We decided to develop the two phase flow solver by starting with the development and the study of one phase flow solver.

First of all we will integrated in the one phase flow solver the permeability as a tensor and the gravity field.

To test this solver we will do several simulation and by varying one parameter and fixing all the other parameters.

After accomplishing the work on the one phase flow solver we will develop a two phase solver using a numerical method called IMPES (Implicit Pressure Explicit Saturation).

Moreover we will study how to reduce or delay the instabilities created by the method IMPES.

The code will be tested in several simulation without capillary pressure and for fluids of different viscosity and different rate flow of pumping.

Finally we will add the capillary pressure and test very simple correlations of capillary pressure.