Reaction Engineering Education in the Digital Age
H. Scott Fogler
The Ame & Catherine Vennema Professor of Chemical Engineering and the Arthur F. Thurnau Professor, The University of Michigan, Ann Arbor
With the advent of COMSOL Multiphysics and other software packages we are now able to take chemical reaction engineering (CRE) to new levels of analysis in our graduate and undergraduate courses as well as for the practicing engineer. We can use COMSOL to solve the partial differential equations that arise in developing models for a variety of reaction engineering problems / systems.
The applications range from physiologically- based-pharmacokinetic models to manufacturing in the microelectronics industry to novel reactors, such as fed-membrane reactors, micro-reactors, and aerosol reactors. For example, there has recently been a major focus on the use of micro-reactors because of their high surface areas for excellent temperature control and safety. Because of the small size of these micro channels, the flow is most always laminar and therefore the plug flow assumption commonly used in reactor modeling cannot be used. Consequently, for micro-reactors, as well as with many full-scale industrial tubular reactors, we must consider both axial and radial gradients, which requires the solution of the coupled partial differential equations (PDEs) for energy, mass and momentum.
Previously an analysis of such reaction systems was not usually carried out in graduate and undergraduate courses because of the inordinate amount of time required to write and debug large computer programs to obtain a numerical solution. However, we have now the capability to develop and easily solve the model equations in both these courses because of development of software tools such as COMSOL Multiphysics to solve PDEs.
In order to facilitate the student´s ability to solve realistic digital age problems of this complexity, COMSOL has developed a COMSOL ECRE version specifically for the 4th edition of my textbook The Elements of Chemical Reaction Engineering (ISBN/0130473944). It is the most used text in the area of chemical reaction engineering in the world.
Figure 1: Exothermic reaction in a laminar flow reactor with heat exchange.
The main thrusts of the 4th edition of The Elements of Chemical Reaction Engineering are to present the fundamentals of CRE in a clear and logical manner, to apply principles to the emerging areas in chemical reaction engineering, and to involve students in solutions to Digital Age [1] problems using state-of-the-art software. With the development of Polymath and COMSOL Multiphysics, we can now have the students focus their time and energy on analyzing the solution to complex reaction engineering problems. The special COMSOL Multiphysics CD-ROM includes six models divided into two groups each with associated on-line documentation: Radial Effects in Tubular Reactors, and Exploring Dispersion with the Dankwert´s Boundary Conditions.
The output from one of the COMSOL Multiphysics tubular reactor modules is shown in Figure 1 in terms of the conversion profiles for an exothermic reaction taking place in a tubular reactor with a heat exchanger. Application of the balance equations for mass and energy results in two coupled highly nonlinear PDEs which are readily solved with COMSOL Multiphysics. Because so little time was spent on programming a numerical solution, the student now has time to focus on the results and analysis. For example, one notes both a maximum and a minimum in the conversion profile near the wall of the tubular reactor. Why do these maximum and minimum points come about? What would accentuate them or cause them to disappear? By changing the parameters in the COMSOL Multiphysics program these and other questions can be readily answered. This special COMSOL ECRE module provides a perfect introduction for the student or practicing engineer to begin to use COMSOL Multiphysics in more advanced modeling.
By posing the above questions related to Figure 1 we see that this type of analysis points out another very important pedagogical enhancement that these software packages bring to CRE. These software tools can also enhance the students´ intellectual development. For example, once the base case for a problem is solved, such as that shown in Figure 1, the students can practice and develop their critical and creative thinking skills by asking “What if...” questions. Here they can use R.W. Paul´s “Six types of Socratic Questions” to probe the assumptions by changing the parameter values and immediately seeing and analyzing their results [2]. These types of problems and solutions are referred to as Living Example Problems because one can obtain multiple outcomes for the same reaction and reactor. For example, one could ask "What is the effect of decreasing the diameter of a laminar flow reactor while at the same time increasing the coolant temperature?" Questions of this type are easily answered using the special COMSOL Multiphysics CD-rom supplied with the 4th edition of The Elements of Chemical Reaction Engineering.
In addition to the COMSOL CD-ROM, the text-related ROM that accompanies the 4th edition has also been greatly expanded in order to facilitate the Felder/Solomon Inventory of Different Learning Styles [3] through interactive summary notes and computer modules. For example, the Global Learner can get an overview from the summary notes; the Sequential Learner can use the “derive” hot buttons; and the Active Learner can interact with the ICMS and the hot buttons in the Summary Notes. A new pedagogical concept is introduced in this edition through expanded emphasis on extending the example problems and using the living example problems. Here, exercises are given to explore all the example problems in the text to fully understand implications and generalizations before proceeding to work the homework problems for that chapter. For example, in the Case Study on safety, the student can use the CD-ROM to carry out a post-mortem on the nitroanaline explosion example to find out what would have happened if the cooling had failed for 5 minutes instead of 10 minutes. Significant effort has been devoted to developing example and homework problems that foster critical and creative thinking.
The greatest expansion of new material in the 4th edition is in the area of the bio-reaction engineering. New material on enzyme kinetics, cell growth, and tissue engineering has been added. There is a bio-reaction engineering homework or example problem in virtually every chapter. In addition there are side notes describing blood coagulation, DNA lab-on-a-chip, and methanol poisoning. Bio-related web modules include physiological-based-pharmaco-kinetic (PBPK) models of alcohol metabolism and venomous snake bites.
Other new material includes density functional theory, micro-reactors, side-fed-membrane reactors, advanced reactor safety screening tool (ARSST), runaway reactions, and tubular reactors with axial and radial gradients (COMSOL Multiphysics). Expanded material includes collision theory, transition state theory, molecular dynamics, and molecular chemical reaction engineering (DTF) to study rate constants. The 4th edition contains more industrial chemistry with real reactors and real reactions. It also extends the wide range of applications to which chemical reaction engineering principles can be applied (i.e., cobra bites, bioreactors, medications, ecological engineering). Most all these applications can be studied in greater depth with the software packages COMSOL Multiphysics and Polymath.
- "Teaching Critical Thinking, Creative Thinking, and Problem Solving the Digital Age," Phillips Petroleum Company Lecture, Oklahoma State University, 1997.
- Paul, R. W., Critical Thinking (Published by the Foundation for Critical Thinking, Santa Rosa, California).
- www.ncsu.edu/felder-public/ILSdir/styles.htm