Mathematical Models of Single Stage Monod Model of Landfill Degradation using Laplace Transform and Homotopy Perturbation Method

Abstract

A mathematical model to predict waste degradation and landfill gas production is discussed. The model is based on two reaction-diffusion equations containing a non-linear term related to Michaelis–Menten kinetics of the enzymatic reaction. In this paper, we present an approximate analytical solution of the non-linear differential equations that describe the diffusion coupled with a Michaelis–Menten kinetics law. Approximate analytical expressions for substrate and biomass concentrations have been derived for all values of parameter using Laplace transform method and homotopy analysis method. These results are compared with the numerical result and satisfactory is noted. The obtained results are valid for the whole solution domain.