A Mixed-dimensional Discontinuous Galerkin Method for Coupled Flow and Transport in Fractured Porous Media

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

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Abstract

Fluid flow and solute transport in fractured porous media are phenomena that control key processes in groundwater monitoring, generating thermal energy, earthquake prediction, and biomedical engineering, e.g. model activities of the heart or brain from noninvasive measurements on the chest or scalp. The mathematical representation of the fluid interaction between fracture and rock matrix domains is not straightforward because these two domains usually possess vastly different flow properties. For instance, fluid conductivity through a system of fractures can be much greater than that of the rock matrix. To tackle this issue, there are three main approaches, (i) equidimensional, (ii) mixed-dimensional representing fractures as split surfaces, and (iii) mixed-dimensional representing
fractures as internal walls [1, 2]. The first method demands excessively refinement of the fracture domain, more computationally burdens, while the second method requires a sophisticated contact model when mechanical deformation is included in the model 3. Hence, the third method is selected in this study because of its favourable computational cost and straightforward implementation when it is incorporated more phenomena. Researchers have traditionally used the continuous Galerkin (CG) method to solve flow and transport in fractured porous media problems for decades. However, it is not suitable for solving the transport equation because it may not satisfy mass conservation. Moreover, it cannot represent fractures that act as flow barriers [4]. This study aims to present the advantages of using the discontinuous Galerkin (DG) method for solving coupled flow and transport in fractured porous media. A mixed DG × CG space is utilised to solve the pressure equation. Subsequently, a velocity field is established using CG or Raviet − T homas function space; then the transport equation is solved on DG space. This procedure provides more accurate solutions in a convection-dominated regime, in which a sharp flood-front of the tracer is established, than those of CG formulation. The result of this work is compared to relatively new numerical methods, including hybrid-finite-element-finitevolume, lowest order Raviart-Thomas mixed finite elements, and multi-Point flux approximation methods as part of “Verification benchmarks for single-phase flow in three-dimensional fractured
porous media [4, 5, 6].”
Original languageEnglish
Publication date2019
Number of pages2
Publication statusPublished - 2019
Event11th Annual Meeting Interpore 2019 Valencia - Valencia Conference Centre, Valencia, Spain
Duration: 6 May 201910 May 2019
Conference number: 11
https://events.interpore.org/event/12/

Conference

Conference11th Annual Meeting Interpore 2019 Valencia
Number11
LocationValencia Conference Centre
CountrySpain
CityValencia
Period06/05/201910/05/2019
Internet address

Bibliographical note

Abstract 185

Cite this

Kadeethum, T., Nick, H., Salimzadeh, S., Richardson, C. N., Ballarin, F., & Lee, S. (2019). A Mixed-dimensional Discontinuous Galerkin Method for Coupled Flow and Transport in Fractured Porous Media. Abstract from 11th Annual Meeting Interpore 2019 Valencia, Valencia, Spain.
Kadeethum, Teeratorn ; Nick, Hamid ; Salimzadeh, Saeed ; Richardson, C N. ; Ballarin, F. ; Lee, S. / A Mixed-dimensional Discontinuous Galerkin Method for Coupled Flow and Transport in Fractured Porous Media. Abstract from 11th Annual Meeting Interpore 2019 Valencia, Valencia, Spain.2 p.
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abstract = "Fluid flow and solute transport in fractured porous media are phenomena that control key processes in groundwater monitoring, generating thermal energy, earthquake prediction, and biomedical engineering, e.g. model activities of the heart or brain from noninvasive measurements on the chest or scalp. The mathematical representation of the fluid interaction between fracture and rock matrix domains is not straightforward because these two domains usually possess vastly different flow properties. For instance, fluid conductivity through a system of fractures can be much greater than that of the rock matrix. To tackle this issue, there are three main approaches, (i) equidimensional, (ii) mixed-dimensional representing fractures as split surfaces, and (iii) mixed-dimensional representingfractures as internal walls [1, 2]. The first method demands excessively refinement of the fracture domain, more computationally burdens, while the second method requires a sophisticated contact model when mechanical deformation is included in the model 3. Hence, the third method is selected in this study because of its favourable computational cost and straightforward implementation when it is incorporated more phenomena. Researchers have traditionally used the continuous Galerkin (CG) method to solve flow and transport in fractured porous media problems for decades. However, it is not suitable for solving the transport equation because it may not satisfy mass conservation. Moreover, it cannot represent fractures that act as flow barriers [4]. This study aims to present the advantages of using the discontinuous Galerkin (DG) method for solving coupled flow and transport in fractured porous media. A mixed DG × CG space is utilised to solve the pressure equation. Subsequently, a velocity field is established using CG or Raviet − T homas function space; then the transport equation is solved on DG space. This procedure provides more accurate solutions in a convection-dominated regime, in which a sharp flood-front of the tracer is established, than those of CG formulation. The result of this work is compared to relatively new numerical methods, including hybrid-finite-element-finitevolume, lowest order Raviart-Thomas mixed finite elements, and multi-Point flux approximation methods as part of “Verification benchmarks for single-phase flow in three-dimensional fracturedporous media [4, 5, 6].”",
author = "Teeratorn Kadeethum and Hamid Nick and Saeed Salimzadeh and Richardson, {C N.} and F. Ballarin and S. Lee",
note = "Abstract 185 ; 11th Annual Meeting Interpore 2019 Valencia, InterPore2019 ; Conference date: 06-05-2019 Through 10-05-2019",
year = "2019",
language = "English",
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Kadeethum, T, Nick, H, Salimzadeh, S, Richardson, CN, Ballarin, F & Lee, S 2019, 'A Mixed-dimensional Discontinuous Galerkin Method for Coupled Flow and Transport in Fractured Porous Media', 11th Annual Meeting Interpore 2019 Valencia, Valencia, Spain, 06/05/2019 - 10/05/2019.

A Mixed-dimensional Discontinuous Galerkin Method for Coupled Flow and Transport in Fractured Porous Media. / Kadeethum, Teeratorn; Nick, Hamid; Salimzadeh, Saeed; Richardson, C N.; Ballarin, F.; Lee, S.

2019. Abstract from 11th Annual Meeting Interpore 2019 Valencia, Valencia, Spain.

Research output: Contribution to conferenceConference abstract for conferenceResearchpeer-review

TY - ABST

T1 - A Mixed-dimensional Discontinuous Galerkin Method for Coupled Flow and Transport in Fractured Porous Media

AU - Kadeethum, Teeratorn

AU - Nick, Hamid

AU - Salimzadeh, Saeed

AU - Richardson, C N.

AU - Ballarin, F.

AU - Lee, S.

N1 - Abstract 185

PY - 2019

Y1 - 2019

N2 - Fluid flow and solute transport in fractured porous media are phenomena that control key processes in groundwater monitoring, generating thermal energy, earthquake prediction, and biomedical engineering, e.g. model activities of the heart or brain from noninvasive measurements on the chest or scalp. The mathematical representation of the fluid interaction between fracture and rock matrix domains is not straightforward because these two domains usually possess vastly different flow properties. For instance, fluid conductivity through a system of fractures can be much greater than that of the rock matrix. To tackle this issue, there are three main approaches, (i) equidimensional, (ii) mixed-dimensional representing fractures as split surfaces, and (iii) mixed-dimensional representingfractures as internal walls [1, 2]. The first method demands excessively refinement of the fracture domain, more computationally burdens, while the second method requires a sophisticated contact model when mechanical deformation is included in the model 3. Hence, the third method is selected in this study because of its favourable computational cost and straightforward implementation when it is incorporated more phenomena. Researchers have traditionally used the continuous Galerkin (CG) method to solve flow and transport in fractured porous media problems for decades. However, it is not suitable for solving the transport equation because it may not satisfy mass conservation. Moreover, it cannot represent fractures that act as flow barriers [4]. This study aims to present the advantages of using the discontinuous Galerkin (DG) method for solving coupled flow and transport in fractured porous media. A mixed DG × CG space is utilised to solve the pressure equation. Subsequently, a velocity field is established using CG or Raviet − T homas function space; then the transport equation is solved on DG space. This procedure provides more accurate solutions in a convection-dominated regime, in which a sharp flood-front of the tracer is established, than those of CG formulation. The result of this work is compared to relatively new numerical methods, including hybrid-finite-element-finitevolume, lowest order Raviart-Thomas mixed finite elements, and multi-Point flux approximation methods as part of “Verification benchmarks for single-phase flow in three-dimensional fracturedporous media [4, 5, 6].”

AB - Fluid flow and solute transport in fractured porous media are phenomena that control key processes in groundwater monitoring, generating thermal energy, earthquake prediction, and biomedical engineering, e.g. model activities of the heart or brain from noninvasive measurements on the chest or scalp. The mathematical representation of the fluid interaction between fracture and rock matrix domains is not straightforward because these two domains usually possess vastly different flow properties. For instance, fluid conductivity through a system of fractures can be much greater than that of the rock matrix. To tackle this issue, there are three main approaches, (i) equidimensional, (ii) mixed-dimensional representing fractures as split surfaces, and (iii) mixed-dimensional representingfractures as internal walls [1, 2]. The first method demands excessively refinement of the fracture domain, more computationally burdens, while the second method requires a sophisticated contact model when mechanical deformation is included in the model 3. Hence, the third method is selected in this study because of its favourable computational cost and straightforward implementation when it is incorporated more phenomena. Researchers have traditionally used the continuous Galerkin (CG) method to solve flow and transport in fractured porous media problems for decades. However, it is not suitable for solving the transport equation because it may not satisfy mass conservation. Moreover, it cannot represent fractures that act as flow barriers [4]. This study aims to present the advantages of using the discontinuous Galerkin (DG) method for solving coupled flow and transport in fractured porous media. A mixed DG × CG space is utilised to solve the pressure equation. Subsequently, a velocity field is established using CG or Raviet − T homas function space; then the transport equation is solved on DG space. This procedure provides more accurate solutions in a convection-dominated regime, in which a sharp flood-front of the tracer is established, than those of CG formulation. The result of this work is compared to relatively new numerical methods, including hybrid-finite-element-finitevolume, lowest order Raviart-Thomas mixed finite elements, and multi-Point flux approximation methods as part of “Verification benchmarks for single-phase flow in three-dimensional fracturedporous media [4, 5, 6].”

M3 - Conference abstract for conference

ER -

Kadeethum T, Nick H, Salimzadeh S, Richardson CN, Ballarin F, Lee S. A Mixed-dimensional Discontinuous Galerkin Method for Coupled Flow and Transport in Fractured Porous Media. 2019. Abstract from 11th Annual Meeting Interpore 2019 Valencia, Valencia, Spain.