Abstract
The Monod equation has been extensively used for modeling microbial growth, but has no mechanistic basis and its derivation is purely empirical. In this work an approach was developed for deriving the Monod equation based on a simple kinetics scheme. The microbial growth process considered involved two consecutive steps, i.e., (i) the formation of a substrate-cell “complex”, and (ii) the metabolism of the substrate for cell reproduction. By departing from the law of mass action, the approach uses a singular perturbation method for derivation of the differential equations governing the microbial growth dynamics. Within this context, a Monod equation corrected by a quadratic term induced by auto-catalyst effects was obtained. The proposed model was validated with experimental data reported in the literature for the degradation of benzene, phenol and toluene by P. putida.
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