Characterization of macro-scale heterogeneity and homogeneity of porous media employing fractal geometry

Othman, Mohd Roslee; Numbere, D.T.

doi:10.1016/s0960-0779(01)00061-3

Cited by 7 publications

(6 citation statements)

References 11 publications

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“…The area dimension Df was determined following the boxcounting method [2,4]. This method is based on the image analysis of a sufficiently large section on the membrane surface.…”

Section: Determination Of Df and Dtmentioning

confidence: 99%

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A flow through behavior of gas across meso-porous membranes

Martunus

Helwani

Wiheeb

et al. 2012

Microporous and Mesoporous Materials

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“…The area dimension Df was determined following the boxcounting method [2,4]. This method is based on the image analysis of a sufficiently large section on the membrane surface.…”

Section: Determination Of Df and Dtmentioning

confidence: 99%

“…Although self-similarity in a global sense is seldom observed in nature, fractal description based on a statistical self-similarity have been used in diverse engineering applications involving physical phenomena in disordered structures and over multiple scales [2][3][4].…”

Section: Introductionmentioning

confidence: 99%

A flow through behavior of gas across meso-porous membranes

Martunus

Helwani

Wiheeb

et al. 2012

Microporous and Mesoporous Materials

Self Cite

View full text Add to dashboard Cite

“…Many natural structures have irregular geometries exhibiting statistical scale invariance over a great range of length scales L [5]. Specifically, it has been proved that naturally fractured reservoirs possess pore and fracture networks whose heterogeneity is almost always fractal [6]. So, there is a complex fluid flow path that cannot be described by traditional geometry [7,8].…”

Section: Introductionmentioning

confidence: 99%

A Mechanical Picture of Fractal Darcy’s Law

Damián Adame,

Gutiérrez-Torres,

Figueroa-Espinoza

et al. 2023

Fractal Fract

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The main goal of this manuscript is to generalize Darcy’s law from conventional calculus to fractal calculus in order to quantify the fluid flow in subterranean heterogeneous reservoirs. For this purpose, the inherent features of fractal sets are scrutinized. A set of fractal dimensions is incorporated to describe the geometry, morphology, and fractal topology of the domain under study. These characteristics are known through their Hausdorff, chemical, shortest path, and elastic backbone dimensions. Afterward, fractal continuum Darcy’s law is suggested based on the mapping of the fractal reservoir domain given in Cartesian coordinates xi into the corresponding fractal continuum domain expressed in fractal coordinates ξi by applying the relationship ξi=ϵ0(xi/ϵ0)αi−1, which possesses local fractional differential operators used in the fractal continuum calculus framework. This generalized version of Darcy’s law describes the relationship between the hydraulic gradient and flow velocity in fractal porous media at any scale including their geometry and fractal topology using the αi-parameter as the Hausdorff dimension in the fractal directions ξi, so the model captures the fractal heterogeneity and anisotropy. The equation can easily collapse to the classical Darcy’s law once we select the value of 1 for the alpha parameter. Several flow velocities are plotted to show the nonlinearity of the flow when the generalized Darcy’s law is used. These results are compared with the experimental data documented in the literature that show a good agreement in both high-velocity and low-velocity fractal Darcian flow with values of alpha equal to 0<α1<1 and 1<α1<2, respectively, whereas α1=1 represents the standard Darcy’s law. In that way, the alpha parameter describes the expected flow behavior which depends on two fractal dimensions: the Hausdorff dimension of a porous matrix and the fractal dimension of a cross-section area given by the intersection between the fractal matrix and a two-dimensional Cartesian plane. Also, some physical implications are discussed.

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“…Characterizing the flow and transport properties in porous media is useful for a wide range of applications in science and engineering from oil recovery and carbon sequestration to fuel cells [1][2][3][4]. Tortuosity, τ , is a parameter frequently utilized in continuum models during estimates of effective flow and transport properties within porous media [5,6].…”

Section: Introductionmentioning

confidence: 99%

“…Li and Yu [16] estimated tortuosity through a deterministic Sierpinski carpet using an analytical method and generated the following exponential relationship between tortuosity and porosity: (8/9) . (2) An advantage of their model is that it can be applied over a full range of porosities (Sierpinski carpet generation: n ∈ {0, 1, 2, . .…”

Section: Introductionmentioning

confidence: 99%