Numerical solution of extended black-oil model incorporating capillary effects based on a high-resolution central scheme

The purpose of this paper is to present an efficient numerical method to solve the extended black-oil model's equations with considering the capillary pressure effects. The governing equations are formulated based on a global pressure concept to account for the capillary effects. The developed equations are conservative and suitable for the control volume approach. To solve the equations, an implicit pressure-explicit saturation scheme is used. The component transport equations are decomposed to a pure convection term driven by the global pressure and a pure diffusion part affected by the capillary pressures. A high-resolution central scheme is employed to discretize the convection term of the component transport equations. The results of the proposed model are compared with several semi-analytical and numerical solutions that were previously published. It is shown that the suggested model is computationally efficient and easy to be implemented for solving convection -diffusion problems. The results illustrate reasonable accuracy in comparison with the reference solutions. As a result of simplicity, low computational cost, and decent accuracy, this method is appropriate for solving complicated problems of reservoir engineering.