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Vertical compaction in a faulted sedimentary basin

Published online by Cambridge University Press:  15 November 2003

Gérard Gagneux ,
Roland Masson ,
Anne Plouvier-Debaigt ,
Guy Vallet  and
Sylvie Wolf
Gérard Gagneux
Affiliation:
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.
Roland Masson
Affiliation:
Institut Français du Pétrole, 1 et 4 avenue de Bois-Préau, BP 311, 92852 Rueil-Malmaison Cedex, France. roland.masson@ifp.fr.
Anne Plouvier-Debaigt
Affiliation:
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.
Guy Vallet
Affiliation:
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.
Sylvie Wolf
Affiliation:
Institut Français du Pétrole, 1 et 4 avenue de Bois-Préau, BP 311, 92852 Rueil-Malmaison Cedex, France. roland.masson@ifp.fr.
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Abstract

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.

Keywords

Porous mediavertical compactionsedimentary basinsfault lines modelling.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 2 , March 2003 , pp. 373 - 388
Copyright
© EDP Sciences, SMAI, 2003

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