Theoretical Analysis of Single-Stage and Multi-Stage Monod Model of Landfill Degradation Through Mathematical Modelling

Abstract

Background: Preventing substantial environmental hazards caused by noxious gases and solutes from sanitary landfills necessitates adequate regulations that require knowledge of the underlying mechanisms involved and the effect of various strategies. Mathematical models have been used to understand the development of landfill gas based on sequential biological growth and certain simple chemical and physical processes. Methods: The single-stage and multi-stage Monod landfill degradation model is based on a coupled system of rate equations containing a nonlinear term related to Michaelis- Menten kinetics of the enzymatic reaction. In this communication, an approximate analytical solution of the nonlinear differential equations is solved using a new approach of the homotopy perturbation method. Results: Substrate and biomass concentrations for the single-stage Monod landfill degradation model as well as biomass, solid, aqueous, acetic, and gases for the multi-stage model are derived for all possible values of parameters. Theoretical evaluations of the kinetic parameters such as the constant of Michaelis- Menten, mass-specific growth rate, half-saturation, and the death rate are reported. Conclusion: The accuracy of the proposed analytical expressions is validated by direct comparison with numerical simulations generated by MATLAB. A sensitivity analysis is presented to report the effect of all parameters on the governing model and the time required to reach the steady-state. The obtained analytical results are expected to contribute to a better understanding of the model and the effect of parameters and hence a better designing of experiments.