Numerical Homogenization of the Absolute Permeability Tensor Around a Well
Wouter Zijl, Anna Trykozko · SPE Journal · 2001
Summary This paper presents an extension of the classical homogenization method of upscaling around a well. The use of homogenization theory has been made possible by a transform of the cylindrical homogenization cell around a well to an "equivalent rectangular cell." First, it is shown by an introductory example for radial flow that direct use of the original homogenization cell leads to more than one coarse-scale permeability. This is at variance with the approach based on the transform to an equivalent rectangular cell, which yields one unique coarse-scale permeability that can be applied consistently both in Darcy's law and in the dissipation equation. The main body of the paper describes the extension of this transformational approach to general 3D permeability tensors, without assuming purely radial flow. The pressure equation is solved numerically; from this solution, classical homogenization algorithms compute the "transformed homogenized permeability tensor" in the equivalent rectangular cell. Finally, a back transform to the original homogenization cell leads to the coarse-scale permeability tensor. Validation examples compare the numerical homogenization with global upscaling.