Mass transport through biocatalytic membrane reactor

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 zeroorder 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 (KM >> C) and zeroorder kinetic (C >> KM), 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.

Pem = 10 0.6 0.4 0.2 0.1 0.0 −0.2 MM-kinetics −0.4 0.1 1.0 10.0 Reaction modulus, Φ, – Fig. 8. The change of the outlet mass transfer rate as a function of reaction rate at different values of membrane Peclet number applying the Michaelis–Menten (MM) reaction kinetics (δm = 100 μm, Dm = 5.4 × 10–10 m2/s, k 0 → ∞, k 0 → ∞, K / C 0 = 1, C 0 / C = 0.2). L δ M b Modeling of membrane bioreactor is now in its starting stage. Exact explicit mathematical equations in order to predict how the mass transport parameters, diffusion coefficients, convective velocity, the bioreaction rate parameters could alter the concentration distribution and the mass transfer rate in a biolayer (enzyme/microorganism membrane layer) is very important. It has been proved that the simultaneous diffusive and convective mass transfer rate can also be expressed as product of a mass transfer coefficient and the driving force, similarly to that of the diffusive mass transfer coefficient given for gas–liquid or liquid–liquid systems. Mass transfer coefficients have been defined for mass transfer without and with biochemical reactions. For the first-order and zero-order reactions, these mass transfer coefficients can be given in closed mathematical form. Applying the mass transfer equations given for single layers, the so-called overall mass transfer rate and mass transfer coefficient can be given making possible to predict the simultaneous effect of the liquid boundary layer and of the biocatalytic membrane layers, on the mass transfer rate. Acknowledgment This work was supported by the Hungarian Research Foundation under Grants OTKA 63615/2006.