Theoretical analysis of inhibition effect on steady states of enzymatic membrane reactor with substrate and product retention for reaction producing weak acid

The aim of this study is to formulate a model of enzymatic membrane reactor (EMR), i.e., a continuous, stirred tank bioreactor with full enzyme recycle, for a reaction producing a weak acid, and to explore the effect of substrate and product inhibition of different mechanisms coupled with transport properties of the membrane on the static behaviour of the system. The inhibition of an enzyme by a substrate leads to the non-monotonicity of reaction rate expression with respect to the substrate concentration. If a product of enzymatic reaction, taking place in the EMR, influences the pH of a reaction mixture this is also the factor causing the non-monotonicity of the substrate and product dependent reaction rate. The character of these dependencies affects substantially the structure of the steady states of the reactor. The bifurcation diagrams, shown in the work, are of different characters depending on the bifurcation parameter. It has been found, that bifurcation diagrams for competitive and uncompetitive inhibition by a substrate differ in the number and position of bifurcation points. Steady states of multiplicity five have been localised in case of uncompetitive inhibition by the substrate at high affinity of the enzyme to this substrate. Retention of reagents, related to transport properties of a membrane, influences significantly the effectiveness of a process. A specially written software in Delphi™ has been used for the calculations.