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Permeability plays a pivotal role in water resources management, oil and gas exploration and production, as well as geological hazard assessment. Previous studies primarily explores the influencing factors of permeability through indirect methods, and lacks direct means to describe the relationship between porous media and permeability, and the relationship between permeability and the internal pore structure of porous media is still unclear. This study developed an experimental system featuring controllable pore space properties to investigate the relationship between permeability in porous media and factors including porosity, the horizontal and vertical distribution of pores, the regularity of particle arrangements, and the aspect ratio of elliptical pores. The experimental results demonstrate a positive correlation between permeability and porosity in porous media. Circular porous media generally adhere to the Kozeny-Carman equation, while variations in particle circularities and arrangements lead to pronounced permeability anisotropy. Due to the transverse arrangement of porous media leading to the fluid with a long flow path, permeability in horizontally arranged pores aligned with the flow direction is significantly higher than that in vertically arranged pores. Irregularly arranged porous media exhibit higher permeability compared to regularly arranged porous media, because 1) the irregular arrangement of the particles can lead to some large pores in the porous media that can provide large channels to facilitate the penetration of the fluid; 2) the irregular arrangement increases the flow path within the porous medium, leading to more fluid paths in the porous medium. Porous media with an aspect ratio of 1 for the long and short axes exhibits the highest permeability. The findings of this study provide essential insights into the evolution of penetration rates in porous media and their relationship with pore space properties.

Copyright of Hydrogeology & Engineering Geology / Shuiwendizhi Gongchengdizhi is the property of Hydrogeology & Engineering Geology Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Three hundred and twenty-four data points on the saturated hydraulic conductivity (k) of various hard rock mine tailings are collected from previous publications. The applicability of existing empirical equations for hard rock mine tailings is assessed based on this database collected. Results show that with a greater exponent of d10, the correlation between the measured and predicted k is greatly improved. An empirically modified version of the Kozeny–Carman equation is then proposed for predicting the saturated k of tailings and compared with the database. The proposed equation gives the best fit with a varying exponent greater than 2 for d10. Finally, the impact of particle shape on k is discussed. [ABSTRACT FROM AUTHOR]

• Investigated permeability of MSWs of diverse food contents, DOBs, and void ratios. • Modified Kozeny-Carman equation with effective void ratio was adopted for MSWs. • Parameters required for Kozeny-Carman equation was correlated with DOBs and d 10. The permeability of municipal solid wastes (MSWs) is important for the design and operation of landfills. This study presented the experimental investigation of the permeability of low food content- (LF-) and high food content- (HF-) MSWs prepared in laboratory-scale bioreactors for up to 5 years. The permeability of MSWs with diverse degrees of decomposition (DOBs), void ratios, and permeation liquids was measured (288 tests). The measured permeability was compared to that predicted from the (modified) Kozeny-Carman (K-C) equations in four different forms. The results indicated that the permeability of both LF- and HF-MSWs decreased significantly (p < 0.05) with decomposition under a given void ratio. The predicted permeability using the original K-C equation fitted well with that of fresh MSWs. The permeability of decomposed MSWs was closer to the predicted results using the modified K-C equation with the effective void ratio. This can be attributed to the increase in the fine fractions due to degradation. The reduction in the effective voids was more significant with HF-MSWs. The parameters required in the (modified) K-C equations showed a good correlation with DOB and effective particle size (d 10). The predicted permeability based on the relationship between DOB (or d 10) and equation parameters was within 3 times the difference compared to the measured values. The above results indicated that the modified K-C equation can be adopted to predict the permeability of fresh and degraded MSWs while more field-scale experiments should be conducted to further evaluate its feasibility. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This study evaluates various methods for estimating soil permeability using microtomography-derived data and compares them to the conventional laboratory approaches. Different methods, including measurement in custom-designed permeameter at micro-CT-compatible scale, empirical equations, simulated sifting, semi-theoretical equations, pore-network modeling, and lattice-Boltzmann simulations, were applied to samples of sandy soils with distinct microstructural properties. The empirical equations showed varied results, highly dependent on the method chosen. The simulated sifting method was able to adequately estimate the granulometric properties of the soil, allowing the use of empirical permeability formulations for substantially small samples. Semi-theoretical equations based on the microstructural properties presented reasonable agreement for some samples. The pore-network modeling approach demonstrated computational efficiency but lacked accuracy. The lattice-Boltzmann method required significant computational resources but did not provide substantially closer alignment with the measured hydraulic properties of some samples. None of the simulations was able to properly determine the permeability of silty and organically contaminated sand. The study highlights the complexity of permeability estimation, emphasizing the need for choosing volumes of interest, resolution of micro-CT scans, and methods that match specific soil characteristics and available computational resources.

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.

Copyright of Journal of Fuzhou University is the property of Journal of Fuzhou University, Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The pressure drop in the ceramic filter system of the after-treatment device has a great effect on automobile engine performance. To predict the pressure drop under various operating conditions, it is necessary to analyze how the structural properties of porous media affect the permeability. The commonly used Kozeny-Carman model correlating permeability and porosity is useful for porous media composed of spherical grains, but exhibits considerable deviations in the actual ceramic filter system with low porosity. In this study, the permeability of overlapped-random structured porous media with low porosity was numerically solved by mesoscopic lattice Boltzmann (LB) method in Darcy flow regime. Based on LB simulation results, a new capillary model modified from Kozeny-Carman model is proposed for practically predicting the permeability of complex porous filter systems, using key structural variables such as porosity, tortuosity, and effective pore-throat radius. [ABSTRACT FROM AUTHOR]

A method was developed to integrate the truncated power-law distribution of solid volumetric fraction into the widely used Kozeny–Carman (KC)-type equations to assess the potential uncertainty of permeability. The focus was on the heterogeneity of porosity (or solid volumetric fraction) in the KC equation. The truncated power-law distribution simulates a heterogeneous scenario in which the solid volumetric fraction varies over different portions of porous media, which is treated as stationary, so its spatial mean can be replaced by the ensemble mean. The model was first compared with the experimental results of 44 samples from the literature and a recent model of KC equation modification that targets the coefficients in the equation. The effects of the fractal dimension of characteristic length of the solid volumetric fraction on the mean and standard deviation of permeability are calculated and discussed. The comparison demonstrates that the heterogeneous solid volumetric fraction can have similar effects as adjusting the empirical constant in the KC equation. A narrow range smaller than mean ± standard deviation from the model agreed with the experimental data well. Incorporating the truncated power-law distribution into the classical KC model predicts a high mean permeability and uncertainty. Both the mean and standard deviation of the permeability decrease with an increasing fractal dimension. [ABSTRACT FROM AUTHOR]

A prediction model of the sound velocity and sound attenuation of underwater cobalt-rich crusts (CRCs) was established to solve the problem that it is difficult to predict the sound velocity in thickness measurements of cobalt-rich crusts. Based on Biot theory and BISQ theory, a simplified Biot and BISQ model was proposed for the prediction of the sound velocity and sound attenuation of CRCs by using the Kozeny–Carman (KC) equation. The models could calculate the sound velocity and attenuation by the porosity and detection frequency. Based on the physical and mechanical properties of CRCs, a similarity model of the sound velocity and sound attenuation of CRCs was made by using the similarity theory to solve the problem that it is difficult to measure the acoustic propagation characteristics of CRCs. The sound velocity and sound attenuation of CRC similarity models with different porosities were measured by an underwater transmission experiment and the results of the simplified model calculation and experimental measurements were compared. The results showed that the simplified Biot model was suitable for the CRC sound velocity prediction and the simplified BISQ model was suitable for the CRC sound attenuation prediction, which had a high prediction accuracy. [ABSTRACT FROM AUTHOR]

This paper describes a new formulation for estimating the permeability of drainages composed of natural sands with no clay content, starting from the parameters obtained from the grain size distribution. The conventional relationships for estimating permeability are functions of granulometric factors and porosity. However, for media typically used as drainage, the grain size grading is a determinant factor, so the porosity dependence can be replaced by a function of the average grain size and grading. The methodology used in this study consists of fitting a set of measured permeability values to a joint expression of the average grain size and the granulometric grading coefficient. To this end, a new effective diameter that can be obtained numerically and graphically is defined, and the permeability relationship is solely dependent on this diameter. To estimate later changes in drainage packing and the consequent variations in porosity, a contrasting modification of the Kozeny–Carman equation is established. This equation considers the grain size grading and is applicable to any granular media. [ABSTRACT FROM AUTHOR]

The study to analyze the heterogeneity of porous medium, especially its influence of main characteristics is conducted in this paper. For this goal computer versions of real porous models, which were available in open source, were used. These models contain several slices at three directions. Re-build and processing of models were performed using the Avizo Software. For analyzing the influence of the heterogeneity of porous medium on basic parameters, each model were divided into several geometrical pieces. These parameters were computed using computational method of pore network modelling (PNM) and Kozeny-Carman (KC) method with purpose of collation. Also, these two methods were collated with available data from direct numerical computation method (DNC). According to analyzing it was set a good match between PNM and DNC for sandstone models, also KC method showed a divergence with DNC. For carbonate models, a divergence was seen between PNM and DNC, and KC method showed very good match with DNC. The relationship between the parameters for each of piece shows inhomogeneous character for the carbonate model.

Predicting the permeability of porous media in saturated and partially saturated conditions is crucial in geoengineering. The Kozeny–Carman equation is a pervasive method used for estimating the saturated hydraulic conductivity of soils. The previously reported modified Kozeny–Carman equation did not consider the influence of a wide range of particle size distribution on the saturated hydraulic conductivity. In this study, we quantified the influence of fine particle content on the saturated hydraulic conductivity and introduced the geometrical parameters to the Kozeny–Carman equation, followed by determining the range of empirical constant in the equation by the results of seepage test. Herein, a modified Kozeny–Carman equation, considering the particle size distribution of the particle system, is proposed based on particle gradation and size characteristic parameters including non-uniformity coefficient, curvature coefficient, and effective grain diameter. A laboratory test was performed to measure the saturated hydraulic conductivity values of sand–gravel mixture with different particle size distribution, using one-dimensional seepage equipment. Data from laboratory experiments performed in this study and available data from the literature were finally used to verify this proposed model. The findings of this study demonstrated the higher prediction accuracy of the proposed modified model. [ABSTRACT FROM AUTHOR]

A method was developed to integrate the truncated power-law distribution of solid volumetric fraction into the widely used Kozeny–Carman (KC)-type equations to assess the potential uncertainty of permeability. The focus was on the heterogeneity of porosity (or solid volumetric fraction) in the KC equation. The truncated power-law distribution simulates a heterogeneous scenario in which the solid volumetric fraction varies over different portions of porous media, which is treated as stationary, so its spatial mean can be replaced by the ensemble mean. The model was first compared with the experimental results of 44 samples from the literature and a recent model of KC equation modification that targets the coefficients in the equation. The effects of the fractal dimension of characteristic length of the solid volumetric fraction on the mean and standard deviation of permeability are calculated and discussed. The comparison demonstrates that the heterogeneous solid volumetric fraction can have similar effects as adjusting the empirical constant in the KC equation. A narrow range smaller than mean ± standard deviation from the model agreed with the experimental data well. Incorporating the truncated power-law distribution into the classical KC model predicts a high mean permeability and uncertainty. Both the mean and standard deviation of the permeability decrease with an increasing fractal dimension.

This paper presents a systematical study of the effect of porosity, pore-level heterogeneity and anisotropy on the absolute permeability of digital images of porous media. The main goal is to develop an analytical formula that estimates permeability as a function of these three parameters at once. Permeability is assessed based on numerical simulations using the lattice Boltzmann equations. Digital models of porous media are generated by a combined method consisting of Monte-Carlo and quartet structure generation set (QSGS) algorithms. Increase in heterogeneity negatively affects permeability. With an increase in porosity, the effect of heterogeneity on flow properties decreases. There was a linear decrease in permeability during the transition between favorable and unfavorable anisotropy. The influence of anisotropy is most pronounced in samples with high porosity and monotonically reduces with decreasing porosity. Heterogeneity negatively influences on the sensitivity of flow properties to changes in anisotropy and independent on porosity. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Mathematics, Mechanics & Computer Science is the property of Al-Farabi Kazakh National University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A prediction model of the sound velocity and sound attenuation of underwater cobalt-rich crusts (CRCs) was established to solve the problem that it is difficult to predict the sound velocity in thickness measurements of cobalt-rich crusts. Based on Biot theory and BISQ theory, a simplified Biot and BISQ model was proposed for the prediction of the sound velocity and sound attenuation of CRCs by using the Kozeny–Carman (KC) equation. The models could calculate the sound velocity and attenuation by the porosity and detection frequency. Based on the physical and mechanical properties of CRCs, a similarity model of the sound velocity and sound attenuation of CRCs was made by using the similarity theory to solve the problem that it is difficult to measure the acoustic propagation characteristics of CRCs. The sound velocity and sound attenuation of CRC similarity models with different porosities were measured by an underwater transmission experiment and the results of the simplified model calculation and experimental measurements were compared. The results showed that the simplified Biot model was suitable for the CRC sound velocity prediction and the simplified BISQ model was suitable for the CRC sound attenuation prediction, which had a high prediction accuracy.

It is very important to notice clay minerals, for resource development, stability evaluation of underground utilization, and others. However, few quantitative data on the effects of clay-mineral type on the swelling characteristics and permeability of clays and clay minerals have been reported to date. This study was conducted to investigate the effects of clay-mineral type on the swelling characteristics and permeability of compacted clays using one-dimensional swelling-pressure and constant-pressure permeability tests. Comparative tests revealed that the difference of clay-mineral type in the clays influences the swelling-pressure and hydraulic conductivity. The swelling-pressure and hydraulic conductivity were closely associated with the specific surface area of clays. Furthermore, hydraulic conductivity was almost consistent that measured with the Kozeny-Carman equation. This result suggests that hydraulic conductivity can be estimated based on a specific surface area and void ratio of compacted clays. [ABSTRACT FROM AUTHOR]

Abstract 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.

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. [ABSTRACT FROM AUTHOR]

This paper is a study of determination of representative elementary volume (REV) size suitable for pore-scale flow simulation (PFS) and evaluation of permeability anisotropy for sand based on Kozeny–Carman (KC) equation. We extracted small digitized samples for PFS from the 3D structures of Toyoura sand and glass beads obtained by X-ray computed tomography. Using the digitized samples with various sizes, we performed a series of flow simulations. We characterized the sample size using the ratio of the porous length L to the median grain diameter D 50 . The L / D 50 of REV was determined on the basis of statistical evaluation on coefficients of variations of the simulated values of void ratio, specific surface, hydraulic conductivity and hydraulic tortuosity. We confirmed that the hydraulic properties obtained from the PFS using the REV size determined agreed well with the past experimental studies. We also conducted PFSs in the horizontal direction to evaluate the permeability anisotropy. We clarified that the shape factor in the KC equation has a strong influence on permeability anisotropy even though previous studies treated hydraulic tortuosity as the only factor that affects the permeability anisotropy. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The stress dependency of the porosity and permeability of porous rocks is described theoretically by representing the preferential flow paths in heterogeneous porous rocks by a bundle of tortuous cylindrical elastic tubes. A Lamé-type equation is applied to relate the radial displacement of the internal wall of the cylindrical elastic tubes and the porosity to the variation of the pore fluid pressure. The variation of the permeability of porous rocks by effective stress is determined by incorporating the radial displacement of the internal wall of the cylindrical elastic tubes into the Kozeny–Carman relationship. The fully analytical solutions of the mechanistic elastic pore-shell model developed by combining the Lamé and Kozeny–Carman equations are shown to lead to very accurate correlations of the stress dependency of both the porosity and the permeability of porous rocks. [ABSTRACT FROM AUTHOR]

The groundwater flow with entrapped air was termed as quasi-saturated flow. The entrapped air in quasi-saturated flow of aquifer had a significant influence on hydraulic conductivity of porous media. In this paper,the relation between entrapped air saturation and hydraulic conductivity was studied by the column experiments with respect to four medium,silt,fine sand,medium sand and coarse sand,respectively. The results illustrated that the entrapped air saturation in a quasi-saturated aquifer was related to the particle size of the medium,and the entrapped air saturation in the fine-grained media was greater than that in the coarse-grained. Within a saturation range of 0-15% of entrapped air saturation,the hydraulic conductivity decreased by 32.82%-56.38% compared with that at entrapped saturation,and the hydraulic conductivity can be expressed as a negative linear correlation with entrapped air saturation. The results also showed that the variation of the quasi-saturated hydraulic conductivity could be generalized as the entrapped air occupied the original effective poresand resulted in a decrease in the original effective porosity and hence in hydraulic conductivity. According to this air entrapment theory,the Kozeny-Carman equation could accurately exhibit the variation of the hydraulic conductivity with entrapped air saturation in the quasi-saturated aquifer,and furthermore,the results illustrated the hydraulic conductivity formula based on the Hagen-Poiseuille equation was not suitable for quasi-saturated hydraulic conductivity. In Addition,the experimental results also showed it was necessary to remove entrapped air in laboratory measurement of hydraulic conductivity. [ABSTRACT FROM AUTHOR]

Based on the similarity in the underlying mechanisms between electrical and hydraulic conduction in porous media, Archie's equation can be combined with the Kozeny-Carman (KC) equation to estimate the hydraulic conductivity (K) of coarse-grained soils. However, the assumption of the exponent m in Archie's equation, which is equivalent to the assumed porosity at specific soil electrical properties, reduces the accuracy of the value of K predicted using the combination of Archie's equation and the KC equation. Therefore, this study introduces a depolarization factor, which allows the exponent m in Archie's equation to be estimated from the shape of the particles. Consequently, this study proposes a formula for estimating K for coarse-grained soils based on the combination of Archie's equation, the KC equation, and the depolarization factor. Data from laboratory experiments performed in this work and available data from the literature were used to validate the proposed model. In addition, the optimal value for the exponent m was recommended for predicting hydraulic conductivity using the proposed K estimating formula in the absence of particle shape data. Data obtained in the experiments and literature revealed that the proposed model is comparatively reliable in predicting K. • Depolarization factor was introduced to estimate the Archie's m exponent. • The formula for estimating hydraulic conductivity of sands is proposed. • Hydraulic conductivity and electrical resistivity of sands were measured. • The proposed model is comparatively reliable in predicting hydraulic conductivity. [ABSTRACT FROM AUTHOR]

Effective characteristics, such as the effective particle diameter and hydraulic radius, are usually used to determine the pressure loss associated with single-phase flow through an isotropic, dense non-spherical granular packing. These quantities can be considered as those of an equivalent spherical particle system. This paper reviews different methods to select effective particle diameters taking into account the effect of particle shape. A new method is proposed to determine an equivalent spherical particle system with both the hydraulic radius and the pressure loss equivalent to those in the actual non-spherical particle packing. This equivalent system can be used to determine the characteristics of flow in the actual system. The analyses provide theoretical justification for adoption of proper effective particle diameters and porosity as well as the dependency of Ergun–Kozeny constant on the shape factor of particles. It is also shown theoretically that the critical Reynolds number for Darcian flow depends on the porosity and the shape factor of particles. [ABSTRACT FROM AUTHOR]

Stress dependency of permeability of porous rocks is described by means of a theoretical elastic cylindrical pore-shell model. This model is developed based on a bundle of elastic capillary tubes representation of the preferential flow paths formed in heterogeneous porous rocks. The radial displacement caused in tubes by the pore fluid pressure applied over the surface of the elastic cylindrical flow tubes is expressed by a Lamé-type equation. The radial displacement is incorporated into the Kozeny-Carman relationship to determine the variation of the permeability of porous rocks by variation of the pore fluid pressure. The solution of this equation yields a semi-analytical equation which provides accurate correlations of the stress dependency of the permeability data of porous rocks. The errors associated with the previous formulation of this problem by Zhu et al. (Transp Porous Med 122:235-252, 2018) are explained in view of the present formulation. [ABSTRACT FROM AUTHOR]

Abstract Frost heave can have a very destructive impact on infrastructure in permafrost regions. The complexity of nanoscale ice-mineral interactions and their relation to the macroscale frost heave phenomenon make ice lens growth modeling an interesting but challenging task. Taking into account the limiting assumption of the constant segregation temperature in the segregation potential model, we propose here a new quasi-static model for ice lens growth under a time varying temperature based on the water activity criterion. In this model, the conventional pressure potential gradient in Darcy's law is replaced by a water activity based chemical potential gradient for the calculation of water flow velocity, which provides a better prediction of ice lens growth and is useful to describe the ice nucleation and the state of water at a specific temperature. Moreover, based on the analysis of the new developed model, a mathematical description of the segregation potential is provided here. The modified Kozeny-Carman equation is applied to determine the water permeability of a given soil. In our new model, the effects of the equivalent water pressure are taken into account to modify the freezing characteristic function. Hence, the temperature- and equivalent water pressure- dependent hydraulic permeability in the frozen fringe is mathematically determined and improved. By coupling the quasi-static model with the modified hydraulic permeability function, the numerical calculation of ice lens growth is validated based on the experimental data of the temperature of the ice lens measured in the laboratory. The prediction of ice lens growth using the proposed method contributes and facilitates the simplified calculation of frost heave in the field and/or laboratory scenarios at a quasi-static state, and thus enables a better understanding of phase change and fluid flow in partially frozen granular media (soils). Highlights • A new quasi-static model for ice lens growth under a time varying temperature is established. • A mathematical description of the segregation potential is provided in this paper. • The temperature- and pressure- dependent hydraulic permeability in the frozen fringe is mathematically determined and improved. [ABSTRACT FROM AUTHOR]

• A modified KC equation is proposed to calculate hydraulic conductivity in nanopores. • Influence of surface activity and pore size on nano-flow is modelled by MD simulations. • A specific function is proposed to quantify the adsorbed proportion based on MD simulation results. • The modified KC equation is valid to be applied to both sandy and clayey soils. Hydraulic conductivity is a critical parameter for studying the behavior of clay-water systems. However, accurately estimating saturated hydraulic conductivity k in clayey soil by using the Kozeny-Carman (KC) equation is challenging due to the neglect of its active surface properties and nanoscale pores. Clay surfaces can have diverse characteristics resulting from various physicochemical processes such as isomorphous substitution and are typically characterized by the Cation Exchange Capacity (CEC). These properties can significantly impact fluid transport through the clay matrix. To address this issue, this study modifies the KC equation by incorporating an adsorbed water proportion φ that considers the occurrence state of pore water and its correlation with pore diameter, making it applicable to clayey soils. Molecular dynamics (MD) models are established to investigate the influence of surface interaction (CEC) and nanopore size (r) on saturated hydraulic conductivity k of seepage flow in clayey soils. Based on the MD results, a specific function is proposed to quantify the adsorbed proportion φ , which is linearly related to the root of CEC and reciprocal of pore size (r), and then incorporated into a proposed hydraulic correction ratio k * to modify the classical KC equation. The modified KC equation is validated using experimental data from literature, showing a high R 2 value of 0.96. This result demonstrates that the proposed correction ratio k * can extend the application scope of the classical KC equation to clayey soils. [ABSTRACT FROM AUTHOR]

Abstract In this study, we report a physics-based model for pore structure typing in which a generalized model is also derived to calculate the specific surface area of the grains. In this model, a new pore-structure-type indicator is defined to characterize the discrepancies of pore structures based on the fractal geometry theory and a modified Kozeny-Carman equation. We compared the proposed model with the conventional model by comprehensive experimental tests in 130 low permeability sandstone cores from the Dongfang gas reservoir in the South China Sea. The fractal dimension of the grain D g was first accurately calculated through thin section analysis. The results show that grains of low-permeability sandstone indeed have the bifractal distribution with constant radius boundaries of approximately 30 μm, potentially accounting for the multiscale of pore spaces. Compared with the conventional model, considering the complex pore and grain size distributions as well as irreducible water saturation, the developed model as a generalized expression performs better in pore structure typing with higher correlation coefficients in porosity-permeability and structural coefficients-pore radius relationships due to the newly identified indicator with a wider range. Finally, a multiscale workflow was proposed to analyze the petrological and structural features of pore structures by two-dimensional core images, thin sections, scanning electron microscope, mercury intrusion tests and three-dimensional micro-computed tomography. This work enables us to explain the genetic types and differences of the pore structure and may help to characterize the internal connection of the grain structure-pore structure-flow mechanism in hydrocarbon exploration and development. Highlights • A new model for pore structure typing was developed based fractal geometry. • A newly defined parameter- PSTI well characterizes the difference in pore structures. • The bifractal structure of the grains was first observed in low-permeability rocks. • Petrological and structure characteristics of each PST were analyzed at multiscales. [ABSTRACT FROM AUTHOR]

Abstract A modified Kozeny–Carman (KC) equation is presented based on a semilog–sigmoid (SS) function of a soil's particle size distribution (PSD). The KC equation is widely used to estimate soil permeability. However, a more effective use of the equation requires the accurate measurement of the specific surface area of the soil per unit volume. In this study, it is demonstrated that the specific surface area can be derived from the SS function, which simply but accurately represents the soil's PSD. The modified KC equation is also extended in terms of uniformity and sorting coefficients for its potential use in geotechnical applications. The applicability of the modified KC equation is confirmed through a comparison of the theoretical results of over 50 permeability tests that yielded values ranging from 1 × 10−5 to 1 × 10−1 m/s. [ABSTRACT FROM AUTHOR]

Toe-to-Heel Air Injection (THAI) is a great potential in improving energy efficiency for heavy oil/bitumen recovery. A 3D cylindrical combustion model with large size is used to carry out several experiments using Xinjiang (China) crude oil. The evolution of the fire chamber, temperature variation rate, and mass of burned carbon were analyzed using temperature measurements and flue gas composition analysis. Coke zone was quantified in the variation of zone thickness and distribution characteristics. The results reveal that there is a prevailing stable propagation of the combustion front during the first one third of the process for varying injector to producer spacing. Oxygen breakthrough is more susceptible for smaller separations and the combustion zone is reduced in length. Larger combustion fronts with greater relative propagation in the horizontal direction occurs when the well spacing is larger. The distribution of coke is significantly influenced by the injector/producer spacing. For a THAI pattern with greater injector/producer spacing, a smaller inclination angle of the coke zone occurs and the likelihood of oxygen breakthrough to the horizontal production well is lessened. Hence, the injector to producer spacing needs to be considered in designing a safe THAI process for potentially larger efficiency and optimum economics. [ABSTRACT FROM AUTHOR]

A new manufacturing concept named multilayered hybrid (MLH) roving was invented in the form of a fiber roving separated evenly into several sublayers by thermoplastic films, which is manufactured by the sequential processes of spreading, fixing, and folding. This concept is aimed to combine the variety in processing of commingled roving and the variety in material configuration of organic sheet. For the review on impregnation basics, the Kozeny–Carman equation was examined on the packed bed of fibers, not of particles, to check out the controllable parameter. Also, the newly derived spreading equation was prepared to prevent the current problem of center splitting during fiber spreading processes. The impregnation quality was practically verified by the bending test on the unbalanced (2/1) woven fabric made of polypropylene (PP) and glass fiber (GF) MLH roving, PP/GF45 vol.% (70 wt%), which had been impregnated by the continuous compression molding machine considering the conditions of mass production. The representative flexural properties were statistically determined with the characteristic behavior of stress–strain curve. The coefficient-of-variation values were in the moderate range of around 5%, except for the strength and strain in minor direction that can be explained by the waving of fibers due to the lack of applied tension during and before impregnation. [ABSTRACT FROM AUTHOR]

Reservoir modeling of carbonate rocks requires a proper understanding of the pore space distribution and its relationship to permeability. Using a pigeonhole fractal model we characterize the fractal geometry of moldic pore spaces and extract the fractal dimension. We apply the Kozeny-Carman equation and equations relating the tortuosity and the porosity to the fractal dimension to derive an empirical relationship between permeability and porosity. [ABSTRACT FROM AUTHOR]

Permeability of hydrate-bearing sediments is the key parameter to determine the gas production performance, which is mainly affected by the pore morphology and hydrate saturation. Existing models of permeability could not well capture the dynamic characteristic of permeability in sediments with changing hydrate saturation and pore morphology. In this paper, a novel normalized permeability model using logistic function linked different hydrate pore morphology evolution was established by modifying tortuosity, surface area and pore shape factor simultaneously in Kozeny-Carman equation. It was verified by different published data and compared with other models. The introduced critical hydrate saturation and transitional intensity of hydrate pore morphology were optimized by genetic algorithm. Results indicated that this model was more powerful than existed models and better captured the permeability evolution in hydrate-bearing sediments at various conditions. The critical hydrate saturation and transitional intensity of hydrate pore morphology dominated the characteristics of permeability evolution. In addition, the effect of porosity would not be ignored especially below the critical hydrate saturation when hydrate pore morphology changed from pore filling to grain coating. The proposed model brings reliable predictions and mechanistic understandings of the permeability evolution in hydrate-bearing sediments, and builds fundamental theory for development of natural gas hydrate in safety and efficiency. • Permeability model considering hydrate saturation and morphology was developed. • Tortuosity, surface area and shape factor in Kozeny-Carman equation were modified. • Model performance validated by experimental data and other models showed better. • Critical hydrate saturation and hydrate pore morphology transition can be obtained. [ABSTRACT FROM AUTHOR]

Permeability is a crucial macroscopic parameter in characterizing fluid flow and mass transfer behavior in porous media. A great theoretical basis for permeability estimation has been provided by many traditional and recently presented fractal models. However, since the influence of overlying sediments, the low-permeability porous media such as natural rock and coal generally have lower permeability and porosity with abundant pores which have more complex structure and rougher surface. The fluid located at surface tends to be bound to form irreducible state. Generally, this natural phenomenon is often ignored in the conventional fractal permeability model. In this study, the improved model was theoretically deduced based on the fractal geometry theory with considering the irreducible water saturation. 133 total sandstone samples from a gas reservoir were used to verify the validity of the developed model. The mercury injection experiment and the conventional physical property test were carried out, and the thin section image of each sample was crafted. The pores were segmented by the proposed color extracted algorithm for calculating pore fractal dimension. The results show that the available fractal model overestimates permeability values. A new form of the classical Kozeny-Carman equation was also developed to accurately estimate permeability. In the low permeable porous media, the empirical Kozeny-Carman constant needs to take 3.5, instead of 5. However, no longer is typical superiority found at very low permeability (<0.5 mD) in the improved fractal model and corresponding reasons are analyzed and discussed. [ABSTRACT FROM AUTHOR]

The permeability of the methane gas hydrate-bearing sand, which reflects the hydrate saturation and morphology of the sediments, significantly influences the rate of gas production. In this study, we formulated permeability reduction models for cubic packs of cylinders and spheres and random sphere packs with the grain-coating (GC) and pore-filling (PF) hydrates. Our models were based on the Kozeny–Carman equation. Three assumptions were made: (1) electrical tortuosity could be used in place of hydraulic tortuosity, (2) the effect of hydrate saturation on the shape factor could be ignored, and (3) the presence of an overlapping surface area of the GC hydrate could also be ignored. To confirm the validity of these assumptions, we conducted a series of computational fluid dynamics simulations of particle packs with the GC and PF hydrates generated by the discrete element method. Assumptions (2) and (3) caused the simulated normalized permeability of the GC hydrate to diverge from the proposed models because the simulated hydraulic tortuosity and shape factor of the PF hydrate were different from their analytical counterparts. However, because these differences canceled out at low hydrate saturations, the simulated normalized permeability of the PF hydrate agreed well with the proposed model. This agreement disappeared as the hydrate saturation increased because the cancellation effect atrophied. We compared the prediction accuracy of the proposed models with that of existing models in our simulations and with published experimental results. The proposed models agreed well with the simulation results and the experimental data. We showed that the parameters of the proposed model had a physical meaning: the average size of small clusters of PF hydrates. Analyzing the values of this parameter, we found that the PF type was the dominant morphology in natural core samples used in previous experimental studies. [ABSTRACT FROM AUTHOR]

This study aimed to develop a low-cost and effective clay liner material for solid waste landfills in Sri Lanka. A locally available clayey soil and its admixtures with 5 and 10% bentonite were examined for this purpose. Laboratory experiments to determine soil plasticity and swell index were carried out on the tested samples. Hydraulic conductivity ( k) tests were carried out in the laboratory using water and an aqueous solution of CaCl on unconsolidated samples prepared by either dry or slurry packing and pre-consolidated samples with five different consolidation pressures ( p) from 10 to 200 kPa. Measured liquid limits for tested admixtures increased with increasing bentonite contents and correlated well with measured values of the swell index. The difference in permeant solutions had little effect on measured k values for both unconsolidated and pre-consolidated samples. The hydraulic conductivities were highly affected by changing p, i.e., the k values decreased on two orders of magnitude as p increased from 10 to 200 kPa. The Kozeny-Carman equation, a theoretical permeability model that expresses the k-porosity relationship, was applied to measured data including reported values. Results showed the Kozeny-Carman equation captured well the porosity-dependent k values for tested soils and their admixtures with bentonite under a wide range of void ratios, suggesting that the Kozeny-Carman equation is a useful tool to estimate the magnitude of k values for differently compacted soil and its bentonite admixtures. [ABSTRACT FROM AUTHOR]

A Kozeny-Carman-based model of permeability for fibrous networks is proposed: the original model is extended by incorporating information about the local structure of the void space. Furthermore, it is demonstrated how in practice this added structural information can be retrieved from a three-dimensional digital image of a fibrous material. The proposed model is then validated for both foam- and water-deposited laboratory sheets of bleached kraft pulp (Scots pine) and chemi-thermo-mechanical pulp (CTMP, Norway spruce). The validation is carried out by comparing the model predictions against computationally determined permeability values. The related fluid-flow simulations are executed using the lattice-Boltzmann method together with high-resolution X-ray microtomography images. For both pulp materials, the sample sets had nearly equal porosities, but deviated substantially in their permeabilities. The proposed model was shown to improve prediction of permeability for the fibrous materials considered: the deviation between the predicted and computationally determined values was no more than 8%. [ABSTRACT FROM AUTHOR]

• A modified K–C equation considering the Poiseuille's law is presented. • Poiseuille's law is modified by adding coefficients to consider changed section. • Predicting formulas of the parameters in the modified K–C equation are discussed. • The modified K–C equation predicts hydraulic conductivity of sand and clay well. The Kozeny–Carman (K–C) equation based on Poiseuille's law is an efficient theoretical equation predicting hydraulic conductivity. Some modified K–C equations were proposed focusing on obtaining the uncertainty parameters in the original K–C equation. However, assumptions of some modified K–C equations are inconsistent with Poiseuille's law. This study proposes a new modified K–C equation considering the derivation principle of the original K–C equation. By applying Poiseuille's law in porous media, the concept of 2D porosity (ε) and a correction coefficient for permeation (f) are presented. During the derivation process, each section's void distribution is assumed to be similar, and void pipes in various directions share similar characteristics, because the effective porosity (n e) is approximately equal to ε only when the change in the cross-section in porous media is small. The parameters in the new modified K–C equation include specific surface area (S 0), tortuosity (1/cosθ), and n e. The prediction formulas of n e are presented according to the soil mineral and bound water features. The prediction formulas for S 0 and 1/cosθ are deduced and verified by comparing them with established formulas proposed by other researchers and experimental data. The new modified K–C equation is adequate for predicting hydraulic conductivity for clay and sand by comparing it with the experimental value and theoretical equations, including the original and other established modified K–C equations. [ABSTRACT FROM AUTHOR]

• Pore ice grows inward from the pore wall in coarse-grained soils. • A new hydraulic conductivity model is presented for frozen coarse-grained soils. • The proposed model makes better predictions than the existing models. Hydraulic conductivity is crucial to revealing the mechanisms of frost damage in cold regions, while the hydraulic conductivity of coarse-grained soils during freezing process has rarely been considered. In this study, a new pattern that ice grows from the pore wall is used to describe ice formation in coarse-grained soils. In this pattern, unfrozen water confined in the pore center provides flow channels for liquid water migration. The relationship between distribution characteristics of flow channels and hydraulic conductivity can be established by redefining parameters such as porosity ϕ e , hydraulic radius R H ¯ and tortuosity Γ in the Kozeny-Carman equation. It thus generates a new hydraulic conductivity model for frozen coarse-grained soils. Comparing with measured result in the literature, it shows that the proposed model gives a better prediction than existing models, especially for sand. The proposed model can provide a useful tool for simulating water-heat transfer process of coarse-grained soils in cold regions. [ABSTRACT FROM AUTHOR]

In the present study, three types of experiments on immiscible CO flooding in porous media were conducted and high-resolution images of asphaltene precipitation obtained using X-ray micro-CT scanner. It was found that the effective oil mobility is reduced due to the adsorption of deposited asphaltene onto the rock which blocks the pore throats, whereby the formation wettability is changed and both the effective porosity and permeability are reduced. The deposited asphaltene cannot be redissolved or displaced by the reinjected crude oil, and the formation damage is irreversible. In addition, the porosity-based permeability model was applied to study the effective permeability reduction that results from porosity reduction. The porosity-based permeability was calculated based on the Kozeny-Carman equation and experimental data. The effective permeability variation rate obtained by the porosity-based permeability model agreed well with the results obtained by Darcy's law, which demonstrates that the method is feasible in evaluating the effective permeability variation rate based on the porosity of the cores acquired from micro-CT images. Graphical abstract: [ABSTRACT FROM AUTHOR]

Pervious concrete (PC) mixtures were designed and prepared to measure and study permeability characteristics at varying head levels using a falling head permeameter. A total of 1092 readings was used to study the permeability properties of eighteen PC mixtures whose porosity was in the range of 15–37%, and permeability in the realm of 0.076–3.5 cm/s. The permeability reduced as the head of water increased, and gradually attained an asymptotic relation with the head. Cement-to-aggregate ratio had largest contribution in controlling permeability of PC mixtures. Nonlinearity in Darcy’s law was observed in respect of permeability of PC mixes, which was modelled using Izbash/power law, and was prominent for gradations consisting of larger sized aggregates due to inconsequential tortuous pore structure. Modified Kozeny-Carman equation was fitted for PC gradations to compare the results with Izbash law, which showed good agreement. This study is deemed to assist in understanding the hydrodynamics of water flow in pervious concrete, which in turn will aid in rational pervious concrete pavement system designs. [ABSTRACT FROM AUTHOR]