Two-Phase Flow: Structure, Upscaling, and Consequences for Macroscopic Transport Properties

Toussaint, Renaud; Måløy, Knut Jørgen; Méheust, Yves; Løvoll, Grunde; Jankov, Mihailo; Schäfer, Gerhard; Schmittbuhl, Jean

doi:10.2136/vzj2011.0123

Cited by 50 publications

(59 citation statements)

References 80 publications

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“…Quantitatively, this implies an inverse relationship between Ca * and disorder, namely that increasing disorder (at a given rate, Ca) produces a more CF-like pattern, increasing the transitional Ca between CF to VF, Ca CF/VF 1821222324. We point to a subtle yet crucial inconsistency in the above: if increasing disorder increases Ca CF/VF , promoting a more CF-like pattern, sweep efficiency should increase (since VF is much less efficient that CF182122232428), contrasting the observations stated above.…”

Section: Current Understanding Of Disorder Effectsmentioning

confidence: 79%

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Effects of Pore-Scale Disorder on Fluid Displacement in Partially-Wettable Porous Media

Holtzman

2016

Sci Rep

123

125

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We present a systematic, quantitative assessment of the impact of pore size disorder and its interplay with flow rates and wettability on immiscible displacement of a viscous fluid. Pore-scale simulations and micromodel experiments show that reducing disorder increases the displacement efficiency and compactness, minimizing the fluid-fluid interfacial area, through (i) trapping at low rates and (ii) viscous fingering at high rates. Increasing the wetting angle suppresses both trapping and fingering, hence reducing the sensitivity of the displacement to the underlying disorder. A modified capillary number Ca* that includes the impact of disorder λ on viscous forces (through pore connectivity) is direct related to λ, in par with previous works. Our findings bear important consequences on sweep efficiency and fluid mixing and reactions, which are key in applications such as microfluidics to carbon geosequestration, energy recovery, and soil aeration and remediation.

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Section: Current Understanding Of Disorder Effectsmentioning

confidence: 79%

“…The finger width w is evaluated by skeletonizing the pattern with a Voronoi algorithm, and measuring the distance (in lattice units a ) of the medial line from the interface. In evaluating w we include small clusters trapped within fingers, unlike some previous studies where these were ignored28 (resulting in larger w ).…”

Section: Resultsmentioning

confidence: 99%

Effects of Pore-Scale Disorder on Fluid Displacement in Partially-Wettable Porous Media

Holtzman

2016

Sci Rep

123

125

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“…This means that the invading fluid displaces the more viscous one in separated finger-like intrusions, while leaving the fluid inbetween the fingers less or not displaced. Following an increased interest in this phenomenon, two-phase flow have been widely studied in quasi-2-dimensional porous media confined in thin cells with circular and rectangular geometries [2][3][4][5][6][7][8][9][10][11][12][13][14]. In horizontal cells containing rigid disordered porous media, the unstable invasion patterns during drainage are found to be fractal and either form an invasion percolation cluster [15] in the capillary fingering regime [16,17], or long thin fingers resembling DLA patterns in the viscous fingering regime [18,19].…”

Section: Introductionmentioning

confidence: 99%

“…In horizontal cells containing rigid disordered porous media, the unstable invasion patterns during drainage are found to be fractal and either form an invasion percolation cluster [15] in the capillary fingering regime [16,17], or long thin fingers resembling DLA patterns in the viscous fingering regime [18,19]. The flow regime during drainage of a horizontal porous medium is dependent on the ratio between the driving and stabilizing forces involved in flow and pore-invasion, usually described by the dimensionless capillary number Ca [3,5]. The capillary number is the ratio of viscous pressure drop over capillary pressure drop at the characteristic pore scale, and can be found by…”

Section: Introductionmentioning

confidence: 99%

Invasion patterns during two-phase flow in deformable porous media

et al. 2015

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We study the formation of viscous fingering and fracturing patterns that occur when air at constant overpressure invades a circular Hele-Shaw cell containing a liquid-saturated deformable porous medium-i.e., during the flow of two non-miscible fluids in a confined granular medium at high enough rate to deform it. The resulting patterns are characterized in terms of growth rate, average finger thickness as function of radius and time, and fractal properties. Based on experiments with various injection pressures, we identify and compare typical pattern characteristics when there is no deformation, compaction, and/or decompaction of the porous medium. This is achieved by preparing monolayers of glass beads in cells with various boundary conditions, ranging from a rigid disordered porous medium to a deformable granular medium with either a semi-permeable or a free outer boundary. We show that the patterns formed have characteristic features depending on the boundary conditions. For example, the average finger thickness is found to be constant with radius in the non-deformable (ND) system, while in the deformable ones there is a larger initial thickness decreasing to the ND value. Then, depending on whether the outer boundary is semi-permeable or free there is a further decrease or increase in the average finger thickness. When estimated from the flow patterns, the box-counting fractal dimensions are not found to change significantly with boundary conditions, but by using a method to locally estimate fractal dimensions, we see a transition in behavior with radius for patterns in deformable systems; In the deformable system with a free boundary, it seems to be a transition in universality class as the local fractal dimensions decrease toward the outer rim, where fingers are opening up like fractures in a paste.

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“…Lenormand et al (1988) performed laboratory experiments using pseudo-2D micro models (pore networks etched in glass plates) and observed a cluster fractal dimension of D = 1.81 at slow invasion rates. See Lovoll et al (2004) and Toussaint et al (2005Toussaint et al ( , 2012 for interesting experiments and discussions involving a broad range of immiscible invasion scenarios. IP is normally performed on a lattice of sites connected by bonds.…”

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confidence: 99%

A Fast Algorithm for Invasion Percolation

Masson

Pride

2014

Transp Porous Med

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We present a computationally fast Invasion Percolation (IP) algorithm. IP is a numerical approach for generating realistic fluid distributions for quasi-static (i.e., slow) immiscible fluid invasion in porous media. The algorithm proposed here uses a binary-tree data structure to identify the site (pore) connected to the invasion cluster that is the next to be invaded. Gravity is included. Trapping is not explicitly treated in the numerical examples but can be added, for example, using a Hoshen-Kopelman algorithm. Computation time to percolation for a 3D system having N total sites and M invaded sites at percolation goes as O(M log M) for the proposed binary-tree algorithm and as O(M N) for a standard implementation of IP that searches through all of the uninvaded sites at each step. The relation between M and N is M = N D/E , where D is the fractal dimension of an infinite cluster and E is Euclidean space dimension. In numerical practice, on finite-sized cubic lattices with invasion structures influenced by the injection boundary and boundary conditions lateral to the flow direction, we observe the scaling M = N 0.852 in 3D (valid through the second decimal place) instead of M = N 0.843 based on the infinite cluster fractal dimension D = 2.53.

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Two-Phase Flow: Structure, Upscaling, and Consequences for Macroscopic Transport Properties

Cited by 50 publications

References 80 publications

Effects of Pore-Scale Disorder on Fluid Displacement in Partially-Wettable Porous Media

Effects of Pore-Scale Disorder on Fluid Displacement in Partially-Wettable Porous Media

Invasion patterns during two-phase flow in deformable porous media

A Fast Algorithm for Invasion Percolation

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