Fluid flows of mixed regimes in porous media

Çelik, Emine; Hoang, Luan; Ibragimov, Akif; Kieu, Thinh

doi:10.1063/1.4976195

Cited by 12 publications

(5 citation statements)

References 25 publications

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“…(1978) classified flow in porous media into three regimes: pre‐Darcy flow, Darcy flow, and post‐Darcy flow (Figure 1a). Pre‐Darcy flow occurs mainly in low‐velocity seepage in low‐permeability media at low pressure gradients (Celik et al., 2017; Neuzil, 1986; Siddiqui et al., 2016; Zeng et al., 2011). Based on many experimental and simulation studies, most current scholars agree that the cause of this phenomenon is the formation of a liquid film by the adsorption of fluid on the pore wall (Afsharpoor & Javadpour, 2016; Cai, 2014; Tokunaga, 2009; S. Yang & Yu, 2020).…”

Section: Introductionmentioning

confidence: 99%

From Pre‐Darcy Flow to Darcy Flow in Porous Media: A Simple Unified Model

Cheng,

Wang,

et al. 2024

Water Resources Research

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Extensive experiments have demonstrated that fluid flow in low‐permeability media deviates from Darcy's law at low pressure gradients, which is called pre‐Darcy flow. Although numerous pre‐Darcy flow models have been proposed, these models generally contain one or more empirical parameters with no clear physical meaning. In this paper, we present a simple unified model to describe pre‐Darcy flow in porous media by introducing the concept of loss permeability. The physical meaning of the loss permeability parameter and its relationship to permeability are analyzed. Based on the statistics of the loss permeability parameter results of 24 core samples, we found that there is a good positive correlation between the loss permeability parameter and the absolute permeability. A smaller loss permeability indicates a stronger fluid‐solid interaction and a stronger nonlinearity between the flow velocity and the pressure gradient. Taking a one‐dimensional linear unsteady flow of a slightly compressible fluid in a homogeneous porous medium as an example, we solve the pressure diffusion equation based on the proposed model using a finite difference method. Our results demonstrate that the rate of pressure propagation for pre‐Darcy flow is slower than that for Darcy flow for the entire observation period, which corrects previous conclusions. This study is highly important for improving the understanding of fluid flow in low‐permeability media.

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Section: Introductionmentioning

confidence: 99%

From Pre‐Darcy Flow to Darcy Flow in Porous Media: A Simple Unified Model

Cheng,

Wang,

et al. 2024

Water Resources Research

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“…Interestingly, there are also physics and engineering problems in which the diffusivity can also vanish when the gradient of the dependent variable vanishes. One example is pre-Darcy flow in saturated porous media [12]. Another example is the spreading of confined layers of non-Newtonian fluids [13,14], for which the complex rheology of the fluid leads to a degenerating gradient-dependent diffusivity (unlike the Newtonian case [8]); see also the review by Ghodgaonkar and Christov [15].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Einstein paradigm of Brownian motion and localization property of solutions

Christov

Hevage

Ibraguimov

et al. 2023

Math Methods in App Sciences

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We employ a generalization of Einstein's random walk paradigm for diffusion to derive a class of multidimensional degenerate nonlinear parabolic equations in nondivergence form. Specifically, in these equations, the diffusion coefficient can depend on both the dependent variable and its gradient, and it vanishes when either one of the latter does. It is known that solutions of such degenerate equations can exhibit finite speed of propagation (so-called localization property of solutions). We give a proof of this property using a De Giorgi-Ladyzhenskaya iteration procedure for nondivergence form equations. A mapping theorem is then established to a divergence-form version of the governing equation for the case of one spatial dimension. Numerical results via a finite-difference scheme are used to illustrate the main mathematical results for this special case. For completeness, we also provide an explicit construction of the one-dimensional self-similar solution with finite speed of propagation function, in the sense of Kompaneets-Zel'dovich-Barenblatt. We thus show how the finite speed of propagation quantitatively depends on the model's parameters.

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“…Transport equations for theoretical treatments of porous media flows exist in all of these fields (e.g. see Bear 1972;Celik et al 2017;Fourar et al 2004;Maier et al 2003), but it is difficult to theoretically calculate the boundary conditions for a particular porous matrix based on the geometry of the pores-although some of such attempts have been undertaken, as evident from Freund et al (2003) and Zeiser et al (2003). The publications show that correct flow boundary conditions are needed to solve the available transport equations.…”

Section: Introduction and Objectivesmentioning

confidence: 99%

Permeability and the Ergun Equation as a Basis for Permeability Measurements of Metallic Foams and Wire Meshes

et al. 2021

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This paper concerns a method and a test set-up to measure the permeability of plates of metal foams and sets of wire meshes used to control flows in fluid filters and other flow systems designed to yield constant velocity distributions over large cross sections of flows. The method is based on permeability considerations using the Ergun equation to describe the pressure losses of packages of mono-dispersed spheres. One correlation is suggested for the permeability k over the entire range of mean velocities U0. A suitable measuring set-up was designed, built and used to measure the permeability of plates of metallic foams and sets of wire meshes. The specific objective of the present investigation was to provide permeability data for combined sets of wire meshes with flow properties that are mainly characterized by the wire meshes with the smallest mesh size. A method of data presentation is suggested that clearly illustrates the ranges of laminar and turbulent flows through the wire meshes. The results are compared with those for technical porous plates. The suggested presentation of the results indicates that the general features of the flows through porous plates of metal foams and wire meshes are the same.

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Fluid flows of mixed regimes in porous media

Cited by 12 publications

References 25 publications

From Pre‐Darcy Flow to Darcy Flow in Porous Media: A Simple Unified Model

From Pre‐Darcy Flow to Darcy Flow in Porous Media: A Simple Unified Model

Nonlinear Einstein paradigm of Brownian motion and localization property of solutions

Permeability and the Ergun Equation as a Basis for Permeability Measurements of Metallic Foams and Wire Meshes

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