A one-field fluid/meso-structure coupling approach for multiscale transport in heterogeneous porous media

Modeling transport phenomena within heterogeneous porous media poses considerable challenges, particularly on account of the complexity of the involved geometries combined with nonlinear transport interactions. In the present study, a novel one-field modeling approach for multiscale fluid-solid interactions is proposed that does not need any a priori information on permeability. This approach implicitly considers the existence of multiscale structures through a penalization function that encompasses merely one single effective parameter. The definition, determination, as well as the response of the effective parameter to influencing factors are elaborated in detail. It is demonstrated that this approach is effective in representing properly the heterogeneity of solids. The method has been successfully applied to both nonlinear porous media flows and Darcian transport problems, exhibiting comparable accuracy but substantial computational savings as opposed to pore-scale simulations. It leads to more accurate interphase mass transfer predictions and lower computational cost in comparison with the Darcy-Brinkmann-Stokes approach. Overall, this method appears to be highly effective in forecasting realistic, industrial-scale porous media transport problems.