A Two‐Dimensional Closed‐Form Analytical Solution for Heat Transport With Nonvertical Flow in Riparian Zones

Shi, Wenguang; Zhan, Hongbin; Wang, Quanrong; Xie, Xuan

doi:10.1029/2022wr034059

Cited by 6 publications

(3 citation statements)

References 88 publications

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“… Simulated results of the field application in an alluvial aquifer: (a) Fitness of the observed BTCs (green circle symbols) by the semi‐analytical solution of Wang et al. (2020); (b) Fitness of the observed thermal BTCs (green circle symbols) by the LTNE model (red solid curve) and the model of Shi, Zhan, Wang, and Xie (2023), Shi, Wang, et al. (2023), and Shi, Zhan, Wang, and Liao (2023) (blue solid curve), the LTE model (black dotted curve) in the legend is generated by the model of Shi, Zhan, Wang, and Xie (2023), Shi, Wang, et al.…”

Section: Resultsmentioning

confidence: 99%

“…(2020); (b) Fitness of the observed thermal BTCs (green circle symbols) by the LTNE model (red solid curve) and the model of Shi, Zhan, Wang, and Xie (2023), Shi, Wang, et al. (2023), and Shi, Zhan, Wang, and Liao (2023) (blue solid curve), the LTE model (black dotted curve) in the legend is generated by the model of Shi, Zhan, Wang, and Xie (2023), Shi, Wang, et al. (2023), and Shi, Zhan, Wang, and Liao (2023) using the same parameters as the LTNE model.…”

Section: Resultsmentioning

confidence: 99%

“…Heat transport in porous media plays a crucial role in numerous hydrogeological investigations and practical applications and has received much attention in recent decades. Notably, it is employed in various areas such as geothermal resource assessment, exploitation and thermal energy storage (Klepikova et al., 2016; Shi, Wang, et al., 2023), quantification of subsurface heat flow (Bredehoeft & Papaopulos, 1965; Lin et al., 2022), estimation of hydraulic and thermal properties of aquifers (McCallum et al., 2012; Park et al., 2015; Somogyvári et al., 2016; Wagner et al., 2013), characterization of streambed thermal properties and vertical streambed fluxes (Rau et al., 2015; Shi & Wang, 2023), and determination of lateral groundwater inflow to streams (Chen et al., 2022; Shi, Zhan, Wang & Xie, 2023). One major advantage of using heat as a tracer as compared to hydraulic approaches is that subsurface thermal properties change over narrower ranges than hydraulic properties, potentially reducing uncertainty in parameter estimations such as groundwater flow rate and thermal conductivity (Simon et al., 2021; Stonestrom & Constantz, 2003).…”

Section: Introductionmentioning

confidence: 99%

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New Criteria to Estimate Local Thermal Nonequilibrium Conditions for Heat Transport in Porous Aquifers

Shi,

Wang,

Klepikova

et al. 2024

Water Resources Research

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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.

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