is very timeconsuming. PBL is usually reported as increasing, not decreasing, the time the professor spends on the course. For students to learn howtolearn and to drasti cally increase the professor's efficiency while retaining course effectiveness, a different paradigm is needed. Fortunately, the efficiency literature gives us a clue as to what this paradigm should includedelegation.[ ,2] Instead of the professor planning the material, picking topics, pre paring material, lecturing, etc., ask the students do this work. 94 With appropriate feedback from the professor, delegation of these responsibilities to the students can result in significant growth in their ability to learn. Delegation can be used for the entire course81] or for a portion of the course. Course projects are an effective way to focus students' attention, and they lend themselves to delegation of respon sibilities. Projects lead to more learning if significant class time is devoted to them. For example, finish the lecture portion of the class before the end of the term and spend the remaining class time on project work. If class time is not devoted to the project, students consider it addon work. Although projects can be done by individuals or groups, group projects result in much more significant efforts. I assign the groups to ensure that they are diverse in ability, learning styles, and work styles. Use the principles of good cooperative group instruction.[4] The professor sets the tone for the project work. Expect graduate students and seniors to deliver professional quality work. Provide examples of papers or reports that surpass the minimal quality standards. Give guidelines for topics and some examples, but expect the students to devise their own topics and titles. Work with the students to narrow the scope of their projects so that they can be finished in the time available. For example, one group that started with the topic of supercritical extraction had 19,000 hits in a computerized search. Two iterations later, the topic supercritical extraction of coffee resulted in 65 hits, which is a much more manage able number. The topic must be something new for the students. Do not allow recycling of projects from other courses and note in writing that recycling projects will be considered a form of cheating. Although allowing students to do a project on their master's or PhD research might seem effi cient, it is unfair to students who are not doing research in an area related to the course. Regular meetings with groups during scheduled class time and periodic student presentations to the entire class help combat procrastination. Final reports will be significantly better if students first turn in a rough draft. Have another group critique each rough report. These critiques help to improve the final reports and give the students practice in the highest level of Bloom's taxonomyevaluation. If the cri tiques are graded, the students will take this exercise seri ously. I also critique the drafts with the idea of showing the groups areas for improvement. Allow about one week for groups to finish their reports after the critiques are returned. I also ask the students to fill out forms to critique oral presentations, but these critiques are not graded. A side benefit of requiring critiques is that everyone pays attention and learns from the projects of all groups. Weekly group meetings instead of lectures help prevent procrastination, keep the professor informed of group progress, and provide an inkling of personal interactions within each group. In addition to commenting on the techni Chemical Engineering Education cal work, take time to discuss work habits when necessary. For example, most graduate students have not learned how to rapidly sort articles so that only the most important are read thoroughly. The professor can also be a cheerleader when groups feel that they will never be able to finish their projects. When the members of a group are not getting along, part of the meeting time can be used to help the students start processing group interactions. Do not try to solve their interpersonal problems, however. Make the stu dents do this work or at least muddle through it. The bane of grading group work is freeloaders. Delegate the responsibility of lowering the grades of freeloaders to the students. My grade assigned to each project is the highest grade students in the group can receive for the project. I require the students in each group to assign what percentage of this grade (ranging from 0 to 100%) each group member should receive. I then average these percentages for each group member and calculate their project grades. This pro cedure reduces freeloading and drastically reduces complaints from other group members when freeloading occurs. This projectbased paradigm is very efficient for profes sors. During the project work I typically spend a total of four hours per week on the course, with most of that time focused on the students. During project work the students spend much more time working on the course than the professor does! Grading reports takes time, but since the reports are better than in other classes it is easier. The students learn their topic in depth, they learn howtolearn, and they actually pay attention to the feedback on their writing. A note of caution is in order, however. Most professors and students are inexperienced with projectbased teaching. Professors need a certain amount of chutzpah to relinquish the normal control of a lecture course. They also need to know the material better than they would for a lecture class since it is impossible to prepare for student questions. Note that this method is not "turning the students loose." Students actually receive increased guidance and support. Despite the support, the freedom and responsibility may overwhelm im mature students. Students, particularly those with high grades, may rebel. Other faculty may be skeptical and probably will not be supportive if the course flounders. Because of these risks, a graduate or seniorlevel elective course is a good place to experiment. IMPROVEMENT AND GROWTH Master teachers may be born, not made; but good, effi cient teaching is a learned skill. Sign up for a teaching workshop. Study and try out new teaching methods. After each class, reflect on what worked and what didn't, and tailor your future actions accordingly. Take notes, with the aim of improving the course next time. Find someone in your department with whom you can discuss teaching on a regular basis. Continual experimentation with teaching meth ods helps to prevent boredom and burnout, which can be major problems. Such experimentation can lead to teaching improvement and eventual recognition as a master teacher. REFERENCES 1. Covey, S.R., The Seven Habits of Highly Effective People, Simon and Schuster, New York, NY (1989) 2. Lakein, A., How to Get Control of Your Time and Your Life, Signet Books, New York, NY (1973) 3. Wankat, P. C., "Effective, Efficient Teaching," Proceedings ASEE 1999 Annual Conference, CD ROM pdf file 000167, (1999) 4. Wankat, P.C. and F.S. Oreovicz, Teaching Engineering, McGrawHill, New York, NY (1993). [Out of print. Avail able free as pdf files at 5. Boice, R., The New Faculty Member, JosseyBass, San Fran cisco, CA (1992) 6. Boice, R., Advice for New Faculty Members: Nihil Nimus, Allyn and Bacon, Boston, MA (2000) 7. Woods, D.R., How to Gain the Most from Problem Based Learning, D.R. Woods, Waterdown, Ontario, Canada, (1994). [Available from McMaster University Bookstore, 905572 7160] 8. Wankat, P.C., "Learning Through Doing: A Course on Writ ing a Textbook Chapter," Chem. Eng. Ed., 27(4), 208 (1993) a for book review Multimedia Fluid Mechanics by G.M. Homsy, et al. Cambridge University Press (2000) $19.95 Reviewed by Hossein HajHariri University of Virginia The CD by Homsy, et al., is a most welcome and timely educational tool for students (and instructors!) of introduc tory fluid mechanics. Fluid mechanics is a very visual disci pline. To date, such visual accompaniment to the mathemati cal equations describing flow physics has either come from labs or from samplings of the fantastic movies put together in the 1960s. Whereas the material of those movies will never become outdated, the innovative multimedia approach adopted by Homsy, et al., adds dimensions to the presenta tion that were simply not available forty years ago. This CD ROM is a true multimedia tool that has no paper counter part. In other words, this is not a book typed on a CDit is truly all that the box cover promises, and then some. The approach is based on modules. Currently, there are three technical modules, with more promised. The current modules are dynamics, kinematics, and boundary layers. There is also a module on history, which should be studied by all students. Continued on page 101. Spring 2001 laboratory A SUPERCRITICAL EXTRACTION EXPERIMENT For the Unit Operations Laboratory RONALD G. GABBARD,* DANA E. KNox New Jersey Institute of Technology Newark, NJ 07103 upercritical fluid extraction (SCFE) is becoming a viable unit operation in the chemical process indus try. It uses the distinguishing properties of a fluid that is above its critical point (critical temperature and pressure) to enhance performance in an extraction process. While the concept of SCFE has been known for over a century,[1] it has not been widely used in industry for a variety of reasons. Foremost among these reasons is the high financial risk involved with SCFEspecifically, high installation and op erating costs for a process with a relatively short track record of commercialscale success. Another reason is that a con ventional separation technique is usually already available. Add to this the difficulties caused by the lack of sound theoretical models available for scaleup and it becomes obvious why there has been no incentive for SCFE develop ment on a widescale industrial level. Even the early com mercial applications, such as propane deasphalting in the 1930s, the SOLEXOL process of the 1940s, and the ROSE process in the 1950s, were not enough to generate large scale interest. 21 While these reasons remain true today, new motivating factors have recently paved the way for SCFE to become a viable extraction alternative. The modern chemical engineer is faced with environmental regulations that require strict control of emissions and reductions in hazardous waste. A change in energy costs has lessened the favorable gap in operating costs conventional highheat separation techniques such as distillation have historically had over highpressure SCFE systems. Increased performance demands, such as lower acceptable limits of either residual solvent or other contaminants in the food and pharmaceutical industries, have increased the popularity of SCFE. Also, SCFE solvents (such Address: BASF Corporation, Polymers Division, South Brunswick, NJ 08831 as carbon dioxide) are often more environmentally friendly. As SCFE becomes more and more popular in industry, it is finding widespread applications from the decaffeination of coffee to the removal of trace organic contaminants in waste water.131 Additional work is going on in many other areas from coal liquefactiont4] to fractionation and purification of polymers.[51 Some of these processes (such as coffee decaffeination) are vastly different from the original deasphalting and ROSE processes, while others (such as coal liquefaction) are very similar. While these widely vary ing applications are using many different solvents, the one used most predominantly is carbon dioxide. Supercritical fluid extraction also presents a unique com bination of highpressure phase equilibrium and mass trans fer. As such, an experiment dealing with SCFE represents a Ronald G. Gabbard is Process and Product Development Manager for the Styropor Busi ness Group in the Polymers Division of BASF Corporation, where he has been doing poly mer related research for the last eleven years. He previously worked as a Process Develop ment Engineer at Maxwell House Coffee, and it was in this capacity that he developed an interest in SCFE technology. He received his BS and MS in Chemical Engineering from New Jersey Institute of Technology. Dana E. Knox is Associate Chair for the Chemi cal Engineering, Chemistry, and Environmen tal Science Department at New Jersey Institute of Technology, where he has been since 1983. His teaching interests are in graduate and un dergraduate thermodynamics and equilibrium stage processes, and his research interests are in fluid phase equilibria and thermodynam ics. He received his BS, ME, and PhD degrees in Chemical Engineering from Rensselaer Poly technic Institute. Copyright ChE Division of ASEE 2001 Chemical Engineering Education ... this article discusses a laboratory experiment that both reinforces fundamental engineering principles and introduces the students to one segment of this growing technologyspecifically solid/SCFE. valuable addition to the traditional unit operations labora tory. With that in mind, this article discusses a laboratory experiment that both reinforces fundamental engineering prin ciples and introduces the students to one segment of this growing technologyspecifically solid/SCFE. The experiment provides an opportunity for the students to explore SCFE and to use their engineering skills to deal with issues of scaleup and highpressure equipment design and operation.1[6 From a thermodynamic point of view, it allows students to explore physicalproperty prediction at high pres sures far away from ideal behavior when experimental data are not available. They are then asked to use these predic tions to correlate an equipment design parameter such as the mass transfer coefficient. Additionally, students have the opportunity to evaluate the usefulness of the data they have collected. They will need to understand that if the data indicates saturation of the exit stream, their analysis of the mass transfer coefficient will be invalid because the equa tion they are using (see Eq. 1 in the "Analysis" section) becomes indeterminate. Finally, they will need to have de veloped a plan to avoid saturation prior to starting the ex periment in order to be successful. As far as we know, the inclusion of a supercritical extrac tion experiment in the senior unit operations laboratory is unique. STUDENT EXPERIMENT The experiment consists of a semicontinuous packedbed extraction of naphthalene by supercritical carbon dioxide. The primary objective is to measure the mass transfer coeffi cient for the extraction at a variety of conditions and to develop a correlation for it as a function of these process conditions. Carbon dioxide was the chosen solvent because of its moderate critical conditions (304.2 K, 73.8 bar), its widespread industrial use, and its environmentally friendly nature. It is also nontoxic, making it a very safe lab solvent. Naphthalene was chosen because of its relatively high solu bility in supercritical carbon dioxide and the availability of sufficient data on the system.[51 Equipment The experiment consists primarily of a supercritical screen ing system (see Figure 1) designed and manufactured by Autoclave Engineers of Erie, Pennsylvania. The preas Figure 1. Flow diagram: supercritical fluid extraction system.  Micrometering Valve Spring 2001 Rupture Disc Vent sembled system includes all the necessary basic compo nents: feed pump, extraction column, extract receiver, in strumentation, and a heated pressure boundary used to de pressurize the exit stream. The cost of an Autoclave (814 8385700) system typical of the one used in this laboratory was slightly lower than a similar system made by ISCO (8002284250). The heated pressure boundary was optional and added to the cost of the ISCO SCF 1200 system. One additional benefit of the Autoclave system is that it is a little larger in size than the ISCO system. Since this is intended to be a unit operations laboratory, we felt that having an ana lyticalscale unit would not do justice to the concept of SCFE as a unit operation. We wanted the students to have some degree of a "handson" experience with the lab that we felt would not be achieved with smaller analytical scale equipment. A standard CO2 cylinder with a liquid dip tube is used as the feed tank. The CO2 is cooled by passing the feed tube through an ice bath prior to entering a Milton Roy 1/4Hp, variablespeed positivedisplacement (PD) pump. The PD pump is capable of operating between 40400 cc/hr. The pump discharge pressure is controlled by an adjustable back pressure control valve that can operate in the range of 8480 bar. Excess flow, which causes a pressure higher than the desired set point, is recirculated back to the suction side of the pump. The pump discharge pressure is measured just upstream of this control valve. A vapor vent valve is sup plied downstream of the backpressure control valve. This allows any vaporized CO2 caught in the pump feed line to be vented off during startup. Without the vent, the feed pump would become vapor bound and cavitate. Additional cooling is obtained by packing the pump head in ice. Four valves around the extraction column isolate the col umn and provide the flexibility needed to operate it in either an upflow or downflow configuration. The column is 12 inches long, has an inside diameter of 0.688 inches (nominal 1 inch OD), and is rated for approximately 700 bar at 1000C. It can be electrically heated with two external band heaters. A surfacemounted thermocouple measures the outer col umn wall temperature, and a Watlow proportional/integral controller is used to control the temperature. The column is protected from overpressurization by a 1/4inch diameter rupture disc that is piped directly to the bottom of the col umn. The disc is nominally rated for 480 bar at 22'C. The pressure boundary on the downstream side of the column is maintained by a micrometering needle valve, also supplied by Autoclave Engineers. The column can be isolated upstream of this valve with a blocking valve. The discharge lines from the column, as well as the body of the micrometering valve, are electrically heat traced with a 110volt heating tape. The heat tracing is in place to counter act the large JouleThomson cooling effect that results when the CO, flashes across the micrometering valve and to prevent the line from freezing. The extracted material is collected in the extract receiver. This vessel has a nominal volume of 99 cubic centimeters and has a drain valve at the bottom. The vessel is protected by a pressure relief valve set to open at 1.4 bar (at 220C). The extract and solvent enter the receiver from the top. The extract, which is no longer soluble in the nonsupercritical solvent, separates from the solvent and is collected in the vessel while the solutefree CO, is discharged from the top of the vessel. It then passes through a small filter to a rotameter and then through the dry test meter. In addition, the temperature in the extract receiver is measured by a thermocouple. The rotameter (calibrated for CO2 at standard temperature and pressure in units of standard cubic feet per minute) measures the instantaneous CO, flow rate. The CO2 flow is then totalized by a dry test meter. This provides total standard cubic feet of CO, used during an experiment. Procedure The students are provided with the equipment, and are given detailed safety instructions and a list of "Discussion Topics" (see Table 1). Additionally, the experiment is con ducted under closerthannormal supervision for the senior unit operations lab. The students must develop their own experimental plan that will allow them to answer the ques tions outlined in the discussion topics. In developing their plan, they must decide on the pressures at which to operate the column, whether to use upflow or downflow through the column, what flow rates to use, and how long each extrac tion should last to provide meaningful data. An individual experiment consists of charging the extrac TABLE 1 Discussion Topics 1. Should the column exit stream be saturated with naphthalene? 2. Discuss how you evaluated the mass transfer coefficient, k. 3. For packed beds, the mass transfer coefficient is often represented as a function of the N, Nsc, and NG, numbers, if that function takes the following form, determine the values of the constants a, b, c, and d. k a(NRe)b NSc) (NGr)d 4. What is the fugacity coefficient of the solute in the condensed phase at its sublimation pressure? 5. Use the PengRobinson or other suitable equation of state to predict the solubility of the solute in the supercritical solvent. How well does the equation of state prediction compare to the solubility reported in the literature? 6. How much energy input is required to maintain isothermal conditions across the micrometering valve? 7. Support your decision to operate the column in either the upflow or downflow configuration. Chemical Engineering Education tion column with a known amount of naphthalene (filling the rest of the column void with sand), reassembling the sys tem, pressurizing the system to the desired operating pres sure at a chosen temperature, and initiating flow of supercritical carbon dioxide. Periodic measurements of feed pump and column pressure, column and extractreceiver temperature, and instantaneous and cumulative carbondiox ide flow rates are taken. Once each individual extraction is completed, the column is reweighed to obtain the quantity of naphthalene extracted. The column, rather than the naphthalene recovered in the extract receiver, is weighed because it is difficult to account for all the naphthalene in the receiver without the addition of another solvent. Some naphthalene usually precipitates on the piping walls after the micrometering valve assembly. (This needs to be cleaned out between each experimental run.) Given this, less error is introduced into the experiment by doing the simple lossinweight measurement on the column. Safety is a key aspect of the laboratory for two reasons. First and foremost is to ensure the safety of the students performing the highpressure experiment; second is the heightened appreciation for safety the students gain from completing a highpressure experiment such as this. To per form this experiment safely, students are required to develop a level of proactive thinking that they are not typically re quired to have in other unit operations laboratory experi ments (i.e., fluid flow, efflux time of a tank, or pressure drop in a packed column). The students must evaluate all the possible outcomes of their actions prior to doing anything with the equipment to make sure that the desired result is obtained safely. Students are not allowed to operate the equipment until they have demonstrated reasonable safety awareness to the instructor. This is not to say that the previ ously mentioned experiments should be performed casually or unsafely, but rather that the chance for serious injury is greater when performing a highpressure experiment such as SCFE. This creates an atmosphere in which the students take lab safety very seriously. Providing this heightened level of safety awareness was a significant underlying objective of the laboratory and was one of the key reasons this experi ment (HighPressure Supercriticial Extraction) was consid ered rather than something such as a simple wettedwall masstransfer experiment. Some of the key safety instructions given to the students are No work can be done on the extraction column or associated piping until the system has been depres surized and then verified. Verification ofdepressur ization is accomplished by opening all valves around the column and making sure that both inlet and outlet pressure gauges read zero and that there is no discharge from either of the two vents. Even if the column discharge is plugged, the inlet pressure Spring 2001 gauge should still read zero when the column is depressurized. If this state is not obtained, the students are required to obtain help from either the instructor or the teaching instructor in the lab. No work should be done on the extraction column while it is plumbed up and in place on the extrac tion unit. All work should be completed while the column is out of service and on the workbench. Additionally, stepbystep instructionsfor loading and unloading the extraction column are located in the appendix of the student laboratory. The maximum operating temperature set in the student laboratory is 55 C. While this was done to make sure that the column operating pressure would not exceed design limits, it also prevents liquid naphthalene from being pushed out of the column because the 55 C limit is significantly lower than the 8082 C naphthalene melting point. Finally, with regard to safety, the students should be made aware of the issue of retrograde condensation within SCF systems. This is the phenomenon that can occur when vapor liquid equilibrium exists at a temperature or pressure above the mixture critical point. In such a situation, increasing the operating temperature at constant pressure may lead to con densation. This can be a problem in the student experiment where the micrometering valve and discharge piping are electrically heat traced to prevent freezing. The students should be cautioned to use the heat tracing only to maintain isothermal conditions in this part of the system and not to add unnecessary heat. Should retrograde condensation occur at the inlet of the micrometering valve, the possibility of the system being plugged increases and the system will need to be depressurized as outlined above in the first bullet. The naphthaleneCO2 system is susceptible to retrograde condensation when the operating pressures are around 125 bar and below. Analysis The first step in the analysis is for the students to ensure that the carbon dioxide exiting the column is not saturated with naphthalene (first discussion topic in Table 1). This could happen if either the naphthalene/sand ratio charged to the column is too large or if the carbon dioxide flow rate is too small. In these cases, the effective contact time may be long enough for saturation to occur. This, of course, would render any mass transfer coefficient calculations meaningless. Students can then determine the mass transfer coefficient, k, from the wellknown relationship Az kACLM (1) where C, is the average naphthalene concentration in the exit stream (as determined by material balance), Vo is the empty column superficial velocity, A is the surface area per unit volume, z is the naphthalene packedbed length, and ACLM is the logmean concentration difference across the column defined as (Cat 0) (Csat C) ACLM = at c( (2) fn  Cat C1 where Csat is the naphthalene concentration at saturation (i.e., the solubility). Thus ACLM represents the effective driving force for the extration. All of these quantities can be determined from measured experimental quantities except for the surfacetovolume ratio A (which is given to the students) and Csat, which the students are asked to estimate from an equation of state such as PengRobinson (discussion topic #5). The subject of highpressure phase behavior, in cluding topics such as equilibrium between a solid and a supercritical fluid phase, is covered in the undergraduate thermodynamics sequence at New Jersey Institute of Tech nology. The pertinent equation is at MI M1 Psat VI0 (p p a 1 C = yI exp (3) 1 V V P RT where Psat is the vapor pressure of the solid phase at the system temperature, V1so1 is its molar volume, M, is its molecular weight, y, is its mole fraction in the supercritical fluid mixture at saturation, V is the molar volume of the supercritical fluid mixture, and 41 is the solute fugacity coefficient in the supercritical fluid mixture. Each of the latter two quantities are determined by the chosen equation of state. The equation must be solved iteratively for y, since the fugacity coefficient is a function of composition. Alter natively, the students could obtain a value for Csat from the literature for this quantity. The value of A, the surfacetovolume ratio for the packed bed, has been experimentally estimated using the student equipment and is given to them. This value is only an order ofmagnitude estimate as it will change each time the col umn is repacked with fresh naphthalene. This is because the naphthalene crystals are not very uniform in size or shape. This estimate could be improved by adding a size reduction/ classification step to the naphthalene to make it more uni form in terms of size and shape. This operation would not necessarily be part of the student experiment, but rather an operation a teaching assistant would perform to ensure that the naphthalene was uniform. During the experiment the students should have evaluated the mass transfer coefficient k at several different sets of operating conditions. This should allow them to correlate k with key operating conditions. A typical correlation for SCF applications might have a form such as17l81 NSh = f(NRe,NSc,NGr) (4) where NsH is the Sherwood number (kz/DA,), NRe is the Reynolds number (DVp/ ), Nsc is the Schmidt number (g/DABP), and NGr is the Grashof number (d3gpAp/p2). Here, DAB is the diffusivity, D is the column diameter, p is the fluid density, Ap is the density difference between the saturated interface and the bulk, unsaturated fluid, g is the fluid viscosity, and d is the average particle diameter. The Grashof number, not generally needed in subcritical fluid applications, is included to account for buoyancy effects. These arise due to the relatively high density and low viscos ity and thus exceptionally low kinematic viscosities of supercritical fluids. The students are thus expected to evaluate the constants in an expression such as S= a(NRe)b (Nc)(NGr)d (5) Obtaining sufficient data to evaluate all four constants should be one of the objectives when the students develop their experimental plan. In preparing for the experiment, they are expected to have consulted the provided references19'01 for determining quantities such as viscosity and diffusivity. In their writeup, the students are expected to address each of the discussion topics listed in Table 1. The first three topics relate to the experimental determination of k, as al ready described. The remaining topics require that the stu dents comprehend various thermodynamic aspects of SCFE. These include fugacities of solids at high pressures, use of equations of state for highpressure phase equilibrium, and the JouleThomson effect. CLOSING REMARKS Student response to this experiment has been generally positive. They enjoy the "handson" experience associated with assembling and disassembling the apparatus, the expo sure to a nontraditional unit operation, and the combination of mass transfer and highpressure thermodynamics in a practical application. The principal experimental difficulty has been deposition of naphthalene in the discharge line and in the micrometer ing valve. This can be alleviated by ensuring that the exiting stream is well removed from saturation. With proper choice of operating conditions, however, the experiment works well as designed. Students can complete several indi vidual experiments in the allotted time of two fivehour laboratory periods. An alternative experimental setup would be to replace the discharge line and condensate receiver with a "Utube" in a cold trap. While this idea is yet to be attempted experimen tally, one can envision weighing the tubing (including the Chemical Engineering Education "Utube") downstream of the micrometering valve before and after each trial as an alternative to obtaining the amount of naphthalene extracted in the experiment. The mass of the extracted naphthalene would be a more significant portion of the total mass of the sample and apparatus being weighed. In this manner, more accurate results may be possible. If multiple groups complete the lab during the semester, another enhancement to the laboratory experience could be to have the different groups use different solute materials. At the end of the semester, a comparison of the correlation constants from each group could be completed and this could be used to create a generalized correlation. Possible alternative solutes include biphenyl and benzoic acid. Should this approach be taken, it is important to remember that the value of A, the surfacetovolume ratio in Eq. (1), must be provided for each system investigated. In summary, this laboratory experiment provides a valu able introduction to a modern unit operation in the chemical process industry while at the same time it encourages cre ative thinking in the synthesis of concepts from disparate areas of chemical engineering. NOMENCLATURE A a,b,c,d C, Surface area per unit volume of a packed bed (m2/m3) Correlating equation parameters Average concentration of naphthalene in exiting carbon dioxide (kg/m3) Cat Concentration of naphthalene in carbon dioxide at saturation (kg/m3) ACLM Log mean concentration driving force (kg/m3) D Column diameter (m) DAB Diffusivity (m2/sec) d Particle diameter (m) g Acceleration due to gravity (m/sec2) k Mass transfer coefficient (m/sec) P Pressure (bar) Psat Vapor pressure of solute (bar) R Ideal gas constant (m3bar/molK) T Temperature (K) V Molar volume of fluid phase (m'/mol) Vs' Molar volume of solute (m3/mol) V Empty column superficial velocity (m/sec) z Packed bed length (m) p Density (kg/m3) [t Viscosity (kg/m sec) Dimensionless Numbers N", Grashof number (d3gpAp /2) NRe Reynolds number (DVOp / ) Nsc Schmidt number (I / DABp) Nsh Sherwood number (kz / DAB) REFERENCES 1. Hannay, J.B., and J. Hogarth, "On the Solubility of Solids in Spring 2001 Gases," Proc. Roy. Soc., 29, 324, London (1879) 2. McHugh, M.A., and V.J. Krukonis, Supercritical Fluid Ex traction, Principles, and Practice, 2nd ed., Butterworth, Stoneham, MA (1994) 3. Eckert, C.A., J.A. Van Alsten, and T. Stoicos, "Supercritical Fluid Processing," Environ. Sci. Tech., 20, 319 (1986) 4. Maddocks, R.R., J. Gibson, and D.F. Williams, "Supercritical Extraction of Coal," Chem. Eng. Prog., 49 (1979) 5. McHugh, M.A., and M.E. Paulaitis, "Solid Solubilities of Naphthalene and Biphenyl in Supercritical Carbon Diox ide," J. Chem. Eng. Data, 25, 326 (1980) 6. Gabbard, R.G., "The Development of a Senior Unit Opera tions Laboratory on the Supercritical Extraction of Solid Naphthalene with Supercritical Carbon Dioxide," M.S. The sis, New Jersey Institute of Technology (1993) 7. Debenedetti, P.G., and R.C. Reid, "Diffusion and Mass Trans fer in Supercritical Fluids," AIChE J., 32, 2034 (1986) 8. Lee, C.H., and G.D. Holder, "The Use of Supercritical Fluid Chromatography for Obtaining Mass Transfer Coefficients in FluidSolid Systems at Supercritical Conditions," Ind. Eng. Chem. Res., 34, 906 (1995) 9. Jossi, J.A., L.I. Stiel, and G. Thodos, "The Viscosity of Pure Substances in the Dense Gaseous and Liquid Phases,"AIChE J., 8, 59 (1962) 10. Funazukuri, Y., Y. Ishiwata, and N. Wakao, "Predictive Correlation for Binary Diffusion Coefficients in Dense Car bon Dioxide,"AIChE J., 38, 1761 (1992) O Multimedia Fluid Mechanics Continued from page 95. The CD is neither a book nor a collection of movie clips. It is truly a seamlessly integrated multimedia tool. The user can read some brief text describing the phenomenon, can look at the equations and see the meaning of each term, and also look at some movie clips that will drive the point home. Most importantly, there are a number of very simple, but cleverly designed, interactive experiments where the user can take data off of a running movie clip and process the automatically tabulated data in order to investigate the di mensional relationships and gain valuable insights. These interactive experiments constitute very nice classroom dem onstrations to supplement lectures. An equation feature that is used cleverly is a rollover feature where as the mouse pointer is dragged over each term of the equation, the term is magnified and highlighted, and its meaning pops up in a small text box. I cannot overemphasize how well this CD is done. The selection of the topics, the level of coverage, and the actual presentation are all superb. There are many hyperlinks throughout the CD; however, unlike some other CDs where the user can hyperlink his/her way into a digital purgatory, on this CD one can always return to the page of interest using the small navigation map at the top of the page. Congratulations to Professor Homsy and his colleagues for undertaking the muchneeded task of creating a new tool for aiding students of fluid mechanics. Also, congratulations for holding the line on the price, which is extremely reasonable in an environment of skyrocketing textbook prices. O Random Thoughts... FAQS. III GROUPWORK IN DISTANCE LEARNING1' RICHARD M. FIELDER, REBECCA BRENT North Carolina State University Raleigh, NC 27695 Of all the instructional methods we advocate in our teaching workshops, the ones we emphasize most involve students working together in small groups. Workshop participants invariably ask whether such collabo ration is possible in distance learning. The answer is that it may take some additional effort by the instructor, but it can be done and done effectively. In this column we offer ideas for getting students at re mote sites to collaborate when attending lectures in a syn chronous course, working through lessons in an asynchro nous course, and doing homework in either distance mode. Other references outline the hows and whys of using groupwork in traditional class settings[2'31 and discuss the educational value of distance learning compared to tradi tional classroom instruction.[41 In synchronous lectures, brief group exercises can be as signed just as they are in traditional classrooms. (Ask a question or assign a short problem to pairs or small groups of students, stop them after 30 seconds3 minutes, collect answers, provide the correct answer if necessary, and move on.) The instructor may announce in the first class that such exercises will be interspersed throughout the lectures to provide practice for the homework and tests, adding that the students at the remote sites can either do the exercises as instructed, in which case they will learn how to do them, or just sit there and watch, in which case they'll quickly get bored and learn little or nothing. If some students choose not to participate, the loss is theirs. A similar procedure may be followed for asynchronous course offerings that go out on videotape or webbased media. When the students come to an exercise in a taped or streamed presentation they can either (a) pause the presenta tion, try the exercise (ideally with others who may be physi cally or virtually present with them), and then fastforward to the point in the presentation where the answer is pre sented, or (b) just do the fastforwarding. The instructor should present both options in the first class and strongly suggest that if the students really want to learn the material they will choose the first one. Students may be helped to connect with one another in small groups to view the classes and work through the exercises via instant messaging, e mail, threaded discussion, and ftp transfers. In addition, growing numbers of online studentsespecially those in industryhave access to videoconferencing facilities with electronic whiteboards. With those tools, virtual teams can almost (but not quite) duplicate the inperson team experience. The first step in getting students at remote sites to collabo rate on problem sets or projects is to organize virtual teams and set them up to interact electronically using any of the tools mentioned above. Simply asking students to do some thing in groups is not enough to guarantee effective learning, however, as anyone who has ever tried it knows. Even in traditional classes students may do little or no work but get the same grade as their more industrious colleagues, and serious conflicts may arise between teammates with varying levels of ability and senses of responsibility. The problems may be even worse when groups are virtual and don't have the selfregulating capability provided by facetoface meet ings. It is therefore particularly important in distance classes to adhere to the defining principles of cooperative learning, Richard M. Felder is Hoechst Celanese Professor Emeritus of Chemical Engineering at North Carolina State University. He received his BChE from City College of CUNY and his PhD from Princeton. He is coauthor of the text Elementary Principles of Chemical Processes (Wiley, 2000) and codirector of the ASEE National Effective Teaching Institute Rebecca Brent is an education consultant specializing in faculty devel opment for effective university teaching, classroom and computerbased simulations in teacher education, and K12 staff development in lan guage arts and classroom management. She codirects the SUCCEED Coalition faculty development program and has published articles on a variety of topics including writing in undergraduate courses, cooperative learning, public school reform, and effective university teaching. Copyright ChE Division of ASEE 2001 Chemical Engineering Education especially positive interdependence (if anyone fails to do his or her part, everyone loses in some way), individual ac countability (all team members are held account able for all the material in the assignment), and regular selfassessment of team functioning. Standard references offer guidance on how to meet the criteria for cooperative learning in tra ditional classes,'31 and tips for making groupwork effective in a distance setting are given by Millis15' and Bailey and Luetkehans.16' The fol lowing suggestions are drawn from these sources. 1. Make it clear to the students why groupwork is being required.15' This admoni tion is particularly important for students in dis tance courses, whose learning preferences tend to favor working independently. 2. Form small teams that are balanced in knowledge and skills.[561 Teams of three or four are large enough to provide adequate diversity of opinions, experiences, and learning styles, but not so large that individual members can successfully hide. Groups of all strong stu dents or all weak students should be avoided. If possible, at least one member of each team should have experience with the computer tools to be used to complete the assignments. had their say, a resolution is sought.) Consider conducting such sessions by videoconference or telephone rather than asynchronously. ... wOrkin togeffier in Uma anddane effi""Ibr 3. Give clear directions regarding both the assignments and the communication tools.15' Virtual groups may find it particularly frustrating to have to decipher muddy directions about what to do and how to do it, and their frustration could hurt both their motivation and their performance. Give short preliminary assignments that require the team members to demonstrate their mastery of the communication software. 4. Monitor team progress and be available to consult when teams are having problems.'5'6 The tendency of some students in traditional classes to let groupwork slide in the face of other time demands is likely to be worse when the team members never see each other facetoface. Appoint team coordinators whose responsibilities are to keep their teams on task and to report on progress and problems at regular intervals. Periodically rotate this role among team members. Prompt groups that are not meeting frequently enough and offer guidance if they appear to be stuck. 5. Intervene when necessary to help teams overcome interpersonalproblems.'6 Suggest strategies like active lis tening to resolve conflicts. (Each side makes its case, and the other side has to repeat that case to the first side's satisfac tion without attempting to counter it. When both sides have 6. Collect peer ratings of individual citizen ship and use the ratings to adjust the team assignment grades."I Rewarding exceptional team members and penalizing noncontribu tors helps avoid many of the conflicts and re sentments that often occur when students work on group projects. A procedure for collecting ratings and using them to adjust team grades is described in the literature.'7] 7. Anticipate problems and get help when necessary.'5' You can be reasonably certain that any problem you encounter in groupwork has already been encountered by others and is ad dressed somewhere in the literature. When a problem arises, check the references12'31 to make sure you have not forgotten any of the ele ments of good practice in cooperative learning and ask knowledgeable colleagues or faculty development center personnel to help you strategize remedies. I References 1. See 2. Cooper, J., and P. Robinson, "Annotated Bibliography on Cooperative Learning," 3. For descriptions of different types of active and cooperative learning exercises and guidance on how to implement them, see (a) Millis, B.J., and P.G. Cottell, Cooperative Learning for Higher Education Faculty, Phoenix, American Council of Education/Oryx Press (1998) (b) Johnson, D.W., R.T. Johnson, and K.A. Smith, Active Learning: Cooperation in the College Classroom, 2nd ed., Edina, MN, Interaction Book Co., (1998) (c) Felder, R.M., and R. Brent, "Cooperative Learning in Technical Courses: Procedures, Pitfalls, and Payoffs," Eric Document ED377038 (1994) Coopreport.html > 4. Felder, R.M., and R. Brent, "Is Technology a Friend or Foe of Learning," Chem. Eng. Ed, 34(4), 326 (2000) 5. Millis, B.J., "Managingand Motivating!Distance Learn ing Group Activities" 6. Bailey, M.L., and L. Luetkehans, "Ten Great Tips for Facili tating Virtual Learning Teams," Distance Learning '98: Pro ceedings of the Annual Conference on Distance Teaching and Learning, Madison, WI, August 57, (1998) ERIC Docu ment ED422838 7. Kaufman, D.B., R.M. Felder, and H. Fuller, "Accounting for Individual Effort in Cooperative Learning Teams," J. Engr. Ed., 89(2), 133 (2000) 0 Spring 2001 All of the Random Thoughts columns are now available on the World Wide Web at http://www2.ncsu.edu/effective_teaching/ and at http://che.ufl.edu/cee/ % 1classroom THE BUSINESS MEETING An Alternative to the Classic Design Presentation JAMES A. NEWELL Rowan University Glassboro, NJ 08028 here is an increasing consensus among academics and practicing engineers that effective communica tion skills should be an integral part of an engineer ing education."'3] When engineers who have been out of school for ten years are asked "What courses do you wish you had taken?", Kranzber'41 reports that the most common answer is "English courses." Both ABET15 and the rest of the technical community[61 recognize that communications are part of a broader package of interpersonal, communica tion, and teamwork skills that Seat and Lord171 refer to as "performance skills." Many educationally focused programs, including the pro grams at Rowan"81 and the University of North Dakota,191 have integrated technical communication into their core en gineering curriculum. In many cases, however, oral commu nication exercises in engineering consist of little more than giving repeated technical Powerpoint' presentations to an audience and answering a few brief questions at the end. Such an exercise emulates a presentation at a technical con ference, but resembles very little else in the business world. There is no doubt that this presentation format is valuable, but it should not be the only experience that an undergradu ate engineering student receives. Jim Newell is Associate Professor of Chemi cal Engineering at Rowan University. His technical research interests are in high performance polymers and carbon materi als. His pedagogical interests focus on com munications and assessment of leading out comes. He currently serves as Secretary/ Treasurer of the Chemical Engineering Divi sion of ASEE. Conducting a business meeting instead of a final presenta tion in a senior plantdesign course provides an alternative to ANOTHER formal oral presentation. In this model, student teams plan and conduct a formal business meeting with faculty and industrial representatives serving in formalized roles. Details of the process are provided below. THE PROCESS Each design team is asked to conduct a business meeting with the Executive Committee of their company/customer. The Executive Committee consists of the Chief Executive Officer Engineering Director Finance Director Marketing/Sales Director Safety/Environmental Director Proposed Plant Manager Obviously, the number of members on the Executive Com mittee and their specific roles can be altered to accommo date the number of faculty and/or industrial representatives attending the presentations. Each group makes a formal pre sentation to this committee, including a description of the proposed process, relevant design issues, an economic analy sis, and recommendations. This presentation should not ex ceed thirty minutes. During the presentation, the committee limits itself to questions of clarification. Following the formal presentation, the members of the committee will ask questions of the design group. Commit tee members may address their questions to the team as a whole, or to specific members. Although there is no time limit to the questioning period, 20 to 25 minutes represents a typical length of time. During the presentation, the speaker Copyright ChE Division of ASEE 2001 Chemical Engineering Education stands at the overhead projector or computer while the other group members are seated facing the committee. All group members are seated during the questioning. TEAM ROLES Each member of the design group should perform a spe cific function on the team. At least three distinct roles that must be filled are The Team Leader This member is responsiblefor providing the introductory materials and anything dealing with the "big picture." Teamleader responsibilities include making sure that all members of the group are given sufficient opportunities to participate in the questioning and that every question receives an adequate answer. The Economics Expert This member is responsible for presenting the economic analysis and fielding detailed questions about economic calculations and other issues. The Engineering Expert This member is responsible for presenting the technical aspects of the process including equipment selection, sizing, and processing issues. This person should be prepared to justify technical assump tions and other process decisions. Teams with four members can divide either the economics or engineering issues between two members, but there must be only one team leader. Obviously, these positions may be further divided, or additional roles may be added to accommodate larger teams. Student learning is disserved if individual members of a design team spend the semester focusing on only a single aspect of the design process. To avoid this dilemma, the faculty member's selection of the engineering expert and the economics expert should be made and announced to the team only 48 hours before the presentation. Using this ap proach, team members cannot know which section of mate rial they will be responsible for discussing and are more likely to work on all aspects. The team may pick its own leader. GRADING An ongoing concern with group projects is how to effec tively account for individual performance in team projects.1101 In this business meeting, grading can account for both team and individual performances. It is reasonable for students to feel that their grades should not be destroyed by a weak performance from an unmotivated student. At the same time, a weak member can negatively impact the effectiveness of the team presentation. Thus, a division between team and individual points seems appropriate. On the presentation itself, the team as a whole is graded on a fivepoint scale based on the following items: [ Visual Aids (Clarity; Font Size; Usefulness) [1 Organization (Appropriate Structure and Flow?) E Introduction (Grabs Attention? Appropriate Content?) E[ Body (Completeness; Accuracy; Clarity; etc.) [x3] E Summary (Concise? Covered Key Points?) El Overall Effectiveness (Speaker's Goals Accomplished?) Total Possible Points: 40 Thus, each team member receives the same score from these 40 points. Individual team members are also evaluated on E Delivery (Volume; Clarity; Rate; etc.) E Poise and Appearance (Appropriate Dress? Nervousness? etc.) Total Possible Points: 10 Thus, every team member can receive up to fifty points from the presentation. Forty of these points are the same for every member, while ten points vary from member to mem ber. This division of team and individual grading makes all members accountable for the success of the team while at the same time it maintains individual distinctions. The questioning period also results in a portion of the grade, but the mechanism is different for the experts and the team leader. Each expert is evaluated on the following aI Poise (Calmness, Ability to "Think on One's Feet") [x2] I Ability to Answer [x2] [ Interaction with Audience (Eye Contact? Demeanor) Total Possible Points: 25 Thus, each expert has 25 possible points for his or her role during questioning. The experts' total for the presentation and questioning is divided by 7.5 to provide a 110 grade. The team leader has additional responsibilities during the questioning, so his or her scoring is more involved. It is evaluated on E Poise (Calmness, Ability to "Think on One's Feet") [x2] a Ability to Answer [x2] E Interaction with Audience E Distribution (All Group Members Used?) [x2] 1 Responsibility (Questions Suitably Answered?) [x2] Total Possible Points: 45 Each team leader has his or her total score divided by 9.5, resulting in the same 110 grading as the experts. It is impor tant to note that the team leader does not receive more credit than the other team members, but that more of the team Spring 2001 leader's grade is determined by the questioning. A sample grading sheet is shown in Table 1. Obviously, the categories can be expanded, altered, or weighted differently to accom modate different priorities of design faculty. SELECTION OF EXPERTS AND TEAM LEADERS Design teams select their own team leaders, while experts are assigned by the faculty member in charge, with only 48 hours advance notice. The team leader is responsible for sending all members of the Executive Committee a brief e TABLE 1 Final Meeting Grade Report (NOTE: x2 = doubleweighting; x3 = triple weighting) Evaluator Project Common Presentation Grades: Visual Aids (Clarity; Font Size; Usefulness) Organization (Appropriate Structure and Flow?) Introduction (Grabs Attention?: Appropriate Content?) Body (Completeness; Accuracy; Clarity; etc.) [x3] Summary (Concise? Covered Key Points?) Overall Effectiveness (Goals Accomplished?) Total Points Team Leader Economics Technical Delivery Poise and Appearance (Questioning) Poise [x2] Ability to Answer [x2] Audience Interaction Distribution [x2] Responsibility [x2} Individual Totals Group Leader Economics Technical Team Total Individual Total Grand Total Score mail that includes A formal invitation to the meeting, including mention of the time and place A statement identifying the team leader and other experts A brief summary of the topic to be discussed during the meeting The email must be sent at least 24 hours before the meeting. RESULTS The businessmeeting format has proven successful at two different universities. Students reported that they "felt more like a team" and were "less stressed" by the presentation format. Students with internship or other industrial experi ence reported that the format was more realistic and closer to what they experienced in their jobs. Overall, the students rated the new format a 4.73 out of a possible 5.00 when asked to rate the effectiveness of the business meeting. The faculty have also enjoyed this method. Because of the group format, there was more time for detailed questioning. It was also easier to evaluate both group and individual performances. Other universities, including the Universidad Nacional de Salta in Argentina, have expressed interest in this idea and it is presently being implemented at the Israel Institute of Technology. Overall, the business meeting pro vided a useful alternative to a classical oral presentation. REFERENCES 1. Bakos, J.D., "A Department Policy for Developing Commu nication Skills of Undergraduate Engineers," J. ofEng. Ed., 75, 101 (1986) 2. Elbow, P., "Teaching Thinking by Teaching Writing," Phi Delta Kappan, p. 37 (1983) 3. Newell, J.A., D.K. Ludlow, and S.P.K. Sternberg, "Progres sive Development of Oral and Written Communication Skills Across an Integrated Laboratory Sequence," Chem. Eng. Ed., 31(2), 116 (1997) 4. Kranzber, M., "Educating the Whole Engineer," ASEE PRISM, p. 28, November (1993) 5. Engineering Criteria 2000, Engineering Accreditation Com mission, Accreditation Board for Engineering and Technol ogy, Inc., Baltimore, MD (1998) 6. "Manufacturing Education Plan: Phase I Report, Industry Identifies Competency Gaps Among Newly Hired Gradu ates," Society of Manufacturing Engineers (SME), Dearborn, MI (1997) 7. Seat, E., and S. Lord, "Enabling Effective Engineering Teams: A Program for Teaching Interaction Skills," J. of Eng. Ed., 88(4), 385 (1999) 8. Newell, J.A., A.J. Marchese, R.P. Ramachandran, B. Sukumaran, and R. Harvey, "Multidisciplinary Design and Communication: A Pedagogical Vision," Internat. J. Eng. Ed., 15(5), 376 (1999) 9. Ludlow, D.K., and K.H. Schulz, "Writing Across the Cur riculum at the University of North Dakota," J. of Eng. Ed., 83(2), 161 (1994) 10. Kaufman, D.B., R.M. Felder, and H. Fuller, "Accounting for Individual Effort in Cooperative Learning Teams," J. of Eng. Ed., 89(2), 133 (2000) O Chemical Engineering Education I Setters to the editor Editorial Note: The "Class and Home Problems" section on pages 366368 of the Fall 2000 issue of CEE presented Erich A. Muller's article, "A Thermodynamics Problem with Two Conflicting Solutions." In it, tanks A isothermall) and B (adiabatic) arefilled with an ideal gas and connected by pipes and a valve. Initially, PA > p,. If the valve is opened and equilibrium attained, will it have been necessary to add (or remove) heat from tank A? Professor Muller's article has elicited the following two letters. His reply is also appended. We appreciate the interest that Professor Muller's problem has generated, and request that any further correspondence on this problem be emailed to him at emuller@usb.ve To the Editor: The recent article by Milller1il presents an interesting dis cussion of pedagogically important issues. We wish to com ment on two aspects of the article. First, we believe that it is pedagogically more sound to treat Miller's "two conflicting solutions" as (nonconflicting) solutions to different prob lems that arise from two different equilibrium models of the situation, as implied in his comments. Second, we believe that his "Comments on the Equation for the Uniform State, Uniform Flow Model" can be improved regarding the basic assumptions underlying use of the unsteadystate energy balance equation for a control volume and its general appli cation in firstlaw analysis. We elaborate on both these points in the following. Concerning the analysis of the situation described in the article, we note that his "Solution #1" relates to a model in which it is stated that "tank B is adiabatic"; that is, there is no heat transfer to or from tank B (Q = o) at any time to any other body, although this does not preclude exchange of energy via flow of matter through the connecting line and valve. Practically speaking, the equilibrium state for the contents of tank B is a partial equilibrium state with respect to the contents of tank A: mechanical, but not thermal, equilibrium. Regardless of where the control surface is placed (around tank A alone or around tanks A and B together), the conclusion reached is as Muller states: QA> 0. Solution #1 is the solution to the problem arising from one particular model of the situation. His "Solution #2" relates to a different model of the situa tion, in which it is stated that there is "a heat transfer be tween the tanks" (presumably through the connecting line and valve). In this case, tank B evidently has an adiabatic enclosure with a (small?) diathermal hole in it. This changes the equilibrium aspect of the model to be addressed, to one allowing for both mechanical and thermal equilibrium with respect to the contents of both tanks. This also changes the conclusion reached for the resulting problem to, as MUller also states, QA = 0. We thus believe that it is pedagogically better to treat the two cases as two different models of the situation and to compare the results of a firstlaw analysis of the resulting problems, rather than to present the results as two conflicting solutions of the same problem. Miller cannot on the one hand state that "tank B is adiabatic" and on the other state that there is "a heat transfer between the tanks." Thermody namics requires precise, rather than "shrewd," statements of models and systematic analysis of resulting problems. Concerning his "Comments on the Equation for the Uni form State, Uniform Flow Model," we feel that Miiller's justification of his starting point for solution #1, as a conse quence of a general firstlaw analysis for a control volume, can be strengthened. This strengthening is pedagogically important, to enable students to appreciate points at which approximations are made to exact equations. His "generalized energy balance," Eq. (7), should be re placed by (we also change the sign of W, in accordance with recommended practice) d Fmniis +e e)= dt msys sys k,sys p, sys)] + W + Y ri(t)[h(t)+ k(t)+ ep(t) inlets e m(t)[h(t) + ek(t)+ ep(t)] (A) exits In Eq. (A), u, ek, ep, and h deote specific internal energy, kinetic energy, potential energy, and enthalpy, respectively, and a tilde (~) denotes an appropriately defined intensive Spring 2001 quantity. Thus, for a property within the control volume (sys) Ju(z,t)p(z,t)dV sys _(t) (B)______ msys(t) Jp(z,t)dV (B) v and similarly for ek,sys and ep,ys In Eq. (B), dV is a vol ume element, p is density, and z denotes a point within the control volume. Correspondingly, for a property at an inlet or exit Sh(x,t)p(x,t)un(x,t)dA h(t)= t p(x, u(x,t)dA (C) A and similarly for ek(t)and ep(t). In Eq. (C), dA is an area element of an inlet or exit area, x denotes a point on the area, and un is the flow velocity normal to dA. Eqs. (A) to (C) must be supplemented with the massconservation equation dmsys dry m(t) mh(t) (D) inlets exits The validity of Eq. (A) rests on two generally accepted concepts not introduced by Muiller: the continuum hypoth esis and a local equilibrium hypothesis. The former allows integration of point properties over volumes and areas, as in Eqs. (B) and (C), and the latter allows calculations using macroscopically based property relationships. Equations (A) and (D) are differential equations. As in some introductory texts,[2'31 it is tempting to deal instead with their integrated forms, between times t, and t2, say, m2( U2 ek,2 ep,2)ml +1 ek,1+ep,l t2 =Q12 +W12 + h(t)[h(t)+ek(t+ep(t)]dt inlets t r m(t)(t)+ek(t)+e (t)]dt (E) exits t, m2 m1= mi I me (F) inlets exits Equations {(A),(D)} and {(E),(F)} are exact. Equation (E) is only formal result and may not always be useful, however. This form is deceiving since it implies neglect of any inter dependence of the left and right sides of Eq. (A). Simplification of Eqs. {(A),(D)} or {(E),(F)} involves invoking appropriate approximations for special cases of the spatial and temporal dependence of the properties at the inlets and exits and of the system. Important special cases are uniformflow, for which the properties at an inlet or exit are independent of position x (giving h(t)=h(t)) (or for each phase of the flow) uniform state, for which the properties of the system are independent of position z (giving uisy (t) Usys (t)) (or for each phase within the system) steadyproperty flow, for which the properties at an inlet or exit are independent of time t steady flow, for which mr at an inlet or exit is indepen dent of time t (steady flow usually implies steady property flow, but the converse is not necessarily true) steady state, for which the properties of the system are independent of time t; this entails the vanishing of the left side of Eq. (A) (steady state usually implies steady flow and steadyproperty flow) The uniform flow (UF) assumption at inlets and exits (incorporated without comment by Miiller in his Eq. 7) and the uniform state (US) assumption for the system are often used in the absence of any information concerning spatial dependence of the properties. (The former is consistent with a plugflow assumption and the latter with a wellstirred vessel assumption.) Together, they form part of the basis for an unsteadystate flow model referred to by Miiller as the "UniformState UniformFlow (USUF) model." This desig nation by itself is misleading, however, since this model includes a third assumption that corresponds to the steady property flow assumption defined above. As essentially pointed out by Miiller, these three assumptions (together with neglect of kinetic and potential energy terms) allow Eq. (E) to be simplified to Miller's Eq. (1), his "working equa tion" of the USUF model. More generally, for unsteadystate flow processes, the steadyproperty flow assumption does not hold, and the USUF model is invalid. We do not believe that it should be empha sized pedagogically since it severely restricts the firstlaw analysis to rather special cases, such as the discharge situa tion described by Miiller in his solution #1 and filling a vessel from a constantproperty source/reservoir. We recom mend instead that a firstlaw analysis deal directly with the differential equations (A) and (D) as such. This approach handles all situations (including the USUF model as a spe cial case), and is consistent with the approach of some intro ductory texts14'51 and recent pedagogical articles.16'71 R.W. Missen University of Toronto W.R. Smith University of Guelph References 1. Miiller, E.A., "A Thermodynamics Problem with Two Con flicting Solutions," Chem. Eng. Ed., 34(4), 366 (2000) Chemical Engineering Education 2. Sonntag, R.E., C. Borgnakke, and G.J. van Wylen, Funda mentals of Thermodynamics, 5th ed., Wiley, New York, NY, pp. 163173 (1998) 3. Cengel, Y.A., and M.A. Boles, Thermodynamics, 3rd ed., McGrawHill, New York, NY, pp. 222229 (1998) 4. Elliott, J.R., and C.T. Lira, Introductory Chemical Engi neering Thermodynamics, PrenticeHall PTR, Upper Saddle River, NJ, pp. 7277 (1999) 5. Sandler, S.I., Chemical and Engineering Thermodynamics, 3rd ed., Wiley, New York, NY, pp. 3036 (1999) 6. Wisniak, J., "Discharge of Vessels: Thermodynamic Analy sis," J. Chem. Ed., 74, 301 (1997) 7. de Nevers, N., "NonAdiabatic Container Filling and Emp tying," Chem. Eng. Ed., 33, 26 (1999) 0 To The Editor: In the Fall 2000 Class and Home Problems Column, E.A. Miillermll proposes a thermodynamics problem designed to demonstrate that two seemingly correct but incompatible solutions can be found from the thermodynamic analysis of a particular process, and furthermore that such incompatible solutions provide an opportunity to improve one's under standing of thermodynamic analysis. Miller proposes the following: Consider two tanks, A and B, connected with a valve and initially filled with (ideal) gas at the same temperature, but the pressure in A is greater than the pressure in B. Tank B is well insulated (adiabatic), but tank A is maintained at constant temperature by thermal contact with a heat source or sink. Miller asks: "If the valve that connects both tanks is opened and equilibrium is attained, will it have been neces sary to add (or to remove) heat from tank A?" (Denoted as QA) For this problem, it is clear that tanks A and B will be at the same pressure at the end of the process. But Mtiller clearly intends that tanks A and B are also at the same temperature when equilibrium is attained. For tanks A and B to reach the same temperature at equilibrium would require that tanks A and B be in thermal contact. Clearly, the contra diction is that tank B cannot be well insultated (adiabatic) and in thermal contact with tank A. This contradiction ap pears in both solutions presented in the paper. Solution #1 is obtained by considering an energy balance on a control volume around tank A and shows that QA > 0. Miller subsequently argues that this solution is incorrect by considering an energy balance on a control volume around tank B; for this system, the paper (correctly) shows that energy must be removed from tank B if the temperature of tank B is unchanged. Since Mtiller is treating the tempera ture of tank B to be the same as tank A (and the temperature of tank A is unchanged), energy must be removed from tank B, which violates the requirement that tank B be adiabatic. Spring 2001 In fact, since tank B is well insulated, the energy balance on tank B in the paper correctly shows that the temperature in tank B will increase at equilibrium. Solution #2 is obtained by considering an energy balance on a control volume around both tanks and the connecting piping, so that the change in internal energy must equal the heat transfer to tank A (QA). Since Miiller intends the tem peratures in the two tanks to be equal at equilibrium, the internal energy is unchanged, and QA = 0. As discussed earlier, the temperature in tank B actually increases during the process, so the internal energy of the system increases, and AA > 0. Another way to show QA # 0 is to consider a system such as the contents of tank A after equilibrium is attained. Now, suppose QA = 0. The contents of such a system could then be considered to undergo an adiabatic reversible expansion (since QA = 0). Note however that (TT/MP)s > 0 for all gases (real and ideal). Therefore, when the pressure in tank A decreases, the temperature in tank A also decreasesbut this is a con tradiction since tank A must be maintained at a constant temperature. Therefore, QA cannot equal 0. Irrespective of the difficulties expressed above, Miiller's point is well made that one's understanding is improved by resolving the dispute between seemingly incompatible ther modynamic analyses. Thomas O. Spicer University ofArkansas Reference 1. Miiller, E.A., "A Thermodynamics Problem with Two Conflicting Solutions," Chem. Eng. Ed., 34(4), 366 (2000) Author's Response to Letters to the Editor I have received many comments, personally and publicly, on the problem I presented in the Fall 2000 issue of CEE. As with Levenspiel's original thermo problem, each and every comment is different, ranging from "You chose the wrong answer" to "Send me another one of these problems." The main message of the paper is that if you use equations straight out of a book and apply them to a problem without fully understanding the assumptions behind the equations, you have a chance of coming to a false conclusion. Never theless, I think some readers "missed the point," and I be lieve further discussion is in order. The initial problem is clearly stated, especially with regard to the final state: "equilibrium is attained." In a simple system such as this, thermodynamic equilibrium requires the simultaneous achievement of three conditions: homogeneity of pressures (mechanical equilibrium), homogeneity of tem perature (thermal equilibrium), and homogeneity in chemi cal potential diffusivee equilibrium); i.e., only if all three conditions (PA = pB, TA = T", and tA = LB) are simulta neously met can we affirm that the system will not change in time if left alone. Solution #1, as Missen and Smith note, pertains to the achievement of mechanical equilibria, but as is also noted in the original article, leaves a temperature gradient among tanks A and B. Given enough time, mass diffusion must take place, transferring energy from tank B to tank A. So, even though tank B has adiabatic walls and thus no heat transfer to the surroundings, it does transfer energy due to a tempera ture difference. In hindsight, the phrase "Given enough time, this tempera ture gradient will produce a transfer between the tanks" should read, "Given enough time, this temperature gradient will produce a mass transfer and consequent energy transfer between the tanks" in order to be unambiguous. It is clear, however, that there are not two solutions to the problem, even if the catchy title implies so. Only one solu tion is possible. Any argument attempting to set solution #1 as the correct one must first disprove solution #2an im possible task. Many students and teachers (and Spicer's note is a clear example) apply the textbook equations directly to a problem without further thought on the problem. It is in this sense that I totally agree with the second point noted by Missen and Smith. I believe that one should teach the general energy balance, and for each particular case simplify it accordingly. The point of the original class problem is that if one starts directly with Eq. (2), one may elude some of the assump tions behind its derivation. One should always start with a generalized equation such as Eq. (7)* and integrate it accord ing to the given problem. Categorizing systems as steady state, uniform flow, etc., and stating formal equations in each case only entices the student to learn a myriad of equations, making things more difficult and prone to errors. Erich A. Miiller Universidad Simon Bolivar *Equation (7) is identical (with the exception of the arbitrary sign given to the work) to Eq. (A) of Missen and Smith, not to Eq. (E) as stated in their comment. W book review Advanced Transport Phenomena by John C. Slattery Published by Cambridge University Press, The Edinburgh Building, Cam bridge, UK; 734 pages; available in paperback and hardcover Reviewed by David C. Venerus Illinois Institute of Technology Advanced Transport Phenomena is a new textbook writ ten by Professor J.C. Slattery that represents a revision of an earlier text by the same author: Momentum, Energy and Mass Transfer in Continua (1981). Transport phenomena is a fascinating and interdisciplinary subject that is covered by at least one required course in all graduate chemical engi neering programs and remains an active area of research. Like its predecessor, the new book is intended for graduate students in engineering. The text is organized into three topics according to the main subjects of transport phenomena: momentum, energy, and mass transfer. In addition, there are two shorter topics that are covered; kinematics (coming before the three main topics) and tensor analysis (an appendix). Each of the three main topics is divided into three subtopics that can roughly be described as the formulation, application, and reduction of transport balance equations. This matrix style of organi zation, where the columns are the main topics (momentum, heat, and mass) of transport phenomena and the rows pro vide the components and applications for each topic, is simi lar to that used in the classic text Transport Phenomena by Bird, Stewart, and Lightfoot (BSL), and allows the instructor/ reader the flexibility to cover the topics by column or by row. The style and teaching philosophy of the author are re vealed in Chapter 1 (kinematics) where concepts such as motion, velocity, and phase interfaces are introduced. Vari ous transport theorems are developed and used to derive the differential mass balance, or continuity equation, and the jump mass balance from the mass conservation postulate. Hence, the approach taken here and throughout the book is to start from general postulates about the physical world and to convert these postulates into useful conservation equations using formal mathematical tools. The subtopic structure is itself instructional in that the reader is forced to recognize the similarities (and differ ences) between momentum, heat, and mass transfer. In Chap ters 2, 5, and 8 (Foundations for...), differential forms of the conservation equations and their corresponding twodimen sional forms (jump balances) are derived simultaneously. Chemical Engineering Education This is followed by rather lengthy developments on the behavior of materials where the most widely used (classi cal) constitutive equations are eventually presented. In Chap ters 3, 6, and 9 (Differential Balances in...), various trans port problems are formulated using the conservation and constitutive equations derived in preceding chapters. These problems, which range in complexity from onedimensional, steadystate problems to twodimensional problems that in clude boundarylayer theory, are solved using both analyti cal and numerical techniques. Chapters 4, 7, and 10 (Inte gral Averaging in...) are devoted to deriving reduced forms of the differential balance equations: timeaveraged (turbu lent flows), areaaveraged, local volumeaveraged (pseudo continuous media), and global volumeaveraged (macro scopic balances). Appendix A provides a comprehensive review of tensor analysis and includes operations in both rectangular Carte sian and curvilinear coordinate systems. Scattered throughout each chapter are several worked examples, and each chapter ends with a series of exercises (for which a solution manual is available). At the end of each "Foundations of..." chapter, there is a summary sub section where the reader will find tables with the conserva tion equations expressed in rectangular Cartesian, cylindri cal, and spherical coordinate systems. There is no question that Advanced Transport Phenom ena is a comprehensive and carefully prepared textbook. The use of material volumes and transport theorems (rather than stationary differential volumes, as is BSL) to derive differential conservation equations is appropriate for gradu atelevel courses. Significant attention is given to the be havior of materials and to the entropy inequality and its use in the formulation of constitutive equations. Another positive aspect of this book is the utilization of jump balances to derive boundary conditions. Jump bal ances are rarely covered in modern texts on transport phe nomena, but are invaluable in situations involving free and/ or moving boundary problems. I particularly like the tables in Chapter 2 where the jump mass and jump linear momen tum balances are given for several special surfaces in the three main coordinate systems. Where the optimal balance is between being mathemati cally rigorous and comprehensive while also developing Spring 2001 physical insight on transport problems is, of course, a mat ter of preference. Many readers of this book might find that there is too much emphasis on the first two at the expense of the third. As I read through certain portions of the book, I sometimes found myself leafing through page after page of derivation to find the punch line. (From my own rough estimate, there are on average a little more than seven equations per page, or, in the 700page book, a total of about 5000 equations!) For example, in section 5.3, roughly ten pages are used to transform some general postulates about the thermal behavior of materials into useful results (i.e., viscosity and thermal conductivity are positive, Fourier's law, internal energy can be expressed in terms of density, pressure, temperature, and a heat capacity). Unfortunately, discussion about the physical implications for the different constitutive assumptions used in the development is scant. Another comment is that the book is almost comprehen sive to a fault. For example, readers may find the results from the integral averaging chapters of marginal value, either because the subject is too complex to be developed at an advanced level (e.g., turbulence and pseudo continuous media), or because it was too simple and therefore inappro priate for a graduatelevel text (e.g., macroscopic balances). Also, it is unlikely that one will find a situation that calls for the macroscopic momentofmomentum balance or the jump entropy inequality. These portions of the book could have been better used to provide more physical insight or to analyze moving boundary problems, which are so prevalent in materials science and engineering. Having said that, edu cators and researchers in this field will be glad to have a single book where the equations needed to handle such a wide variety of transport problems can be found. Advanced Transport Phenomena is a comprehensive text book that provides systematic coverage of a challenging subject. It can be used as a primary text for a firstyear graduate course on transport phenomena; students with prior exposure to the subject at the level provided by BSL will have a sufficient background. It could also serve as a solid reference book for more advanced graduate courses on fluid mechanics or on heat and mass transfer. My overall impres sion of the book is positive; I recommend it to those with an interest in teaching graduatelevel transport phenomena or to those interested in learning advanced topics in this im portant and fascinating field. 0 CALL FOR PAPERS Fall 2001 Graduate Eduction Issue of Chemical Engineering Education We invite articles on graduate education and research for our fall 2001 issue. If you are interested in contributing, please send us your name, the subject of the contribution, and the tentative date of submission. Deadline is June 1. 2001 Respond to: cee@che.ufl.edu e, class and home problems The object of this column is to enhance our readers' collections 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 that elucidate difficult concepts. Manuscripts should not exceed ten doublespaced pages if possible and should be accompanied by the originals of any figures or photographs. Please submit them to Professor James O. Wilkes (email: wilkes@umich.edu), Chemical Engineering Department, University of Michigan, Ann Arbor, MI 481092136. THERMODYNAMIC PROPERTIES INVOLVING DERIVATIVES Using the PengRobinson Equation of State R.M. PRATT The National University of Malaysia Bangi, Selangor, 43600, Malaysia Equations of state are among the marvels of chemical engineering. Though simple and convenient, they may be used to model both liquid and vapor behavior for nonpolar and lowpolar mixtures.1'12] Consequently, such methods are the preferred tools of the hydrocarbon process ing industry. It is not often, especially in thermodynamics, that you can do so much with so little. In this article, we calculate thermodynamic properties that contain derivatives, a topic not normally found in textbooks. There are two motivations for presenting this material. First, the calculations are simple, requiring no iteration or trialanderror solutions. They are, however, useful items to add to the engineer's toolkit, and they require only critical property and idealgas heatcapacity data. Second, it enables the student to use some seemingly abstract equations of thermodynamics to directly make numerical calculations. It is rewarding to see these relationships used to make actual calculations and to observe relative magnitudes of various quantities. To illustrate the methods, we use the PengRobinson equa tion of state applied to a binary vapor hydrocarbon mixture. There is an almost endless number of derivatives that can be calculatedwe will consider only a few of the more com monly encountered ones. It is trivial to simplify the ensuing equations for the special case of a pure component or to apply the equations to any number of components. The equations are valid for both liquid and vapor phases. PROBLEM STATEMENT Using the PengRobinson equation of state, calculate the 1) JouleThompson coefficient, J = a)H ap)H 2) Fluid sonic velocity, c = s for a binary vapor mixture of nbutane and npentane at 390K and 11 bar that consists of 35.630 mole % nbutane. Take kij for this binary pair to be zero. SOLUTION We will solve this problem in three steps. First, we will use the PengRobinson equation of state to evaluate the three derivatives involving P, v, and T, i.e., (P / 3v)T, (aT / 3P)v, Copyright ChE Division ofASEE 2001 Chemical Engineering Education Ronald M. Pratt is a lecturer in the engineer ing department at the National University of Malaysia. He obtained his BS in mathematics and in chemical engineering at the Colorado School of Mines, his MS in mathematics at the Fuxin Mining Institute in Liaoning Province, China, and his PhD in chemical engineering at the Colorado School of Mines. Research inter ests involve molecular dynamics and fractal modeling. and (av / 3T),. Then we will find the real fluid heat capaci ties, C, and Cp, and finally we will apply these results to calculate the two thermodynamic derivatives indicated above. Solution of the PengRobinson Equation of State for (aP/ aV)u, (OT/ P),, and (bv/ )T)p The PengRobinson equation is written as RT a P= vb v(v+b)+b(vb) where R universal gas constant T absolute temperature V molar volume a ac +m[l TI T] a 0.45723553 R2T 2/P m 0.37464 + 1.54226 w 0.26992 co2 b 0.077796074 RT/Pc Tc critical temperature Pc critical pressure c pitzer acentric factor The critical properties for the two components of our sys tem are taken from Smith and Van Ness (Table 1):[31 For convenience, the Peng Robinson equation is often TABLE 1 Critical Property Data f nbutane and npentan nbutane npentan T,(K) 425.1 469.7 P,(bar) 37.96 33.7 c 0.200 0.25 quantities applied to the mixture as a whole, and subscripted values for pure component quantities. From Eq. (1), we calculate the pure component parameters using R=83.14 cm3bar/molK: a, = 15911115 cm'bar/mol2 a, = 23522595 cm6bar/mol2 b, = 72.43235 cm3/mol b, = 90.14847 cm3/mol and then, from Eq. (3), we find that a = 20631852 cm6bar/mol2 b = 83.836216 cm3/mol (1) We now solve Eq. (2) for the compressibility factor, Z. This equation is easily solved using NewtonRaphson itera tion15) or by using the cubic formula.'" In either case we calculate the vapor phase compressibility factor (largest of the three real roots) to be 0.7794 for the vapor. Conse quently, the molar volume, v, of the vapor mixture is ZRT/P = 2297.54 cm3/mol. With knowledge of the molar volume and compressibility, we now calculate the three PVT derivatives, which follow directly from the equation of state. Knowledge of these quantities is prerequisite to finding most any derivative ther modynamic property. We know that these three derivatives for must satisfy the "cyclical rule," which may be written as e 2 written in a cubic polynomial form for the compressibility factor Z=Pv / RT f(Z)=Z3 +aZ2 +pZ+y =0 (2) where a=Bl p A 2B 3B2 y B3 +B2 AB and A aP /(RT)2 BbP/RT For an Ncomponent fluid with composition, {w }, we calculate the mixture parameters, a and b, from the empirical relations: N N N a= I wiwj a ( (1kij) and b= wibi (3) i=lj=l i=1 The binary interaction coefficient, k,, is exactly zero for i=j; for itj, kij is close to zero for hydrocarbons. Values of ki, for many component pairs are available in the literature,"41 al though for most hydrocarbon pairs it is safe to take kj=0. We will henceforth use values without subscripts to refer to (a p)(aT)1 a(4) Therefore, once we have values for any two of the three PVT derivatives, the third may be calculated from Eq. (4). We will evaluate each derivative independently, however, and use Eq. (4) to check our work. The first derivative in Eq. (4) is found by direct differen tiation of Eq. (1), (aPI RT 2a(v+b) I)T (vb)2 [v(v+b)+b(v b)]2 Substituting in the values determined above, we find that 0P) =0.0035459 bar/(cm3/mol) The second derivative in Eq. (4) is also found by direct differentiation of Eq. (1), (aP) R a' (6) 9T), v=b v(v+b)+b(vb) ( and is found to be 0.0434866 bar/K. Therefore, T = 22.99558 K / bar tp)v The third derivative in Eq. (4) is a bit trickier since Eq. (1) is not readily explicit in volume or temperature. It is there fore found implicitly, using Eq. (2), la pR Ti(az +zj (7) Spring 2001 where (M) (BZ)+() (6BZ+2Z3B2 2B+AZ2 OTlp OTlP (az ) Oyjp 3Z2+2(B1)Z+(A2B3B2) tion for the mixture is a mole fraction weighted average of the pure component values, i.e., N C=I WCID (12) Inserting the known temperature of 390K into the above equations, we calculate for each component MA = P ( a 2a) T) P RT2 T) (aB) bP OT)p RT2 CID =113.050 J/molK vi CID =141.376J/molK V2 The derivative term, a'=da/dT, may be evaluated directly from Eq. (3) as a' ij 1kij) ai' aji (8) SdT 2i=ij=1 ai ya where dai miai ai' =T m1= (9) dT [+mi(l JT/Tc) JTT The pure component parameters are found from Eq. (9) as a,'=25547.0 cm6bar/mol2K a,' =38460.2 cm6bar/mol2K and da/dT for the mixture is found from Eq. (8) to be a'=33543.8 cm6bar/mol K. Substituting known values in to Eq. (7), we find that (v = 12.26396 cm3 / mol K vT) If we multiply the three numbers together we will see that we have satisfied Eq. (4). Calculation of the Heat Capacities C, and C, We first find C,. We will consider this real fluid property to be a sum of an ideal gas contribution and a residual correction for nonideal behavior: Cv =CID +C (10) The idealgas contribution is found using heatcapacity data applicable to gases at very low pressures, which are avail able in many thermodynamics textbooks. We will use the simple correlation in Smith and Van Ness[31 CD =R(A+BT+CT2+DT21) (11) which is not recom mended for temperatures TABLE 2 below 298K nor valid for nbutane npentane temperatures over 1500K. A 1.935 2.464 For nbutane and npen B 36.915 x 10' 45.351 x 10i tane, the coefficients are given in Table 2. C 11.402 x 10614.111 x 10 The ideal gas contribu D 0 0 and for the mixture CID131.283J/molK To calculate the residual contribution to Eq. (10), we use the standard equation found in many textbooks14,61 for the residual internal energy derived from the PengRobinson equation of state R T_ [ Z+B(1+V)1 UR= Ta'a ze +(1 ) (13) b,8 Z+B( lf2) The value of CR is calculated from its definition S aR )v Evaluation of the partial derivative of Eq. (13) with respect to temperature yields C Ta n z+B(i 2(14) bF8  I (14) with the temperature derivative of Eq. (8) yielding a" d2a a dT2 I a,aj a 2 .2 a i=1j=l I j a~ + + aj~ a+ i=1 j=, lTaaj 7a, C]a, C. Ca3 where a" d2ai da acimi T (1+ m') a dT2 dT 2TTc, (16) These equations appear complicated, but the calculation is straightforward, albeit tedious. Pure component parameters for a" are found from Eq. (16) to be a'= 53.2619cm6 bar / ol2 K2 a' = 80.7496 cm6 bar/mol2 K2 and a" for the mixture is found from Eq. (15) to be a"= 70.2732cm6 bar/mol2 K2 Chemical Engineering Education If doing hand calculations, very little error (usually less than 2%) is introduced by using the mole fraction weighted aver age in calculating a". In this case, we would calculate a" to be 70.9557 cm6bar/mol2K2. Substituting the above mixture quantities into Eq. (14) (using ZL=0.779438) gives CR=1.152 J/molK. Using Eq. (10), we now obtain Cv=132.436 J/molK. We will use an equation analogous to Eq. (10) to calculate C, Cp =CID +C (17) and since CpDDCID+R, we readily calculate C'D to be 139.597 J/molK. The residual contribution may be calcu lated from the general relationship between C, and Cp, C =CR+T ) ( R (18) The two partial derivatives are already calculated above and can be substituted into Eq. (18); we find that C = C+124.85 cm'bar/molK and therefore Cp=136.37 cm3bar/molK, or 13.637 J/molK. Adding the ideal gas and residual contribu tions according to Eq. (17) yields Cp =153.235J/molK Calculation of Thermodynamic Properties J and c Now that we have values for the three PvT derivatives as well as the two heat capacities, Cv and Cp, we can calculate a large number of thermodynamic derivatives. We will only evaluate two of the more commonly encountered ones, the JouleThompson coefficient, J, and the speed of sound in a fluid, c. It is simple to calculate the JouleThompson coefficient,(dT/ aP)H, using the working equation161 J 1 [T(av v] (19) since all the required values have been calculated. Substitut ing into Eq. (19), we obtain J=1.62195 K/bar The fluid sonic velocity (VP/ap) is calculated from the working equation161 Cp (P c = v C aY (20) All the required values have been calculated. Substituting into Eq. (20) yields c=147.164 (cm3bar/mol)05. Since these Spring 2001 are unusual velocity units, some units conversion is in order. The average molecular weight of the vapor mixture is 67.152 g/mol and we find that the sonic velocity is rkg ) c221657cm bar 0 S2 ) m 1000g Imol mol bar 100cm kg 67.152g 3.2251x108 cm2 s or c=179.586m/s=646.5km/hr We can compare this result with the low pressure (ideal gas) limiting value cID c = IRT=185.683(cm bar/mol)5 =226.590m/s ID glD C v DISCUSSION Calculation of derivative properties is easy if there is an equation of state available to model the PVT behavior of the fluid. Two such properties have been evaluated here using the PengRobinson equation of state. It is trivial to evaluate a large number of other derivative properties once we know the three PVT derivatives and the two heat capacities. In this age of computers, it is worthwhile for the student to develop a spreadsheet or set of computer subroutines to calculate thermodynamic properties of hydrocarbons and hydrocar bon mixtures.171 Including these and other thermodynamic derivatives would be very easy, indeed. It is interesting to estimate some of these derivatives by using their finitedifference approximations and to compare these estimates with results using the equations discussed above. For example, Cp is approximated by evaluating the enthalpy H=HI+UR+RT(Z1) at two nearby temperatures at 11 bar (and same composition) C( AH) 30012.44929705.977 153.236J/molK P AT 391389 which is essentially the same as the result obtained above, with any error due to the finitedifference approximation. REFERENCES 1. Winnick, J., Chemical Engineering Thermodynamics, Wiley, New York, NY (1997) 2. Sandler, I.S., Chemical and Engineering Thermodynamics, 3rd ed., Wiley, New York, NY (1999) 3. Smith, J.M., H.C. Van Ness, and M.M. Abbott, Introduction to Chemical Engineering Thermodynamics, 5th ed., McGraw Hill, New York, NY (1996) 4. Walas, S.M., Phase Equilibria in Chemical Engineering, ButterworthHeinimann, Boston, MA (1985) 5. Carnahan, B., H.A. Luther, and J.O. Wilkes, Applied Nu merical Methods, Wiley, New York, NY (1969) 6. Kyle, B.G., Chemical and Process Thermodynamics, Prentice Hall, NJ (1994) 7. Savage, P.E., "Spreadsheets for Thermodynamics Instruc tion," Chem. Eng. Ed., 29(4) (1995) 0 r M.f laboratory COMPUTER MODELING IN THE UNDERGRADUATE UNIT OPERATIONS LABORATORY Demonstrating the Quantitative Accuracy of the Bernoulli Equation DAVID J. KEFFER University of Tennessee Knoxville, TN 379962200 he purpose of this experiment is to demonstrate the predictive capabilities of the Bernoulli equation in determining the time it takes a liquid to drain, under the influence of gravity, from a tank and through an exit pipe, as a function of initial tank charge, exitpipe diameter, and exitpipe length. The project is comprised of an experi mental component and a modeling component. In the modeling component, predictions of the efflux time are obtained from several different approximate solutions of the Bernoulli equation; in the experimental component, the flux time for water draining from a tank through various exit pipes is measured. Comparisons between the experimental and theoretical values are then made. The purposes of the comparison are To evaluate which terms of the Bernoulli equation are important To test the limits of applicability of the Bernoulli equation To demonstrate the value of a rigorous computer modeling Descriptions of fluidflow experiments appear in the lit erature. For example, Hesketh and Slater described an efflux from a tank experiment where students fit heightversus time data, assuming there are no pressure losses within the system.t11 In this work, we include head losses due to various friction terms. Hanesian and Pera described an experiment in optimizing pipe diameter with respect to capital and oper ating costs.[21 A key difference in the latter experiment is that the system was operating at steady state. In the experiment described here, efflux from a tank, there is no steady state, and thus the resulting equations are differential in nature. EXPERIMENTAL SYSTEM Our system is situated inside a cylindrical tank (tank ra dius = R,) filled with water to height, H. The tank has a cylindrical pipe (pipe radius = Rp) of length L extending from the base of the tank (see Figure 1). The length and the diameter of the stainless steel exit pipe are variables depend ing on which of the eight available pipes is used. The pipe dimensions are given in Table 1. The experimental apparatus is intentionally kept as simple as possible. When the students first see the tank and pipes, they frequently smirk and comment that the experiment is too "lowtech" to teach them anything of value, but through this experiment they learn that "The best experiment is the David Keffer has been an Assistant Profesor at the University of Tennessee since January, 2000. His research involves the computational description of the behavior of nanoscopically confined fluids. He has transferred the tools of his researchsolving algebraic, ordinary, and partial differential equationsto the under graduate engineering curriculum by integrat ing modern computer modeling and simula tion tools, not only in numerical methods courses but in any engineering course. Copyright ChE Division ofASEE 2001 Chemical Engineering Education simplest experiment that still has enough guts to demon strate the underlying physics of the system."131 MATHEMATICAL MODEL The mathematical model used to describe efflux from the tank is based on the mass and mechanical energy balances. If we define our system as the dotted line in Figure 1, and if we stop timing the efflux when the water level reaches H', then the control volume is always full and we have a mass balance of the form in = v AT = VTR. = out= VpApvpntR (1) assuming an incompressible fluid, where vT is the flow average velocity in the tank, AT is the crosssectional area of the tank, and RT is the radius of the tank. The subscript P designates analogous variables and parameters of the exit pipe. The average velocity of the fluid in the tank is defined as dH VT(t)= dt (2) where t is time. Equation (2) can be substituted into Eq. (1) to yield an expression for the velocity in the pipe SdH R ( vp = T (3) Vp dt R2 { P The mechanical energy balance (Bernoulli equation in Figure 1. Schematic of the experimental apparatus. TABLE 1 Pipe Dimensions Length Inside Diameter (inches) (inches) 30 3/16 24 3/16 12 3/16 6 3/16 1 3/16 24 1/8 24 1/4 24 5/16 cluding friction terms) has the general form gAz Av2 AP (4) + ++2h, =0 (4) gc 2gc P where g is gravity, Az = L+H', Av2=vT2Vp2, AP is the pres sure drop, p is the density of the fluid, and h, are the terms contributing to the head loss due to friction. Again, if we define our system as the dotted line in Figure 1, we have the advantage that the accumulation term within the system over which the material and mechanical energy balance is drawn is zero, since the system is constantly full of liquid. This results in a nonzero pressure drop corre sponding to the height of the water in the tank, less H', the final height at which we stop the experiment. In this system, we can consider frictional head loss due to the pipe wall, the contraction, and the tank wall Shf = hf,pipewall +hf,contraction + hf,tankwall (5) We define each term in the Bernoulli equation AP= pg(H H') (6) gc The Darcy equation gives the friction head loss for flow in a straight pipe, hf,pipewall = 4P ) V (7) where fp is a dimensionless friction factor and Dp is the diameter of the pipe.141 If we assume turbulent flow in the pipe, we can obtain an estimate of the friction factor, fp, using an empirical relation, known as the Blasius equation, applicable to turbulent flow with Reynolds numbers in the range of 4000 P N0.25 Re,P The Blasius equation for a smooth pipe is used because it will allow for an analytical solution to the resulting differen tial equation. The friction loss due to contraction is given by"51 2 D2,v 2 h K 05 1 P P (9) f,contraction c 2g 0.5 1 2g gc DT ) gc If we assume laminar flow in the tank, the friction loss due to the tank wall is hftaal =4f f H v2 = 64 (10) takwa 2gc NRe,T D T2g The assumption of turbulent flow in the pipe and laminar flow in the tank can be verified experimentally. For the diameters and lengths used in this experiment, these as sumptions are confirmed. System 2Rp Spring 2001 If we combined Eqs. (1) through (10), we obtain a me chanical energy balance of the form 61 (dH 1.75 2(0.0791)p0.25LD35 g(L+H)+ d p025D75 T + (D4 ) DdH 2 D 2p dH ]2 32HP(dH dt) 2 4 T L dt D p dt (11) Equation (11) is a firstorder nonlinear ordinary differential equation. It has no known analytical solution. If we rely on our engineering intuition to neglect terms of less significance, however, we might omit the kinetic energy term, the friction loss due to contraction, and the friction loss due to laminar flow in the tank. If we make these three assumptions, we will find that we can obtain an analytical solution to the resulting differential equation [2(0.0791)0o.25D3.5 4/7 7 H 3 H(t)3/7() S p.25D3.75 T L 1+ 1+ L L L where Ho is the initial height of the water in the tank at time zero. Thus, we can find the time it takes for the water level in the tank to fall to a height, H, from the initial height, Ho. This approximation is what is often used to describe the system in unit operations laboratories solely because it has an analyti cal solution. We will see in the next section, however, that this approximation gives not only quantitatively but also qualitatively incorrect results. The more rigorous approach is to numerically solve the ordinary differential equation (ODE) in Eq. (11). We can use a standard numerical ODEsolution technique (e.g., Euler's method or a RungeKutta method) if we can arrange the ODE into the form dH = f(H,t) (13) Equation (11) cannot be put in this form. Therefore, we cannot easily solve for the velocity in the tank, DH/dt, at every Euler or RungeKutta time step as is required by those algorithms. But for any given time, t, for which we know the height, H, we can obtain the numerical value of the tank velocity by using a technique to solve a single nonlinear algebraic equation, such as the NewtonRaphson method. Combining the NewtonRaphson and RungeKutta methods is a relatively simple algorithm to implement and involves nesting the iterative algebraic equation solver inside the routine that obtains the tank velocity for the ODE solver. For the undergraduates in the unit operations laboratory, we provide just such a routine, written for MATLAB."61 The students are familiar individually with the RungeKutta and NewtonRaphson techniques and the majority of them di rectly comprehend the combination of the two methods. We have integrated the modeling component of this ex periment with the curriculumwide "Web Resource for the Development of Modern Engineering ProblemSolving Skills" instituted in the Department of Chemical Engineer ing at the University of Tennessee.17 This web resource acts as a standalone selfteaching module that students at any level in the programfrom sophomores to graduate stu dentscan access to obtain the basic algorithms to solve systems of linear algebraic equations, systems of nonlin ear algebraic equations, systems of ordinary differential Figure 2. Efflux time as a function of exit pipe length for the experi mental case, the approximation to the mechanical energy balance with an analytical solution (Eq. 12), and for more complete mechanical en ergy balance, solved numerically (Eq. 11). The data are for water at 85 F draining from a sixinch di ameter baffled tank from an initial height of 11 in. to a final height of 2 in. through a pipe with a nominal diameter of 3/16 in. 180 160 140 1oo 80 60 40 60 o 0 experiment analytical solution,eqn (2) numerical solution, eqn (11) 0 10 20 30 40 50 60 70 80 exit pipe length (cm) Chemical Engineering Education equations, numerical integration, and linear regression and analysis of variance. EXPERIMENTAL RESULTS In the lab the students examine the effects on efflux time of the initial water charge, the exitpipe diameter, and the exitpipe length. Here, we limit ourselves to the effect of the exitpipe length. In Figure 2 we plot the flux time versus exitpipe length for the experimental case, for the approxi mation to the mechanical energy balance with an analytical solution (Eq. 12), and for the complete mechanical energy balance, solved numerically (Eq. 11). The data are for water at 85'F draining from a sixinch diameter baffled tank from an initial height of 11 in. to a final height of 2 in. through a pipe with nominal diameter of 3/16 in. The water density and viscosity were obtained from the literature.[8] At short pipe lengths, we see that the experimental efflux time decreases with increasing pipe length, because gravity and the hydrostatic pressure term in Eq. (11) create a driving force for flow proportional to (L+H). As we increase L, the driving force increases and the tank drains faster. In contrast, at longer pipe lengths, the experimental efflux time in creases with increasing pipe length, because we have reached a point where skin friction due to the pipe wall is the dominating factor. The approximation to the Bernoulli equation that has an analytical solution (Eq. 12) fails to model this behavior both qualitatively and quantitatively. The trend for Eq. (12) is a monotonic increase in efflux time with increasing pipe length. The average relative error of Eq. (12) with respect to the experimental data is 32.6%. The more complete Bernoulli equation in Eq. (11) models the experiment both qualitativelty and quantitatively. The average relative error of Eq. (11) with respect to the experi mental data is 3.1%. Plots have also been generated regarding the dependence of efflux time on pipe diameter and initial water height. Both the analytical solution (Eq. 12) and the numerical solution to Eq. (12) model the behavior qualitatively, namely that efflux time decreases as pipe diameter increases or initial water height decreases. But as was the case with the pipe length, the quantitative agreement is substantially better using Eq. (11). CONCEPTUAL LESSONS OF THE EXPERIMENT After the students have collected the experimental data in the laboratory, they take the data to the computer lab and model it using both Eqs. (11) and (12). Additionally, they look at variant models, adding one term at a timekinetic energy, friction due to contraction, and friction due to the laminar flow in the tank wall. Adding the terms individually allows the student to determine the effect of each term in the mechanical energy balance on the efflux time. The students can also explore the comparison of experi ment and theory in terms of error analysis. For example, they can calculate the Reynolds number at each experimental data point and show that for any given theoretical model the accuracy decreases as the Reynolds number drops and reaches the lower limit of applicability of the expression used for the turbulent friction factor. Finally, the students (primarily juniors) obtain a firsthand demonstration of the quantitative accuracy of the Bernoulli equation. The experience helps them understand the signifi cance, validity, and limitations of the otherwise abstract mathematical expressions with which they are presented in classroom lectures on fluid flow. CONCLUSIONS In this work we have described a very simple efflux from a tank experiment, of the sort commonly employed in under graduate unit operations laboratory courses. We have shown that relying only on a simplified analytical solution to the Bernoulli equation not only fails to quantitatively model the experimental results but also qualitatively fails to capture the correct trends. We have provided a more complete me chanical energy balance, outlined its numerical solution, and shown that it both qualitatively and quantitatively models the experiment. The inclusion of a computer simulation in the experiment allows the students to demonstrate for themselves the conse quences of oversimplified engineering approximations and the value of a rigorous mathematical model. ACKNOWLEDGMENTS The author would like to thank Professor John Prados in the Department of Chemical Engineering at the University of Tennessee for his aid and encouragement in this work. REFERENCES 1. Hesketh, R.P., and C.S. Slater, "Cost Effective Experiments in Chemical Engineering Core Courses," Proc. of ASEE Ann. Conf., Charlette, NC (1999) 2. Hanesian, D., and A. Perna, "Estimation of Optimum Pipe Diameter and Economics for a Pump and Pipeline System," Proc. ofASEE Ann. Conf, Milwaukee, WI (1997) 3. Davis, H.T., University of Minnesota, Department of Chemi cal Engineering and Materials Science, personal communi cation (paraphrased) 4. Perry, R.H., and D. Green, Perry's Chemical Engineering Handbook, 6th ed., McGrawHill, New York, NY (1984) 5. "Flow of Fluids Through Valves, Fittings, and Pipes," Crane Technical Paper No. 410, Crane Co., New York, NY (1979) 6. Keffer, D., "ChE 310 Course Website," at 7. Keffer, D., "AWeb Resource for the Development of Modern Engineering ProblemSolving Skills," at 8. Geankoplis, C.J., Transport Processes and Unit Operations, 3rd ed., Prentice Hall, Englewood Cliffs, NJ (1993) O Spring 2001 2001 ASEE Annual Conference June 24 27, 2001 Albuquerque, New Mexico Technical Sessions SMonday, June 251 Session 1313 10:30 a.m. Capstone Design Issues in Chemical Engineering Moderators: Chris Wiegenstein and David Miller 1. "Capstone Chemical Engineering Laboratory Courses at Michigan Tech" A.J. Pintar, E.R. Fisher, and K.H. Schulz 2. "Open Beginning Projects: A Flexible Approach to Encouraging Student Curiosity and Creativity" S.S. Moor 3. "A HandsOn Multidisciplinary Design Course for Chemical Engineering Students" J.M. Keith, D. Charu, J. Meyer, and N. Norman 4. "The Inclusion of Design Content in the Unit Operations Laboratory" D. Ridgway, V.L. Young, and M.E. Prudich 5. "An Introduction to Process Simulation for the Capstone Design Course" D. Miller, T.N. Rogers, and B.A. Barna 6. "Graduate Bridging and Continuing Eduction in Chemical Engineering via the Web" R.M. Worden, D. Briedis, and C.T. Lira Session 1413 12:30 p.m. NonTraditional Topics in Chemical Engineering Moderators: Nada AssafAnid and Ann Marie Flynn 1. "Introducing Emerging Technologies into the Curriculum Through a Multidisciplinary, IndustriallySponsored Research Experience" J.A. Newell, S.M. Farrell, R.P. Hesketh, and C.S. Slater 2. "Integration and Use of a Novel Semiconductor Procesing Simulator to Teach Stream Recycle Issues to Chemical Engineering Students" P. Blowers and E. Weisman 3. "A Course on Health, Safety, and Accident Prevention" A.M. Flynn, J. Reynolds, and L. Theodore 4. "Training Chemical Engineers in Bioprocessing" C. Preston, D. Briedis, and R.M. Worden 5. "Biotechnology and Bioprocessing Laboratory for Chemical Engineering and Bioengineering" S. Sharfstein and P. Relue 6. "Bacterial Disinfection in the Classroom: EngineeringBased Experimental Design" N.M. AssafAnid Tuesday, June 26 Session 2213 8:30 a.m. Laboratory Automation and Classroom Demonstrations Moderators: Connie Hollein and Jim Henry 1. Laboratory Remote Operation: Features and Opportunities" J.M. Henry 2. "Using WebBased Supplemental Instruction for Chemical Engineering Laboratories" C.R. Nippert 3. "Virtual Reality Laboratory Accidents" J.T. Bell and H.S. Fogler 4. "Exercise in Chemical Engineering for Freshmen" S.M. Farrell and R.P. Hesketh 5. "Teaching Chemical Engineering with Physical Plant Models" K.H. Pang 6. "Engineering Experiments Utilizing an Automated Breadmaker" R.P. Hesketh, C.S. Slater, and C.R. Flynn 7. "Utilizing Experimental Measurements to Introduce Underrepresented PreCollege Students to Science and Engineering" A. Perna and D. Hanesian 120 Chemical Engineering Education Session 2565 2:30 p.m. Math Requirements in the Chemical Engineering Curriculum Moderators: Anton Pintar and Jenna Carpenter 1. "Mathematics and Chemical Engineering Education" A. Pintar, F. Carpenter, M. Cutlip, M. Graham, and J. Puszynski 2. "Mathematics in Chemical Engineering: From the 'BallPark' to the 'LapTop'" R. Toghiani and H. Toghiani Session 2613 4:30 p.m. A Galaxy of Stars Moderators: David Kauffman and Melanie McNeil Senior chemical engineering faculty who have been leaders in the analysis, development, and dissemination of educational techniques will be members of a panel to discuss the current state of chemical engineering education and how it has progressed, or digressed, over the past three decades, and how it will change in the coming decades. They will introduce "rising stars" in the field, who will also participate in the panel discussion. Senior panel members include Richard Felder, James Stice, and Billy Crynes. SWednesday, June 27 1 Session 3213 8:30 a.m. The Latest in Pedagogy in Chemical Engineering Moderators: Joe Shaeiwitz and Wallace Whiting 1. "The Role of Homework" P. Wankat 2. "Using Critical Evaluation and PeerReview Writing Assignments in a Chemical Engineering Process Safety Course" D.K. Ludlow 3. "CriterionBased Grading for Learning and Assessment in the Unit Operations Laboratory" V.L. Young, M.E. Prudich, and D.J. Goetz 4. "MidSemester Feedback Enhances Student Learning" R. Wickramasinghe and W.M. Timpson 5. "Development and Implemmentation of a ComputerBased Learning System in Chemical Engineering" N.L. Book, D.K. Ludlow, and O.C. Sitton 6. "Evaluation of IT Tools in the Classroom" S. Soderstrom and C. Lorenz Session 3413 12:30 p.m. The Master as the First Professional Degree Moderator: David Kauffman There is a great deal of discussion concerning the need for a morethanfouryear program for the first professional level in engineering. A panel of experts will give background information and discuss issues raised by the audience. Panelists include Thomas Hanley, Gerald May, and Paul Penfield. Session 3513 2:30 p.m. Computers and Computation in the Chemical Engineering Curriculum Moderators: Anneta Razatos and Donald Visco 1. "TemplateBased Programming in Chemical Engineering Courses" D.L. Silverstein 2. "Sealing AnalysisA Valuable Technique in Engineering Teaching and Practice" E.M. Kopaygorodsky, W.B. Krantz, and V.V. Guliants 3. "Is Process Simulation Effectively Utilized in Chemical Engineering Courses?" M.J. Savelski, K.D. Dahm, and R.P. Hesketh 4. "Scientific Visualization for Teaching Thermodynamics" K.R. Jolls 5. "Integrating Best Practice Pedagogy with ComputerAided Modeling and Simulation to Improve Undergraduate Chemical Engineering Education" J.L. Gossage, C.L. Yaws, D.H. Chen, K. Li, T.C. Ho, J. Hopper, and D.L. Cocke SoceyWide Picnai ChE Division Lectureship ChE Division Awards Banquet Su; j~n we 24, 5:;00p.m. Monday June 25, 4:30 p.m. Monday, June 25,6:30 pm. :.a lt AWl_ e __i' Moderator: Doug Hirt Albuquerque Petroleum Club __ : ,; : Speakerotolbe announced Speaker to be ianounced 'i a..  _" W  " . "  F _4: p A aeCsE Division Bui2ness ASEE AimuatA eceptkis Baf*st :Luancheon and Awards Banquet :Tusd a, June26, 7:0 an. Tuesday, June 26, 12:30p.m. Wednesday, June 27, 6:00p.m. Spring 2001 ,]1 laboratory USING INBED TEMPERATURE PROFILES FOR VISUALIZING THE CONCENTRATIONFRONT MOVEMENT PAULO CRUZ, ADILIO MENDES, FERNAO D. MAGALHAES University of Porto 4200465 Porto, Portugal Purification of gas streams through adsorption in a packed column is an important process in chemical engineering. The experimental study of such systems involves determination of breakthrough curves for the ad sorbable components in the column. Both theoretical and practical implementations of this process are common in undergraduate courses, but students do not readily assimilate some of its aspects. The retention of a concentration front in an adsorbent bed and its implications on the formation of shock waves, for instance, are not easy to visualize mentally, especially when experimental information concerns only the outlet concentration history. In our senior undergraduate laboratory, we have devel oped an experiment that has been successful in helping stu dents grasp the concepts of concentrationfront movement in fixed beds. Due to the structure of the curricular program, most students actually take this lab course before the ad vanced separation course in which the theory associated with these processes is detailed. This does not seem to im pair the students' ability to interpret and understand the experimental results and theoretical concepts, however. In addition to the measurement of the outlet breakthrough curve, a set of thermocouples within the bed allows for the indirect "visualization" of the advancement of the concen tration front. A process simulation program, developed for this purpose, also lets students gain sensitivity for the relative importance of the different operation parameters and physical proper ties. This easytouse software is available for downloading at http://raff.fe. up.pt/~lepae/simsorb.html In this paper we start by briefly describing the Solute Movement Theory, which is a basic tool for interpreting this kind of process, and the mathematical model used in the software simulation, which involves a more detailed de scription. Later we will illustrate how students can use both in the interpretation of experimental results. THEORETICAL BACKGROUND A certain gas, A, diluted in an inert carrier gas stream travels in a column packed with a non adsorbent solid at the same velocity as the carrier. If, however, the solid adsorbs gas A, then its velocity will be lower than the carrier's. Simply put, the gas is "retained" by the solid, i.e., it cannot proceed along the column while the adsorption sites are not filled. This idea is moreorless simple and intuitive. Things become a bit more complicated, though, when one tries to interpret phenomena such as the formation of differ ent kinds of concentrationfront waves. This is when the Solute Movement Theory (SMT) comes in handy. It predicts (for simplified but meaningful conditions) the solute veloc ity as a function of concentration. Its main result states that an infinitesimal element of solute, with concentration cA, will travel the column at a velocity us, which depends (inversely) on the slope of the adsorption isotherm for cA (dqA/dcA) v us v (1) Us =I 1E dqA Se dcA Paulo Cruz is a PhD student in Chemical Engineering at the University of Porto, Portugal. He received his degree in chemical engineering from the same University in 1998. His research interests are in multicomponent mass transport and sorption in porous solids and membranes. Ad6lio Mendes received his licentiate and PhD from the University of Porto, Portugal, where he is currently Associate Professor. He teaches chemical engineering laboratories and separation processes. His main research interests include membrane and sorption gas separations. Ferndo Magalhies is Assistant Professor of Chemical Engineering at the University of Porto, Portugal. He received his PhD from the University of Massachusetts in 1997. His research interests involve mass transport and sorption in porous solids and membranes. Copyright ChE Division of ASEE 2001 Chemical Engineering Education where v is the interstitial velocity of the inert carrier gas, e is the packing porosity, p is the absorbent's apparent density, and qA is the concentration of A adsorbed in the solid, in equilibrium with cA. The reader can find the details of our approach for deriving Eq. (1), based on a differential mass balance to the column, at http://raff.fe.up.pt/~lepae/simulator.html For other approaches see, for example, the book by Wankat.r11 SMT implies, of course, a series of simplifying assump tions, the major being 1. local adsorption equilibrium 2. plug flow in gas phase 3. negligible pressure drop along the column 4. isothermal operation 5. low adsorbate concentration Assumptions 4 and 5 imply that the interstitial gas velocity can be assumed constant. It is quite clear, from Eq. (1), that stronger adsorption (higher dqA/dcA) implies slower solute movement (lower us). On the other hand, if there is no adsorption, then u, = v, and the solute moves at the same speed as the inert carrier gas. Let us now consider that the column, initially without solute, is subject to an inlet concentration step of magnitude c9. Suppose that two welldefined linear regions, as shown in Figure 1, compose the adsorption isotherm for this solute. Solute elements with concentrations between 0 and c, will, according to Eq. (1), have a velocity uv (2) Us (1 E) q l+p c On the other hand, for solute elements with concentrations On the other hand, for solute elements with concentrations between c, and c2 the velocity is Us2 =  (q2q1 (3) l+p S(C2 Cl, Velocity u,, is lower than us,. Due to the particular shape of the isotherm, high concentrations tend to move faster than low ones. This would apparently lead to the situation de cl c2 q2 . .  ~ ~~ ~ ~ ~~ Cl C2 Figure 1. Idealized adsorption isotherm. Spring 2001 picted in Figure 2: high concentrations moving ahead of low concentrations! This is obviously a physical impossibility. High concen trations cannot exist without the lower ones. What actually occurs is the formation of a shock wave. The concentration front shown on the left in Figure 2 preserves its shape as it moves along the column, with a velocity intermediate be tween ut and us2. This velocity can be derived from a mass balance to the shock wave, the result being u = (4) s +pE q2 e c2 E C2 As will be shown later, dispersion effects (not accounted for in SMT) cause the concentration front to develop some distortion as it moves along the column. And what will happen in the case of desorption, i.e., when, assuming the same isotherm, a negative concentration step is applied at the column entrance (Figure 3)? Once again, the higher concentrations (between c, and c,) tend to move faster. But now these can actually move ahead of the lower ones, causing a progressive deformation of the originally sharp concentration front. We have, then, a dis persive or diffusive wave."I This discussion can be easily extended to the analysis of more realistic systems, where the adsorption equilibrium is described by, say, a Langmuirtype isotherm. Such isotherms, where dq/dc decreases with increasing c, are called favor able isotherms. It is easy to understand that in the opposite case, i.e., for an unfavorable isotherm, the conditions dis cussed here for the formation of shock and diffuse waves would be reversed. The way SMT describes adsorption in a packed column is quite simplistic. More realistic considerations, such as axial C2 ...  .. Cl  <  shock wave z Figure 2. Hypothetical progression of a step in concentra tion, corresponding to the isotherm shown in Figure 1. This is the basis for the formation of shock waves. C 2 ...........   ___ C2 Figure 3. Hypothetical progression of a negative step in concentration, corresponding to the isotherm shown in Figure 1. This would be a dispersive wave. dispersion, intraparticular mass transport resistance, and nonisothermal behavior, can be added if one establishes a more complex mathematical model for this process. The differential mass and energy balances of our "complex model" (CM) are presented in the Appendix. Students are expected to be able to interpret each term in the balance equations, even though the resolution of a sys tem of partial differential equations is beyond their abilities. For that we supply our homemade software simsorb, which uses finite difference discretization of the spatial coordinate (routine PARSET from package FORSIMVI) and performs the time integration with routine LSODA. It uses a MS Excel interface for inputting the data and for plotting the results. This software is available for downloading at http://raff.fe. up.pt/~lepae/simsorb. html The input spreadsheet already contains the set of physical parameters and operating conditions used in simulating our experimental results. The adsorption isotherms (of the type LangmuirFreundlich) were experimentally measured at our lab and the Peclet number (axial dispersion) estimated from an available correlation.2 Values for the global heattransfer coefficient and the intraparticle diffusion coefficient were not measured directly. They were obtained by fitting the model to experimental results. This is done previously by the class tutor, so when the students run the simulator for the first time they observe a good agreement between the model's output and their experimental results. Students can later run the simulator with other input data and analyze its effects on the system's performance. An example of this is given later in this paper. INTERPRETING EXPERIMENTAL RESULTS The previous theoretical introduction is es sentially the first contact that students have with Solute Movement Theory. Even if they seem to understand it relatively well, the sedi mentation of concepts demands a more tan gible, i.e., experimental, approach. Ideally, it would be possible to directly observe the evo lution of a concentration front within a packed column. This is, of course, not the case. Only inlet and outlet concentrations are, in prin ciple, accessible. By measuring the tempera ture at different points in the column's axis, however, one can obtain indirect informa tion on the behavior of the concentration front along it. One may point out that the existence of measurable thermal effects is certainly con trary to the SMT's original hypothesis of iso thermal operation. Nonetheless, as long as Figur these are not excessive, a good compromise can be obtained between the applicability of SMT and an "online visualization" of the progress of the concentration front, as we shall see. For our lab course we use the adsorbate/adsorbent pair CO2/activated carbon. Carbon dioxide was chosen since, in addition to being quite safe to work with and having a low cost, it has a high heat of adsorption in activated carbon. We used activated carbon from Chemviron Carbon in the form of extruded pellets (6.3 mm x 3.6 mm). Our setup is shown schematically in Figure 4. The column is 250 mm long and 50 mm in internal diameter. Seven evenly spaced holes were drilled in its side to allow for insertion of the thermocouples. The column is placed inside an oven. This has a twofold purpose: to keep the surrounding temperature constant (the oven is set to a temperature slightly above room temperature) and to allow for complete regen eration if necessary. Actually, we noticed that for this sys tem (CO2/activated carbon), hightemperature regeneration is not needed; pure helium flow at operation temperature suffices for removing the adsorbed CO2 (within the sensor's detection limit). The inlet flow rates of helium (the carrier gas) and carbon dioxide are controlled with two needle valves and monitored with electronic flow meters. The outlet con centration of carbon dioxide is measured with an infrared CO2 sensor. The inlet feed concentration can be checked before starting a run by directing the feed into the sensor through a column bypass. A dataacquisition system con nected to a computer allows for continuous visualization and, if desired, storage of all data (flow rates, tempera ture, composition). Students are asked to perform two breakthrough experi ments: *e 4. Experimental setup for breakthrough experiments with inbed temperature measurement. Chemical Engineering Education 1. Response to a positive concentration step at the inlet (from pure helium to about 5% molfraction CO,) 2. Response to a negative concentration step at the inlet (from 5% CO2 back to pure helium) after stage 1 has reached steady state. Complete execution time is about 1.5 hours, leaving enough time for the students to plot the data in the computer and start analyzing the results. As an example, we next provide some typical plots ob tained for the operating conditions listed in Table 1. The breakthrough curve (i.e., the history of the CO, con centration measured at the column's outlet) obtained for a positive concentration step is shown in Figure 5. As discussed previously, SMT predicts, for a positive inlet step and a favorable isotherm, the formation of a shock wave (a sharp vertical front). On the other hand, the experimental curve shows a notorious tilt and rounded edges. It is actually noticeablea pronounced "tailing" as the front approaches the steadystate concentration. This departure from "ideal ity" is associated with dispersion effects that oppose the compressive nature of the front, such as axial dispersion, intraparticular mass transfer resistance, and non isothermality. Students are asked to identify and discuss these phenomena. By using the software simulator, they will actually be able to identify the predominant dispersive effect in this case. TABLE 1 Operating Conditions Operation Ambient Operation Helium Carbon Dioxide Temperature Pressure Pressure Flowrate Flowrate (C) (Pa) (Pa) (mN(PTN)/s) (m'(PTN)/s) 38.1 1.00x 10'5 2.60 x 10' 4.35x 105 2.48 x 106 6 5 4 S3 0 0 200 400 600 800 1000 1200 1400 Time (s) Figure 5. Breakthrough curve (exit CO, mol fraction as a function of time) for a positive concentration step at the inlet. The solid line refers to the fit of the complex model. The dashed line is the result from Solute Movement Theory: an ideal shock wave with breakthrough time computed from Eq. (4). Spring 2001 Figure 6 shows the corresponding temperature histories along the column. Data from the last thermocouples are not shown since they are placed at the beginning and at the end of the packed bed where heat is being dissipated through the column's inlet and outlet flanges. This effect masks the temperature information provided by the two thermocouples. Thermocouples 2 and 6, on the other hand, depict quite well the progress of the concentration front along the column. The observed increase in temperature is associated with the exothermal adsorption of CO, at the concentration front. The significant amplitude of the temperature increase (about 7C), as well as the long length of time that it takes for cooling down, usually surprises the students. It is a good way to make them start questioning the validity of the isothermality hypothesis, often applied without proper re flection in chemical engineering problems. A more subtle observation is associated with the succes sive broadening of the temperature peaks along the column or, more clearly visible, the decrease in the temperature maximum measured in each thermocouple. Note: the second peak shown in Figure 6 was recorded with a slightly differ ent thermocouple and therefore it has a different response time. Aside from this deviation from the general trend, one may then conclude that this broadening is associated with the increasing dispersion of the concentration front as it travels along the column. Eventually, the dispersive and compressive effects compensate each other at some point in the column and the shape of the front stabilizes. This is the socalled constant pattern regime.1] Despite the clear evidences of nonisothermality and dis persive effects, students are asked to use SMT (more ex actly, Eq. 4) to predict the time it takes for the shock wave to reach each thermocouple and to compare this with the experi mental results, using the maximum temperature in each peak as a reference for the passage of the concentration front. Note that (for such a comparison to be meaningful) we have 44 S43 41 540 39 37 0 100 200 300 400 500 600 700 800 900 1000 Time (s) Figure 6. Temperature histories obtained at evenly spaced points inside the column, for a positive concentration step at the inlet. The solid lines refer to the fit of the complex model. to assume that the temperature front travels in combination with the concentration front. Under some conditions (mainly for adiabatic systems), the temperature front may lead the concentration front.131 The reasonability of our assumption is reinforced by comparing simulated concentration and tem perature profiles. In addition, as can be seen from Table 2, there is a good agreement between the SMT estimations and the experimental results. It is remarkable that the simple SMT model still seems to have some predictive value under these operating conditions. In relation to the desorption step, the resulting break through curve is shown in Figure 7. SMT predicts that a negative concentration step associated with a favorable iso therm leads to a diffuse wave. The presence of other disper sion phenomenon adds to this effect, causing the experimen tal concentration front to have a very pronounced tilt. Figure 8 shows the temperature history profiles. The peaks are now inverted, since desorption is an endothermic pro cess. Now there is a clear broadening of the peaks as the front travels along the column, agreeing with its disper sive nature (in addition to the aforementioned dispersion phenomena). The qualitative differences between the results obtained from the positive and negative steps are quite evident to the students and contain a lot of material for discussion. The quantitative analysis in terms of SMT is also quite interest ing. In addition, students are asked to run the simulation program and to compare its results to the experimental data (see Figures 5 to 8 and Table 2). The complex model, by considering several dispersion effects and nonisothermality, is able to reproduce quite nicely the shapes of the break through curves and temperature peaks. Students are encouraged to run the simulator with other input parameters and therefore gain sensitivity to how these affect the results. It is particularly interesting to study those TABLE 2 Time for the Concentration Front to Reach Each Thermocouple Position The experimental time refers to the time when the maximum tempera ture is reached, the theoretical time from SMT uses Eq. (4), and the theoretical time from CM uses the results from the complex model simulations. Thermocouple Experimental Theoretical Theoretical position time time from SMT time from Cm (m) (min) (min) (min) 0 0.0 0 0.042 3.0 2.1 2.3 0.083 4.8 4.2 4.2 0.125 6.6 6.3 6.2 0.167 8.4 8.4 8.3 0.208 10.3 10.4 10.5 0.250 12.1 12.5 12.5 6 5 03 0 200 400 600 800 1000 1200 1400 Time (s) Figure 7. Breakthrough curve (exit CO, mol fraction as a function of time) for a negative concentration step at the inlet. The solid line refers to the fit of the complex model; the dashed line is the result from Solute Movement Theory, with breakthrough times for each concentration computed from Eq. (1). 30 327 31 0 100 200 300 400 500 600 700 800 900 1000 Time (s) Figure 8. Temperature histories obtained at evenly spaced points inside the column for a negative concentration step at the inlet. The solid lines refer to the fit of the complex model. 6 4 2 h=7W/(m2K) 1 h = 700W/(m2K) 0 i 0 200 400 600 800 1000 1200 1400 Time (s) Figure 9. Breakthrough curves obtained with the complex model for two different values of the global heattransfer coefficient, h. The value h=7W/(m2K) is the one used in fitting the experimental data (Figures 5 to 8). The value h=700 W/(m2K), on the other hand, is equivalent to assum ing that heat transfer to the exterior is instantaneous. Chemical Engineering Education parameters that are probably more difficult (or impossible) to change experimentally, such as the global external heat transfer coefficient, the heat of sorption, or the intraparticu lar masstransfer coefficient. For example, increasing the global heattransfer coefficient gives rise to a quite different breakthrough curve (see Figure 9). The outlet concentration front is now much closer to a perfect sigmoid, approaching steady state much more rapidly. This seems to indicate that heat accumulation inside the column is the major cause for the "tailing" of the breakthrough curve. As the front passes, the temperature rises significantly, and the amount adsorbed is lower than for isothermal operation. As the column cools down again, the adsorption equilibrium is shifted toward the adsorbed state and more CO2 is retained in the column. The consequence is that the outlet concentration will take longer to reach steady state. In addition to complementing the discussion of the results, using the simulation program has an extra pedagogic pur pose: it shows students how process modeling in general can be useful in helping to understand and optimize a real system. CONCLUDING REMARKS The experimental study of adsorption in packed beds can be complemented if, in addition to measuring the outlet breakthrough curves, one obtains the temperature histories in different points along the bed. Such an experimental setup is quite simple and economic and provides valuable qualita tive and quantitative information that students can process without major difficulties. Solute Movement Theory is a ba sic tool for that analysis. In addition, using a software simula tor based on a more detailed mathematical model provides a better description of the process and allows students to perform "virtual" experiments and understand how different factors influence the behavior of the adsorption system. ACKNOWLEDGMENTS The authors wish to thank the Chemical Engineering De partment for providing financial support for the setup of this experiment. NOMENCLATURE c, concentration of A in the interparticular gas phase (mol/m3) Cp5 heat capacity of gas (J/mol/K) Cp, heat capacity of adsorbent (J/kg/K) Dax axial dispersion coefficient (m2/s) D. intraparticle diffusion coefficient (m2/s) h overall heattransfer coefficient (J/m2/K/s) P pressure (Pa) qA concentration of A adsorbed in the solid (mol/kg) qA Rb rp t T u v Z Greek AH E P average concentration of A adsorbed in the solid (mol/kg) bed radius (m) particle radius (m) time (s) temperature (K) interstitial solute velocity (m/s) interstitial carrier gas velocity (m/s) axial coordinate (m) Letters heat of adsorption (J/mol) packing porosity gas constant adsorbent's apparent density REFERENCES 1. Wankat, P., RateControlled Separations, Elsevier Applied Science, London, pp. 239251 (1990) 2. Edwards, M.F., and J.F. Richardson, "Gas Dispersion in Packed Beds," Chem. Eng. Sci., 23, 109 (1968) 3. Yang, R.T., Gas Separation by Adsorption Processes, Impe rial College Pres, London, pp. 161165 (1997) O  APPENDIX The main assumptions of the model are: 1. Plug flow with axial dispersion 2. Negligible radial gradients 3. Negligible pressure drop 4. Variable interstitial velocity 5. Instantaneous thermal equilibrium between stationary and mobile phases 6. Negligible thermal axial dispersion 7. Constant heat capacities 8. Intraparticular mass transport de scribed by linear driving force model 9. Negligible film mass transfer resistance 10. Helium does not absorb 11. No heat accumulation at the wall Global mass balance (where the total concen tration has already been rewritten as a func tion of total pressure assumed constant and temperature): av v aT a( 1 'aT 1 IT 91T 1 qA az T az zax)z 2 z T t P E at Interparticular solute mass balance a(vcA) Dax A +aA IE aqA az a + at + P = 0 (A2) Intraparticular solute mass balance (using the linear driving force model) (A3) A 15i qA qA) t rp Energy balance E vCpg + E Cpg +p( s AH p( E) + h (T Ta)= 0 (A4) Spring 2001 12 classroom StudentPerformance Enhancement by CROSSCOURSE PROJECT ASSIGNMENTS A Case Study in Bioengineering and Process Modeling GULNUR BIROL, INANQ BIROL, ALI INAR Illinois Institute of Technology Chicago, IL 60616 A wide range of practical, industrial, and medical ap plications has increased the demand for "bio related" courses in the university curriculum. Stu dents from biology, chemical engineering, and electrical engineering departments, all with different interests and ex pectations, enroll in these courses. Due to the diverse nature of the population in such classes, a variety of educational approaches and tools are necessary, both for accumulating knowledge and for implementing the theory. The typical undergraduate student takes four or five courses per semester, but for many students this load may become too difficult to handle because of all the assignments, projects, and midterm examinations. From time to time, this necessi tates a tradeoff among the tasks in the "todo list." This need led us to initiate a crosscourse platform that offered a joint term project to those students taking the "Introduction to Bioengineering" (IB) and "Process Control" (PC) courses. With this initiative, we tested the hypothesis that integrating crosscourse concepts in bioengineering and process control courses through a unified project could provide a stimulat ing learning environment. The integrated project would also challenge the students to think beyond each course in an isolated manner. BACKGROUND Biotechnology/biomedical engineering courses at the un dergraduate and graduate levels are offered regularly in the Chemical and Environmental Engineering Department at the Illinois Institute of Technology. Among the undergraduate level courses, "Introduction to Bioengineering" provides an introductory knowledge of biotechnology and biomedical Copyright ChE Division of ASEE 2001 engineering from a chemicalengineering point of view. One half of the semester is spent on biomedical engineering, while the other half is used for biochemical engineering. Topics covered in the course are listed in Table 1. Typically, twothirds of the IB class population has a strong interest in biomedical engineering, while onethird is interested in biotechnology. The department offers a bio medical specialization program, and students interested in Gilnur Birol holds BSc, MSc, and PhD degrees ,n ,:r em.cal engineering from Bogazici Univer sl Istanbul. She was a senior research associ Sale at1 T's Department of Chemical and Environ mntr a Engineering. She is currently a research prol Sicor in Northwestern University's Biomedi cal Engineering Department. Her research inter e.tl inoiuaO giucoseinsulin interaction in human biJi mriar,.:,l pathway analysis and modeling ard monrri'.lng ,f bioprocesses. Inanc Birol received his BSc and MSc degrees in ElectricalElectronics Engineering and PhD degree in Physics all from Bogazici University, Istanbul, and is currently a senior research as sociate at the Illinois Institute of Technology. His current research interests include study of com plexity via autocatalytic reactions, model order y reduction and webbased programming. A All ginar received his BS degree in chemical S engineering from Robert College, Turkey (1970), Sand his MEngng (1973) and PhD (1976) de grees from Texas A&M University. His teaching and research interests are process modeling and control, statistical process monitoring and fault diagnosis, and use of knowledgebased systems for realtime process supervision and control. Chemical Engineering Education ... we tested the hypothesis that integrating crosscourse concepts in bioengineering and process control courses through a unified project could provide a stimulating learning environment. careers in medicine and in the medical industries are ex pected to take this course. Many undergraduate students who take the IB course register concurrently for the PC course since it is a senioryear core course. Some stu dents take the PC in their sixth semester to avoid poten tial conflicts in their schedules. Table 2 shows the con tent of the PC course. There are roughly 1015 students who register for the IB course each semester, while 2535 students register for the PC course. In both courses, homework assignments are usu ally given on a weekly basis and form 20% of the course grade. Students are encouraged to discuss the problems and to exchange ideas with the instructors and teaching assis tants. Since the number of students is relatively low, it gives them an opportunity to interact with the course instructors on a onetoone basis. In the IB course, the homework assignments are theory intensive and can be solved using a calculator or an Excel worksheet, while in the PC course, homework problems are computationintensive and knowledge of Matlab is required to solve them. In order to have a uniform student profile in Matlab competence, the instructor tutors introductory topics in a computerlaboratory environment, holds office hours in a computer lab, and assigns study hours under the supervi sion of the teaching assistant. Furthermore, supplementary webbased tutorial material about Matlab and a trouble shooting service on the source codes are provided through the Internet. SCOPE We wanted to form a crosscourse platform where stu dents could use their knowledge from two different fields bioengineering and process controlemphasizing the use of common tools from process dynamics, differential equa tions, and computer simulations. Concentrating on a unified project, students would then have an opportunity to analyze the results from a wider perspective. To that end, glucoseinsulin interaction was chosen as the model system to be investigated. Its dynamic behavior is interesting for process modeling and control, and the unique interactions taking place in various organs in the body are of importance in bioengineering. The choice of this model sys tem turned out to be a very attractive project in both courses. Students were quite interested in the project, both because of its academic impact and because of the challenges that it offered in investigating a reallife problem. All of the bioengi TABLE 1 Course Contents: "Introduction to Bioengineering" E Part I: Biomedical Engineering The History of Biomedicine: A Brief Review Overall Description of the Human Body Physical, Chemical, and Rheological Properties of Blood Modeling the Body as Compartments, Sources, and Streams Transport through Cell Membranes Artificial Kidney Devices Artificial HeartLung Devices E[ Part II: Biochemical Engineering Review of Microbiology and Chemicals of Life Kinetics of EnzymeCatalyzed Reactions Kinetics of Key Rate Processes in Cell Cultures Design and Analysis of Biological Reactors Transport Phenomena in Bioprocess Systems TABLE 2 Course Content: "Process Control" E Incentives for chemical process control, design aspects, and control hardware E Analysis of the dynamic behavior of chemical processes Fundamental models, inputoutput models, state space models Linearization of nonlinear systems Laplace transforms, transfer functions Dynamic behavior of first and higherorder systems Time delay, inverse response Empirical models from plant data E[ Analysis and design of feedback control systems Feedback control (PID control, timedomain criteria, internalmodel control) Stability analysis, root locus analysis Frequency response techniques, Bode diagrams Performance of feedback control El Enhancements of singleloop control (cascade, feedforward, inferential control) E Model predictive control [I Multivariable processes: interaction, multiloop control, muiltivariable control E Process control design Spring 2001 129 TABLE 3 Summary of Student Profiles and Project Descriptions (UGUndergraduate: GGraduate) Students (Their backgrounds, special interests, specifications, etc.) UG Biology UG ChE UG ChE UG ChE, Biomedical Program UG ChE, Biomedical Program UG ChE UG ChE, Biomedical Program UG ChE G ChE, Interest in Transport Phe. G ChE, Interest in Biotechnology UG ChE, Attended Medical School UG ChE UG ChE Project ID 1 2 2 and A 3 and A 3 3 4 4 and B B 5 and B C C D Courses ChEIB ChE PC Taking Taken Project ID Project Topic 1 Comprehensive review of glucoseinsulin interactions 1 2 Effect of food on glucose insulin interactions 2 3 Glucose insulin interactions in a healthy man 3 4 Effect of exercise on glucose insulin interactions 2 5 Studying metabolic pathways of liver 1 A Modeling pancreas of a healthy man 2 B Modeling metabolic pathways of liver to control glucose level in blood 3 C Effect of daily activities on dosage of insulin 2 D Optimal timing and dosage of insulin 1 neering students and onefourth of the process control students volunteered to work on this project. PROJECT DESCRIPTION The purpose of this project was to analyze the dy namic behavior of glucoseinsulin interaction in a healthy person and/or in a diabetic patient. A pharma cokinetic model of diabetes mellitus originally devel oped by Puckett'" had been used previously, and an MS student who was working on this project at IIT wrote Matlab codes for it.121 These codes were given to the students so they could spend their time and energy in understanding the fundamental phenomena involved in the glucoseinsulin interaction rather than writing and debugging code. A summary of the student pro files in both courses performing a project, along with the project topic, is given in Table 3. Students were grouped by taking into account their backgrounds and the status of their course registrations. In the IB course we tried to match students so that at least one of them was concurrently taking, or had already taken, the PC course. In the process control course, we rearranged them so that if all the group members were taking both Figure 1. (a) Block diagram representing the pancreas as a PID controller and the human body as a multiinputoutput process; (b) The effect of food intake on blood glucose and insulin regulated by pancreas. Chemical Engineering Education Students Food Intake Blood Insulin + P Blood Glucose + P (a) 250 80  70 S200 0 60 g Upper Limit L0 5 r 150 50 E 40 ..so .so 5 0 30 " Lower Limit " 10 0 o 0 1 2 3 4 Time (hr) (b) courses they switched members to ensure that no student did exactly the same project in both courses. Introduction to Bioengineering The projects were assigned after the instructor covered the topics in the course, and the students were allowed five weeks to work on the projects. At the end of this period, students presented their findings in a tenminute presentation session as a final project, worth 20% of their I GLUCOSE > GLUCOSE S 4. GLUCOSEP GLYCOOEN CO, NEXP \ FRUCTOSE 6.5 OLYCERA HYDE O .p "HY TOROYACETONE ACYL A QLYCERDLM PHOSPHENOLPYRUVATE ACYLA LYCEOL  PYRVWAT. ACETYLCA 0 MALATE OALOACTATE *CrRATE coc Liver Tissue Plasma 0 Q. o * 00 0 00 0 00 100 0 5 o 00 0 50 0o 0 0 100 1rm phr) tiro pr) (mo 5 '00 ,00 00 00 0,0. 0 ;1, (h,, Sn. B (b) Figure 2. (a) A simplified metabolic pathway network of the liver; (b) Concentration profiles of intermediate metabolites for several sample runs. Spring 2001 course grade. A variety of students from different backgrounds participated: there was one graduate student with biotechnology as his area of interest, seven chemical engineering undergraduate students, and one biol ogy undergraduate student. There were also four graduate students auditing the course who did not prepare a project but participated in the work by giving feedback during the presentations. Four of the undergraduate students were registered in the Bio medical Engineering Program and were going to continue their education in medicine. The biology student was registered in the Biotechnology Cer tificate Program. A suggested timeline for these projects was C Literature review (I week): Students were given a brief description for each of the projects and were asked to make a literature survey to provide background material on the specific topic of interest. C Mathematical Model (I week): A mathematical model in Matlab code was provided and the students were expected to spend a week on understanding the code and using it efflii nilv under the supervision of both the instructor and the graduate student who wrote the code. C Modification of the Model (I week): Depending on the project description, some modifications in the Matlab code were needed. Students made such changes to the original code. C Testing and Validating the Results (1 week): The numerical results after the necessary modifications have been produced and vali dated against the available literature data.[13'44J C Preparing the Report (I week): Students were given a week to write their detailed final reports and to prepare their oral presentations. This enhanced their ability to support their work and ideas and provided immediate feedback on what the students learned from this experience. The student from the Biology Department carried out a comprehensive review on glucoseinsulin in teractions in the human body, with an emphasis on the interactions in different organs. The three Bio medical Program students concentrated on glucose insulin interactions in a healthy person and tried to understand the underlying mechanisms (see Figure 1). The graduate student put her efforts into studying the metabolic pathways of the liver using metabolic engineering concepts, initiating a promising research topic"51 (see Figure 2). Other students worked on ," q investigating the effects of exercise or food intake on glucoseinsulin interactions in a diabetic pa tient (see Figure 3). Process Control In the process control course, students were asked to work for two weeks on the project and to report their findings through project reports and presen tations. This would account for two homework assignments and 4% of their overall grade. The description of a suggested project on the control of glucose level in blood was In healthy people, the pancreas controls the glucose level in blood. When the pancreas does not function properly, the person is diagnosed as a diabetic patient, and his blood glucose level is controlled by insulin injections. Such a patient has to be careful about his diet as well as his exercise. Investigate different cases on a model human body: a healthy person, a patient under nominal conditions, the food intake of a patient, and the exercise of a patient. 1 Upper Limt 0 * (a) 0 4 8 12 16 20 24 Tine(hr) 0 50 10 1 ao 10 1 0 ' 0 ) 0 4 8 12 16 20 24 Mme(hr) Figure 3. A typical blood glucose and insulin concentration profile for repetitive intake of food. Test closedloop and openloop controllers on the model equations. Involve tasks such as finding the parameter subspace where the system works in a healthy regime, determine the appropriate dosage of insulin injection for a patient, and find the food and exercise tolerance limits for a patient. The other project titles in the PC course were "Search for a Power Law," "Internal Model Control," "Complex Systems," and "Popula tion Dynamics." Student groups were told to select one of these topics or to come up with their own project proposals. More than one group was allowed to select one title, but all groups were expected to work separately and to pursue different tasks. Students in the IB course were invited to select the "Control of Glucose Level in Blood" project. Apart from the four students in IB, TABLE 4 Project Questionnaire Low High 1. What was your level of competence using Matlab before the project? 2. What is your level of competence using Matlab after the project? 3. What is the difficulty level of this project compared to other course projects? 4. What is the relevance of your project title to your area of interest? 5. How would you rate the challenge of the project? 6. Overall, how would you rate this project? 7. How many hours did you spend on this project? 8. Are you taking Introduction to Bioengineering Are you taking Process Control No Yes No Yes 9. Facilities/tools at IIT were okay. 10. If I had more time, I would prepare a better project. I received help dealing with the project from the instructor and TAs... 11. ...as exchange of ideas 12. ...as exchange of knowledge 13. ...as technical support I received help dealing with the project from my friends... 14. ...as exchange of ideas 15. ...as exchange of knowledge 16. ...as technical support 17. This project was a useful learning tool for me. 18. It is easily applicable to other areas. 19. The goals were reasonable 20. I used my knowledge from other courses 21. 1 would consider engaging further research in this field 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 12345 12345 12345 12345 12345 12345 12345 12345 12345 12345 12345 12345 12345 Chemical Engineering Education four more students picked this topic, signify ing the appeal of biomedical topics among the students. They formed a valuable "control group" similar to IB students involved in the project who were not taking PC, which gave us the opportunity to monitor crosscourse interactions. Student interest in this topic was also evi denced by the contribution of other class mem bers during project presentations. Two of the eight students performing a project on this topic were graduate students with interests in bio technology and transport phenomena. One of the undergraduate students had previously at tended medical school and provided valuable perspective on the subjects. Some of the PC students were assigned the task of devising a control mechanism centered on different organs, such as the pancreas and ... TheproIect plkyedaa imetri gote in  B.._  7 4= ' the liver, as well as investigating the timing and dosage effects of insulin injections. Other students considered projects on topics other than the glucoseinsulin interaction. After the oral presentations in both classes, students were given a questionnaire to provide feedback to the instructors. They were carefully informed that the questionnaire (see Table 4) would be used only for course enhancement and educational research purposes and that it would not have any effect on grading. Evaluation of the returned questionnaires indicated that all students showed improvement by at least one level in their competence in Matlab, accounting for an average increase of 70%. Although they find this project difficult (4.15 out of 5.00) and challenging (4.40) with respect to other class projects, they found it quite relevant to their own area of interest (3.50) and were willing to engage in further re search in the field (3.47). Most of them reported that they needed more time to deliver a better project (4.20), which is an indication of their interest and willingness to be involved in it. The students tended to receive help from instructors and TAs (3.60) rather than their peers (2.50). They found it a useful learning tool (3.75) with quite reasonable goals (3.45), although they were nearneutral to the applicability in other areas (3.35). Overall, the students rated the project an average of 3.90. The fact that they have used their knowledge from other classes (3.70) suggests that the initiation of a crosscourse platform may become a very useful learning tool, supporting our hypothesis. CONCLUSIONS AND FUTURE DIRECTIONS Diversity of interests, technical abilities, and states of knowledge among students provided unique feedback for future improvements in this crosscourse project assignment. The choice of the project topic turned out to be an attractive one due to the popularity of biomedical engineering in education and research. The project played an important role in triggering the scientific curi osities of the students and providing an oppor tunity to adapt their knowledge to different fields. As a followup, we developed addi tional educational software in order to help students to explore many case studies. The crosscourse project approach to teach ing bioengineering and process control de scribed in this paper directly benefited four S students taking both courses concurrently. The other four who had taken the process control S class in the previous semester found that the project helped them integrate their acquired knowledge in process control to a bioengineering project. Hence, eight out of nine bioengineering students were served by this crosscourse initiative. As a result of this experience, we are looking forward to offering such a crosscourse plat form in future courses. ACKNOWLEDGMENTS The Fall 1999 students in the Introduction to Bioengineer ing and Process Control courses are gratefully acknowl edged. Special thanks also go to F. Ceylan Erzen for provid ing the Matlab codes. REFERENCES 1. Puckett, W.R., "Dynamic Modeling of Diabetes Mellitus," PhD Thesis, University of WisconsinMadison (1992) 2. Erzen, F.C., G. Birol, and A. Cinar, "GlucoseInsulin Inter action: An Educational Tool," Proceedings of the World Con gress on Medical Physics and Biomedical Engineering, Chi cago, Illinois, July (2000) 3. Pehling, G., P. Tessari, J.E. Gerich, M.W. Haymond, F.J. Service, and R.A. Rizza, "Abnormal Meal Carbohydrate Dis position in InsulinDependent Diabetes," J. Clinical Invest., 74,985(1984) 4. Sorensen, J.T., "A Physiologic Model of Glucose Metabolism in Man and Its Use to Design and Assess Improved Insulin Therapies for Diabetes," PhD Thesis, MIT, Cambridge, MA (1985) 5. Kizilel, S., R. Kizilel, G. Birol, I. Birol, and A. Cinar, "Glu coseInsulin Interaction in a Healthy Human Body: Investi gation of Stimulating Different Metabolic Pathways of Liver," World Congress on Medical Physics and Biomedical Engi neering, Chicago, IL, July (2000) 6. Erzen, Fetanet Ceylan, Giilnur Birol, and Ali Cinar, "Simu lation Studies on the Dynamics of Diabetes Mellitus," Pro ceedings of the IEEE International Bioinformatics and Bio medical Engineering (BIBE) Symposium, Washington, DC, November (2000) 7. Erzen, F.C., Giilnur Birol, and Ali Cinar, "An Educational Simulation Package for GlucoseInsulin Interaction in Hu man Body," AIChE Annual Meeting, Los Angeles, CA, No vember (2000) O Spring 2001 " laboratory DEVELOPING THE BEST CORRELATION FOR ESTIMATING THE TRANSFER OF OXYGEN FROM AIR TO WATER WAYNE A. BROWN McGill University Montreal, Quebec, Canada H3A 2B2 he study of engineering is usually carried out in a defined sequence. Students are first taught a set of basic tools that includes, for example, mathematical concepts and solution procedures along with the various conservation laws. They then apply these concepts to el ementary problems associated with their chosen discipline. In the final stages of the educational process, the simple concepts are extended to allow the students to apply them to multifaceted engineering problems. Due to the complexity of systems of practical interest, theory developed around simple systems cannot normally be applied in the form derived. Often the theory is used to identify the set of governing variables, and a relationship between these variables is then established empirically. To generalize these solutions over a number of experimental conditions, variables are often gathered into dimensionless groups. Although the number of independent dimensionless groups is governed by Buckingham's "Pi" theorem,'I a num ber of useful groups have already been defined. These di mensionless groups represent ratios of competing effects, expressed in terms of experimental variables. Thus, devel opment of an empirical relationship depends somewhat on the experience of the engineer or researcher. If particular effects are not identified as being important in the primary analysis, then they cannot be reflected in the final solution. It is imperative that students be taught the following re garding problem analysis: There are many different design equations that can be developed, depending on what assumptions are made. These assumptions are choices and are left to the judgment of the process engineer. The engineer should always use the applicable set of data to formulate a process design. More than one approach to a given problem may lead to a reasonable answer. The best approach is to consider many different methods of achieving a solution, but emphasis should be placed on the solution achieved by using the set of data most applicable to the problem at hand. It is often not possible to verify the results of an estimated parameter since a practical and accurate alternative measurement method may not exist. Thus, one may have to accept the results of an empirical correlation. We developed, and describe here, a laboratory exercise in an attempt to convey some of the above messages. It is based on the experimental determination of the overall masstrans fer coefficient describing the transfer of oxygen to water in an agitated tank. OBJECTIVES OF THE LABORATORY The objectives of the laboratory exercise were to Analyze a problem involving the transfer of oxygen to water and formulate a set of mathematical equations to adequately describe the process Fit the developed equations to experimental data to deter Wayne A. Brown has held the position of Assistant Professor in the Department of Chemical Engineering at McGill University since 1999. Prior to that he worked for five years in the oil sand industry, first as a pro cess engineer and then as a research scien tist. He received his formal training at McGill, receiving his BEng (1989), MEng (1991), and PhD (1998) from the Department of Chemical Engineering. Copyright ChE Division of ASEE 2001 Chemical Engineering Education On a practical level, the lab deals with benign materials. As such, there are no fume hood requirements or disposal problems. The lab can easily be extended to examine the effect of other variables, such as temperature, oxygen partial pressure, and liquid volume. mine the masstransfer coefficient Study the influence of the measuring device on estimates of the masstransfer coefficient Develop the semiempirical equations first put forth by Richards to estimate the masstransfer coefficient Compare experimental results with estimates obtained from the Richards equation "Tailor" the Richards relation so that it makes the most use of the data collected EQUATION DEVELOPMENT Mass Transfer Coefficient from Experimental Data The transfer of oxygen from a gas to a liquid phase can be divided into a number of transfer resistances.t21 The set of equations that describes the transfer of oxygen from a gas phase to water in a batch system is dependent on the assump tions applied. Some of the issues to be considered are: The change in concentration of oxygen in the air over the residence time in the liquid phase The transfer of inert components from the air, in addition to oxygen The composition of the particular gases used The change in gas holdup with time The mixing characteristics of the gas phase The mixing characteristics of the liquid phase The presence of additives in the liquid phase The change in volumetric gas flow rate due to the transfer of matter from the gas to liquid phases The resistance to mass transfer across the gasliquid interface The influence of surface aeration The implications of various assumptions on the resulting differential equations are discussed elsewhere.t391 For the current experimental setup, the following assumptions are assumed reasonable: There is negligible change in oxygen concentration in the gas phase. The gas holdup stays constant with time. The concentrations of oxygen in the gas and liquid phases are in equilibrium at the gasliquid interface. The liquid is well mixed. These assumptions lead to the following equations for the gas and liquid phases: dL KLa(C CL) (1) dCG dC 0 (2) dt where KLa is the volumetric masstransfer coefficient. These equations can be integrated subject to the initial conditions CL(O) = 0 and CG(0) = CG to yield CL(t)= C eKLat) (3) C G (t) = C (4) The problem is further complicated when the measure ment method is considered in the analysis. One of the most common and convenient methods for measuring dissolved oxygen is through application of a dissolved oxygen elec trode. To make a measurement, oxygen dissolved in the surrounding fluid must diffuse to the probe membrane, across the membrane, and finally through the probe solution to the active electrode tip. A number of approaches have been applied successfully to model this process, such as Fick's second law.'91 However, if the bulk solution in the tank is not viscous, transport through the electrode membrane can be treated as a firstorder process, described by an equation of the form dC i (5) dCt (CL C) (5) Here, the diffusion through the probe solution is neglected. Substituting Eq. (3) into Eq. (5) and integrating the result subject to the initial condition C(0) = 0 (6) an expression relating the overall masstransfer coefficient to the probe output can be derived C(t)=C + KLa ek P CL+ k KLa k p eK at k p a KL p L" ) Using this equation, the overall liquid masstransfer coef ficient can be determined directly from the probe output. To determine the probe time constant, Eq. (5) is solved, subject to the conditions given by Eq. (6) and Eq. (8): CL (t)= CL (8) In Eq. (8), C* is a constant for a given oxygen partial Spring 2001 pressure and system temperature. Using Eqs. (6) and (8), Eq (5) can be integrated to yield C,(t)= C( 1ekpt) (9) Generalized Correlation of OxygenTransfer Data The volumetric masstransfer coefficient, KLa is a complex function, dependent on the system geometry, the properties of the liquid, and the process operating conditions. In terms of basic variables, the function can be expressed as KLa= KLa(di,ni,hi,wi,li,dT,hL,nB,WB,pf,~f,of,Do2 ,N,vs,vt,g) (10) In developing his correlation, Richards considered KL and "a" separately. For geometrically similar vessels, dimensionless groups related to geometry do not vary. In this particular situation, the overall masstransfer coefficient per unit trans fer area, KL, associated with the transfer of oxygen from a gas phase to a Newtonian fluid is expected to be a function of the variables KL =fn(N,di,pf,tfDo2 (11) From Buckingham's Pi theorem, three dimensionless groups can be created. Thus, as suggested by Rushton,"'l the relation ship can be written KLd Nd2pf ~ (12 D K 9 lD Pf (12) D02 y Do2 f Here, K, is a constant that accounts for the geometry of the particular system. For convective mass transfer between spheri cal particles and a liquid, a has been shown empirically to have a value in the range of 0.4< a 0.6.1 In his derivation, Richards used a value of a =0.5. Thus, for constant diffusivity and fluid properties, and assuming that the gas consists of spherical bubbles, Eq. (12) reduces to KL = K2N05 (13) Richards' development is completed by noting that the inter facial area for mass transfer is correlated adequately by Calderbank's equation1I" a= K3 (PG /VL 0PL (14) As shown through the dimensional analysis performed by Rushton, et al., PG is itself a function of a subset of the variables introduced in Eq. (10).112] For the assumption of constant fluid properties applied above, the Richards correla tion for the overall mass transfer coefficient is obtained by multiplying Eqs. (13) and (14) to yield KLa = K4(PG / VL)4V.5N0.5 (15) Data from a number of different systems have been correlated using the relation developed by Richards.[13,'41 In applying the Richards equation, data on the power requirements of the gassed system are not always readily available. Therefore, as part of the current development, it is useful to express the correlation in terms of the more commonly measured variables as they appear in Eq. (10). Useful for this purpose is the empirical correlation put forth by Michel, et al.,[ 15 (p2Nd3 )0.45 Pi = QO 5 (16) PG K 5 Q 0 .5 6 , Note that this equation is not dimensionless, and thus care should be taken when extrapolating outside the range in which the data was collected. An estimate of the ungassed power requirements can be obtained from the dimension less relationship based on the Rushton's power number.[121 For geometrically similar vessels, function is of the form P (d Np diN2 Po K6 = fn(Re, Fr) (17) N3d p f (7) The Froude number (Fr) is only important if a vortex is formed. As most systems are baffled, the dependence of the power number (Po) on Fr is usually not considered, and Eq. (17) reduces to a function of Re only. This function is often expressed graphically. Since the dimensionless groups Nitrogen  M1 S1 Air Si M2 S2 Figure 1. Experimental apparatus. Temperature (TI), pres sure (PI), gas flow rate (FI), and dissolved oxygen (DO), were measured continuously. Only the signal from the dissolved oxygen probe was sampled by the data acquisi tion board, however. Solenoid valves S1, S2, and S3 were used to choose the source of the gas added to the fermen tor, while valve VI was used to adjust the flow rate. Valve C1 was used to purge the Erlenmeyer flask with nitrogen for determination of the probe time constant. Details of the procedure can be found in the text. Chemical Engineering Education Speed controller To vent * To data acquisition (D/A) board related to geometry have not been included, however, a single curve for each impeller configuration is required. Thus, using Eqs. (15) through (17), an estimate of the mass transfer coefficient can be obtained. EXPERIMENTAL Apparatus A 4L tank was used for all experiments (see Figure 1). The vessel was 13 cm in diameter and had a height of 30 cm. No baffles were installed. All experiments were performed using 2 L of distilled water, resulting in a liquid depth of approximately 15 cm. A flatblade propeller was used that was 6.5 cm in diameter from tip to tip. The propeller had 4 blades and was located 2 cm from the bottom of the vessel. Air was introduced into the bottom of the tank through a sparger that consisted of four equally spaced holes, directed radially outward. The temperature was controlled by means of a 300W heater connected to a controller (Omega Model BS5001J1). Dissolved oxygen was measured using a dis solved oxygen electrode (Ingold DL531) in conjunction with a digital meter equipped with an analog output (Cole Parmer Model 0197100). Data from the meter was logged on a personal computer by means of a dataacquisition board and bundled dataacquisition software (LABTECH notebook for Windows). Experiments were run over a range of gas flowrates (24 L min1) and stirring speeds (1001200 rev min'). Prior to each set of experiments, the probe was calibrated using nitrogen and oxygen saturated solutions of water. All experiments were performed at 300C and at atmospheric pressure. Determination of Probe Time Constant The dissolved oxygen probe was placed into a flask of Figure 2. Fit of Eq. (3) (dotted line) and Eq. (7) (thick solid line) to experimental data (thin solid line). Experimental data were generated at an air flowrate of 3 L min' and a stirring speed of 1100 rev min1. In calculating Kza by Eq. (3), only data between 30 and 98% saturation were consid ered, as described in the text. Spring 2001 water that had been purged to saturation with nitrogen (see Figure 1). After a reading of 0% had been established, the probe was quickly immersed into the vessel containing 2 L of water saturated with oxygen to 100%. Under these condi tions, the dynamics of the probe are described by Eqs. (5), (6), and (8). To facilitate the determination of the probe constant, a linearized form of Eq. (9) ( Cr (n = kpt (18) was used. From Eq. (18), a plot of en(C /i(c Cp) ver sus t should yield a straight line with a slope of kp. The slope of the bestfit line was determined by linear regresion. Determination of Ka The vessel was first purged with nitrogen until the dis solved oxygen probe stabilized at a value of 0%. The purge gas was then switched instantaneously to air through means of a series of solenoid valves (see Figure 1). An estimate of the masstransfer coefficient was then obtained by fitting Eq. (7) to the data collected. As the model function cannot be linearized, a nonlinear regression algorithm was used to extract the best estimate of KLa from each data set. RESULTS AND DISCUSSION As a preliminary exercise to the laboratory, students were asked to develop the appropriate equations with which to estimate KLa. It became apparent to the students during this exercise that the set of equations generated depends on the assumptions that were made with respect to specific aspects of the problem. For instance, if it was assumed that the rate of mass transfer from the gas to liquid is small compared to the dynamic associated with the probe, then (1 / KLa) >> Ip, and the effect of the probe is negligible. Under these circum stances, the rate of mass transfer can be calculated adequately from Eq. (3); but if this is not the case, then the probe dynamics must be taken into account.J61 Thus, a function such as Eq. (7) is required. The probe constant was calculated by each group of stu dents using a graphical approach. Typical values obtained for Tp were between 14 and 17 s. From Eq. (5) the probe output should attain a value of 63% saturation when t = Tp. From the experimental data used to determine Tp, this con dition was verified (data not shown). Therefore, Eq. (5) proved to be an adequate representation of the dynamics of the probe. Typical data obtained by the students for calculation of KLa is shown in Figure 2. It has been shown that truncating data collected early in the experiment can minimize the effect of the probe on the estimate of KLa."71 Therefore, under appropriate conditions, reasonable estimates of KLa can be obtained from Eq. (3) and knowledge of the probe dynamics is not required. Even when these conditions are met, however, due to the exponential nature of Eq. (3) the best estimates of KLa are obtained from Eq. (3) using data collected at times on the order of the time constant, = 1/ KLa. As such, it is recommended that data above 30% saturation never be discarded. ~71 For the current exercise, when neglecting the effect of the probe, only data between 30 and 98% saturation were con sidered when determining KLa using Eq. (3). When the probe dynamics were considered, however, Eq. (7) was applied and all of the data collected were used. Using the data shown in Figure 2, Eq. (3) and Eq. (7) yield KLa estimates of 134 h' and 285 h', respectively. Therefore, serious errors result if the probe dynamics are not considered. This is to be ex pected since the dynamics of the masstransfer process and the probe are on the same order for these data. Thus, the concept that the measuring device is an integral part of a process is reinforced. From Figure 2 it is apparent that Eq. (7) adequately repre sents the data, where Eq. (3) does not. In addition, for two firstorder processes in series, the sum of the time constants of each process should equal the time at which the overall process achieves a value of 63%. For the data presented, a value of 63% is achieved at approximately 30 s. The sum of the time constants, +1 / KLa, is equal to 29 s. Therefore, the assumptions that led to the development of Eq. (7) ap pear to be appropriateother formulations could also fit the data as well or possibly even better, however. For instance, unsteadystate diffusion to the active element in the probe could have been solved using the appropriate form of the diffusion equation.71 The solution to this problem can then be fit to the data to determine the probe time constant. The range over which the dynamics of the probe can be neglected was studied by comparing estimates of KLa ob tained using Eqs. (3) and (7) (see Figure 3). From this figure, it can be seen that the two estimates deviate at relatively low values of KLa. Quantitatively, it is apparent that the impact of the probe becomes important when the probe time con stant is 20% of the time constant associated with the transfer process, 1/KLa. This "rule of thumb" has also been suggested by others.[171 The data generated by the students was then compared with the Richards equation. This was accomplished by plot ting the KLa estimates obtained by the students on the same axes as the data used to generate the relationship in the original work by Richards (see Figure 4). When originally presented, KLa was quoted in units of mML'h'atm.113] This selection of units was most probably related to the sodium sulphite oxidation method that was used to generate the data. Data generated using this technique are often displayed as H'KLa, where H' is Henry's constant."J8 To facilitate com parison with the data generated by the students, data used to generate the original correlation were divided by Henry's constant at 300C (see Figure 4). In the laboratory exercise, axes complete with the data used by Richards were handed out in printed form to each lab group. Thus, the comparison exercise necessitated that the points be plotted by hand. Therefore, the students were forced to critically examine the deviation of the experimental values from the Richards equa tion. The data generated scatters within the bounds of the original data sets. This scatter is rather large, however. For instance, KLa values of between 75 and 250 h' correspond to a value of 300 on the abscissa. Thus, estimates by the corre 500 2.0 0 E 400 S1.5 s o 300 S1 200 S0.5 S100 0 0.0 0 100 200 300 400 500 KLa considering probe dynamics (hr') Figure 3. Comparison of estimates of KLa obtained by considering (Eq. 7) and neglecting (Eq. 3) the probe dy namics. Closed circles represent the KLa estimates, while open circles represent the ratio of the probe time constant to the time constant of the transfer process, where T= 1K La. The solid line indicates a perfect correspondence between the two estimates of KLa. 500 450 400 350 300 250 * . 200 0 150 ** * 100 50 o " 0 100 200 300 400 500 600 700 800 (PGJVL)'04(Vs).'SNo Figure 4. Assessment of the applicability of the Richards equation to experimental apparatus. The ordinate has the units indicated, while the abscissa has units of (HP/1000 L)o04(cm/min)O.5(RPM) 5. Black (Richards't13) and gray (Coo per "8]) circles represent the data originally used by Richards to assess his correlation. Results were divided by Henry's constant at 300C, as described in the text. The solid line represents the best fit to these data, as suggested by Richards. Open circles represent data generated as part of the current laboratory exercise. The dotted line represents the results of Eq. (19). Chemical Engineering Education lation are on the order of 50%. This finding is often diffi cult for many students to accept, as critical analysis of em pirical correlations on this level is new for them. The correlation developed by Richards underestimates the data generated by the students in almost all of the cases (Figure 4). There are two plausible explanations for this result. First, the original development of the correlation was meant to apply to geometrically similar vessels."31 There fore, it is possible that the consistent offset from the Richards correlation is related to geometric differences between the systems used to generate the various data sets. The Richards equation can be tuned for a specific geom etry as follows: For the experimental system at hand, only N and Q are varied; furthermore, for Reynolds numbers associ ated with all stirring speeds, it can be shown that Po is constant in Eq. (17).1141 Thus, Eqs. (15) through (17) can be reduced to KLa = K7N176Q0.4 (19) This equation has one adjustable parameter (K7) that ac counts for geometry and the fluid properties of the system. As a first step to improving the correlation, K, was deter mined using only the student data. The resulting equation was plotted on Figure 4. Because only data specific to the system under study was used, Eq. (19) is a better representa tion of the system used in the study, as is evident in the superior fit. A second plausible explanation to account for the differ ences noted between the Richards correlation and the experi mental data is related to surface effects. In its development, the Richards correlation assumes that the tanks are well 450 400 .350 E300 0 E250 i200 150 5.100 o v9, ^ oa o50 e 0 0 50 100 150 200 250 300 350 400 450 Measured KLa (h1) Figure 5. Ability of various correlation equations to fit the experimental data. Black circles represent results of the Richards correlation as originally presented (Eq. 15). Open circles represent the Richards correlation tailored for the geometry of the experimental system (Eq. 19). Grey circles represent the equation resulting when surface effects are considered through inclusion of the Froude number (Eq. 22). Spring 2001 baffled.1"3 As a result, surface effects are negligible and no dependence on the Froude number is expected. The Froude number was also not considered in application of Eq. (17) for the same reason. The experimental apparatus used by the students had no baffles. Thus, a dependence of the KLa on the Froude number is expected, especially for larger values of N. To address this shortcoming in the original derivation, the Richards correlation is further modified to account for pos sible surface effects. The Froude number is defined as Fr= diN2 (20) The desired equation can be obtained from Eqs. (19) and (20), and has the general form of KLa K7 (di N2+1.76Q0.4 (21) Although the value of X is not known, it is recognized that Eq. (21) is also a function of N and Q only. The specific value of X could be determined through regression using the experimental data collected. In the resulting equation, the exponent of N would be tailored to the data collected by the students, while the functionality of Q would be dictated by the data sets originally used by Richards. Therefore, a more reasonable approach is to tailor all exponents to the experi mental data generated by the students. The result of this exercise is the equation KLa = K8N135Q0.60 (22) The ability of this equation to capture the relevant features of the experiment is readily seen in Figure 5. While the Richards equation represents the data well, the best fit re sults when the equation is tailored to the experimental data collected. Thus, while an adjusted correlation coefficient, r2, of 0.81 is associated with the fit of Eq. (19), this value increases to 0.98 when Eq. (22) is applied. This result may seem obvious, as Eq. (22) has three adjustable parameters, while it appears as if Eq. (19) has only one. In actuality, however, both equations have three adjustable parameters. The difference is that the exponents in Eq. (19) were ob tained from correlations fit using other sets of data, while those in Eq. (22) were fit to the data obtained with the current system only. The difference among the three approaches becomes readily apparent at this point. As the equations are further tailored to the experimental data, the mathematical form better fits the data. Thus, the spectrum of possibilities associated with process design can be elucidated. When no data are avail able, the engineer must rely heavily on data generated from dimensionally similar systems. This approach is only justi fied, however, in the absence of reliable data associated with the system of interest. As data become available, the pre Continued on page 147. curriculum A PROJECTBASED SPIRAL CURRICULUM FOR INTRODUCTORY COURSES IN ChE Part 3. Evaluation DAVID DIBIASIO, LISA COMPARINI,* ANTHONY G. DIXON, AND WILLIAM M. CLARK Worcester Polytechnic Institute Worcester, MA 01609 his series reports on the development, delivery, and assessment of a projectbased spiral curriculum for the first sequence of courses in chemical engineer ing. The program represents significant restructuring of the introductory chemical engineering curriculum. Traditionally, a compartmentalized course sequence designed to build a conceptual foundation is taught during the sophomore and junior years, followed later by more integrated projects. Our new curriculum requires students to learn and apply chemi cal engineering principles by completing a series of open ended design projects starting during their sophomore year. The new curriculum is spiral in that students' understanding of basic concepts is reinforced by revisiting them in different contexts with everincreasing sophistication. A more detailed explanation of the concepts, curriculum design, and implementation behind this effort was described in the first two part of this series.1'21 Part 1 described the curriculum design, and Part 2 detailed the implementation. In this paper we present the details of the assessment design, describe the results of our assessment, and draw conclusions about the success of the new curriculum. BACKGROUND The background describing the need for the new curricu lum, the published research upon which it was based, and the philosophy behind our approach was presented in the first paper of this series.111 In this section we summarize the literature upon which our assessment plan was based. An extensive array of literature exists regarding assess ment of student learning. An excellent bibliography is avail able from the Department of Education[31 and two good resources are available from the National Science Founda * Current Address: School of Family Studies, University of Connecticut, Storrs, CT 062692058 tion.14'51 There are also a number of references that outline the details of assessment plans aimed at continuous im provement.'691 Most of the philosophy and techniques de scribed in those articles are adaptable to individual educa tional research and curriculum reform efforts. Assessment tools are generally categorized according to the types of methods and when they are applied during an educational project. There are two broad classes describing the timing of assessment. Formative assessment refers to periodic data collection and evaluation prior to project completion. It is used to improve the intervention during the project and helps answer the question, "Is it working?" Summative assessment concerns data collection and evalua tion at project completion. It is used to make conclusions about project retention, alteration, or elimination and nor mally answers the question, "Did it work?" There are two general classes of assessment types. Quanti David DiBiasio is Associate Professor of Chemical Engineering at WPI. He received his BS, MS, and PhD degrees in chemical engineering from Purdue University. His educational work focuses on active and cooperative learning and educational assessment. His other research interests are in biochemical engineering, specifically biological reactor analysis. Lisa Comparini is a postdoctoral fellow in the Department of Family Studies at the University of Connecticut. She received her PhD in Develop mental Psychology from Clark University where she focused on issues of language, communication, culture, and development. While her primary area of interest is in communicative practices within the family context, her interest in issues of development and communication extend to other interactive contexts, including the classroom. Anthony G. Dixon is Professor of Chemical Engineering at WPI. He holds a BSc degree in mathematics and a PhD degree in chemical engineering from the University of Edinburgh. His research has included development of interactive graphics software to aid in teaching process design and mathematics to engineers. William M. Clark is Associate Professor of Chemical Engineering at WPI. He holds BS and PhD degrees in chemical engineering from Clemson University and Rice University, respectively, and has thirteen years of experience teaching thermodynamics, unit operations, and separation pro cesses. His educational research focuses on developing and evaluating computeraided learning tools. Copyright ChE Division of ASEE 2001 Chemical Engineering Education tative methods are those familiar to most engineers. They include exams (standardized, course exams, comprehensive, oral); surveys with statistical analysis (particularly pre/post); database analysis; written reports (laboratory, design, or re search project); graded oral presentations; and graded port folios. These methods are generally perfor mancebased and measure what students can actually do. Within a disciplinespecific con ThL text, it is relatively easy to evaluate student CUIT/ performance, but the design of the tool itself may be problematic. These methods can be is used to evaluate both team and individual per in formance. Performancebased tools (authentic stua evaluation) were pioneered at Alverno Col unler lege.'110 O'Connert111 described a design competition approach to performance assess f ment, and Miller, et al.,[12' present a com COi prehensive assessment plan involving mul is rei tiple types of evaluations. by re Qualitative methods typically involve analy the sis of text and visual information. They in di~ clude videotaping, audiotaping, direct obser vation, portfolios, selfreports, openended sur veys, interviews, focus groups, performances, and journals. Engineers have been somewhat iCnr slow, however, in finding productive ways to SopAhi adopt these methodologies that are used in de velopmental psychology and cognitive science. Most of the methods involve qualitative analy sis that is unfamiliar to technologists. The main advan tage of methods such as videotaping is that they record actual worknot student interpretations of what was asked of them in a survey. By observing students doing chemical engineering, we can probe how and why they learn. This can yield rich information about the learning process. Sometimes this information is quantified, but usually the results are qualitative. Marcus1131 summarized the main features of good and poor assessment plans. The keys to a good assessment plan are: use of both control groups and target groups to minimize variation, including control for contaminating elements; mul tiple measurements using multiple tools; a mix of formative, summative, quantitative, and qualitative tools; and use of an external evaluator. Good plans define measurable objectives and design the assessment methods directly from those ob jectives. They implement continuous feedback for improve ment, use pre and postmeasurements, and include longitu dinal studies when possible. The evaluation plan should uncover program flaws as well as attributes. Poor assessment plans overemphasize one set of outcomes (for example, affective rather than cognitive) or one type of measurement (all quantitative); vaguely define the perfor mance criteria; do not link data collection to the program; Spring 2001 rely on traditional tests for nontraditional interventions; and develop inhouse instruments when validated ones are available.[131 Because any single assessment method has advantages and disadvantages, triangulation (the use of multiple mea e new iculum piral that dents' standing. Das. DOS Icep nfoi visi am i Fere rtex iev teas Sfica surements) is a key to valid assessment. Evalua tion events that occur during and after the inter vention are also important. When multiple mea surements taken at different time points con verge on common results, one can confidently draw conclusions about the observed process or outcomes. METHODS iC Our assessment plan was designed to probe ts student learning in basic chemical engineering reed and students' ability to demonstrate learning in i both team and individual contexts. We also ex ing amined attitudes, satisfaction, and confidence In about chemical engineering. For longitudinal nt data, we looked at individual student perfor mS mance in followon courses in the junior and er. senior years. Our overall plan combined forma tive and summative measures and employed both Ing qualitative (interviews, openended question tion. naires, videotaping of student group work) and quantitative (pre/post surveys, standard course evaluation surveys, individual exams, and team problemsolving competitions) tools. External consultants were used extensively throughout the project. Intervention and Comparison Cohorts At the beginning of each implemention year we randomly selected a cohort of incoming sophomores to participate in the spiral curriculum. During the first implementation year, this was about onethird of the class. In the second imple mentation year, half of the incoming class was randomly selected. Selecting half in the second year meant we elimi nated class size as a variable in our analysis. Students not selected were taught in the traditional fashion in a separate section and represented our comparison cohort. Each year we made minor adjustments (prior to the start of the aca demic year) to insure demographic similarity between the intervention and comparison groups. We also examined grades of each cohort in their first year at WPI. There were no significant differences in firstyear performance between the two cohorts. Since participation in the spiral curriculum was voluntary, students could withdraw at any time during the academic year and move into the comparison section. Only one stu dent did that during the two years of implementation. No students were allowed to selfselect into the experimental section. In the following discussion we will refer to the intervention group as the spiraltaught cohort and the tradi tionally taught students (the control group) as the compari son cohort. Spiraltaught thus refers to all the components of the new curriculum, not simply just the spiral topic structure. We did our best to control contaminating variables. Both cohorts were taught essentially the same material, using the same textbooks. Both cohorts met for the same number of class periods each week and, as schedules allowed, during the same class hour each day. When scheduling did not allow the latter, we avoided vastly different meeting times. For example, if the comparison group was scheduled at 11:00 a.m., we scheduled the spiraltaught section for close to that hour and avoided times such as 8:00 a.m. or 4:30 p.m. ProblemSolving Competitions: Team and Individual Team At the end of each implementation year, we held a teambased problemsolving competition. All sophomores were invited to participate. Spiraltaught students were placed in teams and comparison students were placed in separate teams. Most students were teamed with others with whom they had not previously worked. We constructed teams with a mix of abilities (judged by grade records) and gender. All participants were paid, and the winning teams from each cohort were awarded additional prize money. This structure meant that from the student standpoint, they were competing only with peers (not comparison groups versus spiral groups). The participation rate was 75% for the first year and 90% in the second year. Teams were given an openended chemicalprocess prob lem to solve and had two hours to develop their solution. The problem involved a simple reaction/separation process for the production of formaldehyde from the decomposition of methanol. Students were given the reaction and the desired production rate. They had to develop the process flowsheet, make reactor and materialbalance calculations, and choose and design a separation scheme. Each team selected one group member to present its solu tion. These tenminute presentations were videotaped. The presentation videotapes and written student work were sent to three external experts in chemical engineering. Judges were given the problem solution, some guidelines for rating student work, and a form for reporting their analysis of each team's solution. The judges ranked all teams from bestto worst on the basis of the technical work, not on the presenta tion quality. The highest ranked spiral team and the highest ranked comparison team were each awarded prize money. We were interested in the comparative rankings of spiral versus comparison teams. Judges were volunteers from academia and industry and had no knowledge of whether the teams were spiraltaught or comparison teams. We also vid eotaped each team during its twohour working sessions to help us understand something about the process of solving chemical engineering problems. Individual At the end of the second implementation year we held an individual exam competition. Students were given an exam that tested four basic areas of chemical engineering. The exam was openbook and was designed at about Bloom levels 34: application and analysis. Again, all sophomores were invited and paid to participate. The participation rate was 61% of the total sophomore class. We offered the exam to juniors to probe longterm retention of basic knowledge. Only four participated, however, yielding too small a sample to draw conclusions. We blindgraded each individual exam using a numbering system that preserved student anonymity. To promote conscientious participation, we offered more cash to students scoring above 70% on the exam. Questionnaires. Surveys, Interviews We contracted developmental psychologists from the Frances L. Hiatt School of Psychology at Clark University for our external consultants. Kevin O'Connor and Lisa Comparini were the consultants, with Comparini being with us for most of the project. All questionnaires and surveys were designed by the consultants, and all interviews (in person or electronic) were conducted by Comparini. Both O'Connor and Comparini were intimately involved in the design of the competitions described above. Comparini con ducted the analysis of the questionnaires and surveys. RESULTS The results from the major assessment measures are sum marized below. In all cases, the results were positive regard ing the success of the spiral curriculum project. Assess ment design allowed us to probe program effects from a variety of different views. The converging results clearly demonstrate the superior educational benefits the new curriculum provided. Team ProblemSolving Competition Spiraltaught student teams were judged signifi cantly higher than comparison teams in both years of the team competition. In the first year, all three judges ranked the spiral teams as the top three of the six participating teams by a wide margin. In the second year, spiraltaught teams were unanimously ranked as the top two of eight total, and four of the top five teams were spiraltaught groups. This clearly demonstrates the ability of spiraltaught students to perform at higher levels than comparison students on openended problems. In general, the judges' comments indicated that spiral taught teams demonstrated better overall problem analysis than comparison teams. A more global, systemsoriented approach was taken by higherranked teams. Spiraltaught teams also showed more progress in generating a flowsheet, completing material balances, and handling equilibrium con version calculations. Poorer team solutions (primarily com parison groups) were characterized by incomplete flowsheets, Chemical Engineering Education trouble handling reaction products, and an inability to com pletely couple the reaction and separation portions of the process. Very often, comparison teams focused too much on one particular aspect and failed to demonstrate knowledge of the "big picture." This performance assessment was a major milestone in our evaluation. Since one of our objectives was to improve students' abilities to solve openended problems in team situations, the results were very encouraging. Our evaluation plan was not designed to probe individual effects. For ex ample, we did not run a section that had topic spiraling and no cooperative learning. We strongly believe, however, that repeated exposure to spiraled topics (a critical mechanism in improving knowledge retention) coupled with substantive team work is a major reason for the results. Individual Exam Competition Spiraltaught students performed better, as indi viduals, on basic chemical engineering prob lems. We were not able to conduct this competition in the first implementation year, but we did conduct it at the end of the second implementation year. Twenty students participated, ten from each cohort. The results are summarized in Table 1 and Figure 1. As a group, the spiraltaught students showed better understanding of chemical engineering. The average score was higher for spiraltaught students and more of them scored above the 50% and 70% levels. Figure 1 shows that spiraltaught students performed the same or better than comparison students in three of the four areas tested. Those four areas were material balances, classi cal thermodynamics, staged equilibrium separations, and so lution thermodynamics. A clear difference in learning mate rial balances was shown. Spiraltaught students were con tinuously using this material in different contexts throughout the sophomore year. A similar difference, though not as dramatic, was seen for classical thermodynamics. It is sig nificant that for the case of staged separations, the spiral taught students had been exposed to the specific material tested (basic McCabeThiele calculations) several months prior to the exam. The comparison students were enrolled in the traditional course concerning this material at the time of the exam. Spiraltaught students did not do as well on the solution thermodynamics problem. This area was the most difficult to build into the spiral curriculum and we recognize that it is one area of the curriculum needing improvement. A typical criticism of cooperative learning is that some students will be carried by their group. The individual exam results and the longitudinal data shown below serve to dis prove that notion in our case. Again, the combination of topic spiraling, repeated exposure to openended problems, and extensive group work was successful in improving indi vidual student learning. Longitudinal Effects Spiraltaught students received higher grades than comparison students in followon junior and seniorlevel chemical engineering courses. We tracked students throughout their academic programs to understand how participation in the new curriculum corre lated with later performance. Examination of grades in our unit operations laboratory showed that teams comprised of two or more spiraltaught students generally received higher report and oral presentation grades than teams comprised Figure 1. Average score of each cohort on individual problems. Maximum score per problem was 10 points. Spring 2001 Material Bal. Classical Staged Sep. Solution Thermo. Thermo. solid = spiraltaught open = comparison TABLE 1 Average Total Scores for Individual Exam Competition (Total possible points = 40) Average # Scores # Scores Cohort Score >50% >70% SpiralTaught 21.7 5 3 Comparison 18.8 3 2 Examination of grades in our unit operations laboratory showed that teams comprised of two or more spiraltaught students generally received higher report and oral presentation grades than teams comprised mostly of comparison students. mostly of comparison students. WPI's upperlevel program is heavily projectbased. It makes sense that students experienced in projectbased learn ing would show higher levels of performance in similar academic activities as they became juniors and seniors. These projects are similar to seniorlevel research (BS thesis) projects done at other schools. The first cohort of spiral taught students graduated this year. Contaminating factors such as mixing of students among spiraltaught and com parison cohorts and upperlevel project grade inflation (80% of these projects receive A's) made this analysis uninforma tive. Of the nine graduating seniors who received awards for outstanding project work, however, five were from the spi raltaught curriculum. For that class, only a third of the graduates were in the spiraltaught cohort. An alternative to probing project performance is to com pare grades of comparison and spiraltaught students in up perlevel courses. These courses represent the core knowl edge of the discipline and include: fluid, heat, and mass transport; kinetics and reactor design; two process design courses; and two unit operations lab courses. A variety of faculty members, course formats, and teaching methods are used in this mix: large lecture, group work, laboratories, and teambased capstone design. WPI awards only four letter grades (A, B, C, and NR)there is no D grade. The NR (No Record) grade, typically covers the traditional DF range and is a failure grade that results in no course credit. In all cases, spiraltaught students received a higher per centage of A's and a lower percentage of C's than compari son students. For the class of 2000, spiraltaught students represented 33% of the class, yet they accounted for 40% of the A's and only 22% of the C's, from a total of eight core junior and seniorlevel courses. For the class of 2001, spi raltaught students represented 50% of the class and ac counted for 64% of the A's and only 29% of the C's, from a total of five core junior and seniorlevel courses. For both cohorts over two years of data, a total of 35 failing grades were earned in all courses examined. Only three of those were from spiraltaught students, and the same student earned all of them. This data demonstrates the ability of spiraltaught students to perform at higher levels despite different course formats and variable teaching styles and standards in their upper level courses. Attitudes About the Curriculum, the Discipline. and the Faculty Spiraltaught students showed more positive at titudes about chemical engineering and higher confidence in the major than comparison stu dents. Student course evaluations are required for all WPI courses. A standard form is used that primarily examines student satisfaction with the instructor. We examined the aggregate responses from all sophomorelevel chemical engineering courses for sections taught by all instructors. There were no significant differences between spiral instructors and other faculty. In fact, the percent of positive student responses for the spiral curriculum instructors, as a group, was equal to or higher than that for instructors in the traditional sections (i.e., those teaching the comparison cohort). When the project started, we planned to implement pre/ post surveys during each year. During the first implementa tion year we observed that results from these surveys gave little information, particularly for the time invested adminis tering them to each cohort. We also made a philosophical decision that surveys with closed wording, forcedchoice responses, and fixed topics were not appropriate for our project. We felt this type of evaluation tool, which restricts students responses to predetermined questions, did not allow us to probe a range of possible topics and responses from the students' perspectives. Hence, we used openended ques tionnaires for the remainder of the project. All sophomores were given a questionnaire at the end of each implementation year. Students were asked about their TABLE 2 Results from EndofYear Questionnaire [Number of students responding each year is in ()] SpiralTaught Comparison 9798 9899 (n=14) (n=15) Positive comments Number of topics Negative comments Number of topics 45 61 19 19 Confidence in choice of major Positive change Negative change No change 12 12 0 1 0 2 9798 9899 (n=18) (n=ll) Chemical Engineering Education expectations for the year and whether or not they were met. They were asked about their choice of major and their confi dence in pursuing chemical engineering. We asked what were the 2 to 3 mostvaluable and the 2 to 3 leastvaluable aspects of their sophomoreyear classes. Additional ques tions included estimates of work effort, quality of teaching assistants, and any general comments. A summary of the content analysis of the results is shown in Table 2. We should keep in mind that these responses were taken from a fairly openended questionnaire. The numbers in a particu lar category do not necessarily represent responses to the same questions. They represent relatively spontaneous num bers of mentioned topics, rather than responses to forced choice questions. The overall results show that spiraltaught students were more satisfied with their academic experience and more confident with their choice of major than their peers in the comparison section were. There were about twice as many positive comments made by spiraltaught students on a broader number of topics than by comparison students. The positive comments included topics such as group work, lab work, interaction with the professors, and the projects. Many of the negative comments made by spiraltaught students were about problems that they reported improved during the year (such as "kinks" in early course organization and chang ing professors) and were generally not about the quality of their overall learning experience. Negative student comments were particularly revealing. Spiraltaught students complained most about their high workload and about the teaching assistants. The comparison students' complaints were often stated in terms of a deficit (not enough application, not enough material covered, not enough group work, not enough projects, not enough indi vidual attention, not being in the spiral class) and were more suggestive of a dissatisfaction with their overall experience. Retention in CM Spiraltaught students showed higher retention rates in the major than did TA comparison students. Retent Sophomot Retention is a key issue when new cur ricula are implemented. We are probably similar to most departments in that the big gest loss of students from the major occurs Academic Year and Section during the sophomore year. Historically, our retention rate is about 80%, meaning that 9697 20% of the students enrolling in the first No separate secti chemical engineering course leave the major 9798 by the end of their sophomore year. Comparison Spiraltaught We found retention was higher during the 9899 sophomore year for spiraltaught students 9899C Comparison compared to the comparison cohort. Table 3 Spiraltaught shows the retention data. Note that in 9899, Spring 2001 retention in the traditional courses was significantly lower than normal while spiral student retention was maintained at 80%. We interviewed many of the students who left the spiral curriculum and found that reasons were typically re lated to leaving engineering for one of the sciences (chemis try, biochemistry). An interesting anecdote is that one student who left late in the year said she remained in the spiral curricu lum so long only because she liked it so mucheventually it became clear that chemical engineering was not her preferred discipline and she switched to civil engineering. The Process of Learning Chemical Engineering We are currently involved in a detailed analysis of the problemsolving session videotapes taken during the team competition. These are the twohour tapes of each team that were not used for judging team solutions. The tapes have all been transcribed and are being analyzed using techniques similar to Linde, et al., 41 to study the problemsolving pro cess in spiraltaught and comparison teams. Our methodol ogy for this analysis combines the expertise of a develop mental psychologist with that of a chemical engineer.[15 Preliminary results indicate that the spiraltaught teams exhibited significantly different teamwork skills than did the comparison teams. Since spiraltaught teams presented bet ter solutions, we are interested in characterizing their pro cess and connecting it to our curriculum design. We observed that spiraltaught teams behaved more like practicing chemical engineers attacking a problem, while comparison teams behaved like students of chemical engi neering. We've observed significant differences in the use of tools of the profession (authority figures, textbooks, pub lished data, etc.) that points to a model of teamwork some what different than the traditional engineering model. None of the teams (comparison or spiral) exhibited any evidence of team dysfunction due to typical problems such as domi nant individuals (either intellectually or personalitybased), gender bias, lack of participation, or lack of motivation. Successful teams, as rated by _E 3 external judges, had a greater ability to con )ata for struct a framework for solving the problem. iE Students Unsuccessful teams struggled to do so, and such teams were unable to move toward a Total Students framework even when individual members cent at seemed capable of starting the process. We ined Year End are currently articulating the theoretical ba sis for these observations and formulating ;0 62 an indepth description of the model and its relation to the new curriculum. 0 32 Areas Needing Imorovement Despite the success of the curriculum as described above, we are aware of three aeas where improvement is needed. We attempted to incorporate writing into the curriculum to ,BL ion I e Ch Per Reta ons 8 8 88 14 68 17 80 16 exploit the writingtolearn philosophy. But our efforts lacked consistency, and due to time taken to deliver the new cur riculum, we could not implement all we had envisioned. Although spiraltaught students had multiple writing oppor tunities, a concerted program to improve writing was not possible. Some anecdotal evidence from upperlevel writing samples supports the notion that we did have some positive impact on spiraltaught students' writing abilities. We struggled with spiraling the concepts associated with solution thermodynamics. This is some of the most difficult material that sophomores encounter. In fact, many schools do not teach it until the junior year. The optimal time and location in the curriculum for introducing some of these theoretical concepts is not known. We made improvements from the first to the second implementation year, but our sense is that more work is needed to sort out how students may best understand these concepts. The final project, for both implementation years, was a significantly different and more complex project than any of those earlier in the year. We asked students to design a project that could be used in future course offerings. The technical material involved some topics of chemical engi neering (transient material and energy balances) that are not normally a part of the sophomore year. We believe that students showed mastery of the technical material, but they could not translate that knowledge sufficiently into the con text of the project. Hence they developed mediocretopoor projects regardless of the team. There appears to be a general intellectual limit to their ability to integrate concepts from earlier in the year and extrapolate them to new situations. We are currently examining that limit by analyzing our evaluation data from those projects. SUMMARY We believe our assessment results clearly show the ben efits of all the educational activities implemented in the spiral curriculum. In fact, we were quite surprised that dif ferences between spiraltaught and comparison cohorts were so dramatic in so many different areas. Results from a vari ety of measurements and analysis converged upon a consis tent answer. Compared to traditionally taught students, spiraltaught students displayed equal or better understanding of basic chemical engineering principles, were better in teams at solving openended problems, had higher satisfaction levels with their academic experience, had higher retention rates, performed better in upperlevel courses, and were more con fident about their choice of chemical engineering as a major. Although our evaluation plan could not delineate effects of individual curricular improvements, we believe that frequent openended project experiences built around a spiral topic structure were the major reasons for project success. After extensive discussions, the WPI chemical engineer ing department voted to permanently adopt the curriculum described in this series of three papers for all our sophomore students beginning in the fall of 2001. ACKNOWLEDGMENTS The authors would like to thank the Department of Educa tion for support of this work under the Fund for the Improve ment of PostSecondary Education (FIPSE), Award No. P116B60511. REFERENCES 1. Clark, W.M., D. DiBiasio, and A.G. Dixon, "A ProjectBased, Spiral Curriculum for Introductory Courses in Chemical Engineering: 1. Curriculum Design," Chem. Eng. Ed., 34(3), 222 (2000) 2. Dixon, A.G., W.M. Clark, and D. DiBiasio, "A ProjectBased, Spiral Curriculum for Introductory Courses in Chemical Engineering: 2. Implementation," Chem. Eng. Ed., 34(4), 296 (2000) 3. Marcus, D., "Notes on Evaluation Design," Fund for the Improvement of Postsecondary Education, Department of Education, web site, accessed August, 1996, at http://www.ed.gov/offices/OPE/FIPSE/biblio.html updated January 9, (1998) 4. Frechtling, J., editor, UserFriendly Handbook for Project Evaluation, National Science Foundation, NSF 93152 (1996) 5. Frechtling, J., L.S. Westat, eds., UserFriendly Handbook for Mixed Method Evaluations, National Science Founda tion, NSF 97153 (1997) 6. Olds, B.M., and R.L. Miller, "A Measure of Success," ASEE Prism, p. 24., December (1997) 7. Rogers, G., "EC2000 and Measurement: How Much Preci sion is Enough?" J. Eng. Ed., 89(2), 161 (2000) 8. DiBiasio, D., "Outcomes Assessment: An Unstable Process?" Chem. Eng. Ed., 33(2), 116 (1999) 9. Rogers, G., "Outcomes Assessment: Opportunity on the Wings of Danger," Chem. Eng. Ed., 33(2), 106 (1999) 10. Mentkowski, M., and G. Loacker, "Assessing and Validating the Outcomes of College," in Assessing Educational Out comes: New Directions for Institutional Research, Jossey Bass (1985) 11. O'Connor, K., "Overcoming Obstacles to Boundary Crossing in MultiInstitution Product Realization Projects," proceed ings of the Technology Reinvestment Project Grantees Con ference, NSF (1997) 12. Miller, J., D. DiBiasio, J. Minasian, and J. Catterall, "More Students Learning, Less Faculty Work?The WPI Davis Experiment in Educational Quality and Productivity," in Student Assisted Teaching and Learning: Strategies, Mod els, and Outcomes," M. Miller, J. Groccia, and J. Miller, Anker Publishing (2001) 13. Marcus, D., "Evaluation for Second and Third Year and Beyond," Annual FIPSE Project Director's Meeting, Wash ington, D.C., October (1997) 14. Linde, C., J. Roschelle, and R. Stevens, "Innovative Assess ment for Innovative Engineering Education: VideoBased Interaction Analysis," Report to the NSF Synthesis Coali tion, Institute for Research on Learning, Palo Alto, CA (1994) 15. Clark, W., L. Comparini, D. DiBiasio, and A. Dixon, "The Process of Learning Chemical Engineering: What Works and What Doesn't," ASEE meeting, St. Louis, MO, June (2000) 0 Chemical Engineering Education Estimating the Transfer of Oxygen Continued from page 139. ferred approach is to tailor the functional form derived from existing correlations in an attempt to maximize the use of the specific information available. The laboratory exercise also has secondary benefits. First, the exercise bridges the gap between biotechnology and classical chemical engineering. Students are often under the impression that the area of biotechnology represents a radi cal departure from the chemical engineering principles ap plied to other industries. This laboratory serves to demon strate that the "high tech" fields have been developed on the same set of principles as the mature industries. On a practi cal level, the lab deals with benign materials. As such, there are no fume hood requirements or disposal problems. The lab can easily be extended to examine the effect of other variables, such as temperature, oxygen partial pressure, and liquid volume. CONCLUSIONS When faced with a design problem, the chemical engineer often must turn to empirical expressions, generalized through the application of dimensionless groups. But as data become available that are specific to the system of interest, the basic proven empirical expression should be tailored to reflect these data. Extracting the relevant parameters of interest (i.e., KLa) from experimental data generated for this purpose is subjective, based heavily on the assumptions made by the engineer. Although many approaches may be adequate, oth ers may lead to erroneous results. A key variable to consider when analyzing the problem is the influence of the measur ing element on the resulting data set. NOMENCLATURE a area available for mass transfer per unit volume of ungassed liquid (m2m3) CG concentration of oxygen in the gas phase (mol L') C concentration of oxygen in the gas phase at t=0 (mol L ') CL concentration of oxygen in the liquid (mol L') CL concentration of oxygen in the liquid in equilibrium with the gas phase (mol L') C concentration of oxygen in the liquid, as measured by the dissolved oxygen probe (mol L') d. impeller diameter (m) dT tank diameter (m) Do2 diffusivity of oxygen in water (m2s') g acceleration of gravity (m s 2) h height of impeller from bottom of tank (m) hL height of liquid (m) 1i length of impeller blades (m) H' Henry's constant for oxygen and water (mmol L atm') K empirical constant K overall masstransfer coefficient per unit transfer area, Spring 2001 based on the liquid phase (m s') KLa volumetric masstransfer coefficient, based on the liquid volume (hr') k (I / p)(1) n number of baffles n number of blades on impeller N stirring speed (rev s') P power input into ungassed liquid (W) PG power input into gassed liquid (W) vs superficial gas velocity, based on cross section of vessel (m s') v, terminal rise velocity of a gas bubble (m s') w width of baffles (m) w, width of impeller blades (m) Q gas flow rate (L s') t time (s) Greek symbols a, P, y, X exponents in Eqs. (12), (17), and (21) Tp time constant of the dissolved oxygen probe (s) T time constant of the transfer process (l/KLa)(s) lf liquid viscosity (cp) pf liquid density (kg m 3) of surface tension at gasliquid interface (mN m ') REFERENCES 1. Geankoplis, C.J., Transport Processes and Unit Operations, PrenticeHall, Inc., NJ (1993) 2. Bailey, J.E., and D.F. Ollis, Biochemical Engineering Fun damentals, 2nd ed., McGrawHill, Inc., New York, NY (1986) 3. Linek, V., J. Sinkule, and P. Benes, Biotechnol. Bioeng., 38, 323(1990) 4. Linek, V., V. Vacek, and P. Benes, Chem. Eng. J., 34, 11 (1987) 5. Benedek, A., and W.J. Heideger, Biotechnol. Bioeng., 13, 663 (1971) 6. Sheppard, J.D., and D.G. Cooper, J. Chem. Tech. Biotechnol., 48,325 (1990) 7. Ruchti, G., I.J. Dunn, and J.R. Bourne, Biotechnol. Bioeng., 23,277 (1981) 8. Chang, H.N., B. Halard, and M. MooYoung, Biotechnol. Bioeng., 34, 1147 (1991) 9. Wernau, W.C., and C.R. Wilke, Biotechnol. Bioeng., 25, 571 (1973) 10. Rushton, J.H., Chem. Eng. Prog., 47, 485 (1951) 11. Calderbank, P.H., Trans. Instn. Chem. Engrs., London, 36, 443(1958) 12. Rushton, J.H., E.W. Costich, and H.J. Everett, Chem. Eng. Prog., 26, 395 (1950) 13. Richards, J.W., Prog. Ind. Microbiol. 3, 143 (1961) 14. Kargi, F., and M. MooYoung, in Vol 2 of The Principles of Biotechnology, Engineering Considerations, C.O. Cooney and A.E. Humphrey, eds; in Comprehensive Biotechnology: The Principles Applications and Regulations ofBiotechnology in Industry, Agriculture and Medicine, M. MooYoung, ed., Pergamon Press, New York, NY 15. Michel, B.J., and S.A. Miller, AIChE J., 262 (1962) 16. Tribe, L.A., C.L. Briens, and A. Margaritis, Biotechnol. Bioeng., 46, 388 (1994) 17. Merchuk, J.C., S. Yona, M.H. Siegel, and A.B. Zvi, Biotechnol. Bioeng., 35, 1161 (1990) 18. Cooper, C.M., G.A. Fernstrom, and S.A. Miller, Ind. Eng. Chem., 36, 504 (1944) a " classroom UNDERGRADUATE PROCESS CONTROL Clarification of Some Concepts R. RAVI* Indian Institute of Technology Kanpur Kanpur 208 016, India Teaching undergraduate process control can be an en joyable experience for an instructor given the wide range of quality chemical engineering textbooks that are now available.[16 After teaching the course a couple of times, however, I felt there was still a need for clarification of some fundamental concepts, especially in the areas of frequency response and stability. In this article I hope to achieve such a clarification through some simple, yet illus trative, examples. FREQUENCY RESPONSE: ONLY FOR STABLE SYSTEMS? In the context of process control, the frequency response is usually associated with the response of a linear, time invari ant (constant coefficient) system to a sinusoidal input. In the most common way of "deriving" the frequency response result, the output response is shown to be a sinusoidal func tion of the same frequency (c) as the input, once the tran sients have died out. Further, the ratio of the amplitude of the output to that of the input, called the amplitude ratio (AR), is shown to be equal to IG(j(o)], while the phase difference (p) between the output and the input is shown to be arg[G(jo)], where G(s) is the transfer function representation of the system of interest and j=Y1. Thus, the frequency response calculation is reduced to the calculation of the magnitude and phase of the complex num ber, G(jo), as a function of the frequency. This information is usually represented in the form of a Bode diagram or a Nyquist plot. The key point of our discussion is the condition "once the transients have died out." Clearly, this happens if the system is stable, i.e., if all the poles of the transfer function G(s) lie in the left half (of the * Present address: Indian Institute of Technology Madras, Madras 600028, India 148 complex) plane (LHP). Thus it might appear that frequency response makes sense only for stable systems. But we do find Bode diagrams and Nyquist plots for the pure capacity (G(s)=A/s) and the PI controller, G(s)= [Kc(rls+ l)]/Tls, both of which are (openloop) unstable. Do these diagrams mean anything then? In the case of the pure capacity system, one can show that the response to a sinusoidal input is bounded and is a superposition of a con stant and a sinusoidal function whose amplitude and phase are in fact provided by G(jco), as for a stable system. (It should be noted that a system with a zero pole is to be regarded as unstable in spite of a bounded response to a sinusoidal input. Recall that the step response of such a system grows with time.) But what about a system with a pole in the right half plane (RHP) for which the response to a (bounded) sinusoidal input will have a timegrowing component arising out of the unstable pole? Does the Bode diagram (or the Nyquist plot) for such a system obtained from the corresponding G(jw) have any meaning? The answer to the last question is "yes." The common way of deriving the frequency response re sult is only a method of measuring the frequency response for stable systems and does not constitute a fundamental R. Ravi obtained his BTech from the Indian Institute of Technology, Madras, in 1984, and his PhD from Purdue University in 1991. His research interests are in applied statis tical mechanics and process control. For the past few years, his abiding passion has been the understanding of the origins of thermodynamics and fluid mechanics. Copyright ChE Division of ASEE 2001 Chemical Engineering Education definition of it. The fundamental definition is provided by a basic result of linear systems theory.[7] There exists a peri odic solution for a linear time invariant system subjected to a periodic forcing; this periodic solution has the same fre quency as that of the input forcing, and its amplitude and phase at the particular frequency are determined (as ex plained above) from the complex number G(jw). This result holds whether the system is stable or not. In general, the response of a linear system to a periodic forcing will be the superposition of the periodic solution and a nonperiodic component, and the frequency response is defined with respect to the periodic component. Thus, the Bode diagram for an unstable system makes sense in that it represents the same relationship between the periodic com ponent of the (output) response and the input periodic forc ing as it does for a stable system. This point is not of minor significance as it gives universal status to Bode diagrams or Nyquist plots as signatures of systems they represent, be they stable or unstable. The open loop method of measuring the frequency response (after waiting for the transient to die out) will not work for un stable systems (pure capacity being an exception). In the next section, we point out two possible methods of measuring the frequency response of unstable systemsone an openloop method and the other a closedloop method. Although both methods are valid in principle, the latter is more practicable. The reasons are outlined below. Frequency Response of Unstable Systems We illustrate the procedures through a simple system with one unstable pole Go(s)= (1) (s a) OpenLoop Method For the OpenLoop Method we consider a sinusoidal input u(t)= Au sin(o)t+ (u) (2) The response of the system to this input can be shown (for instance, by a straightforward Laplace inversion) to be After teaching [undergraduate process control] a couple of times, I felt there was a need for clarification of some fundamental concepts, especially in the areas of frequency response and stability. In this article I hope to achieve such a clarification through some simple, yet illustrative, examples. KAu(cocos ~u +asin u)eat y(t) = a2 +02 +A IGo(jco)lsin{cot+pu +arg[Go(j(o)]} (3) This suggests a way of "stabilizing" the response by choos ing 0u such that ) cos u +asin Ou =0 (4) so that only the stable periodic component of the solution remains, enabling the determination of its amplitude and phase. In practice, thus, one is left to choose a unique value of ou (between 0 and 27) for each o; this can be problem atic given that the value of the unstable pole, a, is not known a priori. Hence, we discuss a more practicable method in volving closedloop stabilization. ClosedLoop Method We consider the same firstorder unstable system. It is easy to show that the system can be stabilized in a feedback loop using a proportional controller of gain Kc greater than a/K (Figure 1 illustrates the scheme). In fact y(s)_ KcK CL() (5) r(s) s+ CL) ( where b=KKa > 0. If a sinusoidal variation is given in the reference signal, r, r(t)= Ar sin Ct (6' e can show that (by Laplace inversion, for instance) Figure 1. An openloop unstable system in a feedback loop with a proportional controller. Spring 2001 y(t)= Ciebt + Ay sin (wt + Oy) where K KA ro C = r; ; Ay=Ar'GCL(jo);' y=arg[GCL(jc)] (8) The signal u(t) = K,[r(t)y(t)] can be expressed as u(t)= KcClebt + Au sin (ot +( u) (9) It is possible to show that A A = Go(jo)l and y 4u =arg([Go(jc)]) (10) i.e., the amplitudes and the phases of the "input" and the "output" signals of the unstable system, Go(s), are related as before by the complex number Go(jw). The stabilization effect is noted in the eb term (note: b > 0) in both y and u in contrast to the openloop case where we get the timegrow ing term, e", in the output (for the same input Ar sin ot). For concreteness and simplicity, we illustrate the above result with a numerical example.181 We choose Go(2s) (11) It is easy to see that a unity gain (Kc = 1) proportional controller stabilizes the above system in a feedback loop. In fact y(s) 2 (12 r(s) s+l () If we choose the input to be r(t)= 0.5 sin 2t (13) then we can show that y(t)= e +(0.2)12 sin [2t 1.1 (rad)] (14) Further u(t)= r(t)y(t) = et +0.5 sin [2t+0.93(rad)] (15) and IGo(2j)= and arg[Go(2j)]= 2.04 rad (16) Thus, we see that A IGo(2j) = and arg[Go(2j)] = y (u (17) Of course, the above analysis is based on a given system transfer function. This is not known a priori and, in fact, the purpose of the frequency response experiment is to deter mine the transfer function. But what one has to do is to tune the proportional controller to obtain a stable system. Then, for a known sinusoidal input, r(t), at various frequencies, one would have to measure the amplitude and phase of both (7) u(t) and y(t) (after the transients die out) to construct the transfer function, Go(s). FREQUENCY RESPONSE AND STABILITY CRITERIA We now turn to another aspect of frequency response and stability, the famous Nyquist stability criterion. The Nyquist criterion helps one to infer the stability of a feedback control system from the Nyquist (polar) plot of the loop transfer function, GL(s), which is the product of the transfer functions of all the elements in the control loop. The advantage of stability criteria based on frequency response is their ability to deal with nonpolynomial G,(s) that the RouthHurwitz criteria cannot treat rigorously. This advantage is particu larly relevant to chemical engineering systems that often contain a timedelay element. Most chemical engineering textbooks on process control do not give as much prominence to the Nyquist criterion as they do to the Bode stability criterion, which is easier to use. An exception is the Luyben1[2 book where a detailed discus sion with illustrative examples can be found. It is to be noted that the Bode criterion is not general and specifically cannot be applied in cases where the Bode diagram for G,(s) is not monotonically decreasing. It is our objective here to high light the potential sources of error in the application of the Nyquist criterion. It is not uncommon to find special state ments of the criterion that might work in many cases but fail to yield the correct result for at least some systems. Often, these special statements are not accompanied by the conditions under which they hold. Thus it is desirable to always use the general form of the criterion that is given below. Let N be the number of net rotations of the Nyquist plot of G,(s) (mo< << o) about the point (1,0). This is the net angle traced out by the line segment from (1,0) to the Nyquist plot as the frequency changes from  to . The sign convention is a positive value for N if the net rotation is in the counter clockwise direction and negative if it is in the clockwise direction. Let PR be the number of poles of l+GL(S) (note that this is the same as the number of poles of GL(S)) in the RHP. Then ZR =PRN (18) where ZR is the number of zeros of 1+G,(s) in the RHP. Hence, ZR is the number of roots of the characteristic equa tion l+GL(s)=0 that lie in the RHP. Clearly, ZR must be zero for a stable system. It is not our objective here to give a proof of the above statement (see, for instance, Ref. 9), but we illustrate its proper use through a simple example. In our opinion, the following points are crucial:  While the portion of the Nyquist plot from  to 0 is Chemical Engineering Education (a) 0.4 Im Figure 2. 0.2 Nyquist plots for r a) 0.0 (1,0) Re GLI(S)= 2( 1) 0.2 2(s1) and 0.41 1.5 1.0 0.5 0.0 0.5 b) GL2(S) = (s 1) The dotted () portion is for (b) 2.0 < (0 < 0 Im while the solid () 1.0 ,4 ., portion is for S 0< 0)< o <. 0 \ (1,0) Re The direction of o1.0 the arrow is in the direction of 2.0 increasing o. 30 20 1.0 0.0 1.0 increasing 0. simply the mirror image (about the real axis) of the portion from 0 to , not using the full plot can lead to erroneous conclusions. The precise meaning of the commonly used notion of "encirclement" about the (1,0) point must be under stood. It is not uncommon1691 to have cases where the (1,0) point is entirely within Nyquist plot and hence appears "encircled," but the net encirclement is, in fact, zero. Further, the direction of encirclement is crucial. Encirclement in itself does not necessarily mean that the closedloop system is unstable. 1 The number of RHP poles of GL(S) must be known. We demonstrate the above points by choosing a simple systemthe same one we chose in the previous section Go(s)= 2 (19) in a feedback loop with a proportional controller of gain Kc=1/4 and K2=l It is easy to see that the first control system is unstable, while the second is stable, by considering the characteristic equations I+GL](s)=O and I+GL2(s)=0, respec tively. But our objective here is in the application of the Nyquist criterion. Figure 2a shows the Nyquist plot of 2Kci 1 GL1(S)= s1 2(s1) (20) The figure clearly shows that N=0 as the net angle traced out Spring 2001 by the full Nyquist plot (with reference to the (1,0) point) is zero. Since PR=I, we get ZR =PRN=I0=I (21) Thus the closedloop system is unstable with one root of the characteristic equation in the RHP. Note here that even though the Nyquist plot does not encircle the (1,0) point, the closedloop system is unstable. Figure 2b shows the Nyquist plot for GL2(S) 2 Kc s2 (22) Here the Nyquist plot encircles (1,0) once. Note that the net angle traced is 27r, but this is in the counterclockwise direc tion, implying that N=l. Again, since PR=1, we obtain ZR = PR N =0 (23) Thus the closedloop system is stable, even though the Nyquist plot encircles the (1,0) point. Note further that if we restrict ourselves to the 0 to segment, we will not see any encircle ment. Thus, we have highlighted the aspects we set out to illus tratethe importance of considering the entire frequency range ( to ), the importance of the direction of encircle ment, and the necessity of knowing the number of unstable poles of GL(S). CONCLUSIONS We have clarified the concept of frequency response for linear timeinvariant systems, demonstrating its validity for unstable systems as well. We have also highlighted some pitfalls in the use of the Nyquist criterion and pointed out how to avoid them. REFERENCES 1. Coughanowr, D.R., Process Systems Analysis and Control, McGrawHill Book Company, New York, NY (1991) 2. Luyben, W.L., Process Modeling, Simulation, and Control for Chemical Engineers, McGrawHill Book Company, New York, NY (1990) 3. Marlin, T.E., Process Control: Designing Processes and Con trol Systems for Dynamic Performance, McGrawHill Book Company, New York, NY (1995) 4. Ogunnaike, B.A., and W.H. Ray, Process Dynamics, Model ling, and Control, Oxford University Press, New York, NY (1994) 5. Seborg, D.E., T.F. Edgar, and D.A. Mellichamp, Process Dynamics and Control, John Wiley & Sons Inc., New York, NY (1989) 6. Stephanopoulos, G., Chemical Process Control, Prentice Hall, Englewood Cliffs, NJ (1984) 7. Brockett, R.W., Finite Dimensional Linear Systems, John Wiley & Sons, Inc., New York, NY (1970) 8. Wolovich, W.A., Automatic Control Systems: Basic Analysis and Design, Harcourt Brace (1994) 9. D'Azzo, J.J., and C.H. Houpis, Feedback Control System Analysis and Synthesis, McGraw Hill Book Company, New York, NY (1966) 3 Bj, curriculum THE INTERFACE BETWEEN ChE AND MATHEMATICS What Do Students Really Need? MICHAEL D. GRAHAM University of WisconsinMadison Madison, WI 537061691 SUSAN L. GANTER Clemson University Clemson, South Carolina he Mathematical Association of America (MAA), through its Committee on the Undergraduate Pro gram in Mathematics (CUPM), is conducting a Cur riculum Foundations Project, a major analysis of the under graduate mathematics curriculum. The goal of the project is to develop a curriculum document that will assist college mathematics departments as they plan their programs for the next decade. Historically, CUPM curriculum recommenda tions have had a significant influence on the design of undergraduate mathematics programs. These important and influential guidelines were last revised in 1981. There fore, the CUPM curriculum guidelines need to be recon sidered; such a review and the resulting recommenda tions are likely to have widespread impact on the teach ing of undergraduate mathematics. Given the impact of mathematics instruction on engineer ing, the sciences, and the quantitative social sciences (espe cially instruction during the first two years), significant in put from these partner disciplines is needed to inform the MAA curriculum document. The CUPM subcommittee on Calculus Reform and the First Two Years (CRAFTY) gathered much of this necessary information between Fall 1999 and Spring 2001 through a series of invita tional disciplinary workshops funded and hosted by a wide variety of institutions (see Table 1). Each workshop is focused on a particular partner disci pline or on a group of related disciplines, the objective being a clear, concise statement of what students in that area need to learn in their first two years of college mathematics. The workshops are not intended to be dialogues between math ematics and the partner disciplines, but rather a dialogue among representatives of the discipline under consideration, with mathematicians there only to listen to the discussions and to provide clarification on questions about the math ematics curriculum. For this reason, almost all of the indi viduals invited to participate in each workshop are from the partner disciplines. The major product of each workshop is a report or group of reports summarizing the recommendations and conclu sions of the workshop. These are written by the representa tives from the partner disciplines, with the mathematics community as the primary audience, and they address a series of questions formulated by CRAFTY (see Table 2). Uniformity of style is achieved across the reports by using the same basic questions for each workshop. Having a com mon list of questions also aids in comparing the reports of different workshops. The questions are simply designed to guide the workshop discussions, however, and therefore are Mike Graham received his BS from the Univer sity of Dayton in 1986 and his PhD from Cornell University in 1992, both in chemical engineer ing, and did postdoctoral work at the University of Houston and Princeton University. His re search interests encompass instabilities and nonlinear dynamics in flows of complex fluids, molecular and multiscale simulation of polymeric liquids, and interfacial and multiphase flows. Susan L. Ganter is Associate Professor of Math S ematical Sciences at Clemson University. She Shas directed several local and national evalua tion studies, including a recent residency at the National Science Foundation in which she inves tigated the national impact of the calculus reform S initiative and helped to develop the evaluation plan for the Institutionwide Reform Program in the Division of Undergraduate Education. Copyright ChE Division of ASEE 2001 Chemical Engineering Education intentionally vague. In addition, workshop participants are asked to focus primarily on the first question category, "Un derstanding and Contents," with the other questions being of secondary importance. The reports from each workshop are then widely circu lated within the specific disciplines, as well as in the math ematics community, in order to solicit a broad range of comments. At the completion of this process in the spring of 2001, the reports will be published and used in the formula tion of the MAA curriculum document. A curriculum con ference that includes invitees from all disciplines will be convened in Fall 2001 to synthesize the workshop findings and begin writing the MAA curriculum document, sched uled to be published in 2002. In addition to providing input into the larger CUPM re view, the reports serve as valuable resources for initiating discussions at individual institutions between mathematics departments and partner disciplines. Some mathematics de partments have already begun using the reports to stimulate TABLE 1 MAA Curriculum Foundations Workshops Physics and Computer Science Bowdoin College Maine Oct. 2831, 1999 William Barker: barker@bowdoin.edu Interdisciplinary (Math, Physics, Engineering) USMA West Point Nov. 47, 1999 Don Small: ad5712@usma.edu Engineering Clemson University South Carolina May 47, 2000 Susan Ganter: sganter@clemson.edu HealthRelated Life Sciences Virginia Commonwealth University May 1820. 2000 William Haver: whaver@atlas.vcu.edu Technical Mathematics (at two sites) Los Angeles Pierce College California Oct. 58, 2000 Bruce Yoshiwara: byoshiwara@hotmail.com J. Sargeant Reynolds Community Col. Virginia Oct. 1215, 2000 Susan Wood: swood@jsr.cc.va.us Mary Ann Hovis: hovisma@ltc.tec.oh.us Statistics Grinnell College Oct. 1215, 2000 Thomas Moore: mooret@math.grin.edu Business. Finance and Economics University of Arizona Arizona Oct. 2829, 2000 Deborah Hughes Hallett: dhh@math.arizona.edu William McCallum: wmc@math.arizona.edu Mathematics Education Michigan State University Michigan Nov. 13, 2000 Sharon Senk: senk@pilot.msu.edu Biology and Chemistry Macalester College Nov. 25, 2000 David Bressoud: bressoud@macalester.edu Mathematics Preparation for the Major Mathematical Sciences Research Institute Feb. 911, 2001 William McCallum: wmc@math.arizona.edu Spring 2001 interdepartmental discussions. Such discussions, as well as those at the CRAFTY workshops, generate good will be tween mathematicians and colleagues in partner disciplines. In general, colleagues from partner disciplines value math ematics and welcome the opportunity to state their views about mathematics education, provided their opinions are taken seriously. Promoting and supporting informed discus sions with the partner disciplines may ultimately be the most important outcome of the MAA Curriculum Foundations Project. THE CRAFTY ENGINEERING WORKSHOP AT CLEMSON UNIVERSITY One of the CRAFTY workshops was sponsored and hosted by Clemson University on May 47, 2000. It focused on the needs of engineering from the first two years of college TABLE 2 MAA Curriculum Foundations Workshop Questions Understanding and Content What conceptual mathematical principles must students master in the first two years? What mathematical problemsolving skills must students master in the first two years? What broad mathematical topics must students master in the first two years? What priorities exist between these topics? What is the desired balance between theoretical understanding and computational skill? How is this balance achieved? What are the mathematical needs of different student populations and how can they be fulfilled? Technology How does technology affect what mathematics should be learned in the first two years? What mathematical technology skills should students master in the first two years? What different mathematical technology skills are required of different student populations? Instructional Interconnections What impact does mathematics education reform have on instruction in your discipline? How should education reform in your discipline affect mathemat ics instruction? How can dialogue on educational issues between your discipline and mathematics best be maintained? Instructional Techniques What are the effects of different instructional methods in mathematics on students in your discipline? What instructional methods best develop the mathematical comprehension needed for your discipline? What guidance does educational research provide concerning mathematical training in your discipline? mathematics instruction. The workshop had thirtyeight in vited participants, with roughly equal representation from each of four areas in engineering (chemical, civil, electrical, mechanical) and mathematics. The workshop resulted in four documents, one for each of the four engineering areas, addressing the MAA questions specified at the outset of the workshop. This paper focuses on the recommendations of the chemi cal engineering group. It is not intended to be a definitive document, but rather a working paper that generates discus sion among chemical engineers in order to provide addi tional feedback for the mathematics community. Therefore, the authors welcome comments and additional ideas. REPORT OF THE CHEMICAL ENGINEERING GROUP The Chemical Engineering group members are listed in Table 3. What Chemical Engineers Do Since this report was originally written for mathemati cians, an appropriate introduction is to discuss what chemi cal engineers do, why mathematics is needed, and how it is used. A reasonably broad definition is that chemical engi neers design materials and the processes by which mate rials are made. Traditionally, chemical engineers have been associated with the petroleum and largescale chemical industries, but (especially in recent years) chemical engineers have also been involved in pharmaceuticals, foods, polymers and ma terials, microelectronics, and biotechnology. The core sub jects that underlie and unify this broad field are thermody namics, chemical reaction processes, transport processes (i.e., the spatial and temporal distribution of mass, momentum, and energy) and process dynamics, design, and control. On top of this fundamental framework, a central emphasis of chemical engineering education is model building and analysis. A good chemical en gineer brings together the fun damentals to build and refine a T TA mathematical model of a pro Chemical Engine cess that will help him or her understand and optimize its per I Jenna P. Carpenter Inte formance. To be good at model Engineering, Civil Engin building and analysis, students Technological University must have at hand the math I Michael B. Cutlip Profes ematical background to under Director of the Honors Pr stand and work with the core E Michael D. Graham Ass scientific areas, as well as to Engineering University find solutions to the final model leader/recorder) that they build. In this context, E Anton J. Pintar Associal Michigan Technological the "solution" to a mathemati E Jan A. Puszynski Profes, cal problem is often in the un Engineering South Dak derstanding of the behavior of the process described by the mathematics, rather than the specific closed form (or numerical) result. Here is an example: A starting point for understanding any process is writing down the conservation laws that the sys tem or process satisfies...for conserved quantities, accumu lation = input output. Depending on the level of detail of the model, this equation might be, for example, a large set of linear algebraic equations that determine the relationships between fluxes of chemical species throughout the process (a species balance), or it might be a set of parabolic partial differential equations governing the temperature and compo sition of the fluid in a chemical reactor. In the thermodynamics of multiphase systems, energy is conserved but takes on a variety of forms; a good knowledge of multivariable differen tial calculus is essential here to keep track of everything. Mathematics for Chemical Engineering The purpose of the original report was not to prescribe the mathematics curriculumchemical engineers do not want mathematics instruction to provide only what students can "get by" with knowing. Nor is it appropriate to come down on either side of the "traditional" vs. "reform" debateit is likely that both sides are right, to an extent. Instead, some general thoughts on subject matter and emphasis are pre sented here. Precalculus Foundations By foundations, we mean Basic knowledge offamilies offunctions (polynomical, exponential,...) in terms of data, graphs, words and equations, basic trigonometric identities and geometry, properties of logarithms, etc. Equations, inequalities Basic logic and algorithms Small linear systems of equations Coordinate systems Basic arithmetic and manipulation skills Mastery of the above ar eas is crucial. Probably the ,E 3 most important thing the g Group Members mathematics community can do here is to actively investi .cademic Director, Chemical gate the pedagogy of K12 g and Geosciences Louisiana educationto help sort out f Chemical Engineering and which "reforms" are produc n University of Connecticut tive from those that are e Professor of Chemical merely "fads" and to encour isconsinMadison (discussion age schools not to neglect the education of the more math fessor of Chemical Engineering ematically inclined students sity by focusing the curriculum Chemistry and Chemical Chemistry and Chemical too narrowly on the average hool of Mines and Technology too narrow on the average performer. Another impor Chemical Engineering Education BBL erin rim A eering ssor o ograr ociate ofW e Pro Unive sor of ota Sc tant role here is to provide programs that help K12 math ematics teachers understand some applications of the math ematics that they teach (engineering faculty should do much more here). Linear Mathematics Chemical engineering students would benefit from earlier exposure to the basics of linear systems in RN, particularly The geometry of linear spaces partner Vector algebra (especially in 3D) Ax = b (existence and uniqueness, Gausian elimination, geometric interpre tation, over and underdetermined systems, and least squares problems) Ax = Xx (characteristic polynomial and diagonalization, Jordan form, range and nullspace of A, geometry) At the University of WisconsinMadison, for example, there is a course on "linear mathematics" that introduces these notions and applies them to systems of ordinary differential equations (see next section). Many chemical engineering students take this in lieu of the traditional differential equa tions class. Calculus and Differential Equations The importance of visualization in calculus cannot be overemphasized, especially as a guide to differential and vector calculus in multiple dimensions, plotting (e.g., what function is linear on a loglog plot?), working in cylindrical and spherical coordinate systems, and converting between coordinate systems. Somewhat less time could be spent on techniques for evaluating complicated integrals, with the time spent instead on, for example, visualizing the applica tion of the chain rule in multiple dimensions. Understanding of truncated Taylor series for local approximation of func tions is very important and should be seen early and often. In differential equations, a thorough knowledge of linear con stant coefficient systems (initial value problems and bound ary value problems; see previous section) is preferable to emphasis on existence theory and series solutions for non constant coefficient problems. Some qualitative theory for nonlinear systems is also desirable. Probability and Statistics Alumni surveys typically show that this is the most com mon application of mathematics for the practicing chemical engineer with a bachelor's degree, in addition to the exten sive use of spreadsheets. Key issues here include parameter estimation, experimental design, sampling, and the origins and properties of various distribution functions. Spring 2001 Students interested in graduate school should be encour aged by their mathematics professors, as well as their engi neering advisors, to take additional mathematics courses. A final general comment: students should have some idea of the power of a theorem, but for engineers, concepts are more ... [the] discussions ... generate good will between mathematicians and colleagues in irtner disciplines. In general, colleagues from r disciplines value mathematics and welcome the opportunity to state their views about mathematics education, provided their opinions are taken seriously. important than proofs. In other words, it is appropriate for chemical engineering students to learn mathematical facts without always seeing the associated proofs. Technique and Technology A fair amount of the discussion at the MAA engineering workshop, within the chemical engineering group and oth ers, centered around the use of technology in the mathemat ics courses for engineers. In the discussions, "technology" meant a number of different things, from numerical methods to graphing calculators to symbolic manipulation packages. We'd like to emphasize here some points to be kept in mind when thinking of the introduction of these tools into math ematics courses. We do this in the form of responses to two questions, representing both sides of the issue (admittedly, these questions are straw men): "My laptop can do that. Why should I learn to do it by hand?" Sense ofform of mathematical expressions, under standing of what manipulations are available, facility with these manipulations Fluency in the language of mathematical concepts Appreciation and recognition of mathematical rigor Discipline, maturity, confidence of mastery Closed form results are best, if available Recognition of limitations of closed form results, where things get difficult Knowledge of what computers do "Use of computers dumbs down the mathematics course why use them?" Solution of realistic (complex) problems, many of which involve numerical solutions. In upperlevel courses, extensive use is made of programs such as MATLAB, Octave (available at Efficient exploration of solution and design space Visualization, especially in multidimensional and vector calculus Relieffrom tedium Confidence in results derived by hand Ultimately, the technology should take a back seat in mathematics courses until it becomes necessary for solving interesting problems. For example, in a linear algebra course, students should be able to do LU decomposition of a 3x3 system by hand before they are shown that a computer algebra system can complete the process with one com mand. At the same time, it is useful to point out the relation ship between numerical techniques and exact ones (e.g., a Riemann sum can be evaluated numerically to approximate an integral). Students should have a solid understanding regarding limitations of numerical methods and their accu racy. They should clearly see the power of analytical solu tions when such solutions can be found. A Suggestion for Coupling Mathematics and Engineering Education One set of issues that arose repeatedly in the MAA engi neering workshop discussions was the concern that students do not see connections between mathematical tools and con cepts and the wide utility of these in engineering. A related concern was the time lag between exposure to mathematics and its application to the solution of real engineering prob lems. The notion of "justintime" learning was discussed, and the suggestion was made that mathematics courses be more application or exampledriven and be more evenly spread through the curriculum, rather than "front loaded" into the first two years. The chemical engineering group shared these concerns, but also thought that 1) Part of the beauty and power of mathematics is that it is exampleindependentcalculus applies to econom ics just as it does to mechanics 2) The time spent developing the background for engi neering applications is time not spent on mathematical principles and tools 3) A straightforward "justintime" approach will not satisfy all engineering majors (e.g., electrical engi neers do not need Laplace transforms at the same time as chemical engineers). An alternative structure can be considered for addressing these concerns, which are essentially about how to connect mathematics and engineering in the students' minds. Spe cifically, the college mathematics curriculum could include discipline specific supplements, especially in the calculus sequence. These could be workbooks or web pages contain ing, for example, Engineering background material, e.g., some basic thermodynamics, and how specific mathematical principles and/or tools (such as total differentials and partial derivatives in several dimensions) are used Exercises or projects integrating mathematics and engineering Additional disciplinespecific emphases, e.g., trigono metric identities and manipulations for electrical engineering students. These could be used independently by the students, or used in a onecredit course running in parallel with the calculus courses, or simply be resources for mathematics instructors wishing to gain perspective on engineering appli cations or bring engineering applications into the mathemat ics classroom. This is perhaps overambitious, but certainly worth considering. It was suggested that, within chemical engineering, CACHE (Computer Aids for Chemical Engi neering this possibility in conjunction with MAA. CONCLUDING REMARKS It is clear that the application of mathematical concepts and the generation of mathematical solutions to engineering problems are essential to the educational programs of all undergraduate engineering students. Enhanced cooperation between mathematics faculty and engineering faculty can lead to a better experience for our students. Without excep tion, the participants felt that the workshop was a very pro ductive way to promote dialogue between the mathematics and engineering education communities and encouraged the organization of more workshops of this type. Another venue that mathematicians can explore is the American Society for Engineering Education ematics division. On the other hand, it may be productive for engineering educators to attend MAA meetings. Perhaps most importantly, mechanisms need to be imple mented to promote interaction between engineering and math ematics faculty within individual universitiesgood rela tionships at this level will enable mathematics faculty to understand what material the engineering faculty would like to see reinforced and emphasized, as well as enabling engi neering faculty to gain a better understanding of the issues surrounding mathematical preparation of entering freshman engineering majors. ACKNOWLEDGMENTS We are grateful to Professors J.B. Rawlings and W.H. Ray (University of WisconsinMadison) and J.F. Brady (Califor nia Institute of Technology), and to Sangtae Kim (Vice President and Information Officer, Eli Lilly) for their critical reading and insightful comments on an earlier version of this paper. This document reflects the joint efforts of the entire chemical engineering working group. 1 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 American 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. ABSTRACT: KEY WORDS Include an abstract of less than seventyfive words and a list (5 or less) of keywords 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. Send your manuscript to Chemical Engineering Education, c/o Chemical Engineering Department University of Florida, Gainesville, FL 326116005 CALL FOR PAPERS FALL 2001 GRADUATE EDUCATION ISSUE OF CHEMICAL ENGINEERING EDUCATION Deadline is June 1, 2001 
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