In the literature  exists several empirical formula of capillary pressure present in a porous media.

To understand the effect of the capillary pressure on the saturation, we did our simulation with the following simple formula as a first approach :

$P_c=C(S_e)^{-\alpha}$

where :

•  $P_c$ is the capillary pressure
•  $C$ and $\alpha$ are constant
•  $S_e$ is the effective saturation in liquid.
   

Se is defined by :

• where $ S_{min}$ and $S_{max}$ are the minimal and the maximal saturation of the porous media.