Concentration driven phase transitions in multiphase porous media with application to methane oxidation in landfill cover layers

• Published in: Zeitschrift für angewandte Mathematik und Mechanik Vol. 94; no. 7-8; pp. 609 - 622
• Main Authors: Ricken, T., Sindern, A., Bluhm, J., Widmann, R., Denecke, M., Gehrke, T., Schmidt, T.C.
• Format: Journal Article
• Language: English
• Published: Berlin WILEY-VCH Verlag 01-07-2014; WILEY‐VCH Verlag; Wiley Subscription Services, Inc
• Subjects: Bacteria; Constituents; constitutive modeling; coupled problem; Finite element analysis; Finite element method; Gas phases; homogenization; Landfill; Landfills; Mathematical analysis; Mathematical models; Methane; methane oxidation layer; mixture theory; multicomponent; multiphase; phase transition; theory of porous media
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.201200198

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.
This study focusses on a formulation within the Theory of Porous Media for continuum multicomponent modelling 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, oxygen, and carbon dioxide. A thermodynamically consistent constitutive framework is derived by evaluating the entropy inequality, which results in constitutive relations for the stress and pressure states, interaction forces, and mass exchanges. The final set of variables for the derived finite element calculations consists of the displacement of the solid matrix, the partial hydrostatic gas pressure and osmotic concentration pressures. The model is implemented in the finite element code FEAP [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 by representative numerical examples.