no. 2
Vertical compaction in a faulted sedimentary basin
ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 2, pp. 373-388.

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.

DOI : 10.1051/m2an:2003032
Classification : 35Q35, 76S05, 35J65
Mots clés : porous media, vertical compaction, sedimentary basins, fault lines modelling 
@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: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {373--388},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {2},
     year = {2003},
     doi = {10.1051/m2an:2003032},
     mrnumber = {1991207},
     zbl = {1048.35080},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/m2an:2003032/}
}
TY  - JOUR
AU  - Gagneux, Gérard
AU  - Masson, Roland
AU  - Plouvier-Debaigt, Anne
AU  - Vallet, Guy
AU  - Wolf, Sylvie
TI  - Vertical compaction in a faulted sedimentary basin
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 2003
SP  - 373
EP  - 388
VL  - 37
IS  - 2
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/m2an:2003032/
DO  - 10.1051/m2an:2003032
LA  - en
ID  - M2AN_2003__37_2_373_0
ER  - 
%0 Journal Article
%A Gagneux, Gérard
%A Masson, Roland
%A Plouvier-Debaigt, Anne
%A Vallet, Guy
%A Wolf, Sylvie
%T Vertical compaction in a faulted sedimentary basin
%J ESAIM: Modélisation mathématique et analyse numérique
%D 2003
%P 373-388
%V 37
%N 2
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/m2an:2003032/
%R 10.1051/m2an:2003032
%G en
%F 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: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 2, pp. 373-388. doi : 10.1051/m2an:2003032. http://archive.numdam.org/articles/10.1051/m2an:2003032/

[1] 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). | Zbl

[2] 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. | Zbl

[3] C. Bardos, 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. | Numdam | Zbl

[4] A. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic analysis for periodic structures. North-holland, Amsterdam (1978). | MR | Zbl

[5] P.A. Bourque, http://www.ggl.ulaval.ca/personnel/bourque/intro.pt/science.terre.html.

[6] H. Brezis, Analyse fonctionnelle - Théorie et applications. Masson, Paris (1983). | MR | Zbl

[7] P.G. Ciarlet and J.L. Lions, Handbook of Numerical Analysis. Vol. II, Finite Element Methods (Part 1). North Holland (1991). | MR

[8] A.C. Fowler and X. Yang, Fast and slow compaction in sedimentary basins. SIAM J. Appl. Math. 59 (1999) 365-385. | Zbl

[9] 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. | Zbl

[10] G. Gagneux and M. Madaune-Tort, Analyse mathématique de modèles non linéaires de l'ingénierie pétrolière, Mathématiques & Applications No. 22. Springer-Verlag (1996). | Zbl

[11] 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).

[12] D. Gilbart and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin (1977). | MR | Zbl

[13] G. Gödert and K. Hutter, Induced anisotropy in large ice shields: theory and its homogenization. Contin. Mech. Thermodyn. 10 (1998) 293-318. | Zbl

[14] A.T. Ismail-Zade, A.I. Korotkii, B.M. Naimark and I.A. Tsepelev, Implementation of a three-dimensional hydrodynamic model for evolution of sedimentary basins. Comput. Math. Math. Phys. 38 (1998) 1138-1151. | Zbl

[15] E. Ledoux, http://www.emse.fr/environnement/fiches/1_2_2.html.

[16] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Paris (1969). | MR | Zbl

[17] X. Luo, G. Vasseur, A. Pouya, V. Lamoureux-Var and A. Poliakov, Elastoplastic deformation of porous media applied to the modelling of compaction at basin scale. Marine and Petroleum Geology 15 (1998) 145-162.

[18] N.G. Meyers, An Lp-estimate for the gradient of solutions of second order elliptic divergence equations. Ann. Sci. Norm. Sup. Pisa Cl. Sci. 17 (1963) 189-206. | EuDML | Numdam | Zbl

[19] J. Nečas, Écoulements de fluide, Compacité par entropie, Collection Recherche et Mathématiques Appliquées, No. 10. Masson (1989). | MR | Zbl

[20] 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).

[21] O.A. Oleĭnik, Uniqueness and stability of the generalized solution of the Cauchy problem for a quasi-linear equation. Uspekhi Mat. Nauk 14 (1959) 165-170. | Zbl

[22] L. Perez, Modélisation de la compaction dans les bassins sédimentaires : Influence d'un comportement mécanique tensoriel, Thèse de l'ENSAM (1998).

[23] F. Schneider and S. Wolf, 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.

[24] F. Schneider, S. Wolf, I. Faille and D. Pot, A 3D basin model for hydrocarbon potential evaluation: Application to Congo offshore. Oil and Gas Science and Technology 55 (2000) 3-12.

[25] G. Sciarra, F. Dell'Isola and K. Hutter, A solid-fluid mixture model allowing for solid dilatation under external pressure. Contin. Mech. Thermodyn. 13 (2001) 287-306. | Zbl

[26] M. Wangen, Two-phase oil migration in compacting sedimentary basins modelled by the finite element method. Int. J. Numer. Anal. Methods Geomech. 21 (1997) 91-120. | Zbl

[27] M. Wangen, B. Antonsen, B. Fossum and L.K. Alm, A model for compaction of sedimentary basins. Appl. Math. Modelling 14 (1990) 506-517. | Zbl

[28] Z. Wu and J. Yin, 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. | Zbl

[29] E. Zakarian and R. Glowinski, Domain decomposition methods applied to sedimentary basin modeling. Math. Comput. Modelling 30 (1999) 153-178. | Zbl

Cité par Sources :