The fluid transport in porous media is a critical property for oil and gas exploitation, construction engineering, and environmental protection. It is profoundly influenced by pore geometry and mineral properties. Currently, the Kozeny–Carman equation serves as the permeability prediction equation for porous media, established on the circular pores model. However, it fails to fully account for the impact of pore shape and mineral properties of the soil, leading to significant deviations between predicted and measured soil permeability results. In this paper, based on scanning electron microscope image and mercury intrusion porosimetry, the pores were divided into circular pores and narrow slit pores according to the ratios of pore area and circumference. Then, the quantitative expression of the two types of pores and their connectivity and tortuosity were given, and the circular and narrow slit composite pore model was used to describe the soil pore. Subsequently, the electrostatic potential of pore water was calculated by the Poisson–Boltzmann equation to consider the adsorption effect of minerals on pore water. Combined with the Navier–Stokes equation, the permeability prediction equation considering pore geometry, pore connectivity, and tortuosity and mineral properties was established. Finally, the experimental results illustrated that the theoretical prediction results were in good agreement with the experimental results. The proposed permeability prediction equation proves valuable for assessing and predicting the fluid transport in porous media.
REFERENCES
1.
X.
Liu
,
H.
Wang
, and
L.
Chang
, “
Equivalent permeability model of dual-porosity and bi-dispersed porous media based on the intermingled fractal units
,” Phys. Fluids
35
(3
), 033606
(2023
).2.
Y.
Li
,
J.
Yang
,
Z.
Pan
, and
W.
Tong
, “
Nanoscale pore structure and mechanical property analysis of coal: An insight combining AFM and SEM images
,” Fuel
260
, 116352
(2020
).3.
A.
Kashefi
and
T.
Mukerji
, “
Point-cloud deep learning of porous media for permeability prediction
,” Phys. Fluids
33
(9
), 097109
(2021
).4.
J. A.
Khan
,
E.
Padmanabhan
,
I. U.
Haq
, and
M. A.
Franchek
, “
Hydraulic fracturing with low and high viscous injection mediums to investigate net fracture pressure and fracture network in shale of different brittleness index
,” Geomech. Energy Environ.
33
, 100416
(2023
).5.
J.
Kim
,
S. W.
Jeen
,
H. S.
Lim
,
J.
Lee
,
O. S.
Kim
,
H.
Lee
, and
S. G.
Hong
, “
Hydrogeological characteristics of groundwater and surface water associated with two small lake systems on King George Island, Antarctica
,” J. Hydrol.
590
, 125537
(2020
).6.
L.
Liu
,
G. P.
Sheng
,
Z. F.
Liu
,
W. W.
Li
,
R. J.
Zeng
,
D. J.
Lee
,
J.-X.
Lin
, and
H. Q.
Yu
, “
Characterization of multiporous structure and oxygen transfer inside aerobic granules with the percolation model
,” Environ. Sci. Technol.
44
(22
), 8535
–8540
(2010
).7.
L. W.
Gill
,
J.
Mac Mahon
,
J.
Knappe
, and
P.
Morrissey
, “
Hydraulic conductivity assessment of falling head percolation tests used for the design of on-site wastewater treatment systems
,” Water Res.
236
, 119968
(2023
).8.
A.
Garg
,
N. G.
Reddy
,
H.
Huang
,
P.
Buragohain
, and
V.
Kushvaha
, “
Modelling contaminant transport in fly ash–bentonite composite landfill liner: Mechanism of different types of ions
,” Sci. Rep.
10
(1
), 11330
(2020
).9.
S.
Peng
and
J. D.
Rice
, “
Measuring critical gradients for soil loosening and initiation of backward erosion-piping mechanism
,” J. Geotech. Geoenviron. Eng.
146
(8
), 04020069
(2020
).10.
B.
Liu
,
B.
Wei
,
H.
Li
, and
Y.
Mao
, “
Multipoint hybrid model for RCC arch dam displacement health monitoring considering construction interface and its seepage
,” Appl. Math. Modell.
110
, 674
–697
(2022
).11.
B.
Indraratna
,
V. T.
Nguyen
, and
C.
Rujikiatkamjorn
, “
Hydraulic conductivity of saturated granular soils determined using a constriction-based technique
,” Can. Geotech. J.
49
(5
), 607
–613
(2012
).12.
H.
Ni
,
J.
Liu
,
T.
Chen
,
S.
Chen
, and
Q.
Meng
, “
Coal permeability prediction method based on the microscopic pore-fracture dual-porosity structure
,” J. Pet. Sci. Eng.
211
, 110107
(2022
).13.
H.
Song
,
J.
Lao
,
H.
Yang
,
B.
Pan
,
L.
Liu
, and
C.
Xie
, “
The pinning dynamics of a non-wetting droplet penetrating a permeable substrate
,” Phys. Fluids
35
(6
), 062107
(2023
).14.
H.
Song
,
J.
Lao
,
H.
Yang
,
C.
Xie
, and
J.
Wang
, “
Multifractal modeling of gas–water relative permeability considering multiscale and multieffects: Investigation of unconventional gas development
,” Fractals
31
(08
), 2340178
(2023
).15.
H.
Wang
,
H.
Qian
, and
Y.
Gao
, “
Non-Darcian flow in loess at low hydraulic gradient
,” Eng. Geol.
267
, 105483
(2020
).16.
S.
Zhang
,
H.
Pei
,
M.
Plötze
, and
H.
Ying
, “
Molecular dynamics modeling of hydraulic conductivity of soil considering variable viscosity and adsorbed water
,” Appl. Clay Sci.
228
, 106598
(2022
).17.
C.
Xie
,
J.
Zhu
,
H.
Yang
,
J.
Wang
,
L.
Liu
, and
H.
Song
, “
Relative permeability curve prediction from digital rocks with variable sizes using deep learning
,” Phys. Fluids
35
(9
), 096605
(2023
).18.
W. D.
Carrier
III
, “
Goodbye, Hazen; Hello, Kozeny-Carman
,” J. Geotech. Geoenviron. Eng.
129
(11
), 1054
–1056
(2003
).19.
D. W.
Taylor
, Fundamentals of Soil Mechanics
(
John Wiley and Sons, Inc
.,
New York
, 1948
), pp. 97
–123
.20.
R. P.
Chapuis
, “
Predicting the saturated hydraulic conductivity of sand and gravel using effective diameter and void ratio
,” Can. Geotech. J.
41
(5
), 787
–795
(2004
).21.
P.
Xu
and
B.
Yu
, “
Developing a new form of permeability and Kozeny–Carman constant for homogeneous porous media by means of fractal geometry
,” Adv. Water Resour.
31
(1
), 74
–81
(2008
).22.
C. H.
Shin
, “
Permeability variation analysis using the superficial diameter correlation with porosity change
,” Phys. Fluids
33
(5
), 053108
(2021
).23.
H.
Sokol
,
M.
Sprynskyy
,
A.
Ganzyuk
,
V.
Raks
, and
B.
Buszewski
, “
Structural, mineral and elemental composition features of iron-rich saponite clay from Tashkiv deposit (Ukraine)
,” Colloids Interfaces
3
(1
), 10
(2019
).24.
S.
Yuan
,
X.
Liu
,
Y.
Wang
,
P.
Delage
,
P.
Aimedieu
, and
O.
Buzzi
, “
X-ray microtomography of mercury intruded compacted clay: An insight into the geometry of macropores
,” Appl. Clay Sci.
227
, 106573
(2022
).25.
P.
Hou
,
F.
Gao
,
Y.
Ju
,
H.
Cheng
,
Y.
Gao
,
Y.
Xue
, and
Y.
Yang
, “
Changes in pore structure and permeability of low permeability coal under pulse gas fracturing
,” J. Nat. Gas Sci. Eng.
34
, 1017
–1026
(2016
).26.
J.
Goral
,
M.
Andrew
,
T.
Olson
, and
M.
Deo
, “
Correlative core-to pore-scale imaging of shales
,” Mar. Pet. Geol.
111
, 886
–904
(2020
).27.
E.
Jimenez
,
J.
Escandón
,
F.
Méndez
, and
O.
Bautista
, “
Combined viscoelectric and steric effects on the electroosmotic flow in nano/microchannels with heterogeneous zeta potentials
,” Colloids Surf. A
577
, 347
–359
(2019
).28.
F.
Mugele
,
B.
Bera
,
A.
Cavalli
,
I.
Siretanu
,
A.
Maestro
,
M.
Duits
et al, “
Ion adsorption-induced wetting transition in oil-water-mineral systems
,” Sci. Rep.
5
(1
), 10519
(2015
).29.
C.
Li
,
Z.
Liu
,
X.
Liu
,
Z.
Feng
, and
X.
Mo
, “
Combined effect of surface charge and boundary slip on pressure-driven flow and convective heat transfer in nanochannels with overlapping electric double layer
,” Int. J. Heat Mass Transfer
176
, 121353
(2021
).30.
Y.
Gao
,
H.
Qian
,
X.
Li
,
J.
Chen
, and
H.
Jia
, “
Effects of lime treatment on the hydraulic conductivity and microstructure of loess
,” Environ. Earth Sci.
77
, 529
(2018
).31.
M.
Zhang
,
X.
Zhu
,
G.
Yu
,
J.
Yan
,
X.
Wang
,
M.
Chen
, and
W.
Wang
, “
Permeability of muddy clay and settlement simulation
,” Ocean Eng.
104
, 521
–529
(2015
).32.
Y.
Cai
,
D.
Liu
,
Z.
Pan
,
Y.
Che
, and
Z.
Liu
, “
Investigating the effects of seepage-pores and fractures on coal permeability by fractal analysis
,” Transp. Porous Med.
111
(2
), 479
–497
(2016
).33.
N.
Otsu
, “
A threshold selection method from gray-level histograms
,” IEEE Trans. Syst., Man, Cybern.
9
(1
), 62
–66
(1979
).34.
J.
Bouma
,
A.
Jongerius
,
O.
Boersma
,
A.
Jager
, and
D.
Schoonderbeek
, “
The function of different types of macropores during saturated flow through four swelling soil horizons
,” Soil Sci. Soc. Am. J.
41
(5
), 945
–950
(1977
).35.
E. L.
Fay
,
D. J.
Grombacher
, and
R. J.
Knight
, “
Investigating the effect of internal gradients on static gradient nuclear magnetic resonance diffusion measurements
,” Geophysics
82
(5
), D293
–D301
(2017
).36.
J.
Qajar
and
C. H.
Arns
, “
A comparative study of micro-CT and mercury intrusion techniques for predicting permeability and surface area evolution during chemical dissolution
,” Adv. Water Resour.
168
, 104301
(2022
).37.
M.
Jiang
,
F.
Zhang
,
H.
Hu
,
Y.
Cui
, and
J.
Peng
, “
Structural characterization of natural loess and remolded loess under triaxial tests
,” Eng. Geol.
181
, 249
–260
(2014
).38.
J. D.
Wang
,
P.
Li
,
Y.
Ma
, and
S. K.
Vanapalli
, “
Evolution of pore-size distribution of intact loess and remolded loess due to consolidation
,” J. Soils Sediments
19
, 1226
–1238
(2019
).39.
H. M.
Rootare
and
C. F.
Prenzlow
, “
Surface areas from mercury porosimeter measurements
,” J. Phys. Chem.
71
(8
), 2733
–2736
(1967
).40.
X.
Wang
,
M.
Wang
,
Y.
Li
,
J.
Zhang
,
M.
Li
,
Z.
Li
,
Z.
Guo
, and
J.
Li
, “
Shale pore connectivity and influencing factors based on spontaneous imbibition combined with a nuclear magnetic resonance experiment
,” Mar. Pet. Geol.
132
, 105239
(2021
).41.
J.
Marroquin-Desentis
,
F.
Méndez
, and
O.
Bautista
, “
Viscoelectric effect on electroosmotic flow in a cylindrical microcapillary
,” Fluid Dyn. Res.
48
(3
), 035503
(2016
).42.
S. K.
Mehta
and
P. K.
Mondal
, “
Viscoelectric effect on the chemiosmotic flow in charged soft nanochannels
,” Phys. Fluids
35
(11
), 112005
(2023
).43.
D.
Jin
,
Y.
Hwang
,
L.
Chai
,
N.
Kampf
, and
J.
Klein
, “
Direct measurement of the viscoelectric effect in water
,” Proc. Natl. Acad. Sci. U. S. A.
119
(1
), e2113690119
(2022
).44.
P.
Xu
,
L.
Zhang
,
B.
Rao
,
S.
Qiu
,
Y.
Shen
, and
M.
Wang
, “
A fractal scaling law between tortuosity and porosity in porous media
,” Fractals
28
(02
), 2050025
(2020
).45.
B. M.
Yu
and
J. H.
Li
, “
A geometry model for tortuosity of flow path in porous media
,” Chin. Phys. Lett
21
(8
), 1569
–1571
(2004
).46.
D. C.
Standnes
, “
Derivation of the conventional and a generalized form of Darcy's Law from the Langevin Equation
,” Transp. Porous Med.
141
(1
), 1
–15
(2022
).47.
J.
Bear
,
C.
Braester
, and
P. C.
Menier
, “
Effective and relative permeabilities of anisotropie porous media
,” Transp. Porous Med.
2
, 301
–316
(1987
).48.
H.
Li
,
C.
Le Qing
,
S. Q.
Wei
, and
X. J.
Jiang
, “
An approach to the method for determination of surface potential on solid/liquid interface: theory
,” J. Colloid Interface Sci.
275
(1
), 172
–176
(2004
).49.
J.
Hou
,
H.
Li
,
H.
Zhu
, and
L.
Wu
, “
Determination of clay surface potential: a more reliable approach
,” Soil Sci. Soc. Am. J.
73
(5
), 1658
–1663
(2009
).50.
B.
Yu
and
P.
Cheng
, “
A fractal permeability model for bi-dispersed porous media
,” Int. J. Heat Mass Transfer
45
(14
), 2983
–2993
(2002
).51.
R.
Qiao
and
N. R.
Aluru
, “
Ion concentrations and velocity profiles in nanochannel electroosmotic flows
,” J. Chem. Phys.
118
(10
), 4692
–4701
(2003
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
