Optimal Design of a Series of GSTR's Performing Reversible Reactions Catalyzed by Soluble Enzymes: A Theoretical Study

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Abstract
The condition for the minimum overall reactor volume of a given number of CSTR's in series is theoretically determined for a reversible, single reactant-single product (Uni-Uni) enzyme catalyzed reaction. The reactor network is assumed to operate in steady-state, isothermal conditions with a single phase and a constant activity of biocatalyst. The method is based on a mathematical analysis of the discrete substrate concentration profile along the CSTR's assuming complete micromixing. The algebraic equations describing the critical loci are obtained for the general case, the mathematical proof that these equations define a minimum is presented, and an exact solution arising from an asymptotic situation is found. An approximate analytical method of optimization based on the aforementioned critical behavior is reported and its validity and usefulness discussed. The formulae introduced can be used in more general situations as tools for getting the approximate range where the optimal overall volume of the series of CSTR's lies. Hence, the reasoning developed is important for the preliminary CSTR design and relevant in the initial steps of the more involved methods of numerical optimization. Finally, the enzymatic conversion of fumarate to L-malate is examined as a model system in order to assess the usefulness and applicability of the analysis developed.