Comparison of numerical formulations for Two-phase flow in porous media

Numerical approximation based on different forms of the governing partial differential equation can lead to significantly different results for two-phase flow in porous media. Selecting the proper primary variables is a critical step in efficiently modeling the highly nonlinear problem of multiphase subsurface flow. A comparison of various forms of numerical approximations for two-phase flow equations is performed in this work. Three forms of equations including the pressure-based, mixed pressure-saturation and modified pressure-saturation are examined. Each of these three highly nonlinear formulations is approximated using finite difference method and is linearized using both Picard and Newton-Raphson linearization approaches. Model simulations for several test cases demonstrate that pressure based form provides better results compared to the pressure-saturation approach in terms of CPU_time and the number of iterations. The modification of pressure-saturation approach improves accuracy of the results. Also it is shown that the Newton-Raphson linearization approach performed better in comparison to the Picard iteration linearization approach with the exception for in the pressure-saturation form.