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Computers in Chemical Engineering Education, by P.B. Lederman, B. Carnahan & G.B. Williams ( PDF )
The Integrated Use of the Digital Computer in Chemical Engineering Education, by Paul T. Shannon ( PDF ) The Use of Analog Computers in Teaching Process Control, by James E. Stice and Bernet S. Swanson ( PDF ) 
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CHEMICAL ENGINEERING EDUCATION CHEMICAL ENOIIIEERING DIVISION T=E AMfiCAN lOCIT FOR ZNGCUNMNIG EDUCATION  MM4,\/q6 CHEMICAL ENGINEERING EDUCATION March 1963 Chemical Engineering Division American Society for Engineering Education CONTENTS Computers in Chemical Engineering Education by P.B. Lederman, B. Carnahan & G.B. Williams    1 The Integrated Use of the Digital Computer in Chemical Engineering Education, by Paul T. Shannon  11 The Use of Analog Computers in Teaching Process Control, by James E. Stice and Bernet S. Swanson      23 Chemical Engineering Division American Society for Engineering Education Officers 196263 s (Colorado) Chairm Martin (Michigan) Vice C t (Oklahoma State) Secret aan chairmann taryTreasurer CHEMICAL ENGINEERING EDUCATION , Journal of the Chemical Engineering Division, American Society for Engineering Education. Published Quarterly in March, June, September and December, by Albert H. Cooper, Editor. Publication Office : University of Connecticut P.O. Box 445, Storrs, Connecticut Subscription Price, $2.00 per year. Max Peter Joseph J. J. B. Wesa COMPUTERS IN CHEMICAL ENGINEERING EDUCATION P. B. Lederman (1), B. Carnahan, & G. B. Williams Department of Chemical and Metallurgical Engineering University of Michigan The advent of computers has enabled the engineer to broaden his horizons with respect to the types of problems he may study and solve in a given amount of time. As an educational tool, the computer also proves very useful in that it takes over the routine calculations once an appropriate algorithm or proce dure has been established for the problem at hand. Students can investigate problems using numerical methods which before were not presented to them until they were able to solve them by compact ana lytical techniques. These methods are usually not presented in an undergrad uate curriculum. One must, however, choose problems carefully so that the students avoid the numerous pitfalls present when numerical methods of solu tion are used. Computers and Engineering Science Considering the significant impact which the high speed electronic com puter will have on our future technological development, several questions arise concerning the role of computers in engineering education. There seems little doubt that a good fraction of today's engineering graduates (engineers who may well be working as engineers in the year 2000) will have occasion to use computers in their technical work. Considering his probable imminent in volvement with computers as part of his engineering work, the engineer must know a great deal more about computers than he can learn from the "giant brain" articles so prominent in the Sunday supplements. The question which comes to mind first is, Where should he learn about them? On the job or in the engi neering school? Those who feel that onthejob training is adequate, usually claim that computer programming and computerrelated work involves primarily techniques rather than engineering principle. Those who feel that the engineering school is a proper place for such training agree*that there is a significant amount of technique (technique which will incidentally be useful in the student's future engineering work) but that the primary justification for such training, parti cularly at the undergraduate level, is based on the computer as an educational tool useful in the training of problem solvers. Viewed as an educational tool the computer can be considered a language for communicating as well as a machine for solving problems. A better understanding of principles can be at tained because of the rigor required when communicating with the computer. This understanding is also reinforced because the student has a broader exper ience with solved problems. Some features of a computer experience which seem to be related to the educational aspect of problem solving are: a. Precise Definition: The computer is a rather rigid task master which requires precision in the statement of the problem and its method of solution. Preparation of procedures for computer solution introduces the student to a precise formal language (usually a mixture of English and algebraic notation). Because of the nature of such languages, the students communication skill should be enhanced, he should tend to be more accurate, and he should achieve added understanding of mathematical notation and manipulation. b. Logical Organization: Complex engineering problems require both an analytical ability (to subdivide the overall problem into simpler ones which can be handled) and an ability to synthesize (bring together solutions of in dividual parts as the solution of the whole). Preparing algorithms (problem solving procedures, flow diagrams) for a computer requires just such analysis and synthesis abilities. c. Ilnimize Ambiguity: Because a computer solution requires the pre paration of an orderly and detailed stepbystep procedure, the approach to the solution must be an unambiguous one (formal languages used by computers allow no ambiguity). No gaps in the logic are permitted. (1) Present address: Esso Research Laboratories, Baton Rouge, Louisiana. CHEMICAL ENGINEERING EDUCATION March 1963 d. Recognition of Assumptions: During preparation of organized detailed procedures, assumptions which may be overlooked in a hand computation are fre quently brought to the forefront. Of course, a bad assumption in a computer program has just as deleterious an effect as in a hand solution; however, be cause of the great computational speed, some assumptions necessary to permit hand computation may be removed entirely. e. Solution of the General Problem: Because of the nature of the dig ital computer, i.e., its ability to read parameter values as data, it is usu ally possible (with little extra effort) to produce a general program which will solve a whole class of problems rather than a specific problem in a spe cific problem situation. This necessitates an essentially symbolic approach to problem solving and is rather different from the customary solution tech niques involving mostly numbers. Such an approach requires a more abstract analysis which focuses on problem structure, rather than on "slide rule" de tails. f. Problem Complexity: Because of high computational speed, the com puter permits solution of significantly more complex (nd hence, frequently more realistic) problems than can be "hand" solved. The drudgery of tedious repetitive calculations is removed. Unfortunately, it is usually wise (essen tial) to work at least one example problem in detail by hand for checkout pur poses. g. Numerical Solutions: The high speed computer solution permits nu merical approximation of problems which are intractable analytically. h. Logical NonNumeric Problems: Since the digital computer is in fact a symbol manipulator rather than a mere number manipulator, it can solve a large class of logical, essentially nonnumeric problems. Computers and Engineers in Industry Computers, both digital and analog, have wide acceptance in production, design and research. This trend, although still in its infancy, is making rapid strides. For example, the high degree of sophistication in some appli cations is illustrated in a recent announcement that complete engineering draw ings fro roads are being turned out by computers. A recent survey for the Amer ican Petroleum Institute indicated that 86 of 127 responding refineries used off line computers, and several larger refineries have several computers working full time. Today a large percentage 9f the "green light time" can be attributed to accounting and scheduling type functions in those computers associated with pro duption units. More and more time is being used, however, by engineering groups to do repetitive computations and optimization studies. Several on line control computers are operating with some success. In a number of pro ceases, where the reaction scheme is complex, for example, copolymerization, there appears to be great incentive to use either open or closed loop compu ter control. In research organizations computers are widely used in a number of areas. Although Esso Research Laboratories may not be typical because we are fortunate to have access to a great variety of computers, it is not atypical with respect to computer utilization. Therefore, we would like to take the liberty of using this organization as a basis for discussing the needs of the engineer visavis computers in industry. A very brief look at the organization with particular emphasis on com puters, as shown in Pigurel, will help to orient the discussion. The Labora tory is one of the major development groups affiliated with Easo Research & Engineering Co. and does bench scale exploratory work as well as operate small and large pilot plants. To fulfill its mission it has several research groups, an engineering group and an applied mathematics group. Three digital computers are available, an IBM 1620 in the applied math group, an IBM 7074 in the Baton Rouge Refinery, and an IBM 7090 in Florham Park accessible by transceiver. The latter two installations are closed shop and the inhouse facility is open shop. FORTRAN and symbolic assembly programs are available for all machines. Almost all of the professional employees are involved with computers to some degree. Computers are used in two primary areas in our technical comput ing, data workup and engineering studies. For the former some of the pilot plants are tied to a data gathering system. The data tape is used, along with data picked up from a daily analytical results tape, as input to any one of several unit data workup programs. Much of the logic for these operations has been handled by experienced nonengineer programmers. The engineers must, however, supply algorithms for the unit workups. The programmers in the ap plied mathematics group are available to program the algorithms. It is usually more efficient, however, for the engineers to write and debug their own pro grams especially when, as is usually the case, program requirements change fre quently. March 1963 CHEMICAL ENGINEERING EDUCATION 3 The engineering studies include process optimization, reactor stability, control, reaction mechanism and similar studies which require the use of chem icel engineering and related sciences together with a knowledge of mathematics and computer sense to bring them to a successful conclusion. This type of problem hbs increased in importance and will continue to take a greater share of the engineering talent and computer time in the future. The demands on the engineer using computers in industry are many even though specialized help is usually close at hand. To maximize the information obtained froi extensive pilot plant operations he must decide when computer data reduction with or without automatic data gathering is warranted, keeping in mind programrnnng time required and computer cost. It is helpful if he can write and test his own programs because this cuts down lead time, often one of the greatest costs of research, and allows him to make any changes with the least delay. This class of problems does not usually require extensive application of advanced mathematical techniques. It does demand a degree of rigor which we as chemical engineers were not able to exhibit before the computer era. Often the algorithms for this class of problems are simplified by use of simple ma trix manipulation. Engineering studies are becoming much more sophisticated and more encom passing in their scope. Engineers today should have a better understanding of the advanced methemntical techniques used to solve partial differential equa tions. In this area the computer is a great help, and at the same time its own worst enemy. "lany engineers are not aware of the pitfalls which round off er rors and nonconvergence present. In addition to learning sound problem analy sis and efficient algorithm construction, it is important that the engineer be made aware of the pitfalls involved in numerical methods and approximations so often used in digital computation. A third area where the chemical engineer and the computer have found com mon cause is in scheduling and economic optimization. This, of course, re quires a knowledge of linear (or, in general, mathematical) programming. Today there is a need to develop a logic which can be used for ultimate design opti mization by welding together and exercising supervisory control over independ ent routines representing a series of interdependent moduli or operations. Here again there is a need for a sound foundation in logic. The use of computers by engineers in an industrial organization would not be complete without discussing communication between man and the computer. This has been very much simplified in the past few years at Michigan because of an excellent executive routine and a very versatile ilgol language, MAD, with superb diagnostics. Due to the multiplicity of demands on most large in dustrial computers  they do payrolls, accounting and complex engineering cal culations  and the limitations of the smaller computers such as the IBM 1620, communication is usually not quite as simple. This means that precompilation debugging should be more thorough. More important, it is most helpful if the engineer has some knowledge of computer operation or logic so that he can eas ily adapt to different computers, programming systems and methods of searching for errors. The use of computers in engineering calculations and their introduction into the engineering sciences curricula is of great benefit to the young en gineer. It forces him to be more analytical and rigorous in his approach to problems. It is important that along with the use of computers, numerical analysis, logic and some basic concepts of computer operation be introduced so that the engineer can make wise and efficient use of this powerful tool in an industrial atmosphere. FIGURE 1 COMPUTERS IN AN INDUSTRIAL RESEARCH ORGANIZATION Development Section Engineering Secto Praces D.evel pment* Design  Exploratory Work 1 ,Instrumentation* .... ata Gat hiering Systems Analysis* Ap.plied SoOC Ocap Programing Computer Services Special Studies Statistical Analysis* I_____~_____________IBM se1620 Analog IBM 7074 Refinery IBM 7090 Transceiver atUsers Data Route ..... Program Route & Consul.aton Education With Computers At Michigan there has been some contact with computers for the past 10 years. At first this was rather limited but since 1956 when an IBM 650 became available on an openshop basis, the use of computers in the chemical engineer ing science curricula has been ever increasing. At first only limited use was made of the computer in graduate courses because access was rather difficult. With the arrival of a large computer, an IBM 704, and problem oriented languages such as FORTRAN and MAD, the computer became relatively accessible to under graduates. A question which arose is where and how the student should be introduced to the computer. If he is to gain a real computer proficiency, it appears that an introduction to computer organization and computer language should come ear ly enough in his training to allow opportunity for extensive use of the machine in solving some engineering problems. Since it seems impractical (and probably unwise) to remove engineering course material to allow insertion of computer work into engineering courses, it would appear that the student should have an independent introductory course which gives him thorough training in the lan guage and a general understanding of computing procedures. If he is not to be lost in the hopeless mire of detail there seems little doubt that the selected computer language should be of the problemoriented rather than the machine oriented type. If engineering classroom time is not to be wasted, then he must be trained well enough in the first course to eliminate the need for later retraining in the engineering classroom. The solution to this problem at The University of Michigan has been the introduction of a required onehour course at the sophomore level which trains the student in the use of a problemoriented language (MAD) and introduces him to some of the elementary numerical techniques. At the present time at least one problem whose solution is best obtained with the aid of a high speed computer is presented in most every course in chem ical engineering science. As can be seen in Figure 2 this means that students are exposed to computer methods from the beginning of their sophomore year. By applying the techniques learned in the course "Elementary Computer Techniques" immediately we find that students get a better appreciation of computer tech niques. In each succeeding course one or more computer oriented problems are presented to the students. These problems, chosen by the individual instructor, are coordinated so that they illustrate many facets of computer programming and use. Problems which arise in the assignment of computer problems as part of the engineering coursework homework load include timing. While there seems lit tle doubt that a projecttype assignment involving a time period of perhaps two weeks or more causes no significant difficulty, homework assignments done on a daytoday basis do present some problems. Because of the nature of computer languages, i.e., the necessity for very precise grammar and punctuation, It is unusual for an undergraduate student to solve completely correctly an engineer ing problem on the first approach to the computer. The average may be three or four tries before success. The turnaround time, i.e., the elapsed time between submission of a program to the computer and its return for checking and possible resubmission in case of error, must consequently be fairly short if problems are to be completed between class meetings. If computer integration into engineering classrooms is to be successful, the student's overall computer ability is certainly a major factor. The in structor's ability is probably even more important, particularly for undergrad uate training. The selection of appropriate problems and the illustration (by example) of good computer habits (pointing out inadequacies or places where the computer should probably not be used, as well as where it should be) is essen tial. In an attempt to help develop a better appreciation of the computer and computer techniques, a set of problems for use in an undergraduate chemical engineering curriculum is described in the Appendix. It is expected that the student will have had prior to or concurrently with the first of these problems a basic course in programming, as tpo much time taken from course content would be required to learn basic programming techniques. Conclusion It is not wise to attempt to justify the use of a computer as a time saving device when one deals with a single problem operation, common to intro ductory educational endeavors. It is much better to look at the computer and program as a method of introcuding a tool which will enable the student, after some experience, to solve complex problems and will force the student into hab its of careful, detailed problem analysis and logical solution methods. If ex posure to computers and computer programming does nothing else it will be well worth the time and effort required if our students think more logically and precisely. CHEMICAL ENGINEERING EDUCATION March 1963 C C astIR flQSS. ZLKCTIVZ l' LMTUY C (4) OCIAL SC. (1II LAPOCAOO. SOCIAl CrIES, CI) MoS. SCIEanna ____ 6 CHEMICAL ENGINEERING EDUCATION March 1963 It is true that this is a relatively new area in our curricula, but a v e7 essential one. At this stage we have and should raise more questions than we can answer but by proper choice of problems the advantages of the computer will be well demonstrated. The student will gain new insight into many more problems and will become quite at home with the computer, a valuable tool for the engineer. Acknowledgement The authors appreciate the support of their colleagues in the Department of Chemical and Metallurgical Engineering at the University of Michigan and at Esso Research L'boratories for the many helpful discussions about their exper iences. We are especially grateful to Professor D.L. Katz for his many helpful suggestions and Mr. E.A. McCracken for reviewing the original manuscript. APPENDIX A SERIES OF GRADED CHEMICAL ENGINEERING COMPUTER PROBLEMS This series of computer problems is typical of those used during the past four years in the chemical engineering curricula at the University of Michigan. No attempt has been made to be all inclusive as this set, it is hoped, will merely serve as a guide. Complete solutions for many of these problems  mainly written in MAD  may be found in the various reports is sued by the Ford Foundation Project on Computers in Engineering Education (2). PROBLEM FOR A FIRST COURSE IN STOICHIOMETRY A typical first problem after some basic programming experience might be a detailed mass balance as follows: Problem Statement: A countercurrent multiplecontact extraction system is to treat 100 tons per hour of tailings with fresh water as a solvent. The composition of the tailings fed to the extration unit is Component Mass Fraction Water 0.48 Gangue 0.40 Salt 0.12 The strong solution leaving the system is to contain 0.15 mass fraction salt. A 99 per cent recovery of the salt is anticipated. Calculate the number of equilibrium stages required as a function of the solution retained by the gangue. Solution: This problem may be solved by a number of methods, including the method of linear differences. The basic material stagewise balance method of solu tion is discussed in detail by Brown (1) and a computer solution for a similar problem may be found in the First Annual Report of the Project on the Use of Computers in Engineering Education sponsored by the Ford Foundation at the University of Michigan. (2) Basically, the solution requires that an overall balance around the ex traction be made and then stagewise calculations be made until the raffinate from the last stage meets the required concentration specifications. Once the basic program is written, it may be easily enlarged to include either variable solution retention (as a function of the solution composition) or a series of solution retention values. The problem is not difficult to program but does require the use of sub scripts. Students have programmed a similar problem in 15 steps and with rel atively little expenditure of time. It has the added advantage of illustrating the effect of solution carryover. March 1963 CHEMICAL ENGINEERING EDUCATION 7 A SECOND PROBLEM IN STOICHIOMETRY OR A FIRST PROBLEM IN THERMODYNAMICS A second problem in Stoichiometry which could also serve as a first problem in Thermodynamics is the computation of the adiabatic flame tempera ture as a function of the fuel and fuel to air or oxygen ratio. Solution: The solution to this problem requires writing a material balance for the components involved and then making a thermal balance assuming a flame temper ature. If the amount of sensible heat out equals heat of combustion plus the sensible heat in the correct flame temperature has been established. If the heat in and out do not balance, a new flame temperature must be chosen; the NewtonRaphson (3) method for estimating the successive values for the flame temperature will allow for quick convergence on the correct answer. This problem is quite simple to program for a given fuel and fuel to air ratio and should require even less time than the problem discussed above. If it is desired to investigate the effect of fuel to air ratio or type of fuel, a little more thought is required to successfully program the problem. It is still a reasonable problem for people with a minimum of computer experience. A PROBLEM IN THERMODYNAMICS A number of thermodynamic calculations lend themselves readily to solu tion by the computer. The study of nonideality and physical equilibria are probably two of the areas which are often neglected in beginning courses and which with the aid of the computer may be studied quantitatively. A typical request of students might be to require them to determine the degree of non ideality and the per cent vaporization of a ternary mixture of hydrocarbons as a function of pressure and temperature. Solution: The instructor must supply an equation of state which is to be used to compute the properties of the nonideal gases. This equation should be used to obtain densities and fugacities as a function of pressure and temperature. Once this hcs been programmed successfully, the students nay use the equation of state in subroutine form. The information, fugacity and density of the pure components and mixtures, obtained from the equation of state subroutine, may now be used in a larger pro gram which actually calls on the subroutine when required. '.s may be eval uated as a function of the fugacity and estimated composition and these 'nay then bh used in a flashvaporization comiputti on to colcuite the degree of vaporiza tion of a inixture. In aidi tion CF phase densities may be checked ai inst ideal densities to determine coaipressibili ties factor values, 9 measure of nonilpl ity. This program would i be foi rly advanced and it a7y be les rable to 1'ist compute the degree of vaporization based on Raoultts Law, that is, ushn v;'por pressures obtained from a Clapyron reletionship. This pro r"n would be 'ulte simple to write and would serve as a good introduction to tie aenerol prc"'es of physical equilibr'i. PROBLEM In RA.TE PROC eSSE In the area of rate processes, the computer can greatly benefit nd en hance the subject matter discussed in a beginning course. many of the probles involving rates of heat or mass transfer involve partial differential equations which may be reduced to difference equations for numerical solution on the con puter. A good elementary discussion of these methods may be found in "r:umeri cal Methods for Science and Engineering" by Ralph G: Stanton. The first problem in this area which is very suitable for computer solu tion is an unsteadystate heat transfer problem. The time required to quench an odd shaped bar is to be determined. In order to simplify the geometricel concepts, it is probably good to choose a rectangle with irregular insulation or study the converse problem of heating of a rifbt angle bar at one end and determine the time dependence of the temperature at the other end of the angle iron as indicated in Figure 1 where Tf if a function of time. This problem has been programmed by students quite successfully before. A detailed discussion of the method may be found in q paper by Rudd (4). In this problem a grid is established over the piece in question and the method of relaxation is employed to determine the temperature distribution over t grid at any given point in time. CHEMICAL ENGINEERING EDUCATION FIGURE I CROSSSECTION OF RIGHTANGLE BAR T = 80F. h = 2 BTU/hr.ft.2 *F. Insulated Insulated Temp. at Edge T T Bn*_ T = 90F. at 0=0 T ao.t I ? T = 1000*. at 0046 ANOTHER RATE PROCESSES PROBLEM The design of tubular reactors is a very common task undertaken on a computer. In the case usually considered the equations representing the tem perature and volume dependence of the system become somewhat complex for ana lytical solution. It is therefore necessary to use a set of difference equa tions and iterate down the length of the tube. This problem is well suited to computer solution but one word of caution. The choice of increment size is a difficult one. Care must be taken not to introduce roundoff problems when re sults from preceding segments are used as a basis for computing the next seg ment. A typical problem might be: the decomposition of S02CI2 to S02 and C12. The heats of formation and heat capacities for the compounds are s802C2 (g) AHf = 82,040 cal/gm. sole Cp = 13.0O42i.oxlO3Tl4.4xlO62" g02 (g) AHf = 70,920 cal/gm. sole Cp = 8.12+6.825xl93T2.lo3xlo6T2 C12 (g) ANf = 0 Cp = 7.5755+2.4244xlO3To.965xlo6T2 and the rate of decomposition may be expressed as follows: r = A eE/RT here A = 6.427x1015 1/see E = 50610 *K cal/gm. mole Compute the length of .a 1 1/2" I.D. tube required to insure 98,b decomposi tion of 418 pounds per hour of S02012 fed at 2000. and 1.2 atm, heat Is transferred to the tube at the rate of 5000 BIT per square foot per hour. DESIGN PROBLEM IN REACTION KINETICS The use of computers in design courses has been quite successful. After a program of problems in earlier courses, the students often ask to have the computing facility made available to them. The choice of material taught or problems assigned to students is very wide so we include an example for illus trative purposes of what can be done. A typical problem would be to determine the optimum reaction time for a given product if three competing products are formed, that is, mono, di and tri ethanol amine. If one knows the rate constants as a function of temp erature, one can write expressions for the concentration of all the species in the system. This results in this case in a system of five simultaneous linear differential equations. These may be readily solved using the standard Runga Kutta method which is programmed for most large computing facilities and dis cussed in detail in any of a number of texts in numerical analysis (6). The original reaction data for the ethanol amine reactions were deter mined by Ferrero and coworkers (7) and are summarized below with additional data required to solve the problem. The possible reactions are: I March 1963 March 1963 CHEMICAL ENGINEERING EDUCATION 9 0 I + 3E5 1w 22gCE2CHa oCH2 k Cg% 2 ) CH2 kg N(CH22 )3 higher products The velocity constants for the Arrhenius equation EI/RT ki = Aie are: A gm. mole/liter min. E 1. 3.58xlO8 14,500 2. 9.9x109 15,600 3. 2.58x109 15,000 4. 3.93x106 12,650 It is now possible to determine concentrations of each product in the efflu ent of an isothermal reactor as a function of the space velocity and the ini tial concentrations. If sufficient data is available on the heats of reaction and specific heats of the constituents the nonisothermal case may be studied. This problem and similar problems have been very useful in demonstrating the course of reactions. This and similar problems, it should be mentioned, are also very suitable for analog computer analysis. REFERENCES 1. Brown, G.O., et.al., Unit Operations, John Wiley, New York, 1950. 2. Katz, D.L. and Organick, E.I. (ed.), Electronic Computers in Engineering Education, First Annual Report to The Ford Foundation, Ann Arbor, 1960. 3. Stanton, B.G., Numerical Methods for Science and Engineering, PrenticeHall, New York, 1961. Rudd, D.F., "Temperature Distribution in a Conducting Solid," in First Annual Report on Computers, Ford Foundation Project, Ann Arbor, 1960. 5. Burnett, G.M., Mechanism of Polymer Reactions, Intersacence, New York, 1954. 6. Ralston, A. and H.S. Wiff (ed.), Mathematical Methods for Digital Computers. 7. Ferrero, P., F. Berbs and L.F.Flamme, Bul. Soc. Chim. Belg. L6, 349368 (1947). 8. "Use of Computers in Engineering Education," Second Annual Report, Ford Foundation Project, Univ. of Michigan, Dec. 15, 1961. 0 CHEMICAL ENGINEERING EDUCATION March 196i' The following list of problems were prepared by various staff members and vilst ng professors at the University of Michigan under the sponsorship of the Ford Foundation project on "The Use of Computers in Engineering Education" (8). The titles are included to suggest some more areas where computers have been and can be used. 'Complete descriptions and programs are available from the pro ject at the University of Michigan. Title Level(1) Optimization of Reactor Operation Approach to SteadyState of an Othmer Still Temperatures and Heat Flux in a Radiant Thermal Circuit Heat Balance for an Iron Blast Furnace Three Component, Two Phase, CounterCurrent, Liquid Extraction Temperature Distribution in a Three Dimensional Body Solution of a Boundary Value Porblem Using an Initial Value Technique: Temperature Profile in a Circular Transverse Fin Velocity Profiles for Flow in Smooth Pipes Determine Reflux Ratio by McCabeThiele Method Temperature Profile in a Longitudinal Fin Using the Analog Computer Diffualon and Slow Chemical Reaction Number of Theoretical Plates in a MultiComponent Distillation Column Multiple Regression Analysis Solvent Allocation in MultiStage Crosscurrent Extraction Dynamic Heat Exchange Storage of Natural Gas in Aquifers Adiabatic Reactor Predicting the Scrap Requirement for the OxygenSteel Converting Process 2 2 2. 3 3 3 3 3 3 4 4 4 4G 34 G G 4 (1) Year in which normally used. The Integrated Use of the Digital Computer in Chemical Engineering Education by Paul T. Shannon Purdue University Introduction "How do you teach a robot to perform process design and optimization calcu lations involving recycle streams for any arbitrary process sequence for an arbi trary set of equipment?" Our robot has many desirable qualities as well as limi tations. He possesses the ability to do simple arithmetic extremely fast and can remember everything that he is told. He will answer simple questions which have been unambiguously encoded to him in a form that they are either "yes" or "no" and he will do exactly as he is told to do. This last quality is both an asset and a drawback, as any who have done computer programming will testify. Our robot is not yet built to "see" but he may have this ability in the not too distant future. At present, however, he will deal only in numbers. Thus, if we wish to have our robot use any of the visual aids which we as engineers have found so useful in the study of complex engineering problems, we must find a suit able method for numerically encoding our graphical techniques for communication to and use by our robot. We will find that the answer to this problem, of numerical ly encoding graphical aids and their subsequent uses is the key to our problem of robot education in the field of systems analysis. Digital computer programming has evolved as a criterion of excellence of un derstanding. If you are able to tell an idiot how to perform a given calculation, taking into account all the possibilities and ramifications of the problem, then you, as the programmer, truly understand the calculation yourself. I think no one will argue that one of the most effective ways to teach a student a given calcu lational procedure is to ask him to program the problem on a digital computer and assist him in doing so. Digital computer programming is a tremendous amount of work. Even simple problems require a good deal of time and effort and those who have not actually programmed several problems and experienced the frustrations and relations of de bugging have the pat answer, "We'll just solve that set of equations on a compu ter." A digital computer program works or it doesn't work. One receives almost no partial credit. It has been argued that the student should write each of the digital compu ter programs he is to use. Timewise this is just not possible. The engineer in practice or the student in school must of necessity use programs written by others. This,also, is a considerable amount of work but not nearly that involved in writing the program itself. If the digital computer is to be used extensively by the undergraduate stu dent, he must be shown that it is a tool of significant help to him in his course work. To illustrate this point the successful use of the digital computer in the Chemical Engineering Laboratory courses at Purdue will be described. Next we shall consider our question of robot education. A description will be given of the computer executive system currently under development at Purdue aimed at answering the posed question. This executive system allows the arbitrary se quencing of digital computer programs and thus enables the user to write the com puter program for a given problem in essentially the time required in formulating the problem to be solved. We will find that we arrive at some very powerful gener alizations and some fundamental concepts which have bearing on the teaching of chemical engineering. It will be shown that the executive system develops a basic conceptual and calculational frame work which is easily taught to undergraduate students. Use in the Chemical Engineering Laboratory Digital computer programming is presently taught and very effectively used in the Chemical Engineering laboratory course at Purdue. For most students this is their first introduction to programming since there is not a required course in programming and numerical methods for all engineering students in their fresh man or sophomore year. In Chemical Engineering, an elective one credit hour coursein computer programming is offered in the fall semester. This course offers the students additional computer experience and has been taken by about 70 students, both undergraduate and graduate, each fall. 1 11 12 CHEMICAL ENGINEERING EDUCATION March 1963 The first 22 1/2 weeks of the chemical Engineering Laboratory course is spent on an introduction to digital computer programming. Each student is re quired to write and run one or two simple programs. Then the "canned" computer programs (developed by the students and the staff during the last three years) which will be used in conjunction with the laboratory experiments are explained in detail. The laboratory time spent on computer programming is "made up" in that the time formerly allowed during the course for experimental calculations and report writing is correspondingly decreased. In fact, the students now do an additional experiment and perform more runs in a given experiment than before. Sample results from the computer for three of the programs are shown in Appendix A Perhaps of greatest significance have been the very good "side effects" ac companying the integrated use of computers in the laboratory. First, the majority of what the students referred to as the "mickeymouse" and "dog labor" has been eliminated with a corresponding significant increase in student interest and en thusiasm for the course. Second, each computer program has been written incor porating an error analysis. This forces the student to consider the accuracy of his experimental measurements and their effect on his calculated results. Many a student has been amazed when his "simple" heat balances on an exchanger turn out to have an error 50100%. Third, only the input data need be checked in order to check the complete calculations thus eliminating "fudged" results. Finally, since about 90% of the required calculations are done by the "high speed idiot" primary attention can be focused on the more important questions of "what do you want to measure and how accurately can you measure it?" and "what is the significance and use of your results?" There are, of course, problems associated with the use of "canned" programs in the laboratory. One is always concerned that the students understand how the calculations are performed and does not merely follow a "work book" procedure dictated by writeup of the computer program. The laboratory equipment and the large classes, requiring three or four laboratory sections each semester, had made the course quite formalized even before the computer programs were used. It was these facts that justified the effort of writing the computer programs in the first place. Realizing this, the staff has been introducing variety into the laboratory not by constantly changing the equipment and asking each group to per form a different experiment, but by asking the students a variety of questions regarding the interpretation and use of their experimental results. In summary, the integrated use of the digital computer in the Chemical Engineering Laboratory has been very successful. The previously boring, repe titious calculational portion of the course has been eliminated, and the students first encounter with a digital computer is its use as a logical means to an end rather than an end in itself. The subsequent use of the digital computer by the students in other chemical engineering courses at Purdue has been very limited. Let us turn out attention to the generalized executive computer program for doing process design calcula tions which is currently being developed at Purdue. Following a detailed presen tation of executive program, it will be shown how the program serves as a natural guide for the truly integrated use of the digital computer in the undergraduate curriculum. The PACER Executive System PACER Process Assembly GOse Evaluator Routine is a digital computer executive program. PACER is being written to in clude eventually three major phases: (1) material and energy .balances transient and/or steady state; (2) economic analysis; and (3) internal parameter variation. The PACER program is primarily one which furnishes communication between the equip ment subroutines, does a tremendous amount of internal bookkeeping and has the ability to do trial and error recycle calculations automatically. It is similar in its function and purpose to engineering calculational programs currently being developed and used by companies such as C. F. Braun, Humble Oil and Refining, M. W. ellogg, phillips Petroleum, Shell Oil and Union Carbide. Many of the basic ideas employed in PACER came from a paper presented by M. T. Tayyabkham of Union Carbide corporation entitled "Simulating Unsteady State Operation of a plant on a Digital Computer" which was presented at the AIChE meeting in Cleveland, Ohio, on May 9, 1961. The PACER program was developed by studying the structure of the problem of performing process calculations so that we could teach our robot to do the calcu lations for us in the future. The system design specifications which evolved are shown in Table 1. The major features of PACER are in the use of Stream and Equip ment matrices for handling all the information associated with a problem, modular programming, and the use of the Process Matrix by which the processing sequence Itself is supplied as input dta4 Table 2 gives the definition of these and othe7 slessly related tes. a EMarch 1963 CHEMICAL ENGINEERING EDUCATION Table 1 System Design Specifications for Process Assembly Case Evaluator Routine 1. Process Sequence, Set of Equipment, Boundary Conditions to be supplied as Input Data 2. Process Sequence, Equipment Used and /or Operating Conditions to be easily changed by user 3. PACER is to determine calculations required, do them, and print requested results 4. PACER is to be able to do both steadystate and transient behavior calculations 5. PACER must be open ended, i.e., able to be expanded and modified as required 6. PACER must be useable during development 7. PACER must be able to incorporate all past work easily PACER must be easy to use and understand 9. PACER ultimately must have very large information retrieval capacity The Process Matrix is the numerically encoded process flow diagram. It is the heart of the PACER system. By its use, the processing sequence becomes part of the input data. For any given process such as shown in Figure 1, the Process Matrix is readily formed as follows. First each piece of equipment is numbered. Then each stream on the diagram is numbered. The numbering of the equipment is arbitrary except for one or two restrictions when complex second and third order branched parallel equipment loops are involved. The numbering of streams is also arbitrary. However, particular equipment programs may require a certain ordering of stream numbers in the Process Matrix such as noted in Figure 1. These are very minor restrictions and do not limit the PACER program. The equipment numbers are given in the first column of the matrix. Then for each equipment number, the associated input streams numbers (as positive numbers) followed by the output streams numbers (as negative numbers) are listed across the row. The Process Matrix for the flow diagram is also shown in Figure 1. A second more complex example is shown in Figure 2. FIGURE 1 PROCESS SIMULATION SAMPLE PROBLEM #1 PROCESS FLOW DIAGRAM FIRST ORDER RECYCLE DUMMY PRODUCT PRODUCT PROCESS MATRIX Equipment No. Name (Subroutine) Associated Streams 1 MIXER (UNAME3) 1 9 2 2 TOWER (UNAME2) 2 3 4 3 REACTORS (UNAME2) 4 5 6 4 TOWER (UNAME2) 5 7 8 5 TOWER (UNAME2) 7 9 10 NOTE: In subroutine UNAME2: First output stream number is OVERHEADS. Second output stream number is BOTTOMS. 1 CHEMICAL ENGINEERING EDUCATION March 1963 Table 2. Definition of Terms STREAM = ANY CHANNEL OF INFORMATION The information is contained in the following matrices. STREAM PARAMETERS LIST List of values of those variables specifying what you are talking about. STREAM CONTROL VARIABLES LIST 4 list of values of those variables associated with "con trolling" the information in the parameters list. STREAM PARAMETERS MATRIX SN The composite list of all stream parameter lists. Stream number = matrix row number. STREAM CONTROL VARIABLES MATRIX SNC The composite list of all stream control variables lists. Stream number = matrix row number. STREAM FLAG LIST A list of numbers, one for each stream, which srnals its status. Stream number = list row number. NOTE; Format of SN and SNC should be the same for all streams to allow interchange between equipment Stream formats us:elly determined by equipment subroutines. The decision of which variables are "parameters" and which are "control" is arbitrary. ',UIPIFE::T tNY 1:ATI .CCAL IODEL OR SET CF PLS RN INFO9.. TLi'; IODIFIER A UNIT CALCnLTICN An EQUIPM'NT takes known Input information contained in input streams and uses natt.emotici rules to produce output information in output stretns FCIPIE'31T PARAMETERS LIST List of values of variables associated with specifying basic "size" and mode of operation of the 'QUTPMF1NT ,flTe'.T CONTROL VARIABLES LIST List of values of variables ccntrolln e"qui pment operation. "Cn P!:N,'I ?ARAMITEF!.S '!RiuX X Composite list of all equlpret prmneters lists. Fquipment number 1 matrix ro number. '! : IT CO. VAR! ".i 3 _=I , Composite list of all equipment control vrr;=z'es lists. nquIpment number = metrix row, r'rcr. st ot' numeras, one for fn r vit, w ' i slii :lE Its status. equipmentt number = A1}t, 'v utpr. :!ote:Fo'0rt oi' equipment Pnvnters .nJ onri:l V ribloe Lists need .ct be the same for 11 Fe : nt. Equipment sa.wys wr tten ,' :sub :c t 1. Tne decision of .hic 1 vnri bl rr vt"r rn which are control vnri bless i *rb'tr ry. pROCE'ss :i"TRIXE NUTFRICALLY "UIC 1'2Y ' o. 7' AT10' An array of the Fqjipmsent rnnmr i on th'r isocited in put (positive) and output (reat've) store" r'nurers. The Process Matrix defines the .yster processs seq ence) for PACER and is used to determine how the clcultions w 11 be done. The calculational procedure is Independoent o:' 1. the sequence of equipment in Process :I.tr x 2. the numbering of the streams 'nd equ1p'nert March 1963 CHEMICAL ENGINEERING EDUCATION 15 FIGURE 2 PROCESS SIMULATION SAMPLE PROBLEM #2 PROCRSR PLOW DIAGRAM PRODUCT 3 5 7 9 1 1 2 3 5 4 6 8 10 SECOND ORDER RECYLCE DUMMY PRODUCT PRODU PRODUCT 3 REATOS( 2) 15 13 LPG 8 76 MIXER SPLITTER DEBUT TOWERTO 1 14 1 PRODUCT PRODUCT PROCESS MATRIXa to PACER Equi the process matrix row number, the equipmentent SName (Subroutine) Aspndng subrsoited Stre associated 1 MIXER(UNAME3) 1 9 2 23. TOhe Equipment Pa(UNAMrameter2) 2 3nd Equpment Control Varables 3 REACTORS(UNAHE2) 15 5 6 4 TOWER(AME2) 7and Stream Control Variables Matrices 5. TOWER(UNAME2) 7 9 10 6 TOWER(UNAME2) 8 ll 12 7 SPLITTER(UNAME2) 11 13 14 8 MIXER(UNAME3) 4 13 15 ote: t Output Stream Param etumber nd St Overheads 2nLists used Output Stream Number convergence Bottoms Table 3. Input Data to PACER 1. Control Cards describing the size of the problem, number cases to be evaluated and print out desired 2. The Process Matrix. One card for each equipment giving the process matrix row number, the equipment number, name of corresponding subroutine and the associated stream numbers 3. The Equipment Parameter and Equipment Control Variables Matrices 4. The Stream Parameter and Stream Control Variables Matrices 5. The Stream Parameter and Stream Control Variables Test Lists used for testing for convergence in the trial and error recycle computations 6. Preferred Stream Numbers, if any, used in determining the calculational procedure for recycle computations. 16 CHEMICAL ENGINEERING EDUCATION 11 0" The PACER calculational procedure is independent of the numberng of ea v n, and streams. It is also independent of the order of the equipment in ;he Process Matrix. The basic program logic of the PACER system is shoa in Figures 3 and 4. Space and time prohibit a detailed description of PACER which has been written in FORTRAN for an IBM 7090 computer and consists of well over 1000 FORTRAN statements. The description and discussion presented here are independent of the programming language and machine. As shown in Figures 3 and 4, the Process Matrix is used to determine auto matically the sequence of Equipment calculations thus providing the logical re lationships for computations. The basic calculational rule used is that if the input streams are known or have been computed, then the Equipment subroutine can calculate the corresponding output streams. The streams are treated as entities in that if a stream is known, all variables in the corresponding Stream Parameter and Stream Control Variables lists are taken as known, and, when a stream is cal culated, the change in any and all variables are computed by the particular unit calculation alone. During each primary loop the Stream Flags and Equipment Flags are used to indicate the calculational status of each stream and equipment. PACER uses these flags to make decisions in determining the calculational procedure. Following the logic shown in Figures 3 and 4, one would discover that Figure 1 is a first order recycle problem where stream 9 must be assumed known in order to do FIGURE 3 PROGRAM LOGIC FOR PRIMARY LOOP RESET ALL STREAM FLAGS 1 SCAN STREAM MATRIX. CALCULATE SPECIAL STREAMS SET FEED, PRODUCT, SPECIAL STREAM FLAGS SCAN PROCESS MATRIX ROW BY  ROW STARTING AT FIRST ROW HAS EQUIP BEEN CALCULATE ? NO YES ARE ALL INPUT STR AMS KNO7? YES NO CALL EQUIPMENT SUBROUTINE CALCULATE OUTPUT STREAMS AND FLAG AS KNOWN LAST ROW OF PROCESS MATRIX? NO YES II O TO NEXT ROW ARE ALL STREAMS FLAGGED KNOWNt YES 10 PRIMARY LOOP COMPLETED WERE ANY STREAMS FLAGGED KNOWN DURING SCAN? NO YES RECYCLE CALCULATIONS REQUIRED. FIND SHORTEST CLOSED LOOP. SET UP AND PERFORM REQUIRED TRIAL AND ERROR CALCULATIONS BIoh 1963 CHEMICAL ENGINEERING EDUCATION 17 ,"oIjUatji0ons. Tor Sample Problem #2 in Figure 2, Streas Tand5 miiinatbe 5"nfed known so that it is a second order recycle problem.' D The values given in the Equipment and Stream Matrices represent a snapshot picture of the entire process at any given time. In each primary loop, the values of the variables are recomputed. For time independent problems, the pri mary loop is calculated only once. In transient behavior problems, each primary loop corresponds to a small interval of time. The user supplies the initial boun dary conditions and corresponding steady state answers are obtained by repeated primary loop calculations. Tayyabkham discusses the unsteady state case in detail. In his paper he cites the simulation of an organic chemical plant consisting of 50 flow streams and 30 pieces of equipment on a IBM 7090 computer. About 100 sub routines were used. Each primary loop, equivalent to 0.1 hours, could be calcu lated about 20 to 25 times a minute so that 2 hours of computer time corresponds to about 300 hours of real time. As seen in Figures 3 and 4, the Process Matrix is scanned several times in completing a primary loop. PACER recognizes the need for trial and error re cycle calculations when no additional equipment can be calculated by repeated scanning of the Process Matrix and all streams have not been calculated. The executive program then makes an ordered list of unknown input streams. The list is ordered in the sense that the user can supply PACER with a list of preferred stream numbers and these stream numbers are placed at the top of the unknown stream list. PACER then takes the first stream number in the unknown stream list, flags the stream as temporarily known and scans the Process Matrix to see if an equipment calculational loop can be found such that the assumed known stream would be calculated as an output stream. If this is not possible, then the next stream in the unknown stream list is assumed known and the search repeated. First all single streams are assumed known one at a time in trying to find a calculational path. Then all possible combinations of two streams are tried and finally all possible combinations of three streams. Tne order of the recycle equals the number of streams which have to be assumed in order to establish a closed calcu lational loop. Once a calculational loop consisting of an ordered list of equipment numbers is found such that all assumed known streams are calculated output streams, PACER eliminates all equipment from the list which is not required to complete the cal culational loop. This is done since nonrequired equipment merely increases cal culational time. The present values of the variables are taken as the starting values for the trial and error recycle calculations. Once the shortest order list of equipment has been determined, the necessary booking is done and the equipment repeatedly calculated in order until convergence is obtained. Following some ad ditional bookkeeping, PACER returns to the primary loop scan to complete the cal culations for the primary loop. It is emphasized that the term Equipment and Streams must be used in the broadest sense of their definition in order to see the scope and magnitude of the PACER system. An Equipment subroutine may or may not correspond to a piece of real hardware such as a heat exchanger or distillation tower. It can be any set of mathematical rules. For example, it might be a program for changing the format of Stream Parameters and Control Variables Lists so as to be able to incorporate a previously written subroutine into the PACER library without having to rewrite the subroutine. In the same manner, the definition of Stream is used in the broadest sense. The requirement of a uniform format for all Stream Parameter and Stream Con trol Variables lists allows the complete interchange of Streams and Equipments. This gives the PACER user the ability to quickly study various process sequences and so be able to handle a whole new class of problems on the computer. The PACER executive program is independent of the Stream and Equipment Matrices format in that it will handle any consistent set. Appendix B gives a brief description of two simple Equipment subroutines and the format of their associated Stream and Equipment matrices. The relationship between the equipment subroutines and the formats of the Stream and Equipment matrices is typical. These two Equtpment and subroutines are sufficient to simu late the processes shown in Figures 1 and 2. These two simple programs and PACER, could be used effectively to illustrate many, if not most, of the aspects of pro cess design and optimization for students in their first course in chemical engi neering. M1r. Henry Mosler, one of my graduate students at Purdue who is developing PACER, pointed out that Sample Problem 2 is only a first order recycle problem. This was discoveredu when PACER solved the problem. Streams 5 and 15 are common to the two calculations. loops. Assuming 5 or 15 as known, all equipment can be calculated. The author, and perhaps the reader had been conditioned not to guess Intermediate streams in this type of problem. 18 CHEMICAL ENGINEERING EDUCATION Mareh 1963 One of the powerful features of the PACER system lies in the fact that *af t' : eculpment calculations are written as subroutines. Each equipment subrou t. sa a 'unit calculation", a simple extension of the fundamental chemical en. gineering concept of the "unit operation." This gives rise to the concept of modularity in programming which is extremely useful. The subroutines are "com 4 plete" in the sense that they are written to calculate the output streams using only the data contained in the input streams and the Equipment Parameters and Con trol Variables lests. Hence a library of equipment unit calculations may be de veloped consistent with a basic stream and equipment matrices format. Several unit calculations of increasing complexity can be written for a given type of equipment such as a distillation tower calculation. Then the user of PACER may choose the level of mathematical description required by his particular problem. Another great advantage lies in the fact that only one subroutine is required for a given equipment no matter how many times that equipment is used in a process. Input information for the PACER executive program consists of the data listed in Table 3. The routine for reading the input data is such that individual rows in the Process, Equipment, and Stream Matrices are read in separately. Thus, the user can easily change any portion of these matrices with a minimum of effort. If additional equipment subroutines not in the PACER library are to be used, these are read into the computer prior to the data called for in Tqble 3. The process Matrix specifies the problem to be solved and is used to determine the method of solution. The Stream and Equipment Matrices supply the initial boundary conditions for the case to be evaluated and after solution, contain the computed results. With PACER almost all the "bookkeeping" is done within the computer. The program user does not have to be directly concerned with all the intermediate stream results. Previously, assuming the equipment subroutines were available in "closed form," the user would have to prepare the data sheets for the first pro gram, punch the cards, run the problem, examine the results, prepare the data cards for the second program (which probably require a different format), run the problem, etc. This took all of his time and effort. He would only have time to make one or two complete process calculations; his calculations would not have FIGURE 4 PRIMARY LOGIC FOR RECYCLE CALCULATIONS FORM ORDER LIST OF UNKNOWN INPUT STREAMS CHOOSE INPUT STREAMS ASSUMED "KNOWN" TRY ALL COMBINATIONS OF 1,2 or 3 STREAMS RECYCLE ORDER = NUMBER OF STREAMS ASSUMED 1 SCAN PROCESS MATRIX. CAN ASSUMED INPUT STREAMS BE CALCULATED AS OUTPUT STREAMS? NO YES MODIFY CHOICE OF DETERMINE SHORTEST, ORDERED LIST "KNOWN" INPUT STREAMS OF EQUIPMENT HAVING ASSUMED INPUT STREAMS AS OUTPUT STREAMS DO BOODEKEPING REQUIRE D FOR ITERATIVE RECYCLE CALCULATION SELECT EQUIPMENT FROM ORDERED LIST it CALL EQUIPMENT SUBROUTINE AND CALCULATE OUTPUT STREAMS TEST OUTPUT STREAMS FOR CONVERGENCE NO HAS ALL EQUIPMENT BEEN CALCULATED? YES I S HAVE ALL STREAMS CONVERGED?NO  TRANSFER RESULTS TO STREAM MATRIX RETURN TO PRIMARY LOOP March 1963 CHEMICAL ENGINEERING EDUCATION 19 converged, and he would then "adjust" his answers and report his results. This need no longer be the case. When the user of PACER specifies the Process Matrix he has written a complete digital computer program in the time it took him to write the Process Matrix. In most cases, the resulting computer program is of such magnitude as to have been prohibitive if it had had to be written from the beginning. The great advantage of modularity and the "open ended" approach in programming as used in PACER is il lustrated in the fact that for PACER, Sample Problems #1 and #2 are the "same" problem. It is the same problem for any specification of the unit calculation equipment subroutines to be used. Thus PACER' and a library of equipment sub routines gives the user a tremendous computational ability. While it has not been possible to present a detailed description of the PACElR system it is hoped that a clear picture has been given of the basic approach and fundamental concepts involved. It is hoped to have the first phase of PACER opera tional on the IBM 7044 at Purdue next Spring. A more detailed description of the PACER system will be made available at that time. Now let us consider how the PACER system might be effectively used in the un dergraduate chemical engineering curriculum. At the same time we shall see how this would lead to the integrated use of digital computers in the students under graduate courses and be of tremendous use in his senior year courses in Process Design and Process Dynamics and Control. The basic ideas and operation of PACER are simple and could easily be taught to students in their first course in chemical engineering. What more effective way to teach a student process recycle calculations then have him learn to teach a stupid robot? The use of the Stream and Equipment Matrices certainly represents an orderly way to handle the information associated with a problem. Using simple unit calculations such as given in Appendix B, the students could very quickly be introduced to the concepts and problems of process design. The decision aspects of engineering and the description function of science are dramatically illustra ted in this approach. The Equipment Unit calculations are the scientific descrip tion. It can be pointed out that the majority of his future courses are aimed at giving him the ability to understand and develop specific unit calculations. The engineering decision aspects come in his ability to decide what should be studied in the first place and his ability to interpret the results of the calcu lations in arriving at a decision. A series of decisions results in a design, the essential function of an engineer which distinguishes him from the scientist and the technician and operator. In fact, the fundamental ideas of PACER, particular ly the use of the Process Matrix and the concept of the unit calculation, could well serve as a basis conceptual framework for all of his subsequent engineering courses. In his courses in heat transfer, fluid flow, equilibrium stage calculations, kinetics, etc. the use of the digital computer would arise naturally. Following a thorough grounding in the fundamental concepts, specific unit calculations are generally developed in detail. It would then only be required that the student be asked to write a digital computer program for the specific calculational techni que just studied. This would serve as an acid test of his understanding of the material. Or, he might simply be shown the computer program and be required to use it in solving several problems. This would be done in each of his courses. Thus he would be building up a library of Equipment unit calculations, each of which he had studied in depth at the time the fundamental concepts, basic assump tions, and limitations were his primary concern. The PACER framework would serve to show where and how each course fits into the total picture and emphasize to the student the interrelationships between his courses and that what he is being taught today in fluid mechanics will be used tomorrow in design. In the student's senior year design course he would have at his disposal a large library of unit calculations, each of which he had previously studied in depth. Emphasis could then be shifted back to consideration of the behavior of the total system. He would thus be in a position to attack a wide variety of de sign problems of increasing complexity. The PACER system would provide the abili ty to write the complex digital computer programs required for specific problems in the time required to write the Process Matrix and assemble the appropriate in put data. In addition, he would be able to do a great many problems which our present seniors cannot even attempt. In this approach, the use of a digital com puter would become as natural to the student as the use of his slide rule, text books and the library in the solution of the engineering problems he faces today and will face tomorrow. (Authors note: Copies of the PACER program accompanied by extensive documentation for use by university staffs for educational purposes will be available in the near future. Requests should be addressed to the author at his present address.) CHEMICAL ENGINEERING EDUCATION CH. E. 339 UNIT OPERATIONS LABORATORY SHELL AND TUBE HEAT EXCHANGER IDENTIFICATION NO. A. EXPERIMENTAL CONDITIONS 1. KEROSENE RATE REYNOLDS NO. 2. STEAM RATE 3. WATER RATE PROBABLE UNCERTAINTIES 1. KEROSENE RATE 2. STEAM RATE 3. WATER RATE B. HEAT BALANCES 1. HEAT SUPPLIED BY SHELL FLUID 2. HEAT ABSORBED BY KEROSENE 3. HEAT LOST BY RADIATION 4. HEAT LOST BY CONVECTION NET HEAT LOST BY SYSTEM 6. SAME, AS FRACTION OF ABSORPTION PROBABLE UNCERTAINTIES 1. HEAT SUPPLIED BY SHELL FLUID 2. HEAT ABSORBED BY KEROSENE 6. FRACTIONAL HEAT LOSS C. HEAT TRANSFER COEFFICIENTS HEATER EXPERT. PREDICTED 1. SHELL SIDE 5422746421 2. TUBE SIDE 5285549319 3. FOULING 5420000000 4. OVERALL 5291234129 5268398291 PROBABLE UNCERTAINTIES 1. SHELL SIDE 5223215443 2. TUBE SIDE 5116514913 4. OVERALL 5210243823 5112318093 Note: Numbers representation pp nnnnnnnn = 0.nnnnnnnn X 1050 5271200000 7.12 e 4532350000 0.3235 X 10o5 THE ART OF FILTRATION IDENTIFICATION NO. EXPERIMENTAL CONDITIONS SLURRY TEMPERATURE F. PRESSURE DROP PSIG EXPERIMENTAL RESULTS BEST X COORDINATE BEST Y COORDINATE Y INTERCEPT BB SLOPE KP SPECIFIC CAKE RESISTANCE ALPHA FILTER MEDIUM RESISTANCE RM SLURRY CONCENTRATION CS ALUMINUM HYDROXIDE, PERCENT SILICON DIOXIDE, PERCENT OPTIMUM FILTRATE VOLUME OPTIMUM FRAME THICKNESS 5499690884 5424397640 5265856000 5466007552 5324056099 5120164178 5315240014 HEATER COOLER 5562252359 5562707174 5560911125 5560911125 5313457078 5225290935 5310412223 5217344405 5411025411 5417534137 4918100816 4928786429 5419060794 5494464842 5467873174 5467873172 5011768355 5019285625 COOLER ..................... EXPERT. PREDICTED 5345211066 5285549319 5410000000 5242756633 5259197989 5163570229 5116514913 5147876196 5092899487 5250000000 5270000000 5250000000 DEVIATION 5268681988 5230745552 5223721290 6234477353 6126147465 999056835 048642833 5048639873 5013576260 VALUE 5111228350 5330889000 5243191675 5323664055 6312115680' 6172988184 5114352000 5113910505 5084630350 5126604593 5037837050 Note. Numbers representation pp50 +pp nmnnnnnm =t O.nnmnnnnn X 10 5271200000 = 7.12 4532350000o = 0.3235 X 105 20 APPEr'DIX March 1963 CHEMICAL ENGINEERING EDUCATION CH. E. 440 UNIT OPERATIONS LABORATORY COOLING TOWER IDENTIFICATION NO. 0000000002 PERIMENTAL CONDITIONS, ACTUAL AIR MASS FLOW RATE GY TEMPERATURE F. INLET, DRY BULB INLET, WET BULB EXIT, DRY BULB EXIT, WET BULB HUMIDITY INLET EXIT WATER MASS FLOW RATE GX TEMPERATURE F. INLET EXIT EXPERIMENTAL AND THEORETICAL RESULTS THEORETICAL INTERFACE AREA PER UNIT VOLUME A HEAT TRANSFER COEFFICIENT HYA 5287410747 HEAT TRANSFER COEFFICIENT BY 5118436434 MASS TRANSFER COEFFICIENT KYA 5335388967 MASS TRANSFER COEFFICIENT KY 5174641436 5417647408 5278500000 270500000 52705ooooo 5271500000 52705000ooooo0 4913500000 4915500000 5396623275 5271000000 5269000000 ERROR EXPERIMENTAL ERROR 5247411960 5114190322 5286395293 5322719407 5312451326 5118213901 5147919148 512622280k 5335190623 5391981407 5350409656 5173740236 5219400465 5210616399 Note; Numbers representation #4pp nnnnnnnn =" 0.nnnnnnnn X 10'50 5271200000 = 7.12 4532350000 = 0.3235 X 105 APPENDIX B. EXAMPLE SET OF EQUIPMENT SUBROUTINES AND EQUIPMENT AND STREAM MATRICES FOR USE WITH PACER EQUIPMENT SUBROUTINE UNAME2 DISTILLATION AND REACTOR SIMULATION This program can be used to simulate distillation towers and re actors. It is written to handle five components. One FEED stream is split into an OVERHEAD and a BOTTOMS stream. In Process Matrix, first output stream is OVERHEADS, second output stream is BOTTOMS. OVERHEAD Subroutine SOI FEED UME2 STRi(l,13) EN(E,8) STR(1:13)  EC(EE,) TS O(2,13) Method of Calculation 1. Calculate amounts of each component in OVERHEADS and BOTTOMS. 2. Sum component amounts to find total amount of OVERHEADS and BOTTOMS. 3. Calculate percentage compositions of OVERHEADS and BOTTOMS. 4. Calculate Fictitious Head Load. MATRIX formats are shown on the following pages. UNAME2 is compatible with UNAME3. EQUIPMENT SUBROUTINE UNAME3 COMPONENT MIXER UNAME3 is a MIXER subroutine which adds the amounts of each compo nent in each input stream, splits the total input amounts of each component equally between the output streams and then calculates the percentage compositions of the output streams. March 1963 APPENDIX A 22 CHEMICAL ENGINEERING EDUCATION March 1963 STREAM: P RAMETERS LIST SN and STRMI and STRMO (NS,13) Same format required for all streams. MatrIX Row Variable 1 Stream Number always required 2 Stream Flag always required 3 Total Quantity of the stream W percent of Component 1 0. 1.0 SPercent of Component 2 0. 1.0 6 percent of Component 3 0. 1.0 7 Percent of Component 4 0. 1.0 8 percent of component 5 0. 1.0 Y a 1.0 9 Amount of Component 1 10 Amount of Component 2 11 Amount of Component 3 12 Amount of Component 4 13 Amount of Component 5 STREAM CONTROL LIST SNC and STRMCI and STRMCO (NS,3) Matrix Row Variable 1 Stream Number always required 2 Stream Flag 3 Light Key Component Number 1 or 2 or 3 or 4 Note: Stream Type Stream Flag Interequipment 0 Feed +1 product + 2 Special Feed + 3 EQUIPMENT PARAMETER LIST EN(NE,8) Matrix Row Variable 1 Equipment Number always required 2 Equipment Flag 3 Fictitious Head Load Q 4 Fraction of Component 1 in FEED appearing in OVERHEAD 5 Fraction of Component 2 in FEED appearing in OVERHEAD 6 Fraction of Component 3 in FEED appearing in OVERHEAD 7 Fraction of Component 4 in FEED appearing in OVERHEAD 8 Fraction of Component 5 in FEED appearing in OVERHEAD NOTE: (1. Fraction of Component in OVERHEAD) = Fraction of Com ponent in BOTTOMS. Fictitious Read Load Equation: QS A* OVERHEAD B Pkey key 1 x l10) *C EQUIPMENT CONTROL LIST ENC(NE,5) Matrix Row Variable 1 Equipment Number always required 2 Equipment Flag 3 lst Constant of Heat Equation (A in above equation) 4 2nd Constant of Heat Equation (B in above equation) 5 3rd Constant of Heat Equation (C in above equation) The Use of Analog Computers in Teaching Process Control James E. Stice and Bernet S. Swanson Illinois Institute of Technology, Chicago The use of indirect electronic analog computers is steadily increasing in both industry and engineering education. Such computers are used primarily for the solution of linear and nonlinear ordinary and partial differential equations, and for the simulation of systems. An analog computer facility for educational purposes which is reasonably accurate and large enough to handle linear problems of moderate complexity can be obtained for $2,000. Increasingly accurate equip ment with greater capacity and specialized auxiliary components requires a corres1 pondingly larger investment. The minimum equipment requirements include an analog computer with the nec essary computing resistors and capacitors and some sort of readout device. Some of the manufacturers of small analog computers and computer components are Ap plied Dynamics, Inc., 2275 Platt Road, Ann Arbor, Michigan; Donner Scientific Division, SystronDonner Corp., 888 Galindo St., Concord, California; Electron ic Associates, Inc., Long Branch, N. J.; The Heath Company, Benton Harbor, Michi gan; George A. Philbrick Researches, Inc., 127 Clarendon St., Boston 16, Massa chusetts. The necessary computing resistors and capacitors (if not built into the com puter) may be made up by the user or they may be purchased ready to use. The re sistors may be made up by attaching precision resistors having the desired resis tance (one percent tolerance or better) to General Radio double plugs. Computing capacitors may be similarly made up, but it is difficult to obtain capacitors which have exactly the capacitance desired, so that trimming is almost always necessary. Further, condensors of radio quality do not have high enough leekage resistances for accurate computation purposes. Computing resistors and capaci tors may be purchased from several sources, such as Donner Scientific Division of SystronDonner Corp. and Southern Electronics Corp., 239 West Orange Grove Ave., Burbank, California. The precision capacitors are expensive. The readout device may be an oscilloscope or some sort of recorder. A re corder is recommended for educational use, so that the student may obtain a per manent record of the solution. Recorders tested here which are quite acceptable for analog computer readout include the Brush Mark II, the Offndr Type 542 and Type RP DynoCraphs, the sanborn Model 1525460, the Varian G11A, and the EAI Model 1100E variplotter (an XY recorder). The July 1962 issue of Instruments and Control Systems contains a survey of 1,000 recorders. A group of laboratory experiments follows which were developed at Illinois Tech for the process control laboratory course given in the Chemical Engineering curriculum. These experiments introduce the student to the use of the computer gradually. There are eight experiments, and a two or threeman team of students should be able to work all of them in nine threehour laboratory periods without too much supervision. The experiments are written for the 15amplifier Heath Group C Computer ($945), although any computer with nine amplifiers would suffice, with the exception of the Heath Model EC1 Computer, which can be used for only seven of the experiments. The recorder used here was the Offner Type 542 Dynograph ($1,145). This is a twochannel, galvanometertype recorder which is also used for a great variety of other applications around the department. If money is tight, excellent re suits should be obrained with a singlepen, potentiometertype recorder such as the Varian G11A recorder (base price with Type B1 Input Chassis is $540). The range of applications of such recorders is not as broad as that of the galvano. metertype recorders, since the potentiometric recorders cannot be used for sig nals having frequencies above one cycle per second. However, the equations can be timescaled so that good results can be obtained with these recorders. The computing capacitor requirements for these experiments are: one 0.01 ufd, one 0.1 ufd, and four 1.0 ufd capacitors. Resistors required are: two 0.1 megohm, one 0.2 megohm, one 0.4 megohm, four 0.5 megohm, eight 1.0 megohm, two 2.0 megohm, one 5.0 megohm, and one 10.0 megohm resistors (one percent toler ance or better). In addition to the equipment already specified, the second part of Experi ment Two requires a diode function generator (DFG) for the generation of the valve characteristic curve. There are a number of diode function enerators on te mar ket, but by far the least expensive is the Model ES600 (kit) manufactured by the Heath Company ($72.95). This DFG provides only ten straight line segments, and it is understandably less accurate than a DFG costing $450, but it is adeqg"tq r.o instructional purposes and the price is attractive. 23 20 CHEMICAL ENGINEERING EDUCATION Mareh 1963 These experiments have worked out very well; the students have learned how td solve relatively simple process control problems on the computer. There have, in7 addition, been some bonus results which were not anticipated when the program was begun. Students tend to get rather disconcertingly enthusiastic about the compu ter after they begin to understand how to operate it, and they leave the labora tory only after repeated threats of bodily harm. They concoct their own problems and return to the laboratory on their own time. Further, they experience a re newed interest and a more mature understanding for differential equations, and the electrical engineering department reports that our students are'badgering their staff to give them more electronics. This awakening of intellectual curiosity in nearly all the students who have worked with the computer has been a delightful, if somewhat wearing, experience for the staff members who teach this laboratory. Building an analog computer laboratory poses the problem of how many students can be handled at one time. A team should consist of no more than three students, and two is better. A class of twelve students may thus imply four to six compu ters, and this becomes an expensive operation. The Donner Model 3500 and Model 3400 computers have removable problem boards, as do many of the larger computers (Applied Dynamics, Electronic Associates, Berkeley Division of Beckman Instru ments). Also, Prof. James 0. Osburn of the Chemical Engineering Department, State University of Iowa, Iowa City, has devised a plugboard for use with the Heath Group C computer. This plugboard has connections to four of the computer ampli fiers, three of the initial condition power supplies, and a 100volt and a 100 volt supply. Each plugboard also contains four integral coefficient potentio meters. A plugboard costs about $15.50 to make. A team of students can patch up a problem on their own plugboard and when wiring is completed the board is at tached to the computer and the solution can be run off in a short time. In this way one computer can serve a class of perhaps ten to twelve students. Osburn's plugboard is described in the Journal of Chemical Education, 38, 492 (1961), and further details may be obtained direct from Dr. Osburn. The development of these experiments and the manual which accompanied them was supported by a National Science Foundation grant. EXPERIMENT ONE INTRODUCTION TO THE HEATH GROUP C ELECTRONIC ANALOG COMPUTER This experiment is intended to familiarize the student with the basic tech niques of analog computation on the Heath Group C electronic analog computer. After the various mathematical operations which the computer can perform have been studied, they can be utilized to solve a classical rpoblem in physics, such as the body falling freely in a vacuum from a position of rest. EXPERIMENT TWO FUNCTION GENERATION PART I1 Use of the Computer to Generate Functions An analog computer can be used to generate a variety of functions for use as problem inputs. PART II: Use of the Diode Function Generator EXPERIMENT THREE COMPUTER SOLUTION OF LINEAR SECONDORDER DIFFERENTIAL EQUATIONS Ordinary linear differential equations occur commonly in science and engi neering. The examples used here will be limited to differential equations with constant coefficients, so that function multipliers will not be required. A class ioal problem in mechanics is the massspringdamper system, in which a mass is supported by a spring and a dashpot. EXPERIMENT FOUR FREQUENCY RESPONSE DIAGRAM FOR A MECHANICAL SYSTEM In the previous experiment, the analogy between the massspringdamper sys tem and the timescaled R L C circuit was developed, and the transient response of these systems was studied for the case with no forcing function applied. In this experiment, the mechanical system will be forced to oscillate by impressing a ainusoidal forcing function on the mass. The system will be subjected to forcing functions of different frequencies, and a frequency response diagram will be constructed for the system. March 1963 CHEMICAL ENGINEERING EDUCATION 25 EXPERIMENT FIVE COMPUTER SIMULATION OF SYSTEM COMPONENTS One of the most important applications of analog computers is the simulation of physical systems. The computer is programmed to solve the differential equa tion or set of equations which represent the system. When this has been done, it turns out that certain portions of the computer circuit represent identifiable parts of the physical system under study, so that it becomes natural to think of these circuit components as though they were the corresponding components of the physical system. This will be illustrated in the several parts of this experi ment. PART I: SingleTank Liquid Flow Process This is illustrated by a liquid flow process in which liquid flows into a tank at a rate of F (t) cubic feet per minute, and flows out at a rate of Fl(t) cubic feet per minute. The capacity of the tank is C1 cubic feet of liquid per foot of depth, which is numerically equal to the crosssectional area of the tank in square feet. To keep the problem simple, assume that the crosssectional area of the tank is uniform from top to bottom, as would be the case with a vertical cylinder or a rectangular tank. The head of liquid in the tink is hI feet. The Fo(t) Capacity = Ci ft3 per ft of depth Fllt) Figure 51: SingleTank Liquid Flow Process liquid flowing out of the tank suffers head losses due to contract on and expan sion, and friction in the piping and fittings. All of tiese factors are lumped into one equivalent resistance term which is designated 1 (foot) (minutes) per cubic foot of flowing liquid. This equivalent resistance is equal to the slope of the head versus flo curve in the region of interest. This curve is not nor mally linear, but it .y be aproximately linear in the region of interest. gajin in the interests of keeping the problem simple, the curve which relates head to flow F1 will be assumed to be a straight line. PART II: Second SingleTank LiquId Process 1 second tank will be sinulfted, the new tank being similar to the first. The process time constant will be different, since the second d tln will alree a irgeer crosssectlonu l rrea capacityy) and a somewhat different equivalent res p  tbnce. fos before, ciprcity and resistance will be assumed constant. The flow in to Ink 2 will be Fl(t) cubic feet per minute, and the flow out will be F2(t) cu bic feet per minute. PART III: TwoTank Liquid Flow PFrcess Tank 1 is the tank of Part T n1 d Tant: 2 's the tank of prt It it is de sired to know what the traslent response of t 's system will be *f n step input eis applied suddenly inc resa sn flow a (t). "en t ie t islent response curve has been obtained, it will bae use s to ca puacte t e tme c cnstants of' the process. Io(t)he I dCapacity CI Capacity C Figure 53: TwoTank Liquid Flow Process 26 CHEMICAL ENGINEERING EDUCATION March 1963 EXPERIMENT SIX OPENLOOP RESPONSE OF PROCESS The twotank process of Experiment Five is to be instrumented to maintain a flow rate of twenty gallons per minute for flow F2(t). The control valve and the flow sensing device will be simulated in this experiment and the openloop res ponse of the system will be studied. In Experiment Seven the pneumatic controller will be studied. The controller will be added to the rest of the equipment in Experiment Eight, and the e]osedloop behavior of the entire system will be ob served for various controller settings. Flow F2(t) out of Tann 2 will be maintained constant by controlling flow Fo(t) into Tank 1. Flow 21,(t) is an intermittent stream which also flows into Tank 1 Pt Rrb:trsry intervals and for varying lengths of time. To simplify the analysis, it will be assumed that the nature of the process is such that Tank 1 will never run dry or overflow. EXPERIMENT SEVEN CC"'TOTR SIMULTITON OF A PEIUMATIC CONTROLLER In order to control the system in the previous experiment, some sort of con troller is necessary. This controller receives the air pressure signal from the flow sensing device, subtracts this signal from the set point signal to produce an error signal, and acts upon the error signal to reposition the control valve. Pneumatic controllers can be obtained with up to three modes of control, these being proportional, derivative (also called rate or preact), and integral (also called reset rate) modes. The particular process under study can be con trolled very nicely by a controller having proportional and integral action, and this is the type of controller which will be simulated. EXPERIMENT EIGHT BEHAVIOR OF THE CLOSEDLOOP PROCESS The complete process of Experiment 6 will be simulated and the effect of various controller settings will be observed. The pertinent facts about the pro cess are summarized below. (1) It is desired to maintain a constant flow of twenty gallons of liquid per minute out of the bottom of the second of two noninteracting, seriescon nected tanks. This flow is designated Fp(t). To accomplish this a pneumatic con trol valve regulates the flow of liquid Into the top of the first tank, the regu lated stream being Fo(t). (2) In addition to Fo(t) there is an intermittent stream, FL (t), which also flows into the top of the first tank. This flow is unregulated, and occurs in varying amount and on no regular schedule. The amount of this flow is small com pared to Fo(t). Pneunatic Control valve Pneumatic 0 F ( ) Controller 0 )(t) Tank 1 Flow Sensing Device Tank 2 T  F 2Ct) Figure 61: Automatic Control of Flow in Liquid Process 
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