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

Dynamic mathematical models of liquid membrane-immobilized multienzyme reac tion systems involve a large number of algebraic, ordinary and nonlinear pa rtial differential equations with different types of boundary conditions. S olutions of such model equations are often difficult and stand in the way o f realistic modeling efforts in this field. In the present study, attempt h as been made to numerically solve such model equations for a liquid membran e-immobilized sequential bienzymatic reaction system through development of a software (MEMBSOL). In the solution process, partial differential equati ons have been converted into ordinary differential equations by using a fin ite difference technique in which the spatial derivatives have been discret ized while leaving the temporal derivatives unconverted. Through mathematic al manipulations, use of fictitious points at the boundaries has been elimi nated thereby making the solution-approach a general-purpose one. To integr ate the differential equations, Runge-Kutta-Fehlberg method has been applie d. 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.