On the non-linear behavior of a laminar single-phase flow through two and three-dimensional porous media

Fourar, Mostafa; Radilla, Giovanni; Lenormand, R.; Moyne, Christian

doi:10.1016/j.advwatres.2004.02.021

Cited by 131 publications

(71 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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: 64%

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

et al. 2017

View full text Add to dashboard Cite

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.

show abstract

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

confidence: 64%

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

et al. 2017

View full text Add to dashboard Cite

show abstract

“…More realistic flow simulations in three dimensions were performed by Hill and Koch (2002), by means of the lattice-Boltzmann method (which makes use of the relation between fluid flow and kinetic gas theory), and also by Fourar et al (2004). Fourar et al (2004), in their numerical study of high-velocity effects in periodic porous media, state that viscous dissipation in the recirculation area is not preponderant.…”

Section: Theoretical Background and Proposed Relationsmentioning

confidence: 99%

Determination of Forchheimer equation coefficients a and b

Sidiropoulou

Moutsopoulos

Tsihrintzis

2006

Hydrological Processes

128

View full text Add to dashboard Cite

Abstract:This study focuses on the determination of the Forchheimer equation coefficients a and b for non-Darcian flow in porous media. Original theoretical equations are evaluated and empirical relations are proposed based on an investigation of available data in the literature. The validity of these equations is checked using existing experimental data, and their accuracy versus existing approaches is studied. On the basis of this analysis, some insight into the physical background of the phenomenon is also provided. The dependence of the coefficients a and b on the Reynolds number is also detected, and potential future research areas, e.g. investigation of inertial effects for consolidated porous media, are pointed out.

show abstract

“…This equation was obtained by numerical simulations in a two-dimensional periodic porous medium, and by using the homogenization technique for an isotropic homogeneous 3D porous medium. In spite of the numerous attempts to clarify the physical reasons for the non-linear behavior described above, neither Forchheimer equation (2) nor the weak inertia equation (4) have received any physical justification (Fourar et al, 2004). The pressure gradient across the foam is thus a function of system geometry (porosity, pore and ligament size...), as well as physical properties of the fluid phase (viscosity, density).…”

Section: Flow Lawmentioning

confidence: 99%