In this paper, we consider a 2D mathematical modelling of the verticalcompaction effect in a water saturated sedimentary basin. This model isdescribed by the usual conservation laws, Darcy's law, the porosity as afunction of the vertical component of the effective stress and theKozeny-Carman tensor, taking into account fracturation effects. This modelleads to study the time discretization of a nonlinear system ofpartial differential equations. The existence is obtained by a fixed-pointargument. The uniqueness proof, by Holmgren's method, leads to work out a linear, strongly coupled, system of partial differential equations andboundary conditions.
