In porous media research, Modified Brinkman’s equation is a very recent development. It is important as it incorporates the concept of viscous effect to inertial effect in a fluid flow system when Darcy’s, Forchheimer’s and Brinkman’s terms are brought all together. So far, researchers have developed the modified equation in its two-dimensional forms; however, limited to only one phase. In reality, petroleum reservoirs experience the multiphase conditions. Therefore, the simulation of a multidimensional, multiphase scenario is mostly desired, the highlight of this paper. The paper presents the formulation of two-dimensional, transient pressure and saturation equations for oil and water phases, one equation for each phase. The difference between phases is noticeable explicitly in their respective saturation, permeability, viscosity and velocity terms. The equations are then solved numerically to generate relative permeability curves. The simultaneous solution of pressure and saturation terms in the governing equations required additional relationships: the phase saturation constraint and capillary pressure as function of saturation. Finally, the numerical results are compared and validated with the experimental results. The implication of this study is manifold. The formulated equations including the solution part for the multiphase conditions are new. The new comprehensive model will describe fluid flow in reservoirs prone to high velocity or fractures more accurately than ever described by Darcy’s or other aforementioned equations.

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