New Criteria to Estimate Local Thermal Nonequilibrium Conditions for Heat Transport in Porous Aquifers
Abstract A fundamental assumption in numerous studies of heat transfer in porous media is local thermal equilibrium (LTE), which assumes that the temperature of the porous media at the fluid and solid interface is in instantaneous equilibrium. Although significant efforts have been made to quantify...
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Wiley
2024-07-01
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| Series: | Water Resources Research |
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| Online Access: | https://doi.org/10.1029/2024WR037382 |
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| author | Wenguang Shi Quanrong Wang Maria Klepikova Hongbin Zhan |
| author_facet | Wenguang Shi Quanrong Wang Maria Klepikova Hongbin Zhan |
| author_sort | Wenguang Shi |
| collection | DOAJ |
| description | Abstract A fundamental assumption in numerous studies of heat transfer in porous media is local thermal equilibrium (LTE), which assumes that the temperature of the porous media at the fluid and solid interface is in instantaneous equilibrium. Although significant efforts have been made to quantify the occurrence and consequences of local thermal nonequilibrium (LTNE), where the temperatures of the fluid and adjacent solid phases differ, there is no simple expression for quantifying the occurrence and effects of local thermal disequilibrium. Using a numerical model combining LTE and LTNE models, we develop here two simple general criteria based on Darcian velocities (q) and particle sizes (dp) of porous media for determining when LTNE effects occur (denoted as g(dp, q)) and when they become significant (denoted as f(dp, q)). Results show that using an LTE model can result in an underestimation of effective thermal diffusivity and the unaffected Darcian velocities when g(dp, q) > 0. It is possible that using the LTE model can result in an underestimation of the effective thermal diffusivity by more than 200 times within Darcian velocities ranging from 0 to 60 m/d. In the case of g(dp, q) < 0, the use of the LTE model can result in an overestimation of effective thermal diffusivity and Darcian velocities. The performances of the newly developed general criteria are demonstrated using three typical data sets and corresponding numerical models. These data sets include new heat tracer tests conducted in the laboratory and the field, as well as temperature‐time series collected in streambed sediments from a previous study by Shanafield et al. (2012, https://doi.org/10.5194/hessd‐9‐4305‐2012). The potential LTNE effects should be considered when using heat as a tracer to characterize flow and heat transport in porous media in the presence of Darcian velocities less than 2 m/d and particle sizes larger than 10 mm. |
| format | Article |
| id | doaj-art-b086186b16e64e5382a8d84fec9877f5 |
| institution | OA Journals |
| issn | 0043-1397 1944-7973 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | Wiley |
| record_format | Article |
| series | Water Resources Research |
| spelling | doaj-art-b086186b16e64e5382a8d84fec9877f52025-08-20T02:36:39ZengWileyWater Resources Research0043-13971944-79732024-07-01607n/an/a10.1029/2024WR037382New Criteria to Estimate Local Thermal Nonequilibrium Conditions for Heat Transport in Porous AquifersWenguang Shi0Quanrong Wang1Maria Klepikova2Hongbin Zhan3School of Environmental Studies China University of Geosciences Wuhan PR ChinaSchool of Environmental Studies China University of Geosciences Wuhan PR ChinaUniversity Rennes CNRS Géosciences Rennes—UMR 6118 Rennes FranceDepartment of Geology and Geophysics Texas A&M University College Station TX USAAbstract A fundamental assumption in numerous studies of heat transfer in porous media is local thermal equilibrium (LTE), which assumes that the temperature of the porous media at the fluid and solid interface is in instantaneous equilibrium. Although significant efforts have been made to quantify the occurrence and consequences of local thermal nonequilibrium (LTNE), where the temperatures of the fluid and adjacent solid phases differ, there is no simple expression for quantifying the occurrence and effects of local thermal disequilibrium. Using a numerical model combining LTE and LTNE models, we develop here two simple general criteria based on Darcian velocities (q) and particle sizes (dp) of porous media for determining when LTNE effects occur (denoted as g(dp, q)) and when they become significant (denoted as f(dp, q)). Results show that using an LTE model can result in an underestimation of effective thermal diffusivity and the unaffected Darcian velocities when g(dp, q) > 0. It is possible that using the LTE model can result in an underestimation of the effective thermal diffusivity by more than 200 times within Darcian velocities ranging from 0 to 60 m/d. In the case of g(dp, q) < 0, the use of the LTE model can result in an overestimation of effective thermal diffusivity and Darcian velocities. The performances of the newly developed general criteria are demonstrated using three typical data sets and corresponding numerical models. These data sets include new heat tracer tests conducted in the laboratory and the field, as well as temperature‐time series collected in streambed sediments from a previous study by Shanafield et al. (2012, https://doi.org/10.5194/hessd‐9‐4305‐2012). The potential LTNE effects should be considered when using heat as a tracer to characterize flow and heat transport in porous media in the presence of Darcian velocities less than 2 m/d and particle sizes larger than 10 mm.https://doi.org/10.1029/2024WR037382local thermal nonequilibriumheat transport modelingparticle sizeDarcian velocityhyporheic exchangetransport in porous media |
| spellingShingle | Wenguang Shi Quanrong Wang Maria Klepikova Hongbin Zhan New Criteria to Estimate Local Thermal Nonequilibrium Conditions for Heat Transport in Porous Aquifers Water Resources Research local thermal nonequilibrium heat transport modeling particle size Darcian velocity hyporheic exchange transport in porous media |
| title | New Criteria to Estimate Local Thermal Nonequilibrium Conditions for Heat Transport in Porous Aquifers |
| title_full | New Criteria to Estimate Local Thermal Nonequilibrium Conditions for Heat Transport in Porous Aquifers |
| title_fullStr | New Criteria to Estimate Local Thermal Nonequilibrium Conditions for Heat Transport in Porous Aquifers |
| title_full_unstemmed | New Criteria to Estimate Local Thermal Nonequilibrium Conditions for Heat Transport in Porous Aquifers |
| title_short | New Criteria to Estimate Local Thermal Nonequilibrium Conditions for Heat Transport in Porous Aquifers |
| title_sort | new criteria to estimate local thermal nonequilibrium conditions for heat transport in porous aquifers |
| topic | local thermal nonequilibrium heat transport modeling particle size Darcian velocity hyporheic exchange transport in porous media |
| url | https://doi.org/10.1029/2024WR037382 |
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