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

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.

anaerobic biodegradation
compressible two-phase flow
biogas production
coupled model
метод скінченних елементів
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