Volume 5, Issue 4
Algorithms for Coupled Mechanical Deformations and Fluid Flow in a Porous Medium with Different Time Scales

F.-Z. Daïm, D. Hilhorst, J. Laminie & R. Eymard

Int. J. Numer. Anal. Mod., 5 (2008), pp. 635-658.

Published online: 2008-05

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  • 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.

  • Keywords

porous media, Darcy flow, mechanical deformations, Gauss Seidel method, nonlinear conjugate gradient method, inf-sup condition, mixed formulation, multiscale algorithm.

  • AMS Subject Headings

35Q35, 65F15, 65F10, 65F50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-5-635, author = {Daïm , F.-Z. and Hilhorst , D. and Laminie , J. and Eymard , R.}, title = {Algorithms for Coupled Mechanical Deformations and Fluid Flow in a Porous Medium with Different Time Scales}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2008}, volume = {5}, number = {4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/830.html} }
TY - JOUR T1 - Algorithms for Coupled Mechanical Deformations and Fluid Flow in a Porous Medium with Different Time Scales AU - Daïm , F.-Z. AU - Hilhorst , D. AU - Laminie , J. AU - Eymard , R. JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 635 EP - 658 PY - 2008 DA - 2008/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/830.html KW - porous media, Darcy flow, mechanical deformations, Gauss Seidel method, nonlinear conjugate gradient method, inf-sup condition, mixed formulation, multiscale algorithm. AB -

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.

F.-Z. Daïm, D. Hilhorst, J. Laminie & R. Eymard. (1970). Algorithms for Coupled Mechanical Deformations and Fluid Flow in a Porous Medium with Different Time Scales. International Journal of Numerical Analysis and Modeling. 5 (4). 635-658. doi:
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