Numerical simulation of interfacial coupling phenomena in two-phase flow through porous media

This paper provides details of the numerical simulation process for the interfacial coupling effect in multiphase flow through porous media. It covers the theoretical background, description of mathematical formulations, basic assumptions in the models, normalization and transformation between Lagrangian and Eulerian formulations, specification of boundary conditions, discretization and grid system, and solution methods. The main advantage of the Lagrangian formalism is that it eliminates the need for space discretization thereby reducing computation time and error. The numerical simulation process was codified into a stand-alone numerical simulator using the JavaTM Programming language. Numerical examples obtained from the numerical simulator are presented to show the applicability of the computational technique and to investigate the effects of interfacial coupling and hydrodynamic effects. Numerical results show that interfacial coupling (viscous and capillary) and hydrodynamic effects are insignificant in two-phase, cocurrent, horizontal, porous media flow. Sensitivity analyses studies carried out with the simulator show that if the viscous factor in the parameter that control the amount of viscous coupling is taken as the theoretically established value of 2 or below, then the viscous coupling effect is insignificant. Otherwise, the viscous coupling effect would have a greater effect on the physics of flow and might lead to unreasonable results.