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At least in the last 10 years, considerable effort has been given to studying the dynamics of fluid flow in porous media. The phenomena is widely applicable in many areas of science and engineering. In many cases, the effect of capillary pressure and discontinuities in the two-phase flow dynamics is not fully clear, especially in petroleum reservoirs. In this paper, we introduce a new method based on the Chebyshev wavelets collocation method and the so-called operational matrices of integration. The method was implemented specifically for an oil–water-phase flow in heterogeneous reservoir using different capillary pressure treatments. Convergence and accuracy of this method were established and used to simulate the partial differential equations governing the two-phase model. The method incorporates the various conditions of the complex governing equations as a single system. The system is subsequently reduced into a simple set of algebraic equations making the problem easier to solve. Numerical results showed that the method is able to account for the expected discontinuities occurring in the flow process. It was also found that these discontinuities or jumps in the two-phase flow are caused by the capillary pressure as expected physically.

Chebyshev wavelets collocation method for simulating a two-phase flow of immiscible fluids in a reservoir with different capillary effects