A mechanistic derivation of the Monod bioreaction equation for a limiting nutrient

We present a quasi-steady state mechanistic derivation of the Monod bioreaction equation based upon a conceptual model involving aqueous phase diffusive transport of substrate towards a spherical microbe; transport of the substrate across its surface membrane; and reaction depleting the substrate within the microbe. The resulting Monod coefficients K S and μ max are dependent upon substrate-species pairs and the mass transfer properties of the system. Two substrate transport scenarios are investigated: (1) a constant rate model that is a function of a constant flux across the surface of the microbe; and (2) a linear rate model that is the product of a constant transport velocity and the concentration of substrate in contact with the surface of the microbe. The model is verified and parameterized using benzene, toluene, and phenol depletion and biomass growth data obtained from Reardon et al. (Biotechnol Bioeng: 385–400, 2000). Calibration results indicate a normalized surface to bulk concentration ratio of nearly unity in all simulations for benzene, toluene, and phenol when paired with P. putida F1 , implying that the process is not aqueous phase diffusion limited.