A Simplified Numerical Model as a Design Tool for Vertical Single U-Tube Ground Heat Exchangers
Publication: International Journal of Geomechanics
Volume 24, Issue 5
Abstract
Ground heat exchangers (GHEs) are commonly modeled using the finite-element (FE) method for the design and evaluation of the GHE performance. However, one of the disadvantages of these FE models is the huge computational time involved due to the complex transient three-dimensional (3D) transport phenomena of GHEs. Thus, it is essential to develop an FE model that can provide the inlet and outlet fluid temperature and 3D temperature field with high accuracy and yet with minimal computational time. The primary objective of this study was to create a streamlined numerical model that could serve as an effective and practical design tool for simulating vertical GHEs, emphasizing a high degree of numerical accuracy while minimizing computational time. A computationally efficient 3D transient FE model was developed in COMSOL Multiphysics, which uses an equivalent 1D pipe flow instead of fully modeling the borehole grout. The proposed model prioritizes the simulation of fluid and borehole wall temperatures with an accuracy comparable to the conventional model, but it sacrifices the simulation accuracy of the borehole grout to reduce computational time and offer more convenient meshing. The proposed model was compared with a conventional model and verified against field measurements of outlet fluid temperature and spatial subsurface soil temperature at different depths and radial distances from a 132.5-m GHE operated in a full-scale geothermal bridge de-icing system. Two FE mesh cases––optimum and extrafine––were designed in order to compare the models. The results indicated that the computational time was greatly reduced, by 95% and 81% for the two mesh cases, respectively, while the same level of accuracy in the temperature evaluation was maintained. Also, the required number of model elements was decreased by 90% and 67% for the optimum and extrafine-mesh cases.
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Data Availability Statement
All data that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors are grateful for the financial support provided by the Texas Department of Transportation (TxDOT, Award No. 0-6872). We acknowledge the help of our research supervisors, Shelley Pridgen, Sonya Badgley, and James Kuhr, and the TxDOT engineers, Richard Williammee and Justin Thomey. Special thanks go to the Fort Worth maintenance group and Tom Weatherspoon for help with the machinery. We would also like to thank Howard Newton from the Image Engineering Group, Ltd., William McPike from Geothermal Drilling, Inc., and Pile Dynamics for providing consulting, fieldwork, and technical support, respectively, during the field study.
References
Al-Khoury, R., and P. G. Bonnier. 2006. “Efficient finite element formulation for geothermal heating systems. Part II: Transient.” Int. J. Numer. Methods Eng. 67 (5): 725–745. https://doi.org/10.1002/nme.1662.
Al-Khoury, R., P. G. Bonnier, and R. B. J. Brinkgreve. 2005. “Efficient finite element formulation for geothermal heating systems. Part I: Steady state.” Int. J. Numer. Methods Eng. 63 (7): 988–1013. https://doi.org/10.1002/nme.1313.
Austin, W. A. III. 1998. Development of an in situ system for measuring ground thermal properties. Stillwater, OK: Oklahoma State Univ.
Barnard, A. C. L., W. A. Hunt, W. P. Timlake, and E. Varley. 1966. “A theory of fluid flow in compliant tubes.” Biophys. J. 6: 717–724. https://doi.org/10.1016/S0006-3495(66)86690-0.
Bennet, J., J. Claesson, and G. Hellström. 1987. Multipole method to compute the conductive heat flows to and between pipes in a composite cylinder. Notes on heat transfer. Lund, Sweden: Lund Univ.
Bernier, M. A. 2001. “Ground-coupled heat pump system simulation/discussion.” ASHRAE Trans. 107: 605.
Boockmeyer, A., and S. Bauer. 2016. “Efficient simulation of multiple borehole heat exchanger storage sites.” Environ. Earth Sci. 75 (12): 1–13. https://doi.org/10.1007/s12665-016-5773-4.
Brandl, H. 2006. “Energy foundations and other thermo-active ground structures.” Géotechnique 56 (2): 81–122. https://doi.org/10.1680/geot.2006.56.2.81.
Choi, J. C., J. Park, and S. R. Lee. 2013. “Numerical evaluation of the effects of groundwater flow on borehole heat exchanger arrays.” Renewable Energy 52: 230–240. https://doi.org/10.1016/j.renene.2012.10.028.
Churchill, S. W. C. 1977. “Friction-factor equation spans all fluid-flow regimes.” Chem. Eng. 84: 91–92.
Comsol, I. 2018. “COMSOL multiphysics reference manual, version 5.3.” COMSOL AB 564: 565.
Gawecka, K. A., D. M. G. Taborda, D. M. Potts, E. Sailer, W. Cui, and L. Zdravković. 2020. “Finite-element modeling of heat transfer in ground source energy systems with heat exchanger pipes.” Int. J. Geomech. 20 (5): 4020041. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001658.
Gnielinski, V. 1976. “New equations for heat and mass transfer in turbulent pipe and channel flow.” Int. J. Chem. Eng. 16: 359–368.
Habibzadeh-Bigdarvish, O., G. Lei, X. Yu, and A. J. Puppala. Forthcoming. “Temporal and spatial thermal performance of a ground heat exchanger in response to bridge solar recharging and de-icing.” Can. Geotech. J.
Habibzadeh-Bigdarvish, O., X. Yu, T. Li, G. Lei, A. Banerjee, and A. J. Puppala. 2021. “A novel full-scale external geothermal heating system for bridge deck de-icing.” Appl. Therm. Eng. 185: 116365. https://doi.org/10.1016/j.applthermaleng.2020.116365.
Han, C., and X. Yu. 2016. “Sensitivity analysis of a vertical geothermal heat pump system.” Appl. Energy 170: 148–160. https://doi.org/10.1016/j.apenergy.2016.02.085.
Han, Z., B. Li, C. Ma, H. Hu, and C. Bai. 2018. “Study on accurate identification of soil thermal properties under different experimental parameters.” Energy Build. 164: 21–32. https://doi.org/10.1016/j.enbuild.2017.12.067.
He, M., S. J. Rees, and L. Shao. 2009. “Applications of a dynamic three-dimensional numerical model for borehole heat exchangers.” In Proc., Effstock, the 11th Int. Conf. on Thermal Energy Storage. Stockholm, Sweden: Energy and Environmental Technology Association/EMTF Publishers.
Kohl, T., and R. J. Hopkirk. 1995. “‘FRACure’—A simulation code for forced fluid flow and transport in fractured, porous rock.” Geothermics 24 (3): 333–343. https://doi.org/10.1016/0375-6505(95)00012-F.
Lamarche, L., S. Kajl, and B. Beauchamp. 2010. “A review of methods to evaluate borehole thermal resistances in geothermal heat-pump systems.” Geothermics 39 (2): 187–200. https://doi.org/10.1016/j.geothermics.2010.03.003.
Lazzari, S., A. Priarone, and E. Zanchini. 2010. “Long-term performance of BHE (borehole heat exchanger) fields with negligible groundwater movement.” Energy 35 (12): 4966–4974. https://doi.org/10.1016/j.energy.2010.08.028.
Li, B., Z. Han, C. Bai, and H. Hu. 2019. “The influence of soil thermal properties on the operation performance on ground source heat pump system.” Renewable Energy 141: 903–913. https://doi.org/10.1016/j.renene.2019.04.069.
Marion, W., and S. Wilcox. 1995. Solar radiation data manual for buildings. Golden, CO: National Renewable Energy Lab.
Omer, A. M. 2008. “Ground-source heat pumps systems and applications.” Renewable Sustainable Energy Rev. 12 (2): 344–371. https://doi.org/10.1016/j.rser.2006.10.003.
Ozudogru, T. Y., C. G. Olgun, and A. Senol. 2014. “3D numerical modeling of vertical geothermal heat exchangers.” Geothermics 51: 312–324. https://doi.org/10.1016/j.geothermics.2014.02.005.
Signorelli, S., S. Bassetti, D. Pahud, and T. Kohl. 2007. “Numerical evaluation of thermal response tests.” Geothermics 36 (2): 141–166. https://doi.org/10.1016/j.geothermics.2006.10.006.
Spitler, J., and M. Bernier. 2011. Ground-source heat pump systems: The first century and beyond. New York: Taylor & Francis.
Zhang, D., P. Gao, Y. Zhou, Y. Wang, and G. Zhou. 2020. “An experimental and numerical investigation on temperature profile of underground soil in the process of heat storage.” Renewable Energy 148: 1–21. https://doi.org/10.1016/j.renene.2019.11.123.
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International Journal of Geomechanics
Volume 24 • Issue 5 • May 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Apr 10, 2023
Accepted: Nov 5, 2023
Published online: Feb 28, 2024
Published in print: May 1, 2024
Discussion open until: Jul 28, 2024
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