Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 94, pp. 1-19.

Title: A model for single-phase flow in layered porous media

Authors: Daniel J. Coffield Jr. (Univ. of Michigan, Flint, MI, USA)
         Anna Maria Spagnuolo   (Oakland Univ., Rochester, MI, USA)

Abstract:  
 Homogenization techniques are used to derive a double
 porosity model for single phase flow in a reservoir
 with a preferred direction of fracture.  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, using a parameter $\epsilon$, based on the
 fracture direction in the reservoir.  The parameter
 $\epsilon$ 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 additional terms in the fracture sheet equation.
 Together, these terms represent the fluid exchange between the
 matrix blocks and the fracture sheet.

Submitted February 23, 2010. Published July 13, 2010.
Math Subject Classifications: 76S05, 35B27.
Key Words: Layered media; naturally-fractured media;
           double-porosity model; homogenization.