A coupled compressible two-phase flow with the biological dynamics modeling the anaerobic biodegradation process of waste in a landfill

Abstract

In this article, we present and study a new coupled model combining the biological and the mechanical aspects describing respectively the process of the biogas production and the compressible two-phase leachate-biogas flow during the anaerobic biodegradation of organic matters in a landfill, which is considered a reactive porous medium. The model obtained is governed by a reaction-diffusion system for the bacterial activity coupled with a compressible two-phase flow system of a non-homogeneous porous medium. We carry out the analysis and the numerical approximation of the model within a variational framework. We propose a full discrete system based on a second-order BDF-time scheme and P1-conforming finite element and we derive an efficient algorithm for the coupled system. We perform some numerical simulations in 2D and 3D examples in agreement with the theoretical analysis.