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.
@article{M2AN_2003__37_2_373_0,
author = {Gagneux, G\'erard and Masson, Roland and Plouvier-Debaigt, Anne and Vallet, Guy and Wolf, Sylvie},
title = {Vertical compaction in a faulted sedimentary basin},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {37},
year = {2003},
pages = {373-388},
doi = {10.1051/m2an:2003032},
mrnumber = {1991207},
zbl = {1048.35080},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2003__37_2_373_0}
}
Gagneux, Gérard; Masson, Roland; Plouvier-Debaigt, Anne; Vallet, Guy; Wolf, Sylvie. Vertical compaction in a faulted sedimentary basin. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 37 (2003) pp. 373-388. doi : 10.1051/m2an:2003032. http://gdmltest.u-ga.fr/item/M2AN_2003__37_2_373_0/
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