Testing a Model of Flow and Heat Transfer for U-shaped Geothermal Exchangers

Testing a Model of Flow and Heat Transfer for U-shaped Geothermal Exchangers

Josephin GiacominiMaria C. Invernizzi Pierluigi Maponi Massimo Verdoya 

School of Science and Technology, Mathematics division, University of Camerino, Via Madonna delle Carceri 9, Camerino (MC) 62032, Italy

School of Science and Technology, Geology division, University of Camerino, Via Gentile III da Varano, Camerino (MC) 62032, Italy

Department of Earth, Environment and Life Sciences (DISTAV), University of Genoa, Viale Benedetto XV 5, Genova 16132, Italy

Corresponding Author Email: 
15 March 2018
28 May 2018
30 September 2018
| Citation



Among renewable resources, geothermal energy is one of the most promising for its independence on weather conditions. However, design and installation of borehole heat exchangers on low enthalpy regions must consider numerous influencing factors. Here, we focus on the efficiency improvement in hot water production and heating and cooling of buildings of a pilot geothermal plant, which was implemented as part of a hybrid system within the frame of a research project at the University of Camerino (Italy). The aims of the geothermal plant were to study the subsoil thermal properties and monitoring the parameters of the system during operation. As an important application for the design and sizing of low enthalpy geothermal systems, we propose a mathematical model to study the heat transfer between the fluid circulating in the pipes and the underground, where the mutual influence between the soil and the exchanger is considered. We present results of these approximated solutions based on experimental measurements acquired in the actual geothermal exchangers. Laboratory and in situ tests were also carried out to investigate the underground thermal properties and thermal regime of the heterogeneous soil sedimentary succession.


borehole heat exchanger, geothermal energy, heat transfer modeling, thermal conductivity

1. Introduction
2. Test Area
3. Modelling of a Borehole Exchanger
4. Conclusions

This work has benefited from the contribution of Unicam FAR 2014-15, PI Invernizzi. The authors are particularly grateful to Stefano Calabrò for suggestions, assistance and scientific contribution to the MATREND project, and to Sara Ciattoni for re-processing of data within her bachelor thesis project.


[1] Borinaga-Treviño R, Pascual-Muñoz P, Castro-Fresno D, Del Coz-Díaz JJ. (2013). Study of different grouting materials used in vertical geothermal closed loop heat exchangers. Appl Therm. Eng. 50(1): 159-167. https://doi.org/10.1016/j.applthermaleng.2012.05.029

[2] Cucumo M, Ferraro V, Kaliakatsos D, Mele M, Barci G. (2016). Performance of a field of geothermal probes to support the air conditioning plant of a public building powered by water/water heat pumps. International Journal of Heat and Technology 34(Sp.2): S535-S544. Oct. 2016. https://doi.org/10.18280/ijht.34S248

[3] Desmedt J, Van Bael J, Hoes H, Robeyn N. (2012). Experimental performance of borehole heat exchangers and grouting materials for ground source heat pumps. Int J Energy Res 36(13): 1238-1246. https://doi.org/10.1002/er.1898

[4] Luo J, Rohn J, Bayer M, Priess A. (2013). Thermal efficiency comparison of borehole heat exchangers with different drillhole diameters. Energies 6(8): 4187-4206. https://doi.org/10.3390/en6084187

[5] Pierantoni P, Deiana F, Galdenzi S. (2013). Stratigraphic and structural features of the Sibillini Mountains. Ital J Geosci 132(3): 497-520. https://doi.org/10.3301/IJG.2013.08

[6] Centamore E, Micarelli A. (1991). Stratigrafia, in L’ambiente fisico delle Marche, Firenze, IT: S.EL. CA., 1-66.

[7] Cantalamessa G, Centamore E, Chiocchini U, Micarelli A, Potetti M, (1986). Il Miocene delle Marche. Studi Geol. Camerti, pp. 35-55.

[8] Chicco JM, Fusari A, Invernizzi MC. (2016). Innovative applications of geothermal energy for direct uses: A pilot study case in Marche region (Italy). Rendiconti Online della Società Geologica Italiana 41: 280-283. https://doi.org/10.3301/ROL.2016.148

[9] Calabrò S. (2018). Thermal and electricity energy storage - a strategy of efficiency in a micro CCHP energy system. PhD dissertation, Phys. Div., University of Camerino, MC, IT.

[10] Pacetti C, Giuli G, Invernizzi MC, Chiozzi P, Verdoya M, (2017). Thermophysical parameters from laboratory measurements and tests in borehole heat exchangers. Proc. EGU2017-12713 19.

[11] Verdoya M, Pacetti C, Chiozzi P, Invernizzi C. (2018). Thermophysical parameters from laboratory measurements and in-situ tests in borehole heat exchangers. Appl. Therm. Eng. 144: 711-720. https://doi.org/10.1016/j.applthermaleng.2018.08.039

[12] Pasquale V, Verdoya M, Chiozzi P, (2014). Measurements of rock thermal conductivity with a Transient Divided Bar. Geothermics 53: 183-189. https://doi.org/10.1016/j.geothermics.2014.05.008

[13] Anderson JD. (1995). Computational Fluid Dynamics. Singapore, SG: McGraw-Hill, Inc. 37-94.

[14] Batchelor JK. (2002). An introduction to Fluid Dynamics. Cambridge, USA. Cambridge University Press 131-173. https://doi.org/10.1017/CBO9780511800955

[15] Liua Y, Zhanga Y, Gonga S, Wanga Z, Zhangb H. Analysis on the performance of ground heat exchangers in ground source heat pump systems based on heat transfer enhancements. Procedia Engineer 121: 19-26. https://doi.org/10.1016/j.proeng.2015.08.1013

[16] Bejan A. (2013). Convection Heat Transfer. Hoboken. USA: John Wiley & Sons, Inc. pp. 96-125, 369-397. https://doi.org/10.1002/9781118671627

[17] Medina YC, Khandy NH, Fonticiella OMC, Morales OFG. (2017). Abstract of heat transfer coefficient modelation in single-phase systems inside pipes. MMEP 4: 126-131. https://doi.org/10.18280/mmep.040303

[18] Egidi N, Giacomini J, Maponi P. (2018). A mathematical model for the analysis of the flow and heat transfer problem in u-shaped geothermal exchangers. Appl Math Model 61: 83-106. https://doi.org/10.1016/j.apm.2018.03.024