A Novel Enriched Galerkin Method for Modelling Coupled Flow and Mechanical Deformation in Heterogeneous Porous Media

Teeratorn Kadeethum, Hamid Nick, S. Lee, C. N. Richardson, S. Salimzadeh, F. Ballarin

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

Coupled fluid flow and solid deformation in porous media modelling is essential in a wide variety of applications. It is also crucial to provide an appropriate discretization for these coupled problems. Therefore, in this study, we provide comparisons between a classical continuous Galerkin (CG), and a new approach, enriched Galerkin (EG) to solve such problem. Even though both the EG and CG methods deliver approximately the same solution for the Terzaghi’s 1-D model, the CG method may produce spurious pressure and volumetric strain oscillations where a vast difference of conductivity property is observed. On the contrary, the EG
method results demonstrate a smooth transition across the mentioned interfaces. These phenomena lead to different reservoir compaction and conductivity effects, which are induced by volumetric strain, on flux approximation in heterogeneous, both porosity and permeability, materials. These impacts are exemplified, and the differences between the EG and CG methods grow larger in softer materials. Although both methods maintain global mass conservation, the EG method guarantees a local mass conservation property by the construction. The EG method, however, demands more computational resources in terms of both degrees of freedom
and number of iterations than the CG method.
Original languageEnglish
Title of host publicationProceedings of 53rd US Rock Mechanics/Geomechanics Symposium
Number of pages10
PublisherAmerican Rock Mechanics Association (ARMA)
Publication date2019
Article numberARMA 19–228
Publication statusPublished - 2019
Event53rd US Rock Mechanics/Geomechanics Symposium - New York Marriott , New York, United States
Duration: 23 Jun 201926 Jun 2019

Conference

Conference53rd US Rock Mechanics/Geomechanics Symposium
LocationNew York Marriott
CountryUnited States
CityNew York
Period23/06/201926/06/2019

Cite this

Kadeethum, T., Nick, H., Lee, S., Richardson, C. N., Salimzadeh, S., & Ballarin, F. (2019). A Novel Enriched Galerkin Method for Modelling Coupled Flow and Mechanical Deformation in Heterogeneous Porous Media. In Proceedings of 53rd US Rock Mechanics/Geomechanics Symposium [ARMA 19–228] American Rock Mechanics Association (ARMA).
Kadeethum, Teeratorn ; Nick, Hamid ; Lee, S. ; Richardson, C. N. ; Salimzadeh, S. ; Ballarin, F. / A Novel Enriched Galerkin Method for Modelling Coupled Flow and Mechanical Deformation in Heterogeneous Porous Media. Proceedings of 53rd US Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association (ARMA), 2019.
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Kadeethum, T, Nick, H, Lee, S, Richardson, CN, Salimzadeh, S & Ballarin, F 2019, A Novel Enriched Galerkin Method for Modelling Coupled Flow and Mechanical Deformation in Heterogeneous Porous Media. in Proceedings of 53rd US Rock Mechanics/Geomechanics Symposium., ARMA 19–228, American Rock Mechanics Association (ARMA), 53rd US Rock Mechanics/Geomechanics Symposium, New York, United States, 23/06/2019.

A Novel Enriched Galerkin Method for Modelling Coupled Flow and Mechanical Deformation in Heterogeneous Porous Media. / Kadeethum, Teeratorn; Nick, Hamid; Lee, S.; Richardson, C. N.; Salimzadeh, S.; Ballarin, F.

Proceedings of 53rd US Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association (ARMA), 2019. ARMA 19–228.

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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AB - Coupled fluid flow and solid deformation in porous media modelling is essential in a wide variety of applications. It is also crucial to provide an appropriate discretization for these coupled problems. Therefore, in this study, we provide comparisons between a classical continuous Galerkin (CG), and a new approach, enriched Galerkin (EG) to solve such problem. Even though both the EG and CG methods deliver approximately the same solution for the Terzaghi’s 1-D model, the CG method may produce spurious pressure and volumetric strain oscillations where a vast difference of conductivity property is observed. On the contrary, the EGmethod results demonstrate a smooth transition across the mentioned interfaces. These phenomena lead to different reservoir compaction and conductivity effects, which are induced by volumetric strain, on flux approximation in heterogeneous, both porosity and permeability, materials. These impacts are exemplified, and the differences between the EG and CG methods grow larger in softer materials. Although both methods maintain global mass conservation, the EG method guarantees a local mass conservation property by the construction. The EG method, however, demands more computational resources in terms of both degrees of freedomand number of iterations than the CG method.

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Kadeethum T, Nick H, Lee S, Richardson CN, Salimzadeh S, Ballarin F. A Novel Enriched Galerkin Method for Modelling Coupled Flow and Mechanical Deformation in Heterogeneous Porous Media. In Proceedings of 53rd US Rock Mechanics/Geomechanics Symposium. American Rock Mechanics Association (ARMA). 2019. ARMA 19–228