# Conclusion

During this project we developed two solvers, one solver in one phase flow and a solver for two phase flow.

The solvers developed take into account the gravity. Moreover as we have seen in the two phase flow, we can have problem of saturation superior to one due to the instabilities created by the IMPES method. One of the solution to delay the apparition of those instabilities is to decrease gradually the rate flow.

In the two phase flow we implemented the capillary pressure with an empirical law. The observations on the capillary pressure were conform to the theory.

In solvers taking into account the gravity, the permeability was not defined as a tensor, because of the need of the inversion of the permeability tensor to put a boundary condition on the pressure gradient on the bottom of the domain. Indeed the operation of tensor inversion is difficult to implement on OpenFoam. Then the permeability was defined as scalar or as a field of scalar.

Through the different simulations we observed the existence of different regimes, in fact the rate flow or the source term has to be adapted to the fluid and to the porous media properties.

The study of viscous flow in a domain with very small permeability has shown that there is a limit on the maximal flow rate of pumping.

This project will be continued to develop a three phase flow solver and to implement the permeability as a tensor.