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

Zakaria Belhachmi (1, 2) , Zoubida Mghazli (3) , Salih Ouchtout (1, 3)

1 IRIMAS - Institut de Recherche en Informatique Mathématiques Automatique Signal - IRIMAS - UR 7499
2 UNISTRA - Université de Strasbourg
3 EIMA - Equipe d'Ingénierie MAthématique [Kenitra]

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 maters in a landfill, considered as a reactive porous medium. The model obtained is governed by a reactiondiffusion 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 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.

Mots clés: Anaerobic biodegradation; Compressible two-phase flow; Biogas production; Coupled model; Finite element method

Domaines: Mathématiques [math]

Zakaria Belhachmi, Zoubida Mghazli, Salih Ouchtout. A coupled compressible two-phase flow with the biological dynamic modelling the anaerobic biodegradation process of waste in a landfill. 2021. ⟨hal-03409786⟩