A model for single phase flow in horizontally fractured porous media using homogenization techniques.

Modified homogenization techniques are used to derive a double porosity model for single phase flow in a reservoir with a preferred direction of fracture, namely horizontal. The equations in the microscopic model are the usual ones derived from Darcy's law in the fractures and matrix (rock). The permeability coefficients over the matrix domain are scaled, by a parameter &egr;, based on the fracture direction in the reservoir. The parameter &egr; represents the size of the parts of the matrix blocks that are being homogenized and the scaling preserves the physics of the flow between matrix and fracture as the blocks shrink. Convergence to the macroscopic model is shown by extracting the weak limits of the microscopic model solutions. The limit (macroscopic) model consists of Darcy flow equations in the matrix blocks and fracture sheet, with two additional terms in the fracture sheet equation. Together, these terms represent the source of fluid coming out of the matrix blocks into the fracture sheet. The techniques developed can be extended to model flow in other reservoirs with one or more preferred directions of fracture.