Two-substrates packed-bed bioreactors: inhibition of enzyme and competitive binding of substrate and product to a ligand

An analytical model is developed to describe the performance of a packed-bed immobilized enzyme reactor in which parallel processes take place. In particular, two-substrate reaction, inhibition of the enzyme by one of the reaction products, and binding of one substrate and/or one product to an added ligand are taken into account. In addition, substrates and product diffusion into the porous catalyst are also considered. Using this model, numerical simulations were performed. The results point to the fact that, when all the above processes occur concomitantly, a variety of performance characteristics can be obtained, depending on the particular values of the related parameters. Moreover, under certain conditions, the reactor performance can be improved by controlled addition of ligand.List of Symbols A total concentration of ligand - C _1,i concentration of Substrate-1 in the pores of stage i - C _2,i concentration of Substrate-2 in its free form in the pores of stage i - _2,i concentration of the Substrate-2-Ligand Complex in the pores of stage i - total concentration of Substrate-2 in the pores of stage i - _i concentration of the Product-Ligand Complex in the pores of stage i - concentration of the free Product in the pores of stage i - total concentration of the Product in the pores of stage i - internal (pore) diffusion coefficient for the Substrate-Ligand Complex - D ₁ internal (pore) diffusion coefficient of Substrate-1 - D ₂ internal (pore) diffusion coefficient of Substrate-2 - effective (pore) diffusion coefficient for Substrate-2 - internal (pore) diffusion coefficient for the Product - internal (pore) diffusion coefficient for the Product-Ligand Complex - effective (pore) diffusion coefficient for the Product - K thermodynamic equilibrium constant for binding Substrate-2 to Ligand - K _m,1,K _m,2 Michaelis constants for Substrates-1 and 2, respectively - effective Michaelis constant for Substrate-2 - K _p thermodynamic equilibrium constant for binding the reaction Product to Ligand - effective equilibrium constant for binding Substrate-2 to Ligand - effective equilibrium constant for binding the reaction Product to Ligand. - K _b inhibition constant - K _q inhibition constant - effective inhibition constant - effective inhibition constant - k _a, k _d association and dissociation rate constants for Substrate-2 — Ligand complex - association and dissociation constants for Product —Ligand complex - n total number of elementary stages in the reactor - Q volumetric flow rate throughout the reactor - R _j,i reaction rate of Substrate-j in stage i, in terms of volumetric units - S _1,0 concentration of Substrate-1 in the reactor feed - total concentration of Substrate-2 in the reactor feed - S _1,i–1,S _1,i concentration of Substrate-1 in the bulk phase leaving stages i–1 and i, respectively - S _2,i concentration of Substrate-2 in its free form, in the bulk phase leaving stage i - _2,i–1, _2,i concentration of Substrate-2 in the bulk phase leaving stage i–1 and i, respectively - total concentration of Substrate-2 in the bulk phase leaving stages i–1 and i, respectively - _i concentration of the Product-Ligand Complex in the bulk phase of stage i - concentration of free Product in the bulk phase of stage i - total concentration of Product in the bulk phase of stage i - V total volume of the reactor - V _m maximal reaction rate in terms of volumetric units - y axial coordinate of the pores - y ₀ depth of the pores Greek Symbols ₁ dimensionless parameter - dimensionless parameter - dimensionless parameter - ₁ dimensionless parameter - dimensionless parameter - _1,i dimensionless concentration of Substrate-1 in pores of stage i - dimensionless total concentration of Substrate-2 (in both free and bound form) in pores of stage i - dimensionless total concentration of the reaction product in the pores of stage i - ₁ dimensionless parameter - dimensionless parameter - dimensionless parameter - dimensionless parameter - dimensionless parameter - dimensionless position along the pore - volumetric packing density of catalytic particles (dimensionless) - porosity of the catalytic particles (dimensionless) - _1,i dimensionless concentration of Substrate-1 in the bulk phase of stage i - dimensionless total concentration of Substrate-2 (in both free and bound form) in the bulk phase of stage i