Strategy for the simulation of batch reactors when the enzyme-catalyzed reaction is accompanied by enzyme deactivation

The balance equations pertaining to the modelling of batch reactors performing an enzyme-catalyzed reaction in the presence of enzyme deactivation are developed. The functional form of the solution for the general situation where both the rate of the enzyme-catalyzed reaction and the rate of enzyme deactivation are dependent on the substrate concentration is obtained, as well as the condition that applies if a maximum conversion of substrate is sought. Finally, two examples of practical interest are explored to emphasize the usefulness of the analysis presented.List of Symbols C_E mol/m³ concentration of active enzyme - C_E,O mol/m³ initial concentration of active enzyme - C_S mol/m³ concentration of substrate - C_S,O mol/m³ initial concentration of substrate - C_S,min mol/m³ minimum value for the concentration of substrate - k 1/s first order rate constant associated with conversion of enzyme/substrate complex into product - k₁ 1/s first order deactivation constant of enzyme (or free enzyme) - k₂ 1/s first order deactivation constant of enzyme in enzyme/substrate complex form - K_m mol/m³ Michaelis-Menten constant - p mol/(m³s) time derivative of C_S - q mol/m³ auxiliary variable - t s time elapsed after reactor startupGreek Symbols 1/s univariate function expressing the dependence of the rate of enzyme deactivation on C_S - mol/m³ dummy variable of integration - mol/m³ dummy variable of integration - 1/s univariate function expressing the dependence of the rate of substrate depletion on C_S - m³/(mol s) derivative of with respect to C_S