Stochastic Analysis of Macrodispersive Solute Flux in Heterogeneous Aquifers With Nonstationary Random Hydraulic Conductivity Fields
Abstract This work develops a theoretical framework for modeling the large‐scale transport of inert solutes in heterogeneous aquifers, where the perturbation field of logarithmic hydraulic conductivity (lnK) is considered nonstationary. Based on the intrinsic hypothesis for the lnK perturbation fiel...
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| Format: | Article |
| Language: | English |
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Wiley
2025-07-01
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| Series: | Water Resources Research |
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| Online Access: | https://doi.org/10.1029/2024WR038722 |
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| author | Ching‐Min Chang Chuen‐Fa Ni Chi‐Ping Lin I‐Hsian Lee Wei‐Cheng Lo |
| author_facet | Ching‐Min Chang Chuen‐Fa Ni Chi‐Ping Lin I‐Hsian Lee Wei‐Cheng Lo |
| author_sort | Ching‐Min Chang |
| collection | DOAJ |
| description | Abstract This work develops a theoretical framework for modeling the large‐scale transport of inert solutes in heterogeneous aquifers, where the perturbation field of logarithmic hydraulic conductivity (lnK) is considered nonstationary. Based on the intrinsic hypothesis for the lnK perturbation field, the variability of the lnK perturbation field can be characterized by the semivariogram. The general expressions for the concentration semivariogram and the macrodispersive flux in Fourier spectral space are derived using the Fourier‐Stieltjes spectral representation approach and the representation theorem. These solutions generalize the previous results presented in the literature on stochastic subsurface hydrology under the assumption of a stationary covariance function of the lnK perturbation field. The theories developed here are applied to the case of solute transport in heterogeneous media, where the variation of the lnK perturbation field exhibits a power‐law semivariogram. It is shown that the nonstationarity of the lnK perturbation field leads to nonstationary perturbation fields of the hydraulic head and thus of the specific discharge, which in turn results in a nonstationary perturbation field of the concentration, leading to a non‐Fickian macrodispersion. The greater the Hurst exponent, the greater the variability of the specific discharge and solute concentration perturbation fields and thus the greater the macrodispersive flux. |
| format | Article |
| id | doaj-art-ecb918a8f41a45d28ddc55c70730f9a0 |
| institution | Matheson Library |
| issn | 0043-1397 1944-7973 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Wiley |
| record_format | Article |
| series | Water Resources Research |
| spelling | doaj-art-ecb918a8f41a45d28ddc55c70730f9a02025-07-29T02:32:50ZengWileyWater Resources Research0043-13971944-79732025-07-01617n/an/a10.1029/2024WR038722Stochastic Analysis of Macrodispersive Solute Flux in Heterogeneous Aquifers With Nonstationary Random Hydraulic Conductivity FieldsChing‐Min Chang0Chuen‐Fa Ni1Chi‐Ping Lin2I‐Hsian Lee3Wei‐Cheng Lo4Graduate Institute of Applied Geology National Central University Taoyuan TaiwanGraduate Institute of Applied Geology National Central University Taoyuan TaiwanCenter for Environmental Studies National Central University Taoyuan TaiwanCenter for Environmental Studies National Central University Taoyuan TaiwanDepartment of Hydraulic and Ocean Engineering National Cheng Kung University Tainan City TaiwanAbstract This work develops a theoretical framework for modeling the large‐scale transport of inert solutes in heterogeneous aquifers, where the perturbation field of logarithmic hydraulic conductivity (lnK) is considered nonstationary. Based on the intrinsic hypothesis for the lnK perturbation field, the variability of the lnK perturbation field can be characterized by the semivariogram. The general expressions for the concentration semivariogram and the macrodispersive flux in Fourier spectral space are derived using the Fourier‐Stieltjes spectral representation approach and the representation theorem. These solutions generalize the previous results presented in the literature on stochastic subsurface hydrology under the assumption of a stationary covariance function of the lnK perturbation field. The theories developed here are applied to the case of solute transport in heterogeneous media, where the variation of the lnK perturbation field exhibits a power‐law semivariogram. It is shown that the nonstationarity of the lnK perturbation field leads to nonstationary perturbation fields of the hydraulic head and thus of the specific discharge, which in turn results in a nonstationary perturbation field of the concentration, leading to a non‐Fickian macrodispersion. The greater the Hurst exponent, the greater the variability of the specific discharge and solute concentration perturbation fields and thus the greater the macrodispersive flux.https://doi.org/10.1029/2024WR038722intrinsic random functionconcentration semivariogrammacrodispersive fluxFourier‐Stieltjes representation |
| spellingShingle | Ching‐Min Chang Chuen‐Fa Ni Chi‐Ping Lin I‐Hsian Lee Wei‐Cheng Lo Stochastic Analysis of Macrodispersive Solute Flux in Heterogeneous Aquifers With Nonstationary Random Hydraulic Conductivity Fields Water Resources Research intrinsic random function concentration semivariogram macrodispersive flux Fourier‐Stieltjes representation |
| title | Stochastic Analysis of Macrodispersive Solute Flux in Heterogeneous Aquifers With Nonstationary Random Hydraulic Conductivity Fields |
| title_full | Stochastic Analysis of Macrodispersive Solute Flux in Heterogeneous Aquifers With Nonstationary Random Hydraulic Conductivity Fields |
| title_fullStr | Stochastic Analysis of Macrodispersive Solute Flux in Heterogeneous Aquifers With Nonstationary Random Hydraulic Conductivity Fields |
| title_full_unstemmed | Stochastic Analysis of Macrodispersive Solute Flux in Heterogeneous Aquifers With Nonstationary Random Hydraulic Conductivity Fields |
| title_short | Stochastic Analysis of Macrodispersive Solute Flux in Heterogeneous Aquifers With Nonstationary Random Hydraulic Conductivity Fields |
| title_sort | stochastic analysis of macrodispersive solute flux in heterogeneous aquifers with nonstationary random hydraulic conductivity fields |
| topic | intrinsic random function concentration semivariogram macrodispersive flux Fourier‐Stieltjes representation |
| url | https://doi.org/10.1029/2024WR038722 |
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