Algorithms for Coupled Mechanical Deformations and Fluid Flow in a Porous Medium with Different Time Scales
Year: 2008
Author: F.-Z. Daïm, D. Hilhorst, J. Laminie, R. Eymard
International Journal of Numerical Analysis and Modeling, Vol. 5 (2008), Iss. 4 : pp. 635–658
Abstract
In this paper, we solve a problem describing the mechanical deformations of a porous medium in the presence of a monophasic linear flow or a two phase nonlinear flow with the purpose of modelizing subsidence of hydrocarbon reservoirs. An essential characteristics of this problem is that the mechanical deformation and the flow have different time scales. In petroleum industry, one uses different very efficient simulators for the flow problem and the mechanical deformations, which enables to handle complex models. Therefore it is necessary to be able to combine as efficiently as possible the exploitation of these simulators. We propose two alternative splitting approaches. The first one is the staggered algorithm used by engineers, which amounts to a Gauss-Seidel method in the one phase linear case. The second approach is based upon the preconditioned conjugate gradient method. We use a numerical multi-scale method in both of these algorithms. We compare these two approaches and we show that the preconditioned conjugate gradient algorithm is faster and more robust than the staggered algorithm. Applying the preconditioned conjugate gradient algorithm therefore seems to compensate for the fact that the inf-sup condition for the mixed discretization method is not satisfied when combining the simulators for the mechanical deformations and for the flow computations.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-IJNAM-830
International Journal of Numerical Analysis and Modeling, Vol. 5 (2008), Iss. 4 : pp. 635–658
Published online: 2008-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: porous media Darcy flow mechanical deformations Gauss Seidel method nonlinear conjugate gradient method inf-sup condition mixed formulation multiscale algorithm.