A diffuse interface model for low solubility binary flows in porous media

Dissolution-driven convection of low solubility fluids separated by a free interface in a porous medium is analyzed via two-dimensional numerical simulations and scaling considerations. Towards this end, we employ a low solubility Darcy-Cahn-Hilliard model with a Helmholtz free energy. The momentum equations are solved in the stream function-vorticity formulation with a pseudospectral method, so that continuity is automatically satisfied, while the diffusion equation is integrated in time by an explicit Runge-Kutta procedure, combined with high order compact finite differences. We validate the simulation approach by comparing the growth rate of the standard deviation of the surface location with experimental measurements for a CO₂-water system in a Hele-Shaw cell. The numerical results for the evolving interfacial shape in density-driven convection flow of low solubility fluids agree significantly better with experimental observations than corresponding fully soluble results. The temporal evolution of the interfacial plumes is accurately captured, and distinct stages with different plume features are identified. The differences in plume features and solute flux of CO₂ between low solubility and fully soluble fluids are discussed, and it is found that the low solubility simulation approach offers clear advantages for the investigation of CO₂-dynamics in porous rock.