Mathematical models have been developed to calculate the mass transfer rates through catalytic membrane layer and through the concentration boundary layer by means of explicit, closed expressions for first-order and zero-order bioreactions as well as even in the case of the nonlinear Michaelis-Menten reaction kinetics and/or in the case of variable mass transport parameters as diffusion coefficient, convective velocity. Some typical examples, applying the Michaelis-Menten kinetics and its limiting cases, namely the first-order kinetic (K-M >> C) and zero-order kinetic (C >> K-M), are shown regarding the concentration distribution and the mass transfer rates as a function of the reaction modulus or of the Peclet numbers of the boundary layer and/or membrane layer. It has been shown that the mass transport parameters and the biochemical reaction rate can essentially alter the mass transfer rates and that significant differences of the results can be obtained by the three different reaction orders.