Ensemble distribution for immiscible two-phase flow in porous media

Savani, Isha; Bedeaux, Dick; Kjelstrup, Signe; Vassvik, Morten; Sinha, Santanu; Hansen, Alex

doi:10.1103/physreve.95.023116

Cited by 10 publications

(10 citation statements)

References 59 publications

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“…In this section, we connect the pseudo-thermodynamic results of section III to the properties of an underlying ensemble distribution. This concept in the context of immiscible two-phase flow was first considered by Savani et al [32]. Here we generalize this concept.…”

Section: Differential Transversal Area Distributionsmentioning

confidence: 67%

Flow-Area Relations in Immiscible Two-Phase Flow in Porous Media

2020

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We present a theoretical framework for immiscible incompressible two-phase flow in homogeneous porous media that connects the distribution of local fluid velocities to the average seepage velocities. By dividing the pore area along a cross-section transversal to the average flow direction up into differential areas associated with the local flow velocities, we construct a distribution function that allows us not only to re-establish existing relationships between the seepage velocities of the immiscible fluids, but also to find new relations between their higher moments. We support and demonstrate the formalism through numerical simulations using a dynamic pore-network model for immiscible two-phase flow with two-and three-dimensional pore networks. Our numerical results are in agreement with the theoretical considerations.

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Section: Differential Transversal Area Distributionsmentioning

confidence: 67%

Flow-Area Relations in Immiscible Two-Phase Flow in Porous Media

2020

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“…Modern network theory has evolved through a synthesis of mathematical graph theory [1][2][3] with problems and methods from social sciences [4,5] and physics [6][7][8][9][10][11][12], into a powerful paradigm for analysis of complex systems consisting of interacting entities. Current interdisciplinary applications include modeling of transport in porous media and composites [13,14], reaction networks in chemical synthesis [15], food webs in ecology [16], transportation and distribution networks [17][18][19], economics and sociology [20], the Internet and the World Wide Web [21], and many more.…”

Section: Introductionmentioning

confidence: 99%

Absorbing random walks interpolating between centrality measures on complex networks

Gurfinkel

Rikvold

2020

Phys. Rev. E

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Centrality, which quantifies the importance of individual nodes, is among the most essential concepts in modern network theory. As there are many ways in which a node can be important, many different centrality measures are in use. Here, we concentrate on versions of the common betweenness and closeness centralities. The former measures the fraction of paths between pairs of nodes that go through a given node, while the latter measures an average inverse distance between a particular node and all other nodes. Both centralities only consider shortest paths (i.e., geodesics) between pairs of nodes. Here we develop a method, based on absorbing Markov chains, that enables us to continuously interpolate both of these centrality measures away from the geodesic limit and toward a limit where no restriction is placed on the length of the paths the walkers can explore. At this second limit, the interpolated betweenness and closeness centralities reduce, respectively, to the well-known current betweenness and resistance closeness (information)centralities. The method is tested numerically on four real networks, revealing complex changes in node centrality rankings with respect to the value of the interpolation parameter. Non-monotonic betweenness behaviors are found to characterize nodes that lie close to inter-community boundaries in the studied networks.ity's preference for geodesics. However, these do not precisely reduce to the betweenness. Kivimäki et al . [45,46] introduce the randomized-shortest-path (RSP) framework, which assigns Boltzmann weights to all paths in the network. Their inverse temperature parameter also tunes the preference for geodesics. In [45], RSP is used to interpolate between graph distance and resistance distance, while in [46] it is used to interpolate between random-walk betweenness and a measure similar to standard betweenness centrality. In [47], Bavaud and Guex accomplish a weighting equivalent to RSP through the minimization of a free-energy functional. Françoisse et al . also reach similar results with a different path-weighting scheme in [48]. Estrada, Higham, and Hatano [25] calculate a version of betweenness centrality by assigning lower weights to longer paths.The remainder of this paper is organized as follows. In Sec. II A, we introduce notations and conventions. In Sec. II B, we discuss well-known centrality measures. In Sec. II C, we develop two new parametrized centralities, based on a specific absorbing random walk, that interpolate between (a) closeness and resistance-closeness centralities and (b) betweenness and random-walk betweenness centralities. In Sec. III A, we report the behavior of these centralities on four example networks. In Sec. III B, we use the numerical examples to explain how the presence of similarly-long paths leads to specific centrality behaviors. In Sec. III C, we provide a model for the non-monotonicity encountered in some of the numerics. In

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“…The REV can be regarded as homogeneous only on the REV scale. With one driving force the variables on this scale can be obtained, knowing the micro-scale ensemble distribution [30,31]. This averaging procedure must keep invariant the entropy production, a necessary condition listed already in the 1990ies [7,12].…”

Section: Defining the Systemmentioning

confidence: 99%

“…We now take the derivative of equation (24) with respect to S w and combine with the two previous equations (30) and (31) to find…”

Section: Consequences Of the Euler Theorem: New Equationsmentioning

confidence: 99%

Relations Between Seepage Velocities in Immiscible, Incompressible Two-Phase Flow in Porous Media

et al. 2018

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Based on thermodynamic considerations we derive a set of equations relating the seepage velocities of the fluid components in immiscible and incompressible two-phase flow in porous media. They necessitate the introduction of a new velocity function, the co-moving velocity. This velocity function is a characteristic of the porous medium. Together with a constitutive relation between the velocities and the driving forces, such as the pressure gradient, these equations form a closed set. We solve four versions of the capillary tube model analytically using this theory. We test the theory numerically on a network model.

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Ensemble distribution for immiscible two-phase flow in porous media

Cited by 10 publications

References 59 publications

Flow-Area Relations in Immiscible Two-Phase Flow in Porous Media

Flow-Area Relations in Immiscible Two-Phase Flow in Porous Media

Absorbing random walks interpolating between centrality measures on complex networks

Relations Between Seepage Velocities in Immiscible, Incompressible Two-Phase Flow in Porous Media

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