Upscaling and large-scale modeling of the dissolution of gypsum cavities
Résumé
The dissolution of geological formations containing gypsum can rapidly create various karstic features, and may potentially generate great risks such as subsidence and collapse. To understand the gypsum dissolution mechanism is very important to develop safety measures. In practical applications, it is not feasible to take into account all the pore-scale details at a large-scale by direct numerical modeling, therefore some sort of macro-scale modeling is necessary. In this study, we will develop a general expression of the macro-scale model for gypsum dissolution, starting from the pore-scale transport problem with boundary condition of thermodynamic equilibrium or non-linear reaction, making use of the method of volume averaging. Then, this macro-scale porous medium model will be used as a diffuse interface model (DIM) to solve for large-scale cavity dissolution examples, typical of situations leading to sinkhole formations, with the mass exchange term for Ca2+ given in the form of a first order reaction. A work-flow is proposed to choose properly the parameters in the model to reflect accurately the interface recession. Additional tests are performed to check which type of momentum balance equation should be used. It is shown that a proper choice for the mass exchange coefficient leads to satisfactory results with the macro-scale model, and that Darcy-Darcy and Darcy-Navier- Stokes formulations give almost the same cavity formation for the studied cases.
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