The aim of this paper is to prove that the framework of generalized functions of Sobolev type is more suitable to pose and solve some PDEs problems with very irregular data, than the one introduced by J.-F. Colombeau, when ${\mathcal{C}}^{\infty}$ estimates are not available or out of reach. In such type of algebras, one shows the existence and some qualitative properties of solutions for problems appearing in the mathematical modelisation of oil activities.