A numerical solution to enzyme emulsion liquid membrane reactor model for sequential bienzymatic reaction

Abstract

Dynamic mathematical models of liquid membrane-immobilized multienzyme reaction systems involve a large number of algebraic, ordinary and nonlinear partial differential equations with different types of boundary conditions. Solutions of such model equations are often difficult and stand in the way of realistic modeling efforts in this field. In the present study, attempt has been made to numerically solve such model equations for a liquid membrane-immobilized sequential bienzymatic reaction system through development of a software (MEMBSOL). In the solution process, partial differential equations have been converted into ordinary differential equations by using a finite difference technique in which the spatial derivatives have been discretized while leaving the temporal derivatives unconverted. Through mathematical manipulations, use of fictitious points at the boundaries has been eliminated thereby making the solution-approach a general-purpose one.

To integrate the differential equations, Runge-Kutta-Fehlberg method has been applied. An automatic step-size adjustment mechanism has been incorporated in the integration process to produce results with a reasonably desired level of accuracy. In the present computations, numerical solutions with 0.1 percent relative error have been obtained.