(581e) Experience with Efficient Solutions of Numerical Problems in Reaction Engineering Courses

Experience in obtaining efficient solutions of problems in undergraduate and graduate reaction engineering courses using Mathcad and Matcont, a utility in Matlab, is discussed to improve understanding of fundamentals of reaction processes. The emphasis is on obtaining solutions with increased confidence and higher precision and with minimum effort by understanding what type of problem has been defined. Students are encouraged to not introduce unnecessary complications when attempting to solve a problem and solve problems using optimal effort. Example problems considered for illustration deal with solution of linear algebraic equations (kinetic parameter estimation and properties of small and large reaction schemes and metabolic networks), nonlinear algebraic equations (computations of equilibria for multiple reactions, isothermal and non-isothermal operations of well-mixed reactors with single and multiple reactions, and kinetic parameter estimation using nonlinear regression), and ordinary differential equations [ODEs] (isothermal, adiabatic, and non-adiabatic batch and steady state continuous flow tubular reactors), application of difference equations (population and system dynamics, stochastic processes), and symbolic algebra (rate expressions for catalytic reactions and characteristics of reaction networks). Illustrations involving ODEs pertain to initial value and boundary value problems. Analysis of multi-reaction networks is based on properties of atomic and stoichiometric matrices. A smart use of relations among atomic and molecular species and molecular species and reactions obviates the need for solving conservation equations for all species in the reaction network, which typically are systems of nonlinear algebraic equations and nonlinear ordinary and partial differential equations. Any independent reactions missing in the reaction network are identified in a systematic fashion. Reduced order reactor models for large reaction networks can be obtained by applying pseudo-steady state hypothesis for highly reactive species, such as free radicals and various forms of catalytically active sites, an approach also useful in flux balance analysis in networks of reactions in living cell cultures (metabolic engineering), extending to genome-scale metabolic networks. Symbolic algebra is very useful in this effort. Mathcad is interactive, with user-friendly graphics capabilities. Students are encouraged to display results using graphics for improved learning and understanding. The capabilities of Mathcad are of significant benefit in accelerating the learning and strengthening the fundamental knowledge base. The nonlinear reaction kinetics can lead to steady state multiplicity, single period and multi-period cyclic steady states, and chaotic attractors (nonlinear phenomena). The pathological behavior of reactors varies with variation in system parameters owing to these nonlinearities, systematic investigation of which can be facilitated by developing parameter continuation methods. This is greatly facilitated by using Matcont, a Matlab utility. Specific illustrations for nonlinear phenomena are provided using symbolic and numerical computations carried out using Mathcad and Matcont.