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# A Fully Coupled Finite Element Model of Landfill Gas Migration in a Partially Saturated Soil

W. J. Ferguson1, B. Palananthakumar2
School of the Built Environment, Heriot-Watt University, Edinburgh, EH14 4AS, United Kingdom
Fault Analysis Group, Department of Geology, University College Dublin, Belﬁeld, Dublin 4, Ireland

Computer Modeling in Engineering & Sciences 2005, 8(3), 201-216. https://doi.org/10.3970/cmes.2005.008.201

### Abstract

Environmental and safety issues associated with landfill gas require the control of off-site migration. Mathematical modelling can assist in the understanding of the processes and mechanisms controlling gas migration from municipal waste disposal sites. This paper presents the development and application of a mathematical model that simulates landfill gas migration within a partially saturated soil. This model accounts for two-phase flow and incorporates multi-component (methane, carbon dioxide, dry air and moisture) transport in the gas and liquid phases together with concomitant heat migration. The governing system of fully coupled non-linear partial differential equations of the model have been derived from a mechanistic approach where the mass and energy conservation laws are defined for a particular phase into which Darcy's law and Fick's law are substituted. Employing the Galerkin finite element method for the spatial discretisation and a finite difference time-stepping scheme for the temporal discretisation, a fully implicit algorithm has been developed for the numerical solution of the governing equations. The model was applied to the Loscoe landfill site to estimate the landfill gas concentration in the vicinity of the gas explosion which occurred in March 1986. An assessment has also been made to determine the relative importance of the gas transport mechanisms (i.e. diffusion, convection and dissolved gas) in this case study.

### Keywords

finite element model, landfill gas migration, partially saturated soil, Loscoe landfill gas explosion, gas transport mechanism

Ferguson, W. J., Palananthakumar, B. (2005). A Fully Coupled Finite Element Model of Landfill Gas Migration in a Partially Saturated Soil. CMES-Computer Modeling in Engineering & Sciences, 8(3), 201–216.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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