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Modeling insulated borehole heat exchangers


In the heating sector, borehole heat exchangers have become popular for supplying renewable energy. They tap into the subsurface to extract geothermal energy for heating purposes. For advanced applications, borehole heat exchangers require insulation in the upper part of the borehole either to meet legal requirements or to improve their performance. A priori numerical heat transport models of the subsurface are imperative for the systems’ planning and design. Only fully discretized models can account for depth-dependent borehole properties like insulated sections, but the model setup is cumbersome and the simulations come at high computational cost. Hence, these models are often not suitable for the simulation of larger installations. This study presents an analytical solution for the simulation of the thermal interactions of partly insulated borehole heat exchangers. A benchmark with a fully discretized OpenGeoSys model confirms sufficient accuracy of the analytical solution. In an application example, the functionality of the tool is demonstrated by finding the ideal length of a borehole insulation using mathematical optimization and by quantifying the effect of the insulation on the borehole heat exchanger performance. The presented method allows for accommodation of future advancements in borehole heat exchangers in numerical simulations at comparatively low computational cost.

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  • Acuña J, Palm B (2013) Distributed thermal response tests on pipe-in-pipe borehole heat exchangers. Appl Energy 109:312–320. doi:10.1016/j.apenergy.2013.01.024

    Article  Google Scholar 

  • Acuña J, Mogensen P, Palm B (2011) Distributed thermal response tests on a multi-pipe coaxial borehole heat exchanger. HVAC&R Res 17:1012–1029. doi:10.1080/10789669.2011.625304

    Google Scholar 

  • Ageb AE (2013) Anwendungsbilanzen für die Endenergiesektoren in Deutschland in den Jahren 2011 und 2012 mit Zeitreihen von 2008 bis 2012. Bundesministerium für Wirtschaft und Technologie, Berlin

    Google Scholar 

  • Angelino L, Dumas P, Latham A (2014) EGEC Market Report 2013/2014 Update, 4 edn. European Geothermal Energy Council—EGEC

  • Bär K, Rühaak W, Welsch B, Schulte D, Homuth S, Sass I (2015) Seasonal high temperature heat storage with medium deep borehole heat exchangers. Energy Procedia 76:351–360. doi:10.1016/j.egypro.2015.07.841

    Article  Google Scholar 

  • Bauer D, Heidemann W, Müller-Steinhagen H, Diersch HJG (2011) Thermal resistance and capacity models for borehole heat exchangers. Int J Energy Res 35:312–320. doi:10.1002/er.1689

    Article  Google Scholar 

  • Bauer S, Beyer C, Dethlefsen F, Dietrich P, Duttmann R, Ebert M, Feeser V, Görke U, Köber R, Kolditz O, Rabbel W, Schanz T, Schäfer D, Würdemann H, Dahmke A (2013) Impacts of the use of the geological subsurface for energy storage: an investigation concept. Environ Earth Sci 70:3935–3943. doi:10.1007/s12665-013-2883-0

    Article  Google Scholar 

  • Bauer S, Pfeiffer T, Boockmeyer A, Dahmke A, Beyer C (2015) Quantifying induced effects of subsurface renewable energy storage. Energy Procedia 76:633–641. doi:10.1016/j.egypro.2015.07.885

    Article  Google Scholar 

  • Boockmeyer A, Bauer S (2014) High-temperature heat storage in geological media: high-resolution simulation of near-borehole processes. Géotechnique Lett 4:151–156. doi:10.1680/geolett.13.00060

    Article  Google Scholar 

  • Brent RP (1973) Algorithms for minimization without derivatives. Dover, Mineola

    Google Scholar 

  • Diersch HJG, Bauer D, Heidemann W, Rühaak W, Schätzl P (2011a) Finite element modeling of borehole heat exchanger systems: part 1. Fundam Comp Geosci 37:1122–1135. doi:10.1016/j.cageo.2010.08.003

    Article  Google Scholar 

  • Diersch HJG, Bauer D, Heidemann W, Rühaak W, Schätzl P (2011b) Finite element modeling of borehole heat exchanger systems: part 2. Numer Simul Comp Geosci 37:1136–1147. doi:10.1016/j.cageo.2010.08.002

    Article  Google Scholar 

  • Eskilson P, Claesson J (1988) Simulation model for thermally interacting heat extraction boreholes. Numer Heat Transf 13:149–165

    Google Scholar 

  • Gehlin SEA, Spitler JD, Hellström G (2016) Deep boreholes for ground source heat pump systems—scandinavian experience and future prospects. Paper presented at the ASHRAE Winter Meeting, Orlando, Florida, 23–27 Jan 2016

  • Haehnlein S, Bayer P, Blum P (2010) International legal status of the use of shallow geothermal energy. Renew Sustain Energy Rev 14:2611–2625. doi:10.1016/j.rser.2010.07.069

    Article  Google Scholar 

  • Kolditz O, Bauer S (2004) A process-oriented approach to computing multi-field problems in porous media. J Hydroinformatics 6:225–244

    Google Scholar 

  • Kolditz O, Bauer S, Bilke L, Böttcher N, Delfs JO, Fischer T, Görke UJ, Kalbacher T, Kosakowski G, McDermott CI, Park CH, Radu F, Rink K, Shao H, Shao HB, Sun F, Sun YY, Singh AK, Taron J, Walther M, Wang W, Watanabe N, Wu Y, Xie M, Xu W, Zehner B (2012) OpenGeoSys: an open-source initiative for numerical simulation of thermo-hydro-mechanical/chemical (THM/C) processes in porous media. Environ Earth Sci 67:589–599. doi:10.1007/s12665-012-1546-x

    Article  Google Scholar 

  • Lee C, Lee K, Choi H, Choi H-P (2010) Characteristics of thermally-enhanced bentonite grouts for geothermal heat exchanger in South Korea. Sci China Ser E-Technol Sci 53:123–128. doi:10.1007/s11431-009-0413-9

    Article  Google Scholar 

  • Lund JW, Freeston DH, Boyd TL (2005) Direct application of geothermal energy: 2005 Worldwide review. Geothermics 34:691–727. doi:10.1016/j.geothermics.2005.09.003

    Article  Google Scholar 

  • Mansure AJ (2002) Polyurethane grouting geothermal lost circulation zones. Paper presented at the IADC/SPE Drilling Conference, Dallas, Texas, 26–28 Feb 2002

  • Nakevska N, Schincariol RA, Dehkordi SE, Cheadle BA (2015) Geothermal waste heat utilization from in situ thermal bitumen recovery operations. Groundwater 53:251–260. doi:10.1111/gwat.12196

    Article  Google Scholar 

  • Reddy JN, Gartling DK (2010) The finite element method in heat transfer and fluid dynamics, 3rd edn. CRC Press, Boca Raton

    Google Scholar 

  • Sass I, Brehm D, Coldewey WG, Dietrich J, Klein R, Kellner T, Kirschbaum B, Lehr C, Marek A, Mielke P, Müller L, Panteleit B, Pohl S, Porada J, Schiessl S, Wedewardt M, Wesche D (2016a) Shallow geothermal systems—recommendations on design, construction, operation and monitoring. Ernst & Sohn, Berlin

    Google Scholar 

  • Sass I, Welsch B, Schulte DO (2016b) Mitteltiefe Erdwärmesondenspeicher—Lösung für den Nutzungskonflikt Grundwasserschutz versus Geothermienutzung? Paper presented at the 7. Bochumer Grundwassertag, Bochum, 17 Mar 2016

  • Schulte DO, Rühaak W, Oladyshkin S, Welsch B, Sass I (2016) Optimization of medium-deep borehole thermal energy storage systems. Energy Technol 4:104–113. doi:10.1002/ente.201500254

    Article  Google Scholar 

  • The MathWorks (2015a) MATLAB 2015b. The MathWorks Inc, Natick

    Google Scholar 

  • The MathWorks (2015b) MATLAB 2015b Global Optimization Toolbox. The MathWorks Inc, Natick

    Google Scholar 

  • Welsch B, Rühaak W, Schulte DO, Bär K, Homuth S, Sass I (2015) A comparative study of medium deep borehole thermal energy storage systems using numerical modeling. In: Proceedings World Geothermal Congress, Melbourne, 19–24 Apr 2015

  • Zawislanski PT, Faybishenko B (1999) New casing and backfill design for neutron logging access boreholes. Ground Water 37:33–37. doi:10.1111/j.1745-6584.1999.tb00955.x

    Article  Google Scholar 

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This study is financially supported by the Deutsche Forschungsgemeinschaft (DFG) in the framework of the Excellence Initiative, Darmstadt Graduate School of Excellence Energy Science and Engineering (GSC 1070).

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Correspondence to Daniel Otto Schulte.

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This article is part of a Topical Collection in Environmental Earth Sciences on “Subsurface Energy Storage”, guest edited by Sebastian Bauer, Andreas Dahmke, and Olaf Kolditz.

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Schulte, D.O., Welsch, B., Boockmeyer, A. et al. Modeling insulated borehole heat exchangers. Environ Earth Sci 75, 910 (2016).

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  • Borehole insulation
  • Borehole heat exchangers
  • Borehole thermal energy storage