We have a mesh 120*120 cells and the a well of 50cm*200cm.

We took in this part of fluid that have properties similar to the water properties but less dense than water.

Here we can see the representation of the domain :

Well and domain representation

 The initial saturation will have the form of this :

Initial saturation in water

 We implemented a first simulation with the following parameters

 phase a :

• Viscosity $\mu_a=1.17 \ kg/(m.s)$
•  density $\rho_a=1.85 \ 10^{-5} kg/m^3$

phase b :

• Viscosity $\mu_b=1 \ 10^{-3} kg/(m.s)$
• density $\rho_b=0.88 \ 10 ^3 Kg/m^3$
   

The initial flow rate qwell was fixed to :

•  $qwell=1 \ 10^{-2} m^3/s$

Moreover we consider that we have an isotropic domain and we set the permeability to :
 

•  $K=1 \ 10^{-10}m^2$

In this part when the saturation in water goes below 0.5, the initial flow rate is gradually decreased. Furthermore  when the water saturation goes below the value 0.1 we stop the well production.

Saturation in water time=300 s

Saturation in water time=350 s

Saturation in water time=650 s

Saturation in water time=4000 s