Homogenization on Two-phase Flow

Example: Homogenization on Two-phase Flow Near a Fracture

Joe Koebbe
Department of Mathematics and Statistics
Utah State University

This page contains examples of flow simulations in homogenized porous media and compares different homogenization strategies for homogenizing the region. In this example The code used to perform the simulation is capable of doing multiphase flow, but

Before breakthrough
After breakthrough

Result I:

The results in the following table show the state of the flow just before breakthrough in the producing well in the upper right hand corner of the region. It should be clear that homogenization of the entire region is not appropriate and that adding one extra cell in the heterogeneous region near the fracture region increases the accuracy of the results. The case without the extra cell in the matrix is not terrible.

Heterogeneous Case	Homogenization of Entire Region
Homogenization of Three Regions	One Cell Boundary Layer Case

Result II:

The results in the following table show the state of the flow just after breakthrough in the producing well in the upper right hand corner of the region. Similar comments to those mentioned above apply in this case.

Heterogeneous Case	Homogenization of Entire Region
Homogenization of Three Regions	One Cell Boundary Layer Case