(232f) Experience with Symbolic Algebra and Smart Computing in Reaction Engineering Courses

Experience in using symbolic algebra and smart numerical computations in chemical reaction engineering and bioprocess engineering courses using Mathcad and Matlab is discussed to improve understanding of process fundamentals. Emphasis is on obtaining solutions with increased confidence and higher precision and with minimum effort by understanding what type of problem is being presented. 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 (equilibrium calculations for multiple reactions, isothermal and non-isothermal operations of well-mixed reactors with single and multiple reactions, and kinetic parameter estimation using nonlinear regression), ordinary differential equations (isothermal, adiabatic, and non-adiabatic batch and steady state continuous flow tubular reactors), and symbolic algebra (rate expressions for catalytic reactions and characteristics of reaction networks). Analysis of multi-reaction networks is based on properties of atomic and stoichiometric matrices. Atomic matrices provide information on the maximum number of and identity of independent reactions. For a given reaction network, a study of the stoichiometric matrix leads to estimation of the number of independent reactions in the given network, relations of the dependent reactions in the network to independent reactions, and understanding of the relations among rates of formation of species participating in the reaction network. A smart use of these relations obviates the need for solving conservation equations for all species in the reaction network, which typically are systems of nonlinear algebraic equations (steady state CSTR) and nonlinear ordinary and partial differential equations (steady state and transient operations of batch reactors and imperfectly mixed flow reactors). In case any independent reactions are missing in the reaction network, these can be identified from the atomic and stoichiometric matrices. Reduced order reactor models for large reaction networks can be obtained by applying pseudo-steady state hypothesis (PSSH) for highly reactive species, such as free radicals and various forms of catalytically active sites. This approach is also useful in flux balance analysis in networks of biochemical reactions in living cell cultures. 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.