Orateur : Mustapha El Ossmani
Établissement : Université Moulay Ismail de Meknes (Maroc)
Dates : 2025-07-09 – 2025-07-09
Heures : 14:00 – 14:00
Lieu : Salle 0-3
Résumé :
This talk is concerned with a numerical method for the modeling of immiscible two-phase flows with temperature variations in heterogeneous porous media. Both compressible and incompressible models are used, incorporating capillary and gravity effects. The mathematical models lead to nonlinear, degenerate parabolic systems involving mass and energy balance equations. Depending on the compressibility of the fluids, the primary unknowns include phase saturations, temperature, and either gas pressure or global pressure in the fractional flow formulation.
Our approach is based on a fully coupled, fully implicit time integration strategy using a first-order implicit Euler scheme. For spatial discretization, we use either a cell-centered two-point flow approximation (TPFA) or a vertex-centered control volume finite element (CVFE) method, depending on the scenario, ensuring accurate resolution of diffusion terms and treatment of anisotropic permeability tensors taking into account the compressibility or not of the non-wetting phase. Convective terms are discretized using upwind schemes.
Under suitable physical assumptions, we prove a discrete maximum principle for saturation and temperature, establish a priori estimates, and demonstrate the well-posedness of the discrete problems. Using compactness arguments, we show convergence of the numerical schemes toward weak solutions of the continuous models.
The algorithms have been implemented in the open-source framework DuMuX. Numerical simulations, including CO₂ injection in 2D and 3D heterogeneous aquifers, validate the convergence, effectiveness, and robustness of the proposed methods. The results support the theoretical analysis and illustrate the capability of the schemes to handle realistic and complex reservoir conditions.