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vertical compaction

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Vertical compaction in a faulted sedimentary basin
Gérard Gagneux, Roland Masson, Anne Plouvier-Debaigt, Guy Vallet, Sylvie Wolf
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 37 / Issue 2 / March 2003

Published online by Cambridge University Press:

15 November 2003, pp. 373-388

Print publication:

March 2003
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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.