Abstract
This paper presents a numerical method to model the coupled thermo-hydro-mechanical (THM) processes in porous media saturated with two immiscible fluids. The basic equations of the system have been derived based on the averaging theory, considering skeleton deformation, two-phase fluid flow, and heat transport. As applying the standard Galerkin finite element method (GFEM) to solve this system of partial differential equations may lead to oscillatory results for saturation and temperature profiles, a hybrid numerical solution is proposed. In this frame, the GFEM is combined with a control volume based finite element (CVFE) approach, and a streamline upwind control volume finite element (SUCVFE) scheme, respectively for the mechanical, hydraulic and thermal part of the system. The CVFEM has been adopted to provide a smooth saturation profile by ensuring local mass conservation, while the streamline upwind scheme has been applied to remove the spurious temperature oscillation by adding stabilizing terms to the thermal part of the system. The CVFE and SUCVFE formulations have been derived using a similar approach as the standard FE practice in the context of weighted residual technique, but using different weighting functions. This will significantly facilitate the implementation of the proposed model in existing FE codes. Accuracy and efficiency of the proposed method have been justified using several numerical examples and comparing the results with available analytical or numerical solutions.
Highlights
Numerical simulation of coupled THM phenomena in geological porous media is of great interest in many engineering disciplines
The control volume based finite element (CVFE) and streamline upwind control volume finite element (SUCVFE) formulations have been derived using a similar approach as the standard FE practice in the context of weighted residual technique, but using different weighting functions
In order to avoid the spurious oscillation of the temperature field in a convection-dominated problem, the weighting function of the CVFEM is modified in a way similar to the Petrov-Galerkin technique (Zienkiewicz et al, 2005): W = W + W* = W + √̅1̅θ5̅̅h‖ev*‖v*T (∇W)
Summary
Numerical simulation of coupled THM phenomena in geological porous media is of great interest in many engineering disciplines. The basic governing equations of the above-mentioned systems, i.e. the mo mentum, mass and energy conservation laws, are derived using either the continuum theory of mixture (Nunziato and Walsh, 1980; Passman, 1977; Wei and Muraleetharan, 2002), local volume averaging theory (Hassanizadeh and Gray, 1979a, 1979b; Lewis and Schrefler, 1998), or a phenomenological extension of Biot’s consolidation theory (McTigue, 1986; Pao et al, 2001; Schiffman, 1971) These approaches are generally suitable for describing coupled THM phenomena in porous media, the formers may introduce a more systematic and flexible framework for further development. The need for the so-called dual mesh system, which is normally necessary in hybrid models, will be obviated In this context, the control volumes are automatically constructed around each node using appropriate weighting functions, and provides a fully conservative solution
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