Optimization of Operating Temperature for Continuous Immobilized Glucose Isomerase Reactor with Pseudo Linear Kinetics

Abstract In this work, the optimal operating temperature for the enzymatic isomerization of glucose to fructose using a continuous immobilized glucose isomerase packed bed reactor is studied. This optimization problem describing the performance of such reactor is based on reversible pseudo linear kinetics and is expressed in terms of a recycle ratio. The thermal deactivation of the enzyme as well as the substrate protection during the reactor operation is considered. The formulation of the problem is expressed in terms of maximization of the productivity of fructose. This constrained nonlinear optimization problem is solved using the disjoint policy of the calculus of variations. Accordingly, this method of solution transforms the nonlinear optimization problem into a system of two coupled nonlinear ordinary differential equations (ODEs) of the initial value type, one equation for the operating temperature profile and the other one for the enzyme activity. The ODE for the operating temperature profile is dependent on the recycle ratio, operating time period, and the reactor residence time as well as the kinetics of the reaction and enzyme deactivation. The optimal initial operating temperature is selected by solving the ODEs system by maximizing the fructose productivity. This results into an unconstrained one‐dimensional optimization problem with simple bounds on the operating temperature. Depending on the limits of the recycle ratio, which represents either a plug flow or a mixed flow reactor, it is found that the optimal temperature of operation is characterized by an increasing temperature profile. For higher residence time and low operating periods the residual enzyme activity in the mixed flow reactor is higher than that for the plug flow reactor, which in turn allows the mixed flow reactor to operate at lower temperature than that of the plug flow reactor. At long operating times and short residence time, the operating temperature profiles are almost the same for both reactors. This could be attributed to the effect of substrate protection on the enzyme stability, which is almost the same for both reactors. Improvement in the fructose productivity for both types of reactors is achieved when compared to the constant optimum temperature of operation. The improvement in the fructose productivity for the plug flow reactor is significant in comparison with the mixed flow reactor.