This study focuses on a formulation within the theory of porus media for continuum multicomponent modeling of bacterial driven methane oxidation in a porous landfill cover layer which consists of a porous solid matrix (soil and bacteria) saturated by a liquid (water) and gas phase. The solid, liquid, and gas phases are considered as immiscible constituents occupying spatially their individual volume fraction. However, the gas phase is composed of three components, namely methane (CH4), oxygen (O2), and carbon dioxide (CO2). A thermodynamically consistent constitutive framework is derived by evaluating the entropy inequality on the basis of Coleman and Noll [8], which results in constitutive relations for the constituent stress and pressure states, interaction forces, and mass exchanges. For the final set of process variables of the derived finite element calculation concept we consider the displacement of the solid matrix, the partial hydrostatic gas pressure and osmotic concentration pressures. For simplicity, we assume a constant water pressure and isothermal conditions. The theoretical formulations are implemented in the finite element code FEAP by Taylor [29]. A new set of experimental batch tests has been created that considers the model parameter dependencies on the process variables; these tests are used to evaluate the nonlinear model parameter set. After presenting the framework developed for the finite element calculation concept, including the representation of the governing weak formulations, we examine representative numerical examples.

Methane (CH4), which has a 25 times higher global warming potential than carbon dioxide (CO2), can be oxidated by methanotrophic bacteria into carbon dioxide and water. The biological oxidation of methane can be considered in the passive aftercare phase of landfills in order to reduce climate‐damaging methane emissions. Methanotrophic bacteria are situated within the landfill cover layer and convert the harmful methane emissions arising from the degradation of organic waste to the less harmful carbon dioxide. Hence, the passive aftercare of landfills in terms of methane oxidation layers is an efficient method to reduce contributions to the greenhouse effect. To model the coupled processes during phase transition from methane to carbon dioxide, the well‐known Theory of Porous Media (TPM) combined with the Mixture Theory has been used in order to develop a multi‐component Finite Element calculation concept, see [1, 3]. The thermodynamic consistent model analyzes the relevant gas productions of methane, carbon dioxide and oxygen. The model also accounts for the driving phenomena of production, diffusion and advection. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Landfill gas is composed of methane (CH 4 ) and (CO 2 ) at a ratio of about (60% -40%), whereby the impact of methane on the greenhouse effect is about 25 times higher than that of carbon dioxide. Bacterial methane oxidation, taking place in the landfill cover layer, helps to reduce the climate active emissions from landfill sites. This contribution presents a theoretical and numerical approach to model the coupled processes of bacterial methane oxidation. An isothermal biphasic model based on the Theory of Porous Media (TPM) and Mixture Theory is introduced as well as the coupled finite element (FE) calculation concept.

Worldwide, the most common sites of waste disposal are landfills. After solid waste is deposited in a landfill, physical, chemical, and biological processes ensue and modify the waste. Due to these reactions, landfill gas is produced inside the landfill body and effuses into the atmosphere at the outer layer. These processes create environmentally harmful landfill pollutants (methane (CH4)) and carbon dioxide (CO2)). The impact of methane on the greenhouse effect is about 20 times higher than that of carbon dioxide.WorldwideIn order to estimate potential environmental risk of the landfill, a second important phenomenon has to be taken into account: the bacterial methane conversion in the porous cover layer which significantly reduces the amount of methane emitted into the atmosphere. Subsequently, the metabolism of different methanotrophic bacteria converts methane and oxygen into carbon dioxide, water, and biomass.WorldwideTo model this highly complex and coupled problem we used the well‐known theory of porous media to obtain a thermodynamically consistent description which in turn leads to a fully‐coupled finite element (FE) calculation concept. The theoretical and numerical framework will be presented in order to describe the coupled processes occurring during the phase transition by bacterial activity in the methane oxidation layer. The model analyzes the relevant gas concentrations of methane, carbon dioxide, oxygen, and nitrogen as well as the driving phenomena of production, diffusion, and convection. Based on a model predicting gas production in landfills, see [1], a multiphase continuum approach for landfill cover layers is presented. In order to validate the model, we compare numerical simulations with experimental data. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)