Prediction of steady state flow in nonuniform geologic media by conditional moments: Exact nonlocal formalism, effective conductivities, and weak approximation

Neuman, Shlomo P.; Orr, Shlomo

doi:10.1029/92wr02062

Cited by 258 publications

(226 citation statements)

References 38 publications

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“…Although this correction overestimates the effective permeabilities, it enlarges significantly the domain of validity of this second-order homogenization. The robustness of the exponential correction has been shown by Neuman and Orr [1993] and Gelhar [1993] for example. The coupling between the fluids is expressed through a matrix À, which clearly shows that in the fluid space (w, n) the interaction between the fluids has a specific symmetry.…”

Section: Discussionmentioning

confidence: 99%

Dual homogenization of immiscible steady two‐phase flows in random porous media

Fadili

Ababou

2004

Water Resources Research

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[1] We develop a dual conductivity-resistivity homogenization for immiscible steady two-phase flow in heterogeneous, spatially correlated, random porous media. The objective is to obtain macroscale equations for an equivalent homogeneous medium. We assume that the flow is governed locally by the generalized Darcy equations. Two formulations are developed, one in terms of capillary pressure p c and the other in terms of saturation s. In each case the perturbation approach is used to express average and fluctuation equations, and the closure problems are solved using the Wiener-Kinchine spectral theory. The macroscale permeability K e a and resistivity R e a tensors are determined for each fluid a, which also yield the relative permeabilities. These dual results provide a physically consistent correction of the perturbation-based tensors. The corrected macroscale tensors are then always positive, symmetric, and reciprocal to each other. We also develop, similarly, the homogenization of the capillary pressure curve p c (x, q) and of its reciprocal q(x, p c ), where q is the wetting fluid content. Finally, these general analytical results are applied to the special case where hrp c i % 0 and/or hrqi % 0, which can be interpreted as a mean capillary equilibrium.

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Section: Discussionmentioning

confidence: 99%

Dual homogenization of immiscible steady two‐phase flows in random porous media

Fadili

Ababou

2004

Water Resources Research

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“…(It is not clear that such a length scale will always exist [Long and . Witherspoon, 1985; see also Neuman and Orr, 1993], since heterogeneities in fracture spacing, aperture, etc. may occur at all length scales.. For our present purposes, we will consider only fractured formations which are macroscopically homogeneous on some scale).…”

Section: Dual-porosity Modelsmentioning

confidence: 99%

Numerical dual-porosity model with semianalytical treatment of fracture/matrix flow

1994

International Journal of Rock Mechanics and Mining Sciences &am

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“…3D: k eff = k g 1 + σ 2 lnk 6 for σ lnk < 2 (11) Neuman and Orr (1993) found that in 2D, away from a pumping well and from the outer boundary, the geometric mean dominates even for σ lnk > 4. In the presence of statistical anisotropy or spatial correlation Eq.…”

Section: Introductionmentioning

confidence: 99%

“…It can be determined for uniform flow while for non-uniform flow (e.g., non-local and non-Darcian) it is not existed (Neuman and Orr 1993). Hence, solving numerically (e.g., by using the finite difference or finite element methods) the governing partial differential flow equations with appropriate boundary conditions can be used for estimating effective permeability (Durlofsky 1991;Dykaar and Kitanidis 1992a, b;Neuman et al 1992).…”

Section: Introductionmentioning

confidence: 99%

Estimation of the Effective Permeability of Heterogeneous Porous Media by Using Percolation Concepts

Masihi

Gago²,

King³

2016

Transp Porous Med

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In this paper we present new methods to estimate the effective permeability (k eff ) of heterogeneous porous media with a wide distribution of permeabilities and various underlying structures, using percolation concepts. We first set a threshold permeability (k th ) on the permeability density function and use standard algorithms from percolation theory to check whether the high permeable grid blocks (i.e., those with permeability higher than k th ) with occupied fraction of "p" first forms a cluster connecting two opposite sides of the system in the direction of the flow (high permeability flow pathway). Then we estimate the effective permeability of the heterogeneous porous media in different ways: a power law (k eff = k th p m ), a weighted power average (with k g the geometric average of the permeability distribution) and a characteristic shape factor multiplied by the permeability threshold value. We found that the characteristic parameters (i.e., the exponent "m") can be inferred either from the statistics and properties of percolation subnetworks at the threshold point (i.e., high and low permeable regions corresponding to those permeabilities above and below the threshold permeability value) or by comparing the system properties with an uncorrelated random field having the same permeability distribution. These physically based approaches do not need fitting to the experimental data of effective permeability measurements to estimate the model parameter (i.e., exponent m) as is usually necessary in empirical methods. We examine the order of accuracy of these methods on different layers of 10th SPE model and found very good estimates as compared to the values determined from the commercial flow simulators.

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Prediction of steady state flow in nonuniform geologic media by conditional moments: Exact nonlocal formalism, effective conductivities, and weak approximation

Cited by 258 publications

References 38 publications

Dual homogenization of immiscible steady two‐phase flows in random porous media

Dual homogenization of immiscible steady two‐phase flows in random porous media

Numerical dual-porosity model with semianalytical treatment of fracture/matrix flow

Estimation of the Effective Permeability of Heterogeneous Porous Media by Using Percolation Concepts

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