anisoImpesFoam tutorials

Exploitation Cases

The examples provided in the directory tutorials/anisoImpesFoam-tutorials/ demonstrate the use of the anisoImpesFoam solver in practical scenarios.

We consider a basic simulation involving a square domain in the horizontal (\(xy\)) plane, where the injection of the wetting phase is introduced. The permeability K in this domain is represented as a second-order tensor:

\[\begin{split}K_1 = \begin{bmatrix} 10^{-11} & 0 & 0 \\ 0 & 10^{-9} & 0 \\ 0 & 0 & 10^{-10} \end{bmatrix} \quad K_2 = \begin{bmatrix} 10^{-9} & 0 & 0 \\ 0 & 5 \times 10^{-11} & 0 \\ 0 & 0 & 10^{-10} \end{bmatrix}\end{split}\]

The computational domain is a square with side length \(L = 10m\), discretized into 800 computational cells, with finer meshing near the center to capture more detailed flow dynamics.

The solver reads an injection event file (injection.evt) that specifies the injection details at different times, coordinates, and flow rates:

date 0
4.95 8.1 0.5 -5e-4
5.05 8.1 0.5 -5e-4

date 20000
4.95 8.1 0.5 -4e-4
5.05 8.1 0.5 -4e-4

The following images show the saturation distribution of the wetting phase for two distinct cases:

• Case 1:

• Case 2:

In these simulations, the anisoImpesFoam solver effectively captures the behavior of anisotropic permeability. In Case 1, the flow predominantly follows the preferential permeability direction, which is aligned with the gravity vector. In contrast, Case 2 exhibits a more uniform spread of the wetting phase due to the modified permeability tensor.