Developing a new form of permeability and Kozeny–Carman constant for homogeneous porous media by means of fractal geometry

Xu, Peng; Yu, Bo

doi:10.1016/j.advwatres.2007.06.003

Cited by 596 publications

(296 citation statements)

References 36 publications

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“…Thus for some rocks, such as highly compacted chalk, the tortuosity can be quite large. A range of empirical descriptions for the dependence of tortuosity on porosity has been proposed [2,3] and for some simple grain shapes, analytical shape factors are used [4]. More recent attempts even take the fractal dimension of the porous media into account [5].…”

Section: Introductionmentioning

confidence: 99%

Particle Diffusion in Complex Nanoscale Pore Networks

et al. 2015

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We studied the diffusion of particles in the highly irregular pore networks of chalk, a very fine grained rock, by combining three dimensional X-ray imaging and dissipative particle dynamics (DPD) simulations. X-ray imaging data were collected at 25 nm voxel dimension for two chalk samples with very different porosities (5% and 26%). The three dimensional pore systems derived from the tomograms were imported into DPD simulations and filled with spherical particles of variable diameter and with an optional attractive interaction to the pore surfaces. We found that diffusion significantly decreased to as much as 60% when particle size increased from 1% to 35% of the average pore diameter). When particles were attracted to the pore surfaces, 2 even very small particles, diffusion was drastically inhibited, by as much as a factor of 100.Thus, the size of particles and their interaction with the pore surface strongly influence particle mobility and must be taken into account for predicting permeability in nanoporous rocks from primary petrophysical parameters such as surface area, porosity and tortuosity.

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Section: Introductionmentioning

confidence: 99%

Particle Diffusion in Complex Nanoscale Pore Networks

et al. 2015

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“…1,2,4,7,8,11,13,[18][19][20] This means that the fractal theory can be used to predict the capillary pressure and water relative permeability of porous media. Besides, the pore size distribution and tortuosity of capillaries have also been proven to follow the fractal scaling laws, 2,4,8,18 i.e. The transfer routes of water in unsaturated porous rocks have fractal characteristics and can be described as random fractal curves.…”

Section: Fractal Characteristics Of Unsaturated Porous Rocksmentioning

confidence: 99%

A Fractal Model for Water Flow Through Unsaturated Porous Rocks

et al. 2018

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In this work, considering the effect of porosity, pore size, saturation of water and tortuosity fractal dimension, an analytical model for the capillary pressure and water relative permeability is derived in unsaturated porous rocks. Besides, the formulas of calculating the capillary pressure and water relative permeability are given by taking into account the fractal distribution of pore size and tortuosity of capillaries. It can be seen that the capillary pressure for water phase decreases with the increase of saturation in unsaturated porous rocks. It is found that the capillary pressure for water phase decreases as the tortuosity fractal dimension decreases. It is further seen that the capillary pressure for water phase increases with the decrease of porosity, and at low porosity, the capillary pressure increases sharply with the decrease of porosity. Besides, it can be observed that the water relative permeability increases with the increase of saturation in unsaturated porous rocks. This predicted the capillary pressure and water relative permeability of unsaturated porous rocks based on the proposed models which are in good agreement with the experimental data and model predictions reported in the literature. § Corresponding author. This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited. 1840015-1 B. Xiao et al.The proposed model improved the understanding of the physical mechanisms of water flow through unsaturated porous rocks.

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“…Soil scientists have shown that (1) and (2) provide estimates of permeability that are superior to some other soil transfer functions [Chapuis and Aubertin, 2003;Dvorkin, 2009]. The estimate given by Carman [1939] of c 0 ¼ 1=5 for the Kozeny coefficient seems adequate for media in a middle range of porosity 0:2 < n < 0:7 ð Þ [Xu and Yu, 2008]. In some circumstances high correlation between tortuousity and porosity makes the simpler Kozeny equation a cost-effective alternative to the Kozeny-Carman equation [Koponen et al, 1996].…”

Section: Physical Evidence For Kozeny Equationmentioning

confidence: 99%

Pedotransfer functions for permeability: A computational study at pore scales

Hyman

Smolarkiewicz

Winter

2013

Water Resources Research

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[1] Three phenomenological power law models for the permeability of porous media are derived from computational experiments with flow through explicit pore spaces. The pore spaces are represented by three-dimensional pore networks in 63 virtual porous media along with 15 physical pore networks. The power laws relate permeability to (i) porosity, (ii) squared mean hydraulic radius of pores, and (iii) their product. Their performance is compared to estimates derived via the Kozeny equation, which also uses the product of porosity with squared mean hydraulic pore radius to estimate permeability. The power laws provide tighter estimates than the Kozeny equation even after adjusting for the extra parameter they each require. The best fit is with the power law based on the Kozeny predictor, that is, the product of porosity with the square of mean hydraulic pore radius.Citation: Hyman, J. D., P. K. Smolarkiewicz, and C. L. Winter (2013), Pedotransfer functions for permeability: A computational study at pore scales, Water Resour.

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Developing a new form of permeability and Kozeny–Carman constant for homogeneous porous media by means of fractal geometry

Cited by 596 publications

References 36 publications

Particle Diffusion in Complex Nanoscale Pore Networks

Particle Diffusion in Complex Nanoscale Pore Networks

A Fractal Model for Water Flow Through Unsaturated Porous Rocks

Pedotransfer functions for permeability: A computational study at pore scales

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