ChE curriculum TEACHING REACTION ENGINEERING USING THE AttAINABLE REGION MATTHEW J. METZGER, BENJAMIN J. GLASSER Rutgers University • Piscataway, NJ 08854 DAVID GLASSER, BRENDON HAUSBERGER, AND DIANE HILDEBRANDT University of the Witwatersrand • WITS, 2050 Johannesburg, South Africa sk a graduating chemical engineering student the fol- Matthew Metzger is pursuing his Ph.D. at Rutgers University. He received lowing question: What makes one reactor different his B.S. from Lafayette College and spent two summers working with the from the next? The answers received will often be chemical engineering department at the University of the Witwatersrand. His interests lie in applying the attainable region approach to particle Aunsatisfactory and vary widely in scope. Some may cite the processing in the pharmaceutical field. difference between the basic design equations, others may Benjamin J. Glasser is an associate professor of chemical and bio- point out a PFR is “longer,” and still others may state that it chemical engineering at Rutgers University. He has earned degrees in all depends on the particular reaction network. Though these chemical engineering from the University of the Witwatersrand (B.S., answers do possess a bit of truth, they do not capture the true M.S.) and Princeton University (Ph.D.). His research interests include granular flows, gas-particle flows, multiphase reactors, and nonlinear difference between reactors: the degree of mixing achieved. dynamics of transport processes. This is the inherent difficulty with teaching chemical reaction Diane Hildebrandt is the co-founder of COMPS at the University of engineering. The students learn the technical skills required the Witwatersrand. She received her B.S., M.S., and Ph.D. from the to perform the calculations to determine maximum yields and University of the Witwatersrand, and currently leads the academic and consultant research teams at the university. She has published more than shortest space-times, but very rarely are they able to grasp and 50 refereed-journal articles on topics ranging from process synthesis to thoroughly understand the theory and underlying differences thermodynamics. between reactors.[1] Often, too much time is devoted to tedious Brendon Hausberger is a director at the Centre of Material and Process and involved calculations to determine the correct answer on Synthesis (COMPS) at the University of the Witwatersrand. He received homework instead of focusing on the concepts to enforce the his B.S. and Ph.D. from the University of the Witwatersrand, and is cur- rently overseeing the launch of Fischer-Tropschs plants in both China benefits offered by each reactor presented. and Australia. Reactor network optimization is traditionally not covered David Glasser is a director of the Centre of Material and Process Syn- [2-4] in any depth at the undergraduate level. The way reactor thesis at the University of the Witwatersrand. He is acknowledged as a network optimization is traditionally taught to graduate stu- world-leading researcher in the field of reactor and process optimization, and is a NRF A1 rated researcher. His extensive publication record and dents often involves large numbers of coupled equations that research areas extend from reactor design and optimization to distillation can sometimes hide the final goal of the analysis. Attempts and process optimization and intensification. © Copyright ChE Division of ASEE 2007 258 Chemical Engineering Education to simplify the situation, such as Levenspiel’s graphical possible reactor configurations. One of its advantages over analysis,[4] do offer some benefit, however their applicability previous approaches is the elimination of laborious and is limited as they can readily only optimize simple reaction counter-productive trial and error calculations. The focus problems. For chemical engineers, it is paramount to know is on determining all possible outlet concentrations, regard- the most promising solution to a real problem in the shortest less of the reactor configuration, rather than on examining a amount of time, and rarely is this accomplished with the cur- single concentration from a single reactor. Approaching the rent teaching methods for reactor network optimization. problem from this direction ensures that all reactor systems Presented here is an approach that addresses the challenges are included in the analysis, removing the reliance on the presented above. The attainable region (AR) approach is a user’s imagination to create reactor structures. Also, for lower powerful research technique that has been applied to optimi- dimensional problems often studied in the undergraduate zation of reactor networks.[5-7] It is also a powerful teaching courses, the final solution can be represented in a clear and tool that focuses on the fundamental processes involved in intuitive graphical form. From this graphical representation, a system, rather than the unit operations themselves. It has the optimal process flow sheet can be read directly. In addi- been used to introduce undergraduate and graduate students tion, once the universal region of attainable concentrations to complex reactor network optimization in a short time, with is known, applying new objective functions on the reactor little to no additional calculations required. system is effortless. No further calculations are required, and the optimal values can be read directly from the graph. BACKGROUND Finally, this general tool can be applied to any problem whose basic operation can be The generic approach to complex reac- The AR analysis method broken down into fundamental processes, tor design and optimization is to build on has been presented in including isothermal and nonisothermal reac- previous experience and knowledge to test [5, 12] [13] undergraduate courses, to tor network synthesis, optimal control, a new reactor configuration against the combined reaction and separation,[14-16] com- previous champion that yielded the best industrial audiences, and in [17, 18] [8] minution, and others. Process synthesis result. If a new maximum is achieved, the masters courses at the Uni- and design usefulness are aided greatly by reactor configuration and process settings versity of the Witwatersrand this alternative approach. are kept. If not, the previous solution is in South Africa, as well as, retained and the entire process is repeated. The AR analysis method has been pre- The biggest issue with this trial and error more recently, as an alterna- sented in undergraduate courses, to indus- approach is the time it takes. Also, there tive to traditional complex trial audiences, and in master’s courses is no way to know if all possible com- reactor design in a graduate at the University of the Witwatersrand in binations of operational parameters and reaction engineering course South Africa, as well as, more recently, as an alternative to traditional complex reactor reactors have been tested. In addition, at Rutgers University. calculations are normally exhausting and design in a graduate reaction engineering general computational techniques are dif- course at Rutgers University. The overall ficult to develop due to the specificity of response from the audiences has been fa- each arrangement. Over time, this mechanism has evolved vorable, and it is the intention of the authors to discuss the into a set of design heuristics that dominate decision processes benefits this approach offers to the field of reaction engineer- throughout industry.[9] ing. To aid with teaching/learning, a detailed attainable region [10] Web site has been set up and the address is given at the end Achenie and Biegler model a reactor superstructure of this article. using a mixed integer nonlinear programming (MINLP), which transforms the task into an optimal control problem. In this paper we will first introduce a moderately chal- Again, this approach is useful if the optimal reactor network lenging reaction engineering problem. Next, the AR analy- is known, but it does not address the issue of choosing the sis will be illustrated by solving the presented problem. optimal reactor network. Finally, the teaching strategy adopted by both institutions will be presented. Horn[11] defines the AR as the region in the stoichiometric subspace that could be reached by any possible reactor sys- PROBLEM STATEMENT tem. Furthermore, if any point in this subspace were used as the feed to another system of reactors, the output from this The following liquid phase, constant density, isothermal system would also exist within the same AR. This framework reaction network will be used to illustrate the AR approach. approaches reactor design and optimization in a simpler, k1 AB k3 →C ()1 easier, and more robust manner. It offers a systematic a priori ↔ k2 approach to determining the ideal reactor configuration based 2ADk4 → ()2 upon identifying all possible output concentrations from all Vol. 41, No. 4, Fall 2007 259 The initial characteristics of the reaction network are shown a feed of pure A. These reaction kinetics were used because in Table 1. The end goal of this exercise is to determine the they represent a reaction network without an intuitively obvi- reactor configuration that maximizes the production of B for ous optimal structure. A PFR will maximize the amount of B produced in the first reaction, but a CSTR will minimize the TABLE 1 amount of A consumed in the second reaction. Reaction Network Constants and Initial Concentrations 0 0 0 0 CA CB CC CD SOLUTION 1 kmol m-3 0 kmol m-3 0 kmol m-3 0 kmol m-3 Determining the candidate attainable region for this reaction scheme involves the completion of the following simplified k1 k2 k3 k4 steps: selecting the fundamental processes, choosing the state 0.01 s-1 5 s-1 10 s-1 100 m3 Figure 1 kmol-1 s-1 variables, defining and drawing the process vectors, construct- ing the region, interpreting the boundary as the process flow (a) 1.2 12 sheet, and finding the optimum. I. Choose the Fundamental Processes ) 1 10 ) 3 3 0.8 8 In this particular example, the fundamental processes are 0.6 6 reaction and mixing.