Darcian, Transitional, and Turbulent Flow through Porous Media

Venkataraman, P.; Rao, Prakash R.

doi:10.1061/(asce)0733-9429(1998)124:8(840)

Cited by 125 publications

(55 citation statements)

References 7 publications

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“…The a Darcy coefficients are in agreement with the a coefficients determined by the Forchheimer fit over the whole dataset (see Table 4), resulting in small relative errors of 2.1 and 1.9%, respectively. This is in agreement with the results of Venkataraman and Rao (1998), who also observed similar coefficients for Forchheimer a and a Darcy . However, other studies showed that the Forchheimer coefficient a in the nonlinear flow regime can significantly differ from the resistance coefficient a Darcy in the Darcy regime (see Bagci et al 2014).…”

Section: Nonlinear Flow Behavior In the Reference Sandssupporting

confidence: 93%

“…Hence, we have plotted the Forchheimer coefficient a, which is equal to μ/ρgk (e.g., Venkataraman and Rao 1998), as a function of coefficient b for all samples (see Fig. 5) where a good correlation between both values is found.…”

Section: Comparison With the Literaturementioning

confidence: 94%

“…In the literature, this nonlinearity in the laminar flow regime is ascribed to different microscale processes (e.g., Hassanizadeh and Gray 1987;Ma and Ruth 1993;Skjetne and Auriault 1999;Hill and Koch 2002;Nield 2002). In general, it is assumed that the deviation from the linear Darcy's law at increased Reynolds numbers is due to the occurrence of microscopic inertial forces (e.g., Bear 1972;Macdonald et al 1979;Venkataraman and Rao 1998). Other studies, such as Panfilov et al (2003) and Panfilov and Fourar (2006), showed that the main mechanisms of energy dissipation that contribute to the nonlinear flow term are due to both recirculation of eddies in closed streamline regions, as well as streamline deformation in the main area of flow.…”

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

confidence: 99%

“…Many experimental datasets on nonlinear flow behavior in granular porous media show that this gradual process can be accurately predicted by the Forchheimer equation (Eq. 2) for various ranges of particle Reynold numbers in the nonlinear laminar flow regime, as well as in the turbulent flow regime (e.g., Venkataraman and Rao 1998;Sidiropoulou et al 2007;Moutsopoulos et al 2009;Bagci et al 2014;Sedghi-Asl et al 2014;Salahi et al 2015;Li et al 2017).…”

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

confidence: 99%

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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 Flow Behavior In the Reference Sandssupporting

confidence: 93%

Section: Comparison With the Literaturementioning

confidence: 94%

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

confidence: 99%

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

confidence: 99%

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

et al. 2017

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“…From a thorough review of the literature, one can find enough evidence confirming the complex variation pattern of the Darcy and non-Darcy coefficients with field and media conditions such as porosity, media size, convergent angle, permeability, and so on [6][7][8][9][10][11]. Efforts are made to relate the Darcy and non-Darcy coefficients with the parameters influencing the flow, but they are observed to be empirical therefore of limited use [12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

An Investigation of Parallel Post-Laminar Flow through Coarse Granular Porous Media with the Wilkins Equation

et al. 2018

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Abstract:Behaviour of flow resistance with velocity is still undefined for post-laminar flow through coarse granular media. This can cause considerable errors during flow measurements in situations like rock fill dams, water filters, pumping wells, oil and gas exploration, and so on. Keeping the non-deviating nature of Wilkins coefficients with the hydraulic radius of media in mind, the present study further explores their behaviour to independently varying media size and porosity, subjected to parallel post-laminar flow through granular media. Furthermore, an attempt is made to simulate the post-laminar flow conditions with the help of a Computational Fluid Dynamic (CFD) Model in ANSYS FLUENT, since conducting large-scale experiments are often costly and time-consuming. The model output and the experimental results are found to be in good agreement. Percentage deviations between the experimental and numerical results are found to be in the considerable range. Furthermore, the simulation results are statistically validated with the experimental results using the standard 'Z-test'. The output from the model advocates the importance and applicability of CFD modelling in understanding post-laminar flow through granular media.

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Darcy's law for two‐dimensional flows: Singularities at corners and a new class of models

Shikhmurzaev

2017

AIChE Journal

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As is known, Darcy's model for fluid flows in isotropic homogeneous porous media gives rise to singularities in the velocity field for essentially two‐dimensional flow configuration, like flows over corners. Considering this problem from the modeling viewpoint, this study aims at removing this singularity, which cannot be regularized via conventional generalizations of the Darcy model, like Brinkman's equation, without sacrificing Darcy's law itself for unidirectional flows where its validity is well established experimentally. The key idea is that as confirmed by a simple analogy, the permeability of a porous matrix with respect to flow is not a constant independent of the flow but a function of the flow field (its scalar invariants), decreasing as the curvature of the streamlines increases. This introduces a completely new class of models where the flow field and the permeability field are linked and, in particular problems, have to be found simultaneously. © 2017 American Institute of Chemical Engineers AIChE J, 2017

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Darcian, Transitional, and Turbulent Flow through Porous Media

Cited by 125 publications

References 7 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

An Investigation of Parallel Post-Laminar Flow through Coarse Granular Porous Media with the Wilkins Equation

Darcy's law for two‐dimensional flows: Singularities at corners and a new class of models

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