Theoretical analysis of intrinsic reaction kinetics and the behavior of immobilized enzymes system for steady-state conditions

• Analytical expressions of concentrations of substrate and product are presented.
• Presented the general analytical expression of effectiveness factor.
• Analytical results are compared with the numerical results and are good in agreement.
• Analytical expressions are very much useful to design the immobilized enzyme reactor.
• It is also a valuable tool to optimize the radius of the catalytic particle.

Mathematical modeling of immobilized enzymes under different kinetics mechanism viz. simple Michaelis–Menten, uncompetitive substrate inhibition, total competitive product inhibition, total non-competitive product inhibition and reversible Michaelis–Menten reaction are discussed. These five kinetic models are based on reaction diffusion equations containing non-linear terms related to Michaelis–Menten kinetics of the enzymatic reaction. Modified Adomian decomposition method is employed to derive the general analytical expressions of substrate and product concentration for all these five mechanisms for all possible values of the parameters ΦS (Thiele modulus for substrate), ΦP (Thiele modulus for product) and α (dimensionless inhibition degree). Also we have presented the general analytical expressions for the mean integrated effectiveness factor for all values of parameters. Analytical results are compared with the numerical results and also with the limiting case results, which are found to be good in agreement.