From creeping to inertial flow in porous media: a lattice Boltzmann–finite element study

Narváez, Ariel; Yazdchi, K.; Luding, Stefan; Harting, Jens

doi:10.1088/1742-5468/2013/02/p02038

Cited by 33 publications

(34 citation statements)

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“…It is commonly being reported that the Forchheimer equation consistently overestimates pressure gradients in the so‐called weak inertia regime

scriptO (1 0^{- 1}) < Re < scriptO (1 0^{1})

, where R e is based on the average velocity and a microscopic length scale depending, e.g., on the grain size. In particular, various numerical [e.g., Narváez et al , ; Rojas and Koplik , ; Andrade et al , ; Firdaouss et al , ; Mei and Auriault , ] as well as experimental studies [e.g., Skjetne and Auriault , ; Lage et al , ] articulate the use of a leading cubic term in the weak inertia regime in the form of

- J_{1}^{c} \equiv \frac{\partial}{\partial X_{1}} P - ϱg = - \frac{μ}{κ} q_{1} - \frac{ϱ^{2} ζ}{μ} q_{1}^{3},

with ζ being a material‐dependent fitting coefficient. Others have used nonconstant Forchheimer coefficients c F = c F ( q ) to account for higher‐order contributions [e.g., Chukwudozie and Tyagi , ; Mattis et al , ].…”

Section: Motivationmentioning

confidence: 99%

Transition of effective hydraulic properties from low to high Reynolds number flow in porous media

Sivanesapillai

Steeb

Hartmaier

2014

Geophysical Research Letters

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We numerically analyze fluid flow through porous media up to a limiting Reynolds number of scriptO(103). Due to inertial effects, such processes exhibit a gradual transition from laminar to turbulent flow for increasing magnitudes of Re. On the macroscopic scale, inertial transition implies nonlinearities in the relationship between the effective macroscopic pressure gradient and the filter velocity, typically accounted for in terms of the quadratic Forchheimer equation. However, various inertia‐based extensions to the linear Darcy equation have been discussed in the literature; most prominently cubic polynomials in velocity. The numerical results presented in this contribution indicate that inertial transition, as observed in the apparent permeability, hydraulic tortuosity, and interfacial drag, is inherently of sigmoidal shape. Based on this observation, we derive a novel filtration law which is consistent with Darcy's law at small Re, reproduces Forchheimer's law at large Re, and exhibits higher‐order leading terms in the weak inertia regime.

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“…It is commonly being reported that the Forchheimer equation consistently overestimates pressure gradients in the so‐called weak inertia regime

scriptO (1 0^{- 1}) < Re < scriptO (1 0^{1})

- J_{1}^{c} \equiv \frac{\partial}{\partial X_{1}} P - ϱg = - \frac{μ}{κ} q_{1} - \frac{ϱ^{2} ζ}{μ} q_{1}^{3},

Section: Motivationmentioning

confidence: 99%

Transition of effective hydraulic properties from low to high Reynolds number flow in porous media

Sivanesapillai

Steeb

Hartmaier

2014

Geophysical Research Letters

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“…We follow the procedure to measure permeabilities as described in Narváez et al [28,29], Frijters [30] and Frijters and Harting [31]. The LB method itself has proven to be very successful for modeling fluid flow in porous media [32].…”

Section: The Lattice Boltzmann Methodsmentioning

confidence: 99%

“…[29,34]. Narváez et al [28,29] have shown that relaxation times of τ = 1 and τ bulk = 0.84 provide useful results for permeability calculations. The porous sample is positioned between two fluid chambers which serve as in-and output to avoid artifacts, cf.…”

Section: The Lattice Boltzmann Methodsmentioning

confidence: 99%

Hydraulic properties of porous sintered glass bead systems

et al. 2017

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In this paper, porous sintered glass bead packings are studied, using X-ray Computed Tomography (XRCT) images at 16 µm voxel resolution, to obtain not only the porosity field, but also other properties like particle sizes, pore throats and the permeability. The influence of the sintering procedure and the original particle size distributions on the microstructure, and thus on the hydraulic properties, is analyzed in detail. The XRCT data are visualized and studied by advanced image filtering and analysis algorithms on to the extracted sub-systems (cubes of different sizes) to determine the correlations between the microstruc- Institute of Applied Mechanics (CE), University of Stuttgart, Pfaffenwaldring 7, 70569 Stuttgart, Germany ture and the measured macroscopic hydraulic parameters. Since accurate permeability measurements are not simple, special focus lies on the experimental set up and procedure, for which a new innovative multi-purpose cell based on a modular concept is presented. Furthermore, segmented voxel-based images (defining the microstructure) are used for 3D (three-dimensional) lattice Boltzmann simulations to directly compute some of the properties in the creeping flow regime. A very good agreement between experimental and numerical porosity and permeability could be achieved, in most cases, validating the numerical model and results. Porosity and permeability gradients along the sample height could be related to gravity acting during sintering. Furthermore, porosity increases in the outer zones of the samples due to the different contact geometry between the beads and the confining cylinder wall during sintering (which is replaced by a membrane during permeability testing to close these pores at the surface of the sample). The influence of different filters on the gray scale distributions and the impact of the segmentation procedure on porosity and permeability is systematically studied. The complex relationships and dependencies between numerically determined permeabilities and hydraulic influence parameters are investigated carefully. In accordance to the well-known Kozeny-Carman model, a similar trend for local permeability values in dependence on porosity and particle diameter is obtained. Other than statistical models, which estimate the pore throat distribution on the basis of the particle size distribution, in this study XRCT scans are used to determine the pore throats in sintered granular systems, which are finally linked to the intrinsic permeability through the lattice Boltzmann simulations. From the μXRCT analysis two distinct peaks in pore throat distributions could be identified, which can be clearly assigned to typical pore throat areas occurring in polydisperse granular systems. Moreover, a linear dependency between average pore throat diameter and porosity as well as between permeability and pore throat diameter is reported. Furthermore, almost identical mean values for porosity and permeability are found from sub-system and full-system REV analysis. For sintered granular...

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“…Here simulations of the complex fluid-fluid and fluid-rock interfaces are also needed to gain further insight [40,41,42].…”

Section: Big Data For World-wide and Multiscale Problemsmentioning

confidence: 99%

From human mobility to renewable energies

Raischel

Moreira

Lind

2014

Eur. Phys. J. Spec. Top.

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Abstract.We address and discuss recent trends in the analysis of big data sets, with the emphasis on studying multiscale phenomena. Applications of big data analysis in different scientific fields are described and two particular examples of multiscale phenomena are explored in more detail. The first one deals with wind power production at the scale of single wind turbines, the scale of entire wind farms and also at the scale of a whole country. Using open source data we show that the wind power production has an intermittent character at all those three scales, with implications for defining adequate strategies for stable energy production. The second example concerns the dynamics underlying human mobility, which presents different features at different scales.For that end, we analyze 12-month data of the Eduroam database within Portuguese universities, and find that, at the smallest scales, typically within a set of a few adjacent buildings, the characteristic exponents of average displacements are different from the ones found at the scale of one country or one continent. Big data: the emergence of a new paradigmIn some sense, the notion of Information Age is slowly fading from the perception of our society. For decades, national and international research has been creating impressive amounts of data, and often from various unrelated measurement sources [1]. Computational methods have been serving the needs of the scientific community and the need for higher computational power has driven the invention of more efficient computational codes and triggered the development of new hardware. Simultaneously, the internet has been instrumental in fostering international research collaborations and divulging scientific knowledge.Today, obtaining data is no longer a problem. Information is there, available for everyone at any time. Given the computational power of today's computers and clusters, even single research groups can create and store large data volumes. The challenge in today's research is more often what to do with the data we have. How to manage all the information we have in such large data sources? Which phenomena can we now study? The recent technological progress together with the new challenges naturally lead to a new paradigm in computational sciences, which is partially described by the term big data.In this paper we discuss the utility of big data for approaching the empirical study of phenomena up to now unreachable. We discuss the usage of big data in the study of two specific phenomena, that up to now were unreachable, namely wind energy production and human

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From creeping to inertial flow in porous media: a lattice Boltzmann–finite element study

Cited by 33 publications

References 50 publications

Transition of effective hydraulic properties from low to high Reynolds number flow in porous media

Transition of effective hydraulic properties from low to high Reynolds number flow in porous media

Hydraulic properties of porous sintered glass bead systems

From human mobility to renewable energies

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