| Issue |
ESAIM: M2AN
Volume 37, Number 2, March/April 2003
|
|
|---|---|---|
| Page(s) | 373 - 388 | |
| DOI | https://doi.org/10.1051/m2an:2003032 | |
| Published online | 15 November 2003 | |
Vertical compaction in a faulted sedimentary basin
1
Laboratoire de Mathématiques
Appliquées, Université de Pau et des Pays de l'Adour, BP 576,
64012 Pau Cedex, France.
gerard.gagneux@univ-pau.fr.,
guy.vallet@univ-pau.fr.
2
Institut Français du Pétrole,
1 et 4 avenue de Bois-Préau, BP 311, 92852 Rueil-Malmaison Cedex, France. roland.masson@ifp.fr.
Received:
10
July
2002
Revised:
22
January
2003
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.
Mathematics Subject Classification: 35Q35 / 76S05 / 35J65
Key words: Porous media / vertical compaction / sedimentary basins / fault lines modelling.
© EDP Sciences, SMAI, 2003
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