Distribution of shortest paths at percolation threshold: application to oil recovery with multiple wells

Soares, R. F.; Corso, Gilberto; Lucena, L. S.; Freitas, J. E.; Silva, L.R. da; Paul, Gerald; Stanley, H. Eugene

doi:10.1016/j.physa.2004.05.050

Cited by 10 publications

(4 citation statements)

References 8 publications

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“…They analyzed the traveling time probability density function for two values of the fraction of connecting bonds, namely the homogeneous case and the inhomogeneous critical threshold case. Soares et al [2004] investigated the distribution of shortest paths in percolation systems at the percolation threshold from one injector well to multiple producer wells. They calculated the probability distribution of the optimal path length.…”

Section: Breakthrough and Post Breakthrough Behaviormentioning

confidence: 99%

Percolation Approach in Underground Reservoir Modeling

Masihi¹,

King²

2012

Water Resources Management and Modeling

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Section: Breakthrough and Post Breakthrough Behaviormentioning

confidence: 99%

Percolation Approach in Underground Reservoir Modeling

Masihi¹,

King²

2012

Water Resources Management and Modeling

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“…Nevertheless, the available studies considering the P2P and L2L connectivity are restricted to breakthrough time and hydrocarbon recovery prediction and not connectivity and conductivity evaluation as well as their critical properties (e.g. [10][11][12][13][56][57][58][59][60][61][62][63][64][65]).…”

Section: Point To Point (P2p) Versus Line To Line (L2l) Connectivitymentioning

confidence: 99%

Point to point continuum percolation in two dimensions

Sadeghnejad

Masihi

2016

J. Stat. Mech.

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The outcome of the classic percolation approach is several powerlaw curves with some universal (critical) exponents. Here, the universality means that these power laws as well as their critical exponents, which control the global properties of a system, are independent of its details. Classic percolation considers the connectivity between two lines and two faces at opposite sides of a system in 2-and 3D problems, respectively; whereas, in practice (e.g. hydrocarbon formations), production and injection wells are represented by points (in 2D areal models) and lines (in 3D models). This study presents the results of Monte Carlo simulations of a 2D percolation model wherein the connection locations (i.e. wells) are represented by two points, called pointto-point (P2P) connectivity. The main contribution is to find the percolation threshold as well as the geometrical and dynamical critical exponents of a continuum percolation system with a P2P connection, which is closer to reality in some applications. The result shows that in comparison to classical percolation, some critical exponents definitely changes in the P2P connection.

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“…Percolation refers to the formation of long-range connectivity across a lattice or network, and applies to various complex physical systems, including aerogel [1], polymers [2], superconductors [3,4,5,6], and magnets [7,8]. Outside physics, percolation also arises in the context of ecology [9], complex networks [10,11,12,13] and social science [14,15,16].…”

Section: Introductionmentioning

confidence: 99%

Fractal dimension and threshold properties in a spatially correlated percolation model

Yang,

Zhang,

Bray-Ali

et al. 2009

Preprint

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We consider the effects of spatial correlations in a two-dimensional site percolation model. By generalizing the Newman-Ziff Monte Carlo algorithm to include spatial correlations, percolation thresholds and fractal dimensions of percolation clusters are obtained. For a wide range of spatial correlations, the percolation threshold differs little from the uncorrelated result. In contrast, the fractal dimension differs sharply from the uncorrelated result for almost all types of correlation studied. We interpret these results in the framework of long-range correlated percolation.

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Distribution of shortest paths at percolation threshold: application to oil recovery with multiple wells

Cited by 10 publications

References 8 publications

Percolation Approach in Underground Reservoir Modeling

Percolation Approach in Underground Reservoir Modeling

Point to point continuum percolation in two dimensions

Fractal dimension and threshold properties in a spatially correlated percolation model

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