The numerical simulation has been carried out for the process of the recovery of a reservoir with non-Newtonian Petroleum in terms of the stablized bi-conjugate gradient approach. To propose the governing equations for the problem on hand, the traditional Darcy law for flow in porous media is used to describe the flow behavior of water as the driving fluid, and the rheological relation for the so-called Bingham fluid is employed to describe the flow behavior of the driven non-Newtonian petroleum. The pressure potential and the water saturation are used as the primary variables. The two phase fluids system is considered to be a subsurface immiscible and micro compressible one. The solutions of the transient planar two phase flow problem in porous media have been sought with the corresponding outer and inner boundary conditions. The finite difference scheme has been used to approximate the governing equations for the problem considered. To keep the approximation physically effective, the upwind weighted treatment for the relative permeability at mesh surface is provided. Newton-Raphson iteration is used in view of the existence of non-linearity. And finally, the stablized bi-conjugate gradient approach is applied to seek the solutions of the corresponding algebraic equations required. A good agreement is obtained between the results of non-Newtonian model and production data, but results of the Newtonian model were unable to yield good agreement with the data.

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