Mathematical modeling and numerical simulation of a bioreactor landfill using Feel++

Guillaume Dollé (1) , O Duran (2) , Nelson Feyeux (3) , Emmanuel Frénod (4) , Matteo Giacomini (5, 6, 7) , Christophe Prud'Homme (1)

1 IRMA - Institut de Recherche Mathématique Avancée
2 UNICAMP - Universidade Estadual de Campinas = University of Campinas
3 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
4 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique
5 DeFI - Shape reconstruction and identification
6 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
7 IPSA - Institut Polytechnique des Sciences Avancées

In this paper, we propose a mathematical model to describe the functioning of a bioreactor landfill, that is a waste management facility in which biodegradable waste is used to generate methane. The simulation of a bioreactor landfill is a very complex multiphysics problem in which bacteria catalyze a chemical reaction that starting from organic carbon leads to the production of methane, carbon dioxide and water. The resulting model features a heat equation coupled with a non-linear reaction equation describing the chemical phenomena under analysis and several advection and advection-diffusion equations modeling multiphase flows inside a porous environment representing the biodegradable waste. A framework for the approximation of the model is implemented using Feel++, a C++ open-source library to solve Partial Differential Equations. Some heuristic considerations on the quantitative values of the parameters in the model are discussed and preliminary numerical simulations are presented.

Mots clés: Coupled problem; Multiphysics problem; Finite Element Method; Feel++; Bioreactor landfill

Domaines: Modélisation et simulation; Analyse numérique [math.NA]; Ingénierie de l'environnement

Guillaume Dollé, O Duran, Nelson Feyeux, Emmanuel Frénod, Matteo Giacomini, et al.. Mathematical modeling and numerical simulation of a bioreactor landfill using Feel++. ESAIM: Proceedings and Surveys, 2016, CEMRACS 2015: Coupling multi-physics models involving fluids, 55, pp.83-110. ⟨10.1051/proc/201655083⟩. ⟨hal-01258643v2⟩