Flow of non‐Newtonian fluids in fractured porous media: Isogeometric vs standard finite element discretisation

Understanding fluid flow in fractured porous media is of great importance in the fields of civil engineering in general or in soil science particular. This study is devoted to the development and validation of a numerical tool based on the use of the finite element method. To this aim, the problem of fluid flow in fractured porous media is considered as a problem of coupling free fluid and fluid flow in porous media or coupling of the Stokes and Darcy equations. The strong formulation of the problem is constructed, highlighting the condition at the free surface between the Stokes and Darcy regions, following by the variational formulation and numerical integration using the finite element method. Besides, the analytical solutions of the problem are constructed and compared with the numerical solutions given by the finite element approach. Both local properties and macroscopic responses of the two solutions are in excellent agreement, on condition that the porous media are sufficiently discretized by a certain level of finesse. The developed finite element tool of this study could pave the way to investigate many interesting flow problems in the field of soil science.

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Adaptive mixed finite element methods for Darcy flow in fractured porous media

Water Resources Research ◽

10.1002/2015wr018450 ◽

2016 ◽

Vol 52 (10) ◽

pp. 7851-7868 ◽

Cited By ~ 4

Author(s):

Huangxin Chen ◽

Amgad Salama ◽

Shuyu Sun

Keyword(s):

Finite Element ◽

Porous Media ◽

Finite Element Methods ◽

Mixed Finite Element ◽

Mixed Finite Element Methods ◽

Fractured Porous Media ◽

Darcy Flow

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A comparative study on simulating flow-induced fracture deformation in subsurface media by means of extended FEM and FVM

Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles ◽

10.2516/ogst/2020037 ◽

2020 ◽

Vol 75 ◽

pp. 41

Author(s):

Tingyu Li ◽

Dongxu Han ◽

Fusheng Yang ◽

Bo Yu ◽

Dongliang Sun ◽

...

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Porous Media ◽

Finite Volume ◽

Fractured Porous Media ◽

Single Fracture ◽

Diverse Range ◽

Advantages And Disadvantages ◽

Fracture Deformation ◽

Element Method

Accurate and efficient simulation on the fluid flow and deformation in porous media is of increasing importance in a diverse range of engineering fields. At present, there are only several methods can be used to simulate the deformation of fractured porous media. It is very important to know their application scopes, advantages, and disadvantages for solving the practical problems correctly. Therefore, in this paper, we compared two numerical simulation methods for flow-induced fracture deformation in porous media. One is the Extended Finite Element Method (XFEM), which is based on the classical finite element method and can simulate strong or weak discontinuous problems. The other is developed within the finite-volume framework, termed Extended Finite Volume Method (XFVM). We designed three test cases, including single fracture, cross fractures and eight discrete fractures, to investigate the accuracy and efficiency of XFEM and XFVM. The reference solutions were provided by the commercial software, COMSOL, where the standard finite element method is implemented. The research findings showed that the accuracy of the XFEM was slightly higher than that of the XFVM, but the latter was more efficient. These results are likely to be useful in decision making regarding choice of solving methods for the multi-field coupling problem in fractured porous media.

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