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Varieties of pore‐scale numerical and empirical approaches have been proposed to predict the rock permeability when the pore structure is known, for example, microscopic computerized tomography (micro‐CT) technology. A comparative study on these approaches is conducted in this paper. A reference dataset of nine micro‐CT images of porous rocks is generated and processed including artificial sandpacks, tight sandstone, and carbonate. Multiple numerical and empirical approaches are used to compute the absolute permeability of micro‐CT images including the image voxel‐based solver (VBS), pore network model (PNM), Lattice Boltzmann method (LBM), Kozeny‐Carman (K‐C) equation, and Thomeer relation. Computational accuracy and efficiency of different numerical approaches are investigated. The results indicate that good agreements among numerical solvers are achieved for the sample with a homogeneous structure, while the disagreement increases with an increase in heterogeneity and complexity of pore structure. The LBM and VBS solver both have a relative higher computation accuracy, whereas the PNM solver is less accurate due to simplification on the topological structure. The computation efficiency of the different solver is generally computation resources dependent, and the PNM solver is the fastest, followed by VBS and LBM solver. As expected, empirical relation can over‐estimate permeability by a magnification of 50 or more, particularly for those strong heterogeneous structures reported in this study. Nevertheless, empirical relation is still applicable for artificial rocks. A comprehensive comparative study on multiple numerical and empirical approaches for permeability prediction is carried out in this study, including the image voxel‐based solver (VBS), Lattice Boltzmann method (LBM), pore network method (PNM), Kozeny‐Carman equation (K‐C), and Thomeer's relation. In addition, the differences on computed permeability of different approaches are quantified including computational accuracy and efficiency.

Various processes such as heterogeneous reactions or biofilm growth alter a porous medium’s underlying geometric structure. This significantly affects its hydrodynamic parameters, in particular the medium’s effective permeability. An accurate, quantitative description of the permeability is, however, essential for predictive flow and transport modeling. Well-established relations such as the Kozeny–Carman equation or power law approaches including fitting parameters relate the porous medium’s porosity to a scalar permeability coefficient. Opposed to this, upscaling methods directly enable calculating the full, potentially anisotropic, permeability tensor. As input, only the geometric information in terms of a representative elementary volume is needed. To compute the porosity–permeability relations, supplementary cell problems must be solved numerically on this volume and their solutions must be integrated. We apply this approach to provide easy-to-use quantitative porosity–permeability relations that are based on representative single grain, platy, blocky, prismatic soil structures, porous networks, and real geometries obtained from CT-data. As a discretization method, we use discontinuous Galerkin method on structured grids. To make the relations explicit, interpolation of the obtained data is used. We compare the outcome with the well-established relations and investigate the ranges of the validity. From our investigations, we conclude whether Kozeny–Carman-type or power law-type porosity–permeability relations are more reasonable for various prototypic representative elementary volumes. Finally, we investigate the impact of a microporous solid matrix onto the permeability.

In this article we investigate the permeability of a porous medium as given in Darcy’s law. The permeability is described by an effective hydraulic pore radius in the porous medium, the fluctuation in local hydraulic pore radii, the length of streamlines, and the fractional volume conducting flow. The effective hydraulic pore radius is related to a characteristic hydraulic length, the fluctuation in local hydraulic radii is related to a constriction factor, the length of streamlines is characterized by a tortuosity, and the fractional volume conducting flow from inlet to outlet is described by an effective porosity. The characteristic length, the constriction factor, the tortuosity, and the effective porosity are thus intrinsic descriptors of the pore structure relative to direction. We show that the combined effect of our pore structure description fully describes the permeability of a porous medium. The theory is applied to idealized porous media, where it reproduces Darcy’s law for fluid flow derived from the Hagen–Poiseuille equation. We also apply this theory to full network models of Fontainebleau sandstone, where we show how the pore structure and permeability correlate with porosity for such natural porous media. This work establishes how the permeability can be related to porosity, in the sense of Kozeny–Carman, through fundamental and well-defined pore structure parameters: characteristic length, constriction, and tortuosity.

Permeability and formation factor are important properties of a porous medium that only depend on pore space geometry, and it has been proposed that these transport properties may be predicted in terms of a set of geometric measures known as Minkowski functionals. The well-known Kozeny–Carman and Archie equations depend on porosity and surface area, which are closely related to two of these measures. The possibility of generalizations including the remaining Minkowski functionals is investigated in this paper. To this end, two-dimensional computer-generated pore spaces covering a wide range of Minkowski functional value combinations are generated. In general, due to Hadwiger’s theorem, any correlation based on any additive measurements cannot be expected to have more predictive power than those based on the Minkowski functionals. We conclude that the permeability and formation factor are not uniquely determined by the Minkowski functionals. Good correlations in terms of appropriately evaluated Minkowski functionals, where microporosity and surface roughness are ignored, can, however, be found. For a large class of random systems, these correlations predict permeability and formation factor with an accuracy of 40% and 20%, respectively.

The absolute permeability of rock depends on several factors, including porosity, \\[ \\], the geometry of the pore network (tortuosity), and the grain geometry, dimension and composition. The mineralogical composition plays an important role, mostly with respect to clay, which involves several components including illite, smectite, kaolinite and chlorite. The presence of quartz and feldspar increases permeability, while clay minerals and calcite tend to have the opposite effect. Essentially, permeability decreases with asmaller grain radius, increasing tortuosity of the pore space and decreasing porosity. As the specific surface area of the pores increases, permeability decreases. Here, we compare four expressions for permeability based on clay content, grain dimension, tortuosity and mineral composition. All the expressions somehow contain the Kozeny–Carman (KC) factor \\[ ^3 /(1 - )^2\\], which is obtained on physical grounds, and relies on fitting parameters related to the geometric characteristics of the rock and its composition. The Herron model is based on geochemical mineralogy composition. Despite the highly idealized parameters on which these models are based, the results support the predictive power of the Kozeny–Carman equation, provided that proper calibration is performed.

Compacted bentonite is envisaged as engineering buffer/backfill material in geological disposal for high-level radioactive waste. In particular, Na-bentonite is characterised by lower hydraulic conductivity and higher swelling competence and cation exchange capacity, compared with other clays. A solid understanding of the hydraulic behaviour of compacted bentonite remains challenging because of the microstructure expansion of the pore system over the confined wetting path. This work proposed a novel theoretical method of pore system evolution of compacted bentonite based on its stacked microstructure, including the dynamic transfer from micro to macro porosity. Furthermore, the Kozeny–Carman equation was revised to evaluate the saturated hydraulic conductivity of compacted bentonite, taking into account microstructure effects on key hydraulic parameters such as porosity, specific surface area and tortuosity. The results show that the prediction of the revised Kozeny–Carman model falls within the acceptable range of experimental saturated hydraulic conductivity. A new constitutive relationship of relative hydraulic conductivity was also developed by considering both the pore network evolution and suction. The proposed constitutive relationship well reveals that unsaturated hydraulic conductivity undergoes a decrease controlled by microstructure evolution before an increase dominated by dropping gradient of suction during the wetting path, leading to a U-shaped relationship. The predictive outcomes of the new constitutive relationship show an excellent match with laboratory observation of unsaturated hydraulic conductivity for GMZ and MX80 bentonite over the entire wetting path, while the traditional approach overestimates the hydraulic conductivity without consideration of the microstructure effect.

The pore structure of loess is crucial for understanding the transport of water in soil and affects soil permeability. In this study, X-ray computed tomography (X-ray CT) technology was used to establish the macropore structure of remolded loess, and analyze the influence of macropore on permeability. A new specific and efficient workflow for constructing macropore structure of loess samples was established. The workflow improves the precision of image segmentation and provides a new method for creating 3D soil macropore structure. The macropore structure showed that the macro-porosity variation of loess sample was clearly anisotropic. Based on the macropore structure model, a modified Kozeny–Carman equation was suggested to investigate the hydraulic conductivity anisotropy of the loess sample. Subsequently, permeability test was used to verify the results calculated by equation. Both the results showed that hydraulic conductivity was positively correlated with the uniformity of the porosity changes in each direction. It provides a new method to estimate the anisotropy of hydraulic conductivity based on macropore structure model.

Six different commercial powders, finer than 45 μm, were used for examining the effects of particle characteristics on mean particle size and specific surface area. The measurements were carried out using the most commonly used air permeability- and laser light diffraction (scattering) techniques. As the air permeability method has been used as a benchmark for decades in the powder metallurgy (P/M) industry, the physical phenomena that govern the passage of gas through the powder bed under laminar flow conditions were also presented. The experimental data indicate that both methods give similar results for spherical powders. The advantage of laser light systems over gas permeameters is the ability to provide additional information on particle size distribution. Irregularly shaped powders should be analyzed by both techniques, relying on gas permeametry for surface area measurements and on laser light diffraction for the estimation of mean particle size and size distribution. Application of scanning electron microscopy as a complementary technique was found very helpful in the interpretation of data through visualization of individual particles.

As the first attempt in Iran, the combination of electrical resistivity measurement of groundwater and aquifer matrix with pumping tests and stochastic modeling of hydrofacies was used to estimate hydraulic conductivity (K) and porosity (φ). The stochastic simulation of stratigraphy using transition probability geostatistical simulation (T-PROGS) program shows that this aquifer is mainly composed of three dominant facies including fine sand, medium-coarse sand, and silt-clay. Fine sand has the highest volume proportion (42%) compared to the other two facies. The simulation results show that this alluvial medium shows great heterogeneity as well as anisotropy, which has led to many changes in the values of φ and K. This probabilistic model provided the particle sizes concerning the facies distribution, and these values were then used to calculate K. The average K measured in 54 pumping tests (about 10 m/day) was used as a criterion for inversely determining the optimal values of Archie's equation parameters (i.e., electrical tortuosity (α) and cementation factor (m)), which were 0.6 and 1.4, respectively. Calculations using the Kozeny–Carman–Bear (KCB) equation show that the minimum, maximum and average K values at 180 points are about 0.1, 91, and 10.6 m/day, respectively. Also, the porosity varies between 0.1 and 0.59 (with an average of 0.28). The Voronoi entropy map shows that the lowest amount of K entropy is found in the northern half of this area and the highest entropy is found in the northern coastal parts, a small part in the south as well as the northwest of the region. The proportion of the two medium and high entropy classes is higher than the other three classes, indicating significant changes in calculated K due to the heterogeneity of the porous medium.

Kozeny-Carman permeability equation is an important relation for the determination of permeability in porous media. In this study, the permeabilities of porous media that contains rectangular rods are determined, numerically. The applicability of Kozeny-Carman equation for the periodic porous media is investigated and the effects of porosity and pore to throat size ratio on Kozeny constant are studied. The continuity and Navier-Stokes equations are solved to determine the velocity and pressure fields in the voids between the rods. Based on the obtained flow field, the permeability values for different porosities from 0.2 to 0.9 and pore to throat size ratio values from 1.63 to 7.46 are computed. Then Kozeny constants for different porous media with various porosity and pore to throat size ratios are obtained and a relationship between Kozeny constant, porosity and pore to throat size ratio is constructed. The study reveals that the pore to throat size ratio is an important geometrical parameter that should be taken into account for deriving a correlation for permeability. The suggestion of a fixed value for Kozeny constant makes the application of Kozeny-Carman permeability equation too narrow for a very specific porous medium. However, it is possible to apply the Kozeny-Carman permeability equation for wide ranges of porous media with different geometrical parameters (various porosity, hydraulic diameter, particle size and aspect ratio) if Kozeny constant is a function of two parameters as porosity and pore to throat size ratios.