Nonlinear corrections to Darcy's law at low Reynolds numbers

Firdaouss, Mouaouia; Guermond, Jean‐Luc; Quéré, Patrick Le

doi:10.1017/s0022112097005843

Cited by 184 publications

(151 citation statements)

References 5 publications

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“…2) is obtained for flow experiments on sand and gravel for a wide range of Reynold numbers (e.g., Moutsopoulos et al 2009;Sedghi-Asl et al 2014). Similar conclusions can be obtained from numerical studies, such as Firdaouss et al (1997) and Fourar et al (2004), which consider the Forchheimer equation (Eq. 2) valid over a wide range of Reynolds numbers.…”

Section: Nonlinear Laminar Flow and Fully Turbulent Flow In Porous Mediasupporting

confidence: 78%

The Effect of Grain Size Distribution on Nonlinear Flow Behavior in Sandy Porous Media

et al. 2017

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The current study provides new experimental data on nonlinear flow behavior in various uniformly graded granular materials (20 samples) ranging from medium sands (d 50 > 0.39 mm) to gravel (d 50 = 6.3 mm). Generally, theoretical equations relate the Forchheimer parameters a and b to the porosity, as well as the characteristic pore length, which is assumed to be the median grain size (d 50 ) of the porous medium. However, numerical and experimental studies show that flow resistance in porous media is largely determined by the geometry of the pore structure. In this study, the effect of the grain size distribution was analyzed using subangular-subrounded sands and approximately equal compaction grades. We have used a reference dataset of 11 uniformly graded filter sands. Mixtures of filter sands were used to obtain a slightly more well-graded composite sand (increased C u values by a factor of 1.19 up to 2.32) with respect to its associated reference sand at equal median grain size (d 50 ) and porosity. For all composite sands, the observed flow resistance was higher than in the corresponding reference sand at equal d 50 , resulting in increased a coefficients by factors up to 1.68, as well as increased b coefficients by factors up to 1.44. A modified Ergun relationship with Ergun constants of 139.1 for A and 2.2 for B, as well as the use of d m − σ as characteristic pore length predicted the coefficients a and b accurately.

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Section: Nonlinear Laminar Flow and Fully Turbulent Flow In Porous Mediasupporting

confidence: 78%

The Effect of Grain Size Distribution on Nonlinear Flow Behavior in Sandy Porous Media

et al. 2017

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“…That means that the pressure drop is considered as the sum of two terms: viscous (u, Darcy law) and inertia (u 2 ) terms. Several authors have shown that the onset of the non-linear behavior (that is sometime called the weak inertia regime) may be described by a cubic law (Firdaous et al, 1997;Mei & Auriault, 1993;Wodie & Levy, 1991):…”

Section: Flow Lawmentioning

confidence: 99%

Metal Foam Effective Transport Properties

Hugo¹,

Brun²,

Topin³

2011

Evaporation, Condensation and Heat Transfer

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“…4, was demonstrated by Schneebeli (1955). The nonlinear seepage flow law will be parabolic at Re [ 13, with deviation from linearity (Barenblatt et al 1990;Couland et al 1986); also nonlinear corrections to Darcy's law at low Reynolds numbers for periodic porous media have been described (Firdaouss et al 1997). Values of Reynolds number between 5 and 13 were calculated with numerical experiments based on the Navier-Stokes equations (Couland et al 1986;Stark 1972).…”

Section: Darcy and Couette Equationmentioning

confidence: 99%

Fluid dynamics in naturally fractured tectonic reservoirs

Barros-Galvis

Samaniego

Cinco-Ley

2017

J Petrol Explor Prod Technol

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This study presents analytical models for naturally fractured tectonic reservoirs (NFTRs), which essentially correspond to type I fractured reservoirs, including the effects of the nonlinear gradient term for radial flow, single phase (oil), for constant rate in an infinite reservoir. Using an exact solution of Navier-Stokes equation and Cole-Hopf transform, NFTRs have been modeled. Our models are applied for fissured formations with extensive fractures. Smooth and rough extension fractures were analyzed using single and slab flow geometries. The motivation for this study was to develop a real and representative model of a NFTR, with extension fractures to describe its pressure behavior. A discussion is also presented with field examples, regarding the effect of a quadratic gradient term and the difference between the nonlinear and linear pressure solutions, comparing the Darcy laminar flow equation, with the exact solution of the Navier-Stokes equation applied to the diffusion equation and boundary conditions in wellbore. Keywords

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Nonlinear corrections to Darcy's law at low Reynolds numbers

Cited by 184 publications

References 5 publications

The Effect of Grain Size Distribution on Nonlinear Flow Behavior in Sandy Porous Media

The Effect of Grain Size Distribution on Nonlinear Flow Behavior in Sandy Porous Media

Metal Foam Effective Transport Properties

Fluid dynamics in naturally fractured tectonic reservoirs

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