A discussion on Darcy-scale modeling of porous media dissolution in homogeneous and heterogeneous systems

The unstable dissolution of a porous medium leads to complex patterns which are difficult to model quantitatively. A Darcy-scale dissolution model is proposed involving a local non-equilibrium dissolution equation. A 3D numerical model has been developed to solve for the resulting PDEs using an operator splitting technique and high resolution TVD schemes. Results are shown for 2D and 3D configurations for both homogeneous and heterogeneous systems. The qualitative and quantitative features of the numerical results are discussed with respect to the published literature. Based on the 2D results, a first attempt is made at deriving a core-scale dissolution model based on cross-sectional averages. Several possibilities are explored including one-equation models, i.e., the core-scale medium incorporates the wormholes and the remaining porous matrix, and two-equation models for which the wormholes are treated separately. Theoretical implications are discussed based on numerical experiments.