Finite-difference method Stokes solver (FDMSS) for 3D pore geometries: Software development, validation and case studies

Gerke, Kirill M.; Vasilyev, Roman; Khirevich, Siarhei; Collins, Daniel; Karsanina, Marina V.; Sizonenko, Timofey O.; Корост, Д. В.; Lamontagne, Sébastien; Mallants, Dirk

doi:10.1016/j.cageo.2018.01.005

Cited by 75 publications

(29 citation statements)

References 86 publications

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“…As discussed by previous studies the accuracy of permeability prediction improves with increasing numerical resolution (Gerke et al, 2018;Keehm, 2003;Eichheimer et al, 2019). To investigate this effect with respect to our samples, we computed the permeability of two subsamples (Ex35_04 & Ex36_02 see supplement material) using an increased resolution of 1024 3 grid points.…”

Section: Permeability Predictionmentioning

confidence: 85%

“…To achieve this goal, various experimental and numerical approaches have been developed over the years (e.g. Keehm, 2003;Andrä et al, 2013a;Gerke et al, 2018;Saxena et al, 2017). 1 https://doi.org/10.5194/se-2019-199 Preprint.…”

Section: Introductionmentioning

confidence: 99%

“…Using these images it is possible to compute fluid flow and several microstructural properties like porosity and specific surface as well as fluid properties including tortuosity and permeability. For this purpose several numerical methods including Finite Elements (FEM), Finite Differences (FDM) and Lattice Boltzmann method (LBM) (Saxena et al, 2017;Andrä et al, 2013a;Gerke et al, 2018;Shabro et al, 2014;Manwart et al, 2002;Bird et al, 2014) can be used.…”

Section: Introductionmentioning

confidence: 99%

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Combined numerical and experimental study of microstructure and permeability in porous granular media

Eichheimer¹,

Thielmann²,

Fujita³

et al. 2020

Preprint

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Abstract. Fluid flow on different scales is of interest for several Earth science disciplines like petrophysics, hydrogeology and volcanology. To parameterize fluid flow in large-scale numerical simulations (e.g. groundwater and volcanic systems), flow properties on the microscale need to be considered. For this purpose experimental and numerical investigations of flow through porous media over a wide range of porosities are necessary. In the present study we sinter glass bead media with various porosities. The microstructure, namely effective porosity and effective specific surface, is investigated using image processing. We determine flow properties like hydraulic tortuosity and permeability using both experimental measurements and numerical simulations. By fitting microstructural and flow properties to porosity, we obtain a modified Kozeny-Carman equation for isotropic low-porosity media, that can be used to simulate permeability in large-scale numerical models. To verify the modified Kozeny-Carman equation we compare it to the computed and measured permeability values.

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Section: Permeability Predictionmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Combined numerical and experimental study of microstructure and permeability in porous granular media

Eichheimer¹,

Thielmann²,

Fujita³

et al. 2020

Preprint

View full text Add to dashboard Cite

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“…) necessary to create a three-dimensional pore space. The subsequent computation of fluid flow through the reconstructed three-dimensional pore space is tackled with either Lattice-Boltzmann (Bosl et al, 1998;Pan et al, 2004;Guo and Zhao, 2002), finite difference (Manwart et al, 2002;Shabro et al, 2014;Gerke et al, 2018) or finite element methods (Garcia et al, 2009;Akanji and Matthai, 2010;Bird et al, 2014). The computed velocity field is then used to estimate permeability (Keehm, 2003;Saxena et al, 2017) and other physical properties (Saxena and Mavko, 2016;Knackstedt et al, 2009).…”

Section: Introductionmentioning

confidence: 99%

Pore-scale permeability prediction for Newtonian and non-Newtonian fluids

et al. 2019

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Abstract. The flow of fluids through porous media such as groundwater flow or magma migration is a key process in geological sciences. Flow is controlled by the permeability of the rock; thus, an accurate determination and prediction of its value is of crucial importance. For this reason, permeability has been measured across different scales. As laboratory measurements exhibit a range of limitations, the numerical prediction of permeability at conditions where laboratory experiments struggle has become an important method to complement laboratory approaches. At high resolutions, this prediction becomes computationally very expensive, which makes it crucial to develop methods that maximize accuracy. In recent years, the flow of non-Newtonian fluids through porous media has gained additional importance due to, e.g., the use of nanofluids for enhanced oil recovery. Numerical methods to predict fluid flow in these cases are therefore required. Here, we employ the open-source finite difference solver LaMEM (Lithosphere and Mantle Evolution Model) to numerically predict the permeability of porous media at low Reynolds numbers for both Newtonian and non-Newtonian fluids. We employ a stencil rescaling method to better describe the solid–fluid interface. The accuracy of the code is verified by comparing numerical solutions to analytical ones for a set of simplified model setups. Results show that stencil rescaling significantly increases the accuracy at no additional computational cost. Finally, we use our modeling framework to predict the permeability of a Fontainebleau sandstone and demonstrate numerical convergence. Results show very good agreement with experimental estimates as well as with previous studies. We also demonstrate the ability of the code to simulate the flow of power-law fluids through porous media. As in the Newtonian case, results show good agreement with analytical solutions.

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“…necessary to create a three dimensional pore space. The subsequent computation of fluid flow through the reconstructed three dimensional pore space is tackled with either Lattice-Boltzmann (Bosl et al, 1998;Pan et al, 2004;Guo and Zhao, 2002) , Finite Difference (Manwart et al, 2002;Shabro et al, 2014;Gerke et al, 2018) or Finite Element methods (Garcia et al, 2009;Akanji and Matthai, 2010;Bird et al, 2014). The computed velocity field is then used to estimate permeability (Keehm, 2003;Saxena et al, 2017) and other physical properties (Saxena and Mavko, 2016;Knackstedt et al, 2009).…”

Section: Introductionmentioning

confidence: 99%

Pore-scale permeability prediction for Newtonian and non-Newtonian fluids

Eichheimer¹,

Thielmann²,

Попов³

et al. 2019

Preprint

View full text Add to dashboard Cite

Abstract. The flow of fluids through porous media such as groundwater flow or magma migration are key processes in geological sciences. Flow is controlled by the permeability of the rock, thus an accurate determination and prediction of its value is of crucial importance. For this reason, permeability has been measured across different scales. As laboratory measurements exhibit a range of limitations, the numerical prediction of permeability at conditions where laboratory experiments struggle has become an important method to complement laboratory approaches. At high resolutions, this prediction becomes computationally very expensive, which makes it crucial to develop methods that maximize accuracy. In recent years, the flow of non-Newtonian fluids through porous media has gained additional importance due to e.g., the use of nanofluids for enhanced oil recovery. Numerical methods to predict fluid flow in these cases are therefore required. Here, we employ the open-source finite difference solver LaMEM to numerically predict the permeability of porous media at low Reynolds numbers for both Newtonian as well as non-Newtonian fluids. We employ a stencil rescaling method to better describe the solid-fluid interface. The accuracy of the code is verified by comparing numerical solutions to analytical ones for a set of simplified model setups. Results show that stencil rescaling significantly increases the accuracy at no additional computational cost. Finally, we use our modeling framework to predict the permeability of a Fontainebleau sandstone, and demonstrate numerical convergence. Results show very good agreement with experimental estimates as well as with previous studies. We also demonstrate the ability of the code to simulate the flow of power law fluids through porous media. As in the Newtonian case, results show good agreement with analytical solutions.

show abstract

Finite-difference method Stokes solver (FDMSS) for 3D pore geometries: Software development, validation and case studies

Cited by 75 publications

References 86 publications

Combined numerical and experimental study of microstructure and permeability in porous granular media

Combined numerical and experimental study of microstructure and permeability in porous granular media

Pore-scale permeability prediction for Newtonian and non-Newtonian fluids

Pore-scale permeability prediction for Newtonian and non-Newtonian fluids

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