Numerical modeling of unsaturated flow in porous media using a thermodynamical approach
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Abstract
The Richards equation has been widely used to describe unsaturated flow in porous media, but its thermodynamical consistency has been scarcely investigated. In this paper, a thermodynamically consistent formulation of Richards equation is established on the basis of the free energy concept and the second law of thermodynamics. The capillary effect is described by an interfacial free energy and its corresponding chemical potential. The formulation takes the water saturation as the primary variable as well as chemical potential gradient as the primary driving force. An appealing feature is that the formulation follows an energy dissipation law, which implies the consistency to the second law of thermodynamics. Furthermore, a linearized and energy stable time discretized method is proposed for the model. Numerical results confirms the thermodynamical consistency of the formulation.
Document Type: Original article
Cited as: Kou, J., Wang, X. Numerical modeling of unsaturated flow in porous media using a thermodynamical approach. Capillarity, 2024, 11(3): 63-69. https://doi.org/10.46690/capi.2024.06.01
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