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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 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.

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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References

S.N. Antontsev and A.V. Domansky, Uniqueness generalizated solutions of degenerate problem in two-phase filtration. Numerical methods mechanics in continuum medium. Collection Sciences Research, Sbornik, t. 15, No. 6 (1984) 15-28 (in Russian).
L. Badea, Adaptive mesh finite element method for the sedimentary basin problem. In honour of Academician Nicolae Dan Cristescu on his 70th birthday, Rev. Roumaine Math. Pures Appl. 45 (2000), No. 2 (2001) 171-181.
Bardos, C., Problèmes aux limites pour les équations aux dérivées partielles partielles du premier ordre à coefficients réels. Ann. Sci. École Norm. Sup. 3 (1970) 185-233. CrossRef
A. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic analysis for periodic structures. North-holland, Amsterdam (1978).
P.A. Bourque, http://www.ggl.ulaval.ca/personnel/bourque/intro.pt/science.terre.html.
H. Brezis, Analyse fonctionnelle - Théorie et applications. Masson, Paris (1983).
P.G. Ciarlet and J.L. Lions, Handbook of Numerical Analysis. Vol. II, Finite Element Methods (Part 1). North Holland (1991).
Fowler, A.C. and Yang, X., Fast and slow compaction in sedimentary basins. SIAM J. Appl. Math. 59 (1999) 365-385. CrossRef
G. Gagneux, Sur l'analyse de modèles de la filtration diphasique en milieu poreux, in Équations aux dérivées partielles et applications : Articles dédiés à J.L. Lions. Gauthier-Villars, Elsevier (1998) 527-540.
G. Gagneux and M. Madaune-Tort, Analyse mathématique de modèles non linéaires de l'ingénierie pétrolière, Mathématiques & Applications No. 22. Springer-Verlag (1996).
G. Gagneux, A. Plouvier-Debaigt and G. Vallet, Modélisation et analyse mathématique d'un écoulement 2D monophasique dans un bassin sédimentaire faillé sous l'effet de la compaction verticale, Publication Interne du Laboratoire de Mathématiques Appliquées CNRS-ERS 2055, No. 2000-31 (2000).
D. Gilbart and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin (1977).
Gödert, G. and Hutter, K., Induced anisotropy in large ice shields: theory and its homogenization. Contin. Mech. Thermodyn. 10 (1998) 293-318.
Ismail-Zade, A.T., Korotkii, A.I., Naimark, B.M. and Tsepelev, I.A., Implementation of a three-dimensional hydrodynamic model for evolution of sedimentary basins. Comput. Math. Math. Phys. 38 (1998) 1138-1151.
E. Ledoux, http://www.emse.fr/environnement/fiches/1_2_2.html.
J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Paris (1969).
Luo, X., Vasseur, G., Pouya, A., Lamoureux-Var, V. and Poliakov, A., Elastoplastic deformation of porous media applied to the modelling of compaction at basin scale. Marine and Petroleum Geology 15 (1998) 145-162. CrossRef
Meyers, N.G., Lp-estimate, An for the gradient of solutions of second order elliptic divergence equations. Ann. Sci. Norm. Sup. Pisa Cl. Sci. 17 (1963) 189-206.
J. Necas, Écoulements de fluide, Compacité par entropie, Collection Recherche et Mathématiques Appliquées, No. 10. Masson (1989).
H. Obelembia Adande, Contribution à l'étude de l'unicité pour des systèmes d'équations de conservation. Cas des écoulements diphasiques incompressibles en milieu poreux, Thèse de l'Université de Pau (1996).
Oleinik, O.A., Uniqueness and stability of the generalized solution of the Cauchy problem for a quasi-linear equation. Uspekhi Mat. Nauk 14 (1959) 165-170.
L. Perez, Modélisation de la compaction dans les bassins sédimentaires : Influence d'un comportement mécanique tensoriel, Thèse de l'ENSAM (1998).
Schneider, F. and Wolf, S., Quantitative HC potential evaluation using 3D basin modelling application to Franklin structure, central Graben, North Sea. UK Marine and Petroleum Geology 17 (2000) 841-856. CrossRef
Schneider, F., Wolf, S., Faille, I. and Pot, D., A 3D basin model for hydrocarbon potential evaluation: Application to Congo offshore. Oil and Gas Science and Technology 55 (2000) 3-12. CrossRef
Sciarra, G., Dell'Isola, F. and Hutter, K., A solid-fluid mixture model allowing for solid dilatation under external pressure. Contin. Mech. Thermodyn. 13 (2001) 287-306. CrossRef
Wangen, M., Two-phase oil migration in compacting sedimentary basins modelled by the finite element method. Int. J. Numer. Anal. Methods Geomech. 21 (1997) 91-120. 3.0.CO;2-L>CrossRef
Wangen, M., Antonsen, B., Fossum, B. and Alm, L.K., A model for compaction of sedimentary basins. Appl. Math. Modelling 14 (1990) 506-517. CrossRef
Wu, Z. and Yin, J., Some properties of functions in BV x and their applications to the uniqueness of solutions for degenerate quasilinear parabolic equations. Northeast. Math. J. 5 (1989) 395-422.
Zakarian, E. and Glowinski, R., Domain decomposition methods applied to sedimentary basin modeling. Math. Comput. Modelling 30 (1999) 153-178. CrossRef