An Efficient Permeability Scaling-Up Technique Applied to Discretized Flow Equations
Denise Urgelli, Yu Ding, 1999. "An Efficient Permeability Scaling-Up Technique Applied to Discretized Flow Equations", Reservoir Characterization—Recent Advances, Richard A. Schatzinger, John F. Jordan
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Grid-block permeability scaling-up for numerical reservoir simulations has been discussed for a long time in the literature. It is now recognized that a full permeability tensor is needed to get an accurate reservoir description at large scale; however, two major difficulties are encountered: (1) grid-block permeability cannot be properly defined because it depends on boundary conditions and (2) discretization of flow equations with a full permeability tensor is not straightforward, and little work has been done on this subject.
In this paper, we propose a new method that allows us to get around both difficulties. As the two major problems are closely related, a global approach will preserve the accuracy. In the proposed method, the permeability up- scaling technique is integrated in the discretized numerical scheme for flow simulation. The permeability is scaled-up via the transmissibility term, in accordance with the fluid flow calculation in the numerical scheme. A finite- volume scheme is particularly studied, and the transmissibility scaling-up technique for this scheme is presented.
Two numerical examples are tested for flow simulation. This new method is compared with two published numerical schemes for full permeability tensor discretization where the full permeability tensor is scaled-up through various techniques. Comparing the results with fine grid simulations shows that the new method is more accurate and more efficient.