Permeability from 3D Porous media images: a fast two-step approach

Umang Agarwal, Faruk Omer Alpak, J.M.Vianney A. Koelman

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)

Abstract

An efficient methodology to calculate absolute permeability of porous media using a two-step algorithm is developed. In the first step, the creeping flow equations over the pore space are translated into a Darcy flow problem with the pore space being represented by appropriately chosen local flow conductivities. In the next step, a combined renormalization group and multi-level iterative Laplace solver approach is used to upscale the local conductivities to obtain the effective permeability for the full domain. The accuracy and computational efficiency of the proposed two-step local conductivity–Laplace scheme (LC-LAP) are tested against a FFT (fast Fourier transform) accelerated solver which uses a semi-implicit method for the pressure-linked equation (SIMPLE-FFT) and against a solver that features the GPGPU implementation of the multiple-relaxation-time lattice Boltzmann method (MRT-LBM). A detailed comparison is made by computing permeabilities from all three methods over model geometries and digitized images obtained from micron-scale-resolution computerized tomography (micro-CT) of sandstone rocks of varying porosities and heterogeneity levels. We observe an agreement between our method and either benchmark methods (SIMPLE-FFT and MRT-LBM) that is similar to the agreement between both benchmarks. On the samples tested, the computational performance advantage of the LC-LAP approach ranges from 10- to 40-fold compered to SIMPLE-FFT and 8- to 25-fold compared to MRT-LBM. The proposed method is suitable for fast computations and for computations over very large volumes (due to much lower memory and compute resource requirements) for determining single-phase permeabilities of medium- to high-permeability rocks.

LanguageEnglish
Pages1017-1033
Number of pages17
JournalTransport in Porous Media
Volume124
Issue number3
DOIs
StatePublished - 1 Sep 2018

Fingerprint

Fast Fourier transforms
Porous materials
Relaxation time
Rocks
Computerized tomography
Computational efficiency
Sandstone
Porosity
Data storage equipment
Geometry

Cite this

Agarwal, Umang ; Alpak, Faruk Omer ; Koelman, J.M.Vianney A./ Permeability from 3D Porous media images : a fast two-step approach. In: Transport in Porous Media. 2018 ; Vol. 124, No. 3. pp. 1017-1033
@article{4f9688b6509b40cbaa2e58d457a9594e,
title = "Permeability from 3D Porous media images: a fast two-step approach",
abstract = "An efficient methodology to calculate absolute permeability of porous media using a two-step algorithm is developed. In the first step, the creeping flow equations over the pore space are translated into a Darcy flow problem with the pore space being represented by appropriately chosen local flow conductivities. In the next step, a combined renormalization group and multi-level iterative Laplace solver approach is used to upscale the local conductivities to obtain the effective permeability for the full domain. The accuracy and computational efficiency of the proposed two-step local conductivity–Laplace scheme (LC-LAP) are tested against a FFT (fast Fourier transform) accelerated solver which uses a semi-implicit method for the pressure-linked equation (SIMPLE-FFT) and against a solver that features the GPGPU implementation of the multiple-relaxation-time lattice Boltzmann method (MRT-LBM). A detailed comparison is made by computing permeabilities from all three methods over model geometries and digitized images obtained from micron-scale-resolution computerized tomography (micro-CT) of sandstone rocks of varying porosities and heterogeneity levels. We observe an agreement between our method and either benchmark methods (SIMPLE-FFT and MRT-LBM) that is similar to the agreement between both benchmarks. On the samples tested, the computational performance advantage of the LC-LAP approach ranges from 10- to 40-fold compered to SIMPLE-FFT and 8- to 25-fold compared to MRT-LBM. The proposed method is suitable for fast computations and for computations over very large volumes (due to much lower memory and compute resource requirements) for determining single-phase permeabilities of medium- to high-permeability rocks.",
author = "Umang Agarwal and Alpak, {Faruk Omer} and Koelman, {J.M.Vianney A.}",
year = "2018",
month = "9",
day = "1",
doi = "10.1007/s11242-018-1108-0",
language = "English",
volume = "124",
pages = "1017--1033",
journal = "Transport in Porous Media",
issn = "0169-3913",
publisher = "Springer",
number = "3",

}

Permeability from 3D Porous media images : a fast two-step approach. / Agarwal, Umang; Alpak, Faruk Omer; Koelman, J.M.Vianney A.

In: Transport in Porous Media, Vol. 124, No. 3, 01.09.2018, p. 1017-1033.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Permeability from 3D Porous media images

T2 - Transport in Porous Media

AU - Agarwal,Umang

AU - Alpak,Faruk Omer

AU - Koelman,J.M.Vianney A.

PY - 2018/9/1

Y1 - 2018/9/1

N2 - An efficient methodology to calculate absolute permeability of porous media using a two-step algorithm is developed. In the first step, the creeping flow equations over the pore space are translated into a Darcy flow problem with the pore space being represented by appropriately chosen local flow conductivities. In the next step, a combined renormalization group and multi-level iterative Laplace solver approach is used to upscale the local conductivities to obtain the effective permeability for the full domain. The accuracy and computational efficiency of the proposed two-step local conductivity–Laplace scheme (LC-LAP) are tested against a FFT (fast Fourier transform) accelerated solver which uses a semi-implicit method for the pressure-linked equation (SIMPLE-FFT) and against a solver that features the GPGPU implementation of the multiple-relaxation-time lattice Boltzmann method (MRT-LBM). A detailed comparison is made by computing permeabilities from all three methods over model geometries and digitized images obtained from micron-scale-resolution computerized tomography (micro-CT) of sandstone rocks of varying porosities and heterogeneity levels. We observe an agreement between our method and either benchmark methods (SIMPLE-FFT and MRT-LBM) that is similar to the agreement between both benchmarks. On the samples tested, the computational performance advantage of the LC-LAP approach ranges from 10- to 40-fold compered to SIMPLE-FFT and 8- to 25-fold compared to MRT-LBM. The proposed method is suitable for fast computations and for computations over very large volumes (due to much lower memory and compute resource requirements) for determining single-phase permeabilities of medium- to high-permeability rocks.

AB - An efficient methodology to calculate absolute permeability of porous media using a two-step algorithm is developed. In the first step, the creeping flow equations over the pore space are translated into a Darcy flow problem with the pore space being represented by appropriately chosen local flow conductivities. In the next step, a combined renormalization group and multi-level iterative Laplace solver approach is used to upscale the local conductivities to obtain the effective permeability for the full domain. The accuracy and computational efficiency of the proposed two-step local conductivity–Laplace scheme (LC-LAP) are tested against a FFT (fast Fourier transform) accelerated solver which uses a semi-implicit method for the pressure-linked equation (SIMPLE-FFT) and against a solver that features the GPGPU implementation of the multiple-relaxation-time lattice Boltzmann method (MRT-LBM). A detailed comparison is made by computing permeabilities from all three methods over model geometries and digitized images obtained from micron-scale-resolution computerized tomography (micro-CT) of sandstone rocks of varying porosities and heterogeneity levels. We observe an agreement between our method and either benchmark methods (SIMPLE-FFT and MRT-LBM) that is similar to the agreement between both benchmarks. On the samples tested, the computational performance advantage of the LC-LAP approach ranges from 10- to 40-fold compered to SIMPLE-FFT and 8- to 25-fold compared to MRT-LBM. The proposed method is suitable for fast computations and for computations over very large volumes (due to much lower memory and compute resource requirements) for determining single-phase permeabilities of medium- to high-permeability rocks.

UR - http://www.scopus.com/inward/record.url?scp=85049150882&partnerID=8YFLogxK

U2 - 10.1007/s11242-018-1108-0

DO - 10.1007/s11242-018-1108-0

M3 - Article

VL - 124

SP - 1017

EP - 1033

JO - Transport in Porous Media

JF - Transport in Porous Media

SN - 0169-3913

IS - 3

ER -