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