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Search Results (7)

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Keywords = Kozeny–Carman formula

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17 pages, 3888 KB  
Article
Effective Measurement of the Influence of an Ovoidal Particle Shape on the Tortuosity and Permeability: Theoretical and Numerical Studies
by Jiangnan Hao, Xiangshang Chen and Jianjun Lin
Materials 2026, 19(16), 3498; https://doi.org/10.3390/ma19163498 - 18 Aug 2026
Abstract
An ovoid is a common particle, which is usually formed by constant extrusion and friction during running water handling. However, there is still debate over how the form of ovoidal particles affects the tortuosity and water permeability of particle packing systems. The tortuosity [...] Read more.
An ovoid is a common particle, which is usually formed by constant extrusion and friction during running water handling. However, there is still debate over how the form of ovoidal particles affects the tortuosity and water permeability of particle packing systems. The tortuosity and permeability of the particle packing system are examined in relation to the shape and volume fraction of the particles in this work. The ovoid particle packing system is built using the Monte Carlo approach, and the tortuosity is obtained numerically. Then, the accuracy of the tortuosity prediction model is evaluated by comparing the theoretical derived tortuosities with the simulated results in this work and other literature. By combining the widely used Kozeny–Carman (K-C) formula with the derived theoretical tortuosity prediction model, we develop a modified K-C formula to predict the permeability of ovoidal particle packing systems. By comparing the model outputs with published experimental data and self-conducted lattice Boltzmann method (LBM) numerical simulations, we verify that the modified K-C formula achieves high prediction accuracy. According to the findings, when the aspect ratio c/a rises, the tortuosity first decreases and then increases, and the permeability first increases and then decreases. Full article
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14 pages, 1573 KB  
Article
Study on Permeability Coefficient of Saturated Clay Modified by Fractal Theory and Poiseuille Theory
by Lu Guo, Xiaoyang Xin and Keqiang He
Materials 2026, 19(1), 21; https://doi.org/10.3390/ma19010021 - 20 Dec 2025
Cited by 3 | Viewed by 994
Abstract
The permeability coefficient of saturated clay plays a crucial role in practical engineering applications. In this paper, based on the fractal geometry theory and combined with the relationship between the flowing water volume and non-flowing water volume in saturated clay, the theoretical formulas [...] Read more.
The permeability coefficient of saturated clay plays a crucial role in practical engineering applications. In this paper, based on the fractal geometry theory and combined with the relationship between the flowing water volume and non-flowing water volume in saturated clay, the theoretical formulas for the effective pore specific surface area and the effective void ratio of saturated clay are established. Based on the capillary seepage channel model of saturated clay, combined with Poiseuille’s law and the concept of equivalent hydraulic radius, the theoretical formula for the permeability coefficient of saturated clay is established. Finally, the physical parameters of the remolded clay samples are measured and substituted into the modified Kozeny–Carman equation and the equivalent capillary seepage equation of saturated clay before and after the modification. Through the comparative analysis of the above theoretical values and the measured values of indoor seepage tests, it is found that the saturated clay seepage equation established in this paper is more suitable for dense saturated clay with relatively small pores. It has the characteristics of higher calculation accuracy and easier acquisition of basic parameters. The research results provide important references for practical engineering and the study of saturated clay seepage theory, and have broad prospects for practical engineering applications. Full article
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18 pages, 5867 KB  
Article
Meandering Flow Filter for Phosphorus Removal as a Component of Small Wastewater Treatment Plants—A Case Study
by Beata Zawadzka, Tadeusz Siwiec, Michał Marzec, Krzysztof Jóźwiakowski and Agnieszka Listosz
Water 2023, 15(15), 2703; https://doi.org/10.3390/w15152703 - 27 Jul 2023
Cited by 5 | Viewed by 2272
Abstract
Chemical phosphorus removal in wastewater treatment plants can be carried out by precipitation with iron or aluminum salts or by filtering wastewater through a bed of active sorptive material. This work aimed to investigate whether using a meander flow filter filled with the [...] Read more.
Chemical phosphorus removal in wastewater treatment plants can be carried out by precipitation with iron or aluminum salts or by filtering wastewater through a bed of active sorptive material. This work aimed to investigate whether using a meander flow filter filled with the sorption material Rockfos® would improve phosphorus removal efficiency in a selected wastewater treatment plant. Tests were performed under laboratory conditions using a model of a meander flow filter and a similar filter under field conditions at full technical scale. This filter was the final element of a hybrid constructed wetland located in the village of Białka in the municipality of Dębowa Kłoda in southeastern Poland. A laboratory model of a phosphorus removal filter with vertical incomplete baffles forcing a meandering water flow was constructed to determine the hydraulic conditions of the flow. After one year of operation, the filter with horizontal wastewater flow operating at its full technical scale (without meanders) was modified by inserting appropriate baffles that were analogous to those in the laboratory model. The analysis of the hydraulic conditions in the laboratory model showed that, under the assumed conditions, wastewater flows through the filter layer in a laminar motion, so such filters can be modeled using the Kozeny–Carman formula. It was shown that, after approximately a year of operation in a filter operating at full technical scale, before modification, dead spaces formed, thus causing the channel and primarily surface flow of wastewater. The phosphorus removal efficiency during this test period averaged 9.4%. After introducing baffles and forcing meander flow in the filter chamber, the efficiency increased to 40.6%. The results indicate that meander flow filters can improve phosphorus removal efficiency in small wastewater treatment plants. Full article
(This article belongs to the Section Wastewater Treatment and Reuse)
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16 pages, 2815 KB  
Article
A Fractal Entropy-Based Effective Particle Model Used to Deduce Hydraulic Conductivity of Granular Soils
by Gang Zhang, Hongyu Wang, Jahanzaib Israr, Wenguo Ma, Youzhen Yang and Keliang Ren
Fractal Fract. 2022, 6(9), 474; https://doi.org/10.3390/fractalfract6090474 - 28 Aug 2022
Cited by 6 | Viewed by 2568
Abstract
In this study, a rigorous mathematical approach used to compute an effective diameter based on particle size distribution (PSD) has been presented that can predict the hydraulic conductivity of granular soils with enhanced rigor. The PSD was discretized based on an abstract interval [...] Read more.
In this study, a rigorous mathematical approach used to compute an effective diameter based on particle size distribution (PSD) has been presented that can predict the hydraulic conductivity of granular soils with enhanced rigor. The PSD was discretized based on an abstract interval system of fractal entropy, while the effective diameter of soil was computed using the grading entropy theory. The comparisons between current entropy-based effective diameter (DE) and those computed using existing procedures show that the current DE can capture the particle size information of a given soil more accurately than others. Subsequently, the proposed DE was successfully implicated into Kozeny–Carman’s formula to deduce the saturated hydraulic conductivity of soils with enhanced accuracy. The proposed model was tested using current and previously published experimental data from literature. Not surprisingly, the results of the current model and those from previous experimental studies were found to be consistent, which can sufficiently verify the proposed entropy-based effective diameter model. Full article
(This article belongs to the Special Issue Fractal and Fractional in Geomaterials)
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14 pages, 3411 KB  
Article
Experimental Verification of Reservoirs with Different Wettability Using an Oil–Water Relative Permeability Model
by Jianya Pei, Yunfeng Zhang, Jin Hu, Jian Zhang, Xiaomeng Zhu, Qiang Wang and Hua Gong
Processes 2022, 10(6), 1211; https://doi.org/10.3390/pr10061211 - 17 Jun 2022
Cited by 3 | Viewed by 3423
Abstract
Oil–water relative permeability is an important parameter that affects fluid flow in porous media. It is usually obtained in a laboratory. Since rock resistivity and relative permeability are both effects of water saturation, they should theoretically have a relationship. Based on the parallel [...] Read more.
Oil–water relative permeability is an important parameter that affects fluid flow in porous media. It is usually obtained in a laboratory. Since rock resistivity and relative permeability are both effects of water saturation, they should theoretically have a relationship. Based on the parallel conduction principle of fluid and skeleton in porous media, the pore structure and fluid distribution can be simplified using the Kozeny–Carman permeability correction equation and the Archie formula, and the relative permeability model of the water phase can be deduced under different wetting conditions. In this study, the resistivity and relative permeability experimental data of 20 rock samples from four inspection wells were compared and verified. The results show that the proposed oil–water relative permeability model agrees well with a reservoir having a porosity range of 17.6–30.7% and an air permeability of 0.16–973 × 10−3 μm, and it may explain why the relative permeability of the water phase decreases as water saturation increases. This model could provide a new technique to construct the relative permeability curves of sandstone reservoirs. Full article
(This article belongs to the Special Issue Multiphase Flow Assurance in Porous Media and Production Operations)
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17 pages, 6044 KB  
Article
Suitability of Engineering-Geological Environment on the Basis of Its Permeability Coefficient: Four Case Studies of Fine-Grained Soils
by Marian Marschalko, Zofia Zięba, Dominik Niemiec, David Neuman, Jakub Mońka and Jolanta Dąbrowska
Materials 2021, 14(21), 6411; https://doi.org/10.3390/ma14216411 - 26 Oct 2021
Cited by 10 | Viewed by 2987
Abstract
The aim of the article is to compare two classifications systems of engineering-geological environment sustainability in terms of its permeability evaluated on the basis of permeability coefficient. The first evaluated classification assumes a permeable environment to be a positive characteristic in the engineering-geological [...] Read more.
The aim of the article is to compare two classifications systems of engineering-geological environment sustainability in terms of its permeability evaluated on the basis of permeability coefficient. The first evaluated classification assumes a permeable environment to be a positive characteristic in the engineering-geological assessment, while the other considers an impermeable environment as favourable. The four fine-grained soil materials were selected, as they had very similar, almost identical grains-size distribution, but different microstructure characterized by grains sphericity, angularity, and roughness. At the same time, the influence of changes in the density of soil materials (density index 10%, 30%, 60%, 90%) was analysed. Permeability coefficient was determined using six methods (empirical formulae, laboratory and microscopic analysis). The laboratory method falling head test (FHT) was taken as a reference test that reflected the actual water flow through the soil. It was found that with an increase in grain angularity and roughness (and a decrease in sphericity), the permeability coefficient was decreasing and this trend culminated along with gradual compaction. Moreover, the research shows that unsuitable methods may classify soil materials into wrong engineering-geological permeability classes, which may have negative consequences during engineering-geological or geotechnical assessment and cause subsequent problems in foundation engineering. Full article
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9 pages, 2746 KB  
Article
The Investigation of Permeability Calculation Using Digital Core Simulation Technology
by Lei Zhang, Wenlong Jing, Yongfei Yang, Hainan Yang, Yaohao Guo, Hai Sun, Jianlin Zhao and Jun Yao
Energies 2019, 12(17), 3273; https://doi.org/10.3390/en12173273 - 26 Aug 2019
Cited by 71 | Viewed by 5720
Abstract
Digital core simulation technology, as an emerging numerical simulation method, has gradually come to play a significant role in the study of petrophysical properties. By using this numerical simulation method, the influence of micro factors on seepage properties of reservoir rock is taken [...] Read more.
Digital core simulation technology, as an emerging numerical simulation method, has gradually come to play a significant role in the study of petrophysical properties. By using this numerical simulation method, the influence of micro factors on seepage properties of reservoir rock is taken into consideration, making up the shortcomings of the traditional physical experiment. Three-dimensional core images are reconstructed by a computed tomography scanning technique. Different sizes of the sub-region were simulated by three methods including the direct computation of Navier-Stokes equations, the simulation of the pore network model, and the lattice Boltzmann method. The permeability computed by each simulation was compared. After comparison between these three methods, the results of the direct computation method based on Navier-Stokes equations were found to be higher than the other two methods. The pore network model simulation has an obvious advantage on the computation speed and the simulation area. The lattice Boltzmann method shows the low efficiency due to the time-consuming process. At last, the permeability calculated by the three methods is matched by the Kozeny-Carman equation. A more accurate formula can be obtained by a series of numerical simulations, which can be applied to marco-scale simulation. Full article
(This article belongs to the Section H: Geo-Energy)
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