Influence of the anisotropy

As we know the large majority of porous media that we can find in industry or in the nature present an anisotropy. It's why it is interesting to understand the influence of the anisotropy on the flow.

In order to take into account the anisotropy, we define the permeability as a tensor field in $m^2$:

 

First of all we study a case with K defined as a tensor but without anisotropy in $m^2$:

Then we can notice, that in the anisotropic K introduced, the permeability is more important in the horizontal direction than in the vertical or perpendicularly direction. Which means that we should have a more important velocity in the horizontal direction.

 

In the following study the gravity influence was neglected.

 

 

Influence of the anisotropy on the velocity field

 

 

Velocity field in anisotropic case :

 

Velocity field in isotropic case :

We observe that in the anisotropic case the velocity magnitude is more important in the horizontal direction than in the vertical one as it was predicted in theory. Indeed this result is normal because the permeability is more important in the horizontal direction than in the other directions.

 

Influence of the anisotropy on the pressure field

 

Pressure field in the case of isotropy :

 

Pressure field in the case of anisotropy :

As we have decreased the permeability in the vertical direction in the anisotropic case, the velocity is decreased which increases the pressure.