Thermodynamically consistent numerical method for two-phase carbonate acidizing with capillarity effects

Matrix acidizing is an effective technique to promote the porosity and permeability in carbonate formations, thereby enhancing the oil production rate. In oil-saturated reservoirs, the carbonate acidizing process could be a typical oil–water two-phase flow rather than the widely investigated single-phase flow. The existence of capillarity effects makes numerical modeling of the coupled two-phase carbonate acidizing process more complicated and challenging compared to the single-phase flow. In this paper, we first introduce the concept of free energies for reactive two-phase flow with capillarity, and then, guided by the second law of thermodynamics, we establish a thermodynamically consistent mathematical model for the coupled two-phase carbonate acidizing process, which satisfies an energy dissipation law. Due to the complexity of the physical process, the model consists of a number of strongly nonlinear and fully coupled equations. To efficiently solve this model in practice, we further propose a linearized and decoupled numerical method that is able to inherit the thermodynamical consistency, i.e., the energy dissipation law. Numerical results are also provided to show the potential applicability of the model and numerical method, especially demonstrating that capillarity between binary fluids has significant effects on the carbonate acidizing process.