The Use of Higher-Order Differencing Techniques in Reservoir Simulation

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Abstract
Summary: Uniformly second- and third-order finite-difference schemes are developed for convection-dominated flows in porous media. The schemes are applied to immiscible and miscible displacements characterized by low levels of physical dispersion. The high-order schemes developed are shown to reduce significantly both dispersion of sharp fronts and sensitivity to grid orientation when compared with solutions obtained with the commonly used one-point upwind differencing schemes. Moreover, for explicit timestepping simulators, such as those based on implicit-pressure, explicit-saturation (IMPES) formulations, the improved performance of the high-order methods is obtained with only a modest increase in computational effort.

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