Articles | Volume 29, issue 5
https://doi.org/10.5194/hess-29-1359-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-29-1359-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
12 Mar 2025
Research article |
| 12 Mar 2025
| 12 Mar 2025
Laboratory heat transport experiments reveal grain-size- and flow-velocity-dependent local thermal non-equilibrium effects
Institute of Applied Geosciences (AGW), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Manuel Gossler
Stadtwerke München (SWM), Munich, Germany
Kai Zosseder
Chair of Hydrogeology, Technical University of Munich, Munich, Germany
Philipp Blum
Institute of Applied Geosciences (AGW), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
Peter Bayer
Department of Applied Geosciences, Martin Luther University of Halle Wittenberg, Halle, Germany
Gabriel C. Rau
School of Environmental and Life Sciences, The University of Newcastle, Callaghan, Australia
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Cited articles
Alnaes, M. S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C. N., Ring, J., Rognes, M. E., and Wells, G. N.: The FEniCS project version 1.5, Archive of Numerical Software, 3, 9–23, https://doi.org/10.11588/ans.2015.100.20553, 2015. a
Bandai, T., Hamamoto, S., Rau, G. C., Komatsu, T., and Nishimura, T.: The effect of particle size on thermal and solute dispersion in saturated porous media, Int. J. Therm. Sci., 122, 74–84, https://doi.org/10.1016/j.ijthermalsci.2017.08.003, 2017. a
Bear, J.: On the tensor form of dispersion in porous media, J. Geophys. Res., 66, 1185–1197, https://doi.org/10.1029/JZ066i004p01185, 1961. a
Buntebarth, G. and Schopper, J.: Experimental and theoretical investigations on the influence of fluids, solids and interactions between them on thermal properties of porous rocks, Phys. Chem. Earth, 23, 1141–1146, https://doi.org/10.1016/S0079-1946(98)00142-6, 1998. a
Clauser, C.: Thermal Storage and Transport Properties of Rocks, I: Heat Capacity and Latent Heat, Springer International Publishing, Cham, 1760–1768, https://doi.org/10.1007/978-3-030-58631-7_238, 2021a. a, b, c
Clauser, C.: Thermal Storage and Transport Properties of Rocks, II: Thermal Conductivity and Diffusivity, Springer International Publishing, Cham, 1769–1787, https://doi.org/10.1007/978-3-030-58631-7_67, 2021b. a, b
Gossler, M. A., Bayer, P., Rau, G. C., Einsiedl, F., and Zosseder, K.: On the limitations and implications of modeling heat transport in porous aquifers by assuming local thermal equilibrium, Water Resour. Res., 56, e2020WR027772, https://doi.org/10.1029/2020WR027772, 2020. a, b, c, d, e, f, g, h, i, j, k, l, m
Hamidi, S., Heinze, T., Galvan, B., and Miller, S.: Critical review of the local thermal equilibrium assumption in heterogeneous porous media: dependence on permeability and porosity contrasts, Appl. Therm. Eng., 147, 962–971, https://doi.org/10.1016/j.applthermaleng.2018.10.130, 2019. a
Heinze, T.: Multi-phase heat transfer in porous and fractured rock, Earth-Sci. Rev., 251, 104730, https://doi.org/10.1016/j.earscirev.2024.104730, 2024. a, b, c, d
Kim, S. J. and Jang, S. P.: Effects of the Darcy number, the Prandtl number, and the Reynolds number on local thermal non-equilibrium, Int. J. Heat Mass Tran., 45, 3885–3896, https://doi.org/10.1016/S0017-9310(02)00109-6, 2002. a
Lee, H.: LTE- and LTNE-Model code, figshare [code], https://doi.org/10.6084/m9.figshare.28548197.v1, 2025a. a
Lee, H.: Measurement data, figshare [data set], https://doi.org/10.6084/m9.figshare.26094061.v1, 2025b. a
Levec, J. and Carbonell, R. G.: Longitudinal and lateral thermal dispersion in packed beds. Part I: Theory, AIChE J., 31, 581–590, https://doi.org/10.1002/aic.690310408, 1985a. a, b, c, d
Levec, J. and Carbonell, R. G.: Longitudinal and lateral thermal dispersion in packed beds. Part II: Comparison between theory and experiment, AIChE J., 31, 591–602, https://doi.org/10.1002/aic.690310409, 1985b. a, b, c, d
Menberg, K., Steger, H., Zorn, R., Reuß, M., Pröll, M., Bayer, P., and Blum, P.: Bestimmung der Wärmeleitfähigkeit im Untergrund durch Labor- und Feldversuche und anhand theoretischer Modelle, Grundwasser, 18, 103–116, https://doi.org/10.1007/s00767-012-0217-x, 2013. a, b, c
Metzger, T., Didierjean, S., and Maillet, D.: Optimal experimental estimation of thermal dispersion coefficients in porous media, Int. J. Heat Mass Tran., 47, 3341–3353, https://doi.org/10.1016/j.ijheatmasstransfer.2004.02.024, 2004. a
Molina-Giraldo, N., Bayer, P., and Blum, P.: Evaluating the influence of thermal dispersion on temperature plumes from geothermal systems using analytical solutions, Int. J. Therm. Sci., 50, 1223–1231, https://doi.org/10.1016/j.ijthermalsci.2011.02.004, 2011. a
Nield, D. A. and Bejan, A.: Convection in Porous Media, 5th edn., Springer International Publishing, https://doi.org/10.1007/978-3-319-49562-0, 2017. a
Novak, A., Schunert, S., Carlsen, R., Balestra, P., Slaybaugh, R., and Martineau, R.: Multiscale thermal-hydraulic modeling of the pebble bed fluoride-salt-cooled high-temperature reactor, Ann. Nucl. Energy, 154, 107968, https://doi.org/10.1016/j.anucene.2020.107968, 2021. a
Pastore, N., Cherubini, C., Giasi, C., and Allegretti, N.: Experimental investigations of heat transport dynamics in a 1d porous medium column, Energy Proced., 97, 233–239, https://doi.org/10.1016/j.egypro.2016.10.063, 2016. a
Pati, S., Borah, A., Boruah, M. P., and Randive, P. R.: Critical review on local thermal equilibrium and local thermal non-equilibrium approaches for the analysis of forced convective flow through porous media, Int. Commun. Heat Mass, 132, 105889, https://doi.org/10.1016/j.icheatmasstransfer.2022.105889, 2022. a
Pophillat, W., Attard, G., Bayer, P., Hecht-Méndez, J., and Blum, P.: Analytical solutions for predicting thermal plumes of groundwater heat pump systems, Renew. Energ., 147, 2696–2707, https://doi.org/10.1016/j.renene.2018.07.148, 2020a. a
Pophillat, W., Bayer, P., Teyssier, E., Blum, P., and Attard, G.: Impact of groundwater heat pump systems on subsurface temperature under variable advection, conduction and dispersion, Geothermics, 83, 101721, https://doi.org/10.1016/j.geothermics.2019.101721, 2020b. a
Rau, G. C., Andersen, M. S., and Acworth, R. I.: Experimental investigation of the thermal time-series method for surface water-groundwater interactions, Water Resour. Res., 48, W03530, https://doi.org/10.1029/2011WR011560, 2012b. a, b
Rau, G. C., Andersen, M. S., McCallum, A. M., Roshan, H., and Acworth, R. I.: Heat as a tracer to quantify water flow in near-surface sediments, Earth-Sci. Rev., 129, 40–58, https://doi.org/10.1016/j.earscirev.2013.10.015, 2014. a, b
Schumann, T.: Heat transfer: a liquid flowing through a porous prism, J. Frankl. Inst., 208, 405–416, https://doi.org/10.1016/S0016-0032(29)91186-8, 1929. a
Shi, W., Wang, Q., Klepikova, M., and Zhan, H.: New criteria to estimate local thermal nonequilibrium conditions for heat transport in porous aquifers, Water Resour. Res., 60, e2024WR037382, https://doi.org/10.1029/2024WR037382, e2024WR037382 2024WR037382, 2024. a
Stallman, R. W.: Steady one-dimensional fluid flow in a semi-infinite porous medium with sinusoidal surface temperature, J. Geophys. Res., 70, 2821–2827, https://doi.org/10.1029/JZ070i012p02821, 1965. a
Stauffer, F., Bayer, P., Blum, P., Giraldo, N. M., and Kinzelbach, W.: Thermal Use of Shallow Groundwater, CRC Press, https://doi.org/10.1201/b16239, 2013. a
Tatar, A., Mohammadi, S., Soleymanzadeh, A., and Kord, S.: Predictive mixing law models of rock thermal conductivity: applicability analysis, J. Petrol. Sci. Eng., 197, 107965, https://doi.org/10.1016/j.petrol.2020.107965, 2021. a
Vafai, K.: Handbook of Porous Media, 2nd edn., CRC Press, https://doi.org/10.1201/9780415876384, 2005. a
van Genuchten, M. T. and Alves, W. J.: Analytical Solutions of the One-Dimensional Convective-Dispersive Solute Transport Equation, vol. 1661, US Department of Agriculture, Washington, DC, https://doi.org/10.1016/0378-3774(84)90020-9, 1982. a
Wagner, W. and Pruß, A.: The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use, J. Phys. Chem. Ref. Data, 31, 387–535, https://doi.org/10.1063/1.1461829, 2002. a, b, c
Wakao, N., Kaguei, S., and Funazkri, T.: Effect of fluid dispersion coefficients on particle-to-fluid heat transfer coefficients in packed beds: correlation of nusselt numbers, Chem. Eng. Sci., 34, 325–336, https://doi.org/10.1016/0009-2509(79)85064-2, 1979. a, b
Wang, C. and Fox, P. J.: Validity of local thermal equilibrium assumption for heat transfer in a saturated soil layer, J. Geotech. Geoenviron., 149, 06023002, https://doi.org/10.1061/JGGEFK.GTENG-11152, 2023. a, b
Whitaker, S.: Improved constraints for the principle of local thermal equilibrium, Ind. Eng. Chem. Res., 30, 983–997, https://doi.org/10.1021/ie00053a022, 1991. a, b
Zhu, J., Hu, K., Lu, X., Huang, X., Liu, K., and Wu, X.: A review of geothermal energy resources, development, and applications in China: current status and prospects, Energy, 93, 466–483, https://doi.org/10.1016/j.energy.2015.08.098, 2015. a
Short summary
A systematic laboratory experiment elucidates two-phase heat transport due to water flow in saturated porous media to understand thermal propagation in aquifers. Results reveal delayed thermal arrival in the solid phase, depending on grain size and flow velocity. Analytical modeling using standard local thermal equilibrium (LTE) and advanced local thermal non-equilibrium (LTNE) theory fails to describe temperature breakthrough curves, highlighting the need for more advanced numerical approaches.
A systematic laboratory experiment elucidates two-phase heat transport due to water flow in...
