Uncertainty of Kozeny–Carman Permeability Model for Fractal Heterogeneous Porous Media
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 eq...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Hydrology |
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| Online Access: | https://www.mdpi.com/2306-5338/10/1/21 |
| _version_ | 1797441701793497088 |
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| author | Jianting Zhu |
| author_facet | Jianting Zhu |
| author_sort | Jianting Zhu |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T12:28:54Z |
| format | Article |
| id | doaj.art-a32d76f9e3294a34afb2e6c9e0bc9367 |
| institution | Directory Open Access Journal |
| issn | 2306-5338 |
| language | English |
| last_indexed | 2024-03-09T12:28:54Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Hydrology |
| spelling | doaj.art-a32d76f9e3294a34afb2e6c9e0bc93672023-11-30T22:31:37ZengMDPI AGHydrology2306-53382023-01-011012110.3390/hydrology10010021Uncertainty of Kozeny–Carman Permeability Model for Fractal Heterogeneous Porous MediaJianting Zhu0Department of Civil and Architectural Engineering and Construction Management, University of Wyoming, Laramie, WY 82071, USAA 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.https://www.mdpi.com/2306-5338/10/1/21Kozeny–Carman equationheterogeneous porous mediatruncated power-law distributionsolid volumetric fraction |
| spellingShingle | Jianting Zhu Uncertainty of Kozeny–Carman Permeability Model for Fractal Heterogeneous Porous Media Hydrology Kozeny–Carman equation heterogeneous porous media truncated power-law distribution solid volumetric fraction |
| title | Uncertainty of Kozeny–Carman Permeability Model for Fractal Heterogeneous Porous Media |
| title_full | Uncertainty of Kozeny–Carman Permeability Model for Fractal Heterogeneous Porous Media |
| title_fullStr | Uncertainty of Kozeny–Carman Permeability Model for Fractal Heterogeneous Porous Media |
| title_full_unstemmed | Uncertainty of Kozeny–Carman Permeability Model for Fractal Heterogeneous Porous Media |
| title_short | Uncertainty of Kozeny–Carman Permeability Model for Fractal Heterogeneous Porous Media |
| title_sort | uncertainty of kozeny carman permeability model for fractal heterogeneous porous media |
| topic | Kozeny–Carman equation heterogeneous porous media truncated power-law distribution solid volumetric fraction |
| url | https://www.mdpi.com/2306-5338/10/1/21 |
| work_keys_str_mv | AT jiantingzhu uncertaintyofkozenycarmanpermeabilitymodelforfractalheterogeneousporousmedia |