A 3D filtration law for power-law fluids in heterogeneous porous media

Fadili, Ali; Tardy, Philippe Michel Jacques; Pearson, J. R. A.

doi:10.1016/s0377-0257(02)00085-x

Cited by 52 publications

(33 citation statements)

References 10 publications

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“…Regarding the mean capillary equilibrium assumption (section 6), our results may be applied for homogenizing regions of the reservoir far from the boundaries and far from the flooding (w/n) front where changes in saturation are expected to be small, as it is also suggested by Ekran and Aasen [2000]. Finally, we point out that this dual homogenization has been recently applied to treat the homogenization problem of non-Newtonian fluids in heterogeneous porous materials, and numerical simulations have been found to be in very good agreement with the predicted values [Fadili et al, 2002a[Fadili et al, , 2002b[Fadili et al, , 2002c.…”

Section: Discussionsupporting

confidence: 77%

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: Discussionsupporting

confidence: 77%

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

Fadili

Ababou

2004

Water Resources Research

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“…In simple geometries like capillary tubes, the corresponding Taylor dispersion coefficient D is then lower than for a Newtonian fluid although one has still D ∝ P e 2 [16]. On the other hand, numerical investigations suggest that the flow of shear thinning fluids is localized in a smaller number of flow paths than for Newtonian fluids [17,18]. As a result, geometrical dispersion reflecting the distribution of the local velocities should increase as is indeed observed experimentally [10,11].…”

Section: Dispersion Mechanisms In 3d Porous Media and 2d Networkmentioning

confidence: 85%

Pore scale mixing and macroscopic solute dispersion regimes in polymer flows inside two-dimensional model networks

et al. 2007

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A change of solute dispersion regime with the flow velocity has been studied both at the macroscopic and pore scales in a transparent array of capillary channels using an optical technique allowing for simultaneous local and global concentration mappings. Two solutions of different polymer concentrations (500 and 1000 ppm) have been used at different Péclet numbers. At the macroscopic scale, the displacement front displays a diffusive spreading: for P e ≤ 10, the dispersivity l d is constant with P e and increases with the polymer concentration; for P e > 10, l d increases as P e 1.35 and is similar for the two concentrations. At the local scale, a time lag between the saturations of channels parallel and perpendicular to the mean flow has been observed and studied as a function of the flow rate. These local measurements suggest that the change of dispersion regime is related to variations of the degree of mixing at the junctions. For P e ≤ 10, complete mixing leads to pure geometrical dispersion enhanced for shear thinning fluids; for P e > 10 weaker mixing results in higher correlation lengths along flow paths parallel to the mean flow and in a combination of geometrical and Taylor dispersion.

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“…Hua and Schieber [61] used a combined finite element and Brownian dynamics technique (CONNFFESSIT) to predict the steady-state viscoelastic flow field around an infinite array of squarely-arranged cylinders using two kinetic theory models. Fadili et al [62] derived an analytical 3D filtration formula for up-scaling isotropic Darcy's flows of power-law fluids to heterogeneous Darcy's flows by using stochastic homogenization techniques. They then validated their formula by making a comparison with numerical experiments for 2D flows through a rectangular porous medium using finite volume method.…”

Section: Methodsmentioning

confidence: 99%

Flow of non‐newtonian fluids in porous media

Sochi

2010

J Polym Sci B Polym Phys

123

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The study of flow of non‐Newtonian fluids in porous media is very important and serves a wide variety of practical applications in processes such as enhanced oil recovery from underground reservoirs, filtration of polymer solutions and soil remediation through the removal of liquid pollutants. These fluids occur in diverse natural and synthetic forms and can be regarded as the rule rather than the exception. They show very complex strain and time dependent behavior and may have initial yield‐stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. Non‐Newtonian fluids are generally classified into three main categories: time‐independent whose strain rate solely depends on the instantaneous stress, time‐dependent whose strain rate is a function of both magnitude and duration of the applied stress and viscoelastic which shows partial elastic recovery on removal of the deforming stress and usually demonstrates both time and strain dependency. In this article, the key aspects of these fluids are reviewed with particular emphasis on single‐phase flow through porous media. The four main approaches for describing the flow in porous media are examined and assessed. These are: continuum models, bundle of tubes models, numerical methods and pore‐scale network modeling. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010

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A 3D filtration law for power-law fluids in heterogeneous porous media

Cited by 52 publications

References 10 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

Pore scale mixing and macroscopic solute dispersion regimes in polymer flows inside two-dimensional model networks

Flow of non‐newtonian fluids in porous media

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