A Monte Carlo paradigm for capillarity in porous media

Lu, Ning; Zeidman, B.; Lusk, Mark T.; Willson, Clinton S.; Wu, David T.

doi:10.1029/2010gl045599

Cited by 28 publications

(44 citation statements)

References 24 publications

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“…For example, Lu et al . verified the prediction results of the SAM against X‐ray CT observations, Sukop et al . compared the MCMP LBM with X‐ray CT results, and Sukop and Or declared that SCMP LBM can produce realistic multiphase distributions.…”

Section: Introductionsupporting

confidence: 58%

“…The global interfacial energy E of the system can be calculated as

E = true {true\sum}_{i, j} true {true\sum}_{k, \overset{true¯}{k}} J_{k \overset{k}{true}} n_{i}^{k} n_{j}^{\overset{k}{true}}

which is the interfacial energy between the pixel site i and all its nearest neighbor sites j , with phases of k and

\overset{k}{true}

that span all the sites, where

n_{i}^{k} = 1

if the pixel site is in phase k and 0 otherwise.

J_{k, \overset{k}{true}}

is the interfacial free energy of the contact surface between different phases and is defined as

J_{k, \overset{k}{true}} = ({, \begin{array}{c} center & - 1 & ((), k = 1, \overset{k}{true} = 1) \\ center & 1 & ((), k = 1, \overset{k}{true} = - 1) \\ center & - 2 & ((), k = 1, \overset{k}{true} = 0) \\ center & 0 & else \end{array})

which reproduces the perfect wetting condition .…”

Section: Methodsmentioning

confidence: 99%

“…The system approaches equilibrium (Figure (c)) when the energy change between two Markov chains satisfies ( E m − E m − 1 )/ E m − 1 < 10 − 5 . After reaching equilibrium, another 200 Markov chains are performed, and the profiles generated from each of the Markov chains are averaged to create a smooth curve of the interface, which is called anti‐aliasing (Figure (d)). The simulated annealing is a commonly used methodology for multi‐parameter global optimization problems.…”

Section: Methodsmentioning

confidence: 99%

“…Later, Silverstein and Fort applied the method to study the fluid distribution in sphere packs, Berkowitz and Hansen extended the SAM to the water distribution in a partially saturated sandstone, and Lu et al . investigated the capillarity phenomenon in porous media. Recently, the LBM has become a promising solution for multiphase problems for porous media .…”

Section: Introductionmentioning

confidence: 99%

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Numerical study of two-phase fluid distributions in fractured porous media

Yin

Zhao

2015

Int. J. Numer. Anal. Meth. Geomech.

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Summary Two‐phase fluid distributions in fractured porous media were studied using a single‐component multiphase (SCMP) lattice Boltzmann method (LBM), which was selected among three commonly used numerical approaches through a comparison against the available results of micro X‐ray computed tomography. The influence of the initial configuration and the periodic boundary conditions in the SCMP LBM for the fluid distribution analysis were investigated as well. It was revealed that regular porous media are sensitive to the initial distribution, whereas irregular porous media are insensitive. Moreover, to eliminate the influence of boundaries, the model's buffer size of an SCMP LBM simulation was suggested to be taken as approximately 12.5 times the average particle size. Then, the two‐phase fluid distribution of a porous medium was numerically studied using the SCMP LBM. Both detailed distribution patterns and macroscopic morphology parameters were reasonably well captured. Finally, the two‐phase fluid distributions in a fractured porous media were investigated. The influence of the degree of saturation, fracture length, and fracture width on the fluid distributions and migration was explored. Copyright © 2015 John Wiley & Sons, Ltd.

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Section: Introductionsupporting

confidence: 58%

“…The global interfacial energy E of the system can be calculated as

E = true {true\sum}_{i, j} true {true\sum}_{k, \overset{true¯}{k}} J_{k \overset{k}{true}} n_{i}^{k} n_{j}^{\overset{k}{true}}

which is the interfacial energy between the pixel site i and all its nearest neighbor sites j , with phases of k and

\overset{k}{true}

that span all the sites, where

n_{i}^{k} = 1

if the pixel site is in phase k and 0 otherwise.

J_{k, \overset{k}{true}}

is the interfacial free energy of the contact surface between different phases and is defined as

J_{k, \overset{k}{true}} = ({, \begin{array}{c} center & - 1 & ((), k = 1, \overset{k}{true} = 1) \\ center & 1 & ((), k = 1, \overset{k}{true} = - 1) \\ center & - 2 & ((), k = 1, \overset{k}{true} = 0) \\ center & 0 & else \end{array})

which reproduces the perfect wetting condition .…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical study of two-phase fluid distributions in fractured porous media

Yin

Zhao

2015

Int. J. Numer. Anal. Meth. Geomech.

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“…Advancements in microtomographic image acquisition and processing methods over the past two decades have provided the means to accurately characterize fluid‐fluid interfacial area in three‐dimensional porous‐media systems. High‐resolution industrial X‐ray microtomography (XMT) and in particular synchrotron XMT have been used to measure air‐water and organic liquid‐water interfacial areas for synthetic media (Aferka et al, ; Al‐Raoush & Willson, ; Culligan et al, ; Culligan et al, ; Landry et al, ; Lu et al, ; Lyu et al, ; Narter & Brusseau, ; Patmonoaji et al, ; Porter et al, ; Prodanovic et al, ; Wang et al, ) and natural porous media (Schnaar & Brusseau, , , ; Brusseau et al, , Brusseau et al, , Brusseau et al, , Brusseau et al, ; Costanza‐Robinson et al, ; Al‐Raoush, , ; Russo et al, ; Willson et al, ; Carroll et al, ; McDonald et al, ; Lyu et al, , Patmonoaji et al, ).…”

Section: Introductionmentioning

confidence: 99%

Assessing XMT‐Measurement Variability of Air‐Water Interfacial Areas in Natural Porous Media

Araujo

Brusseau

2020

Water Resources Research

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This study investigates the accuracy and reproducibility of air-water interfacial areas measured with high-resolution synchrotron X-ray microtomography (XMT). Columns packed with one of two relatively coarse-grained monodisperse granular media, glass beads or a well-sorted quartz sand, were imaged over several years, encompassing changes in acquisition equipment, improved image quality, and enhancements to image acquisition and to processing software. For the glass beads, the specific solid surface area (SSSA-XMT) of 31.6 ± 1 cm −1 determined from direct analysis of the segmented solid-phase image data is statistically identical to the independently calculated geometric smooth-sphere specific solid surface area (GSSA, 32 ± 1 cm −1 ) and to the measured SSSA (28 ± 3 cm −1 ) obtained with the N 2 -Brunauer, Emmett, and Teller method. The maximum specific air-water interfacial area (A max ) is 27.4 (±2) cm −1 , which compares very well to the SSSA-XMT, GSSA, and SSSA-N 2 -Brunauer, Emmett, and Teller values. For the sand, the SSSA-XMT (111 ± 2 cm −1 ) and GSSA (113 ± 1 cm −1 ) are similar. The mean A max is 96 ± 5 cm −1 , which compares well to both the SSSA and the GSSA values. The XMT-SSSA values deviated from the GSSA values by 7-16% for the first four experiments but were essentially identical for the later experiments. This indicates that enhancements in image acquisition and processing improved data accuracy. The A max values ranged from 74 cm −1 to 101 cm −1 , with a coefficient of variation (COV) of 9%. The maximum capillary interfacial area ranged from 12 cm −1 to 19 cm −1 , for a COV of 10%. The COVs for both decreased to 5-6% for the latter five experiments. These results demonstrate that XMT imaging provides accurate and reproducible measurements of total and capillary interfacial areas.

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Realistic modeling of cemented granular materials with a lattice spring model by developing a digital 3D reconstruction approach

Wei

Deng

Zhao

2022

Num Anal Meth Geomechanics

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Three-dimensional (3D) geometric reconstruction is a fundamental requirement to realistically predict the mechanical behavior of cemented granular materials (CGMs). In this work, a four-phase geometric reconstruction method for CGMs, involving aggregate, cement, in-between interfacial transition zone (ITZ), and void phases, is developed by using digital image processing techniques and an optimization algorithm. The reconstruction method includes four steps. (1) The planar outlines of aggregates are extracted from a two-dimensional (2D) aggregate image (e.g., gravels, pebbles, and crushed stones) based on the image segmentation algorithm. (2) Through spatial geometric transformations on the acquired planar outlines, the 3D aggregates are generated, whose reliability is verified by comparison with those obtained by a 3D scanner. (3) According to the volume ratio of each phase, the initial four-phase model is reconstructed by randomly placing aggregates into the user-defined domain with considering the size distribution of aggregates, followed by the generation of the ITZ represented by their surrounding minimum envelope surface, and the insertion of voids in the rest cement phase. (4) The final realistic CGM is reconstructed by optimizing the spatial distribution of the void and cement phases based on a simulated annealing algorithm. Afterwards, the rationality of the reconstructed CGM is verified by comparing two-point probability functions between the physical model and the reconstructed model. With the aid of a four-dimensional lattice spring model (4D-LSM), the feasibility of the reconstructed CGM to reproduce its mechanical behavior is demonstrated by numerical examples and a comparison with existing experimental or other numerical solutions.

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A Monte Carlo paradigm for capillarity in porous media

Cited by 28 publications

References 24 publications

Numerical study of two-phase fluid distributions in fractured porous media

Numerical study of two-phase fluid distributions in fractured porous media

Assessing XMT‐Measurement Variability of Air‐Water Interfacial Areas in Natural Porous Media

Realistic modeling of cemented granular materials with a lattice spring model by developing a digital 3D reconstruction approach

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