We did all the  simulations in this part with the same parameters as in 3.3.1 and by taking into accounting the presence of a capillary pressure with $\alpha=0.2$ and $C=10.10^3 Pa$.

We are going to compare the oil saturation over a vertical line from the domain with capillary pressure and without capillary pressure.

Plot line :


Simulations with capillary pressure and qwell=0

In order to observe the effect of the capillary pressure on the saturation we set the source term equal to 0.


Oil saturation t=0 s

Oil saturation t=130000 s


We observe that saturation is increased in the boundary region between oil and air. Indeed the water goes up due to the capillary pressure, after certain time the water stop going up due the balance by gravity

Simulations with capillary pressure with pumping

We compare the influence the case with capillary and the case without capillary pressure.

Saturation without $P_c$, time=100000 s

Saturation with $P_c$,  time=100000 s


We observe that the capillary pressure allows the oil to go up and help to the pumping .
Moreover we know that pumping create a lack of oil which increases the influence of the capillary pressure.