Permeability determination of porous media using large‐scale finite elements and iterative solver

Karim, Md. Rezaul; Krabbenhøft, K.; Lyamin, A. V.

doi:10.1002/nag.2245

Cited by 7 publications

(3 citation statements)

References 69 publications

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“…For this reason, many authors seek to use stabilization techniques to make use of this type of discretization. As an example, we can cite the works of Andreassen and Andreasen [1], Yang et al [5], Karim et al [12], Braack and Schieweck [13], Codina and Blasco [14], and Becker and Hansbo [15].…”

Section: Computational Fluid Dynamics With Finite Element Methods (Fem)mentioning

confidence: 99%

Computing Effective Permeability of Porous Media with FEM and Micro-CT: An Educational Approach

Vianna

Cunha

Azeredo

et al. 2020

Fluids

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Permeability is a parameter that measures the resistance that fluid faces when flowing through a porous medium. Usually, this parameter is determined in routine laboratory tests by applying Darcy’s law. Those tests can be complex and time-demanding, and they do not offer a deep understanding of the material internal microstructure. Currently, with the development of new computational technologies, it is possible to simulate fluid flow experiments in computational labs. Determining permeability with this strategy implies solving a homogenization problem, where the determination of the macro parameter relies on the simulation of a fluid flowing through channels created by connected pores present in the material’s internal microstructure. This is a powerful example of the application of fluid mechanics to solve important industrial problems (e.g., material characterization), in which the students can learn basic concepts of fluid flow while practicing the implementation of computer simulations. In addition, it gives the students a concrete opportunity to work with a problem that associates two different scales. In this work, we present an educational code to compute absolute permeability of heterogeneous materials. The program simulates a Stokes flow in the porous media modeled with periodic boundary conditions using finite elements. Lastly, the permeability of a real sample of sandstone, modeled by microcomputed tomography (micro-CT), is obtained.

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Section: Computational Fluid Dynamics With Finite Element Methods (Fem)mentioning

confidence: 99%

Computing Effective Permeability of Porous Media with FEM and Micro-CT: An Educational Approach

Vianna

Cunha

Azeredo

et al. 2020

Fluids

View full text Add to dashboard Cite

show abstract

“…[4][5][6] Various numerical methods have been implemented for predicting the effective permeability of porous medium. For example, Karim et al, 7 Vianna et al 8 used the finite element method (FEM) to solve the incompressible viscous Navier-Stokes equation that described the fluid flow in pores. Due to the imposed incompressibility constraint for the fluid, various stabilization techniques should be introduced.…”

Section: Introductionmentioning

confidence: 99%

An FFT‐based Galerkin method for the effective permeability of porous material

Tong

Wang

et al. 2022

Numerical Meth Engineering

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A numerical scheme which is a combination of FFT and Galerkin methods is proposed for calculating the effective permeability of periodic porous material. First, a periodic stress field whose divergence is equal to the subtraction of body force from prescribed pressure gradient is introduced to reformulate the governing equations. Then, an auxiliary problem is established to replace the prescribed pressure gradient with the resulting initial prescribed stress. An FFT-based Galerkin method of stress control type, the associated projection operator for zero divergence condition and the treatment of composite pixels/voxels are presented for solving the viscous flow in periodic porous material. Finally, numerical examples of viscous flows in 2D parallel fissured medium, 2Dmedium with regularly packed squares, 2D medium with regularly packed and rotated squares, 3D medium with regularly packed ellipsoids, and 3D medium with randomly packed ellipsoids are implemented. Numerical results calculated by FFT-based Galerkin method agree well with analytical solutions and finite element results. The proposed FFT-based Galerkin method is effective for predicting the macro permeability of porous material with complex meso structures.

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“…In some early works, estimates for Among numerical methods for the computation of the effective permeability, finite-difference schemes (Martys et al, 1994) and, more recently, fast multipole expansions (Koo and Sangani, 2002) as well as Boltzmann Lattice Methods (Belov et al, 2004;Lee and Lee, 2013) have been used. Recently, largescale computations have been carried out using a finite element method (Karim et al, 2014). Interestingly, several Fourier-based algorithms have been devised to treat Stokes flow (Wiegmann, 2007;Monchiet et al, 2009;N'guyen et al, 2013;Bignonnet and Dormieux, 2014).…”

Section: Introductionmentioning

confidence: 99%

Stokes Flow Through a Boolean Model of Spheres: Representative Volume Element

2015

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The Stokes flow is numerically computed in porous media based on 3D Boolean random sets of spheres. Two configurations are investigated in which the fluid flows inside the spheres or in the complementary set of the spheres. Full-field computations are carried out using the Fourier method of Wiegmann (2007). The latter is applied to large system sizes representative of the microstructure. The overall permeability of the two models as well as the Representative Volume Element (RVE) are estimated as a function of the pore volume fraction. We give numerical estimates for the asymptotic behavior of the permeability in the dilute limit for the solid phase, and close to the percolation threshold of the pores. FFT maps of the velocity field are presented, for increasing values of the pore volume fraction. The patterns of the local velocity field is analysed using various morphological criteria. The tortuosity of the streamlines is found to be much higher than the geometrical tortuosity, for both models. The histograms of the velocity field are computed at increasing pore volume fraction. The covariance of orientation is used to characterize the spatial correlation of the velocity field.

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Permeability determination of porous media using large‐scale finite elements and iterative solver

Cited by 7 publications

References 69 publications

Computing Effective Permeability of Porous Media with FEM and Micro-CT: An Educational Approach

Computing Effective Permeability of Porous Media with FEM and Micro-CT: An Educational Approach

An FFT‐based Galerkin method for the effective permeability of porous material

Stokes Flow Through a Boolean Model of Spheres: Representative Volume Element

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