Modeling Fluid Flow Through Complex Reservoir Beds

Abstract

Summary Complex beds can significantly affect the flow of fluids in reservoirs. However, current simulators generally are not well-suited to model such flows, in part because they typically do not model permeability as a tensor quantity. This paper demonstrates the importance of treating permeability as a full tensor quantity in simulating flow through complex beds by considering two related problems. First, fluid flow through cross-stratified beds is studied. In this case, heterogeneities appear on the fine scale, and a scale-up procedure is required to model explicitly the effects of these beds. A general numerical procedure, which properly preserves the tensor nature of the effective permeability of such strata, is presented for this computation. The method is based on a finite-element solution of the fine-scale pressure equation with periodic boundary conditions imposed. Second, the modeling of flow through anisotropic, inclined reservoir beds is studied. It is shown that the commonly used techniques for modeling flow through such features, stratigraphic and horizontal layering, implicitly assume principal directions (or orientations) for the permeability tensor. With simple model problems, the differences between simulation results for different orientations of the permeability tensor and differences between results from horizontal and stratigraphic layering are quantified. These differences, which are substantial in the case of high reservoir dip and high anisotropy, emphasize the importance of a knowledge of the full permeability tensor in predicting flow through complex reservoir features.