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Efficient simulation of multiple borehole heat exchanger storage sites

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In this paper, an adapted model is developed for borehole heat exchangers (BHEs) to simulate geothermal applications such as heat storage on a large scale efficiently and with high accuracy. The adapted numerical model represents all BHE components, allowing for a detailed representation of the governing processes. The approach is calibrated and validated for a single U-tube BHE using a high-resolution experimental data set from a laboratory thermal response test. It is found that the computational effort can be reduced by factors of ~50, ~50 and ~25 for single U-tube, double U-tube and coaxial BHEs, respectively, if an absolute deviation of less than 1 % compared to a conventional fully discretised model is allowed. Computation times can be reduced further by accepting higher deviations. The adapted modelling approach allows for a detailed and correct representation of the temporal and spatial temperature distribution under highly transient conditions by applying it to a high-temperature heat storage scenario using multiple BHEs. The model is especially suited to represent coupled flow and heat transport processes, to account for groundwater flow in the BHE region as well as geological heterogeneities and especially interaction between a large number of BHEs.

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a :

Solid compressibility (Pa−1)

b :

Fluid compressibility (Pa−1)


Volumetric heat capacity (J m−3 K−1)

d :

Thickness (m)

D :

Heat diffusion dispersion tensor

g :

Gravitational acceleration (m s−1)

k :

Intrinsic permeability (m)

L :

Length (m)

m :

Side length (m)

n :

Porosity (–)

p :

Pressure (Pa)

Q :

Sources and sinks (kg m−3 s−1)

Q H :

Heat sources and sinks (W m−3)

r :

Radius (m)

R th :

Thermal resistance (K W−1)

T :

Temperature (K)

v :

Transport velocity (m s−1)

z :

Depth (m)

α :

Dispersivity (m)

λ :

Thermal conductivity (W m−1 K−1)

μ :

Fluid dynamic viscosity (N s m−2)

ρ :

Density (kg m−3)


Hollow cuboid


Hollow cylinder

i :





  1. Abdelaziz SL, Ozudogru TY, Olgun CG, Martin JR (2014) Multilayer finite line source model for vertical heat exchangers. Geothermics 51:406–416

    Article  Google Scholar 

  2. AGEB (2013) Anwendungsbilanzen für die Energiesektoren in Deutschland in den Jahren 2011 und 2012 mit Zeitreihen von 2008 bis 2012. Arbeitsgemeinschaft Energiebilanzen e.V, Berlin 40p

    Google Scholar 

  3. Al-Khoury R, Bonnier P (2006) Efficient finite element formulation for geothermal heating systems. Part II: transient. Int J Numer Methods Eng 67(5):725–745

    Article  Google Scholar 

  4. Al-Khoury R, Bonnier P, Brinkgreve R (2005) Efficient finite element formulation for geothermal heating systems. Part I: steady-state. Int J Numer Methods Eng 63(7):988–1013

    Article  Google Scholar 

  5. Bandos TV, Montero Á, Fernández E, Santander JLG, Isidro JM, Pérez J, de Córdoba PJF, Urchueguía JF (2009) Finite line-source model for borehole heat exchangers: effect of vertical temperature variations. Geothermics 38(2):263–270

    Article  Google Scholar 

  6. Bauer D, Heidemann W, Marx R, Nußbicker-Lux J, Ochs F, Panthalookaran V, Raab S (2008) Solar unterstützte Nahwärme und Langzeit-Wärmespeicher (Juni 2005 bis Juli 2008). Forschungsbericht zum BMU-Vorhaben 0329607J, Stuttgart

  7. Bauer D, Marx R, Nußbicker-Lux J, Ochs F, Heidemann W, Müller-Steinhagen H (2010) German central solar heating plants with seasonal heat storage. Sol Energy 84:612–623

    Article  Google Scholar 

  8. Bauer S, Beyer C, Dethlefsen F, Dietrich P, Duttmann R, Ebert M, Feeser V, Görke UJ, 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(8):3935–3943. doi:10.1007/s12665-013-2883-0

    Article  Google Scholar 

  9. 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 

  10. Bayer P, de Paly M, Beck M (2014) Strategic optimization of borehole heat exchanger field for seasonal geothermal heating and cooling. Appl Energy 136:445–453

    Article  Google Scholar 

  11. Bear J (2007) Hydraulics of groundwater. Dover Publications, Mineola

    Google Scholar 

  12. Bear J, Bachmat Y (1990) Introduction to modeling and transport phenomena in porous media. Kluwer Academic Publishers, Dortrecht

    Book  Google Scholar 

  13. Beck M, Bayer P, de Paly M, Hecht-Méndez J, Zell A (2013) Geometric arrangement and operation mode adjustment in low-enthalpy geothermal borehole fields for heating. Energy 49:434–443

    Article  Google Scholar 

  14. Beier RA (2014) Transient heat transfer in a U-tube borehole heat exchanger. Appl Therm Eng 62:256–266

    Article  Google Scholar 

  15. Beier RA, Smith MD, Spitler JD (2011) Reference data sets for vertical borehole ground heat exchanger models and thermal response test analysis. Geothermics 40:79–85

    Article  Google Scholar 

  16. Beyer C, Popp S, Bauer S (submitted) Simulation of temperature effects on groundwater flow and reactive contaminant dissolution, transport and biodegradation due to shallow geothermal use. Environ Earth Sci (this issue)

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

    Article  Google Scholar 

  18. Carslaw HS, Jaeger JC (1959) Conduction of heat in solids, 2nd edn. Oxford University Press, New York

    Google Scholar 

  19. Cimmino M, Bernier M (2014) A semi-analytical method to generate g-functions for geothermal bore fields. Int J Heat Mass Transf 70:641–650

    Article  Google Scholar 

  20. Diersch HJG, Bauer D, Heidemann W, Rühaak W, Schätzl P (2011) Finite element modeling of borehole heat exchanger systems: part 1. Fundamentals. Comput Geosci 37:1122–1135

    Article  Google Scholar 

  21. Doherty J (2015) Calibration and uncertainty analysis for complex environmental models. PEST: complete theory and what it means for modelling the real world. Watermark Numerical Computing, Brisbane

    Google Scholar 

  22. Eskilson P (1987) Thermal analysis of heat extraction boreholes. Ph.D. Thesis, University of Lund. Lund, Sweden

  23. Hein P, Kolditz O, Görke UJ, Bucher A, Shao H (2016) A numerical study in the sustainability and efficiency of borehole heat exchanger coupled ground source heat pump systems. Appl Therm Eng 100:421–433

    Article  Google Scholar 

  24. IEA (2008) Worldwide trends in energy use and efficiency. IEA/OECD, Paris

    Google Scholar 

  25. Ingersoll LR, Zoeble OJ, Ingersoll AC (1954) Heat conduction with engineering, geological and other applications. University of Wisconsin Press, Madison

    Google Scholar 

  26. Javed S, Claesson J (2011) New analytical and numerical solutions for the short-term analysis of vertical ground heat exchangers. ASHRAE Trans 117(1):3–12

    Google Scholar 

  27. Kabuth A, Bauer S, Dahmke A (submitted) Energy storage in the geological subsurface: dimensioning, risk analysis and spatial planning—the ANGUS+ project. Environ Earth Sci (this issue)

  28. Kohl T, Brenni R, Eugster W (2002) System performance of a deep borehole heat exchanger. Geothermics 31:687–708

    Article  Google Scholar 

  29. Kolditz O, Bauer S (2004) A process-oriented approach to computing multi-field problems in porous media. J Hydroinf 6(3):225–244

    Google Scholar 

  30. 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 

  31. Li M, Lai ACK (2012) Parameter estimation of in-situ thermal response tests for borehole ground heat exchangers. Int J Heat Mass Transf 55:2615–2624

    Article  Google Scholar 

  32. Lienen T, Hebbeln K, Halm H, Westphal A, Köber R, Würdemann H (submitted) Effects of thermal energy storage on shallow aquifer systems—temporary increase in abundance and activity of sulfate reducing and sulfur oxidizing bacteria. Environ Earth Sci (this issue)

  33. Marcotte D, Pasquier P (2008) On the estimation of thermal resistance in borehole thermal conductivity test. Renew Energy 33:2407–2415

    Article  Google Scholar 

  34. Molina-Giraldo N, Blum P, Ke Zhu K, Bayer P, Fang Z (2011) A moving finite line source model to simulate borehole heat exchangers with groundwater advection. Int J Therm Sci 50:2506–2513

    Article  Google Scholar 

  35. Pannike S, Kölling M, Panteleit B, Reichling J, Scheps V, Schulz HD (2006) Auswirkungen hydrogeologischer Kenngrößen auf die Kältefahnen von Erdwärmesondenanlagen in Lockersedimenten. Grundwasser 1(2006):6–18. doi:10.1007/s00767-006-0114-2

    Article  Google Scholar 

  36. Popp S, Beyer C, Dahmke A, Bauer S (2015) Model development and numerical simulation of a seasonal heat storage in a contaminated shallow aquifer. Energy Procedia 76:361–370. doi:10.1016/j.egypro.2015.07.842

    Article  Google Scholar 

  37. Popp S, Beyer C, Koproch N, Köber R, Dahmke A, Bauer S (2016) Temperature dependent dissolution of residual non-aqueous phase liquids—model development and verification. Environ Earth Sci 75:953. doi:10.1007/s12665-016-5743-x

    Article  Google Scholar 

  38. Poulsen SE, Alberdi-Pagola M (2015) Interpretation of ongoing thermal response tests of vertical (BHE) borehole heat exchangers with predictive uncertainty based stopping criterion. Energy 88:157–167

    Article  Google Scholar 

  39. Rivera JA, Blum P, Bayer P (2015) Ground energy balance for borehole heat exchangers: vertical fluxes, groundwater and storage. Renew Energy 83:1341–1351

    Article  Google Scholar 

  40. Rivera JA, Blum P, Bayer P (2016) A finite line source model with Cauchy-type top boundary conditions for simulating near surface effects on borehole heat exchangers. Energy 98:50–63

    Article  Google Scholar 

  41. Sass I, Lehr C (2011) Improvements on the thermal response test evaluation applying the cylinder source theory. In: Proceedings of the thirty-sixth workshop on geothermal reservoir engineering, Stanford University, Stanford, California

  42. Schulte DO, Welsch B, Boockmeyer A, Rühaak W, Bär K, Bauer S, Sass I (2016) Modelling insulated borehole heat exchangers. Environ Earth Sci 75:910. doi:10.1007/s12665-016-5638-x

    Article  Google Scholar 

  43. Seibertz KSO, Dietrich P, Vienken T (submitted) High resolution temperature monitoring around and within borehole heat exchanger physical models using bre-optic distributed temperature sensing. Environ Earth Sci (this issue)

  44. Shonder JA, Beck JV (1999) Determining effective soil formation thermal properties from field data using a parameter estimation technique. ASHRAE Trans 105(1):458–466

    Google Scholar 

  45. Signorelli S, Bassetti S, Pahud D, Kohl T (2007) Numerical evaluation of thermal response tests. Geothermics 36:141–166. doi:10.1016/j.geothermics.2006.10.006

    Article  Google Scholar 

  46. Sørensen PA, Larsen J, Thøgersen L, Dannemand Andersen J, Østergaard C, Schmidt T (2013) Boreholes in Brædstrup. Final report

  47. Sternberg A, Bardow A (2015) Power-to-What? Environmental assessment of energy storage systems. Energy Environ Sci 8:389–400

    Article  Google Scholar 

  48. VDI (2010) Thermal use of the underground - fundamentals, approvals, environmental aspects. VDI 4640 Part I

  49. Vienken T, Schelenz S, Rink K, Dietrich P (2015) Sustainable intensive thermal use of the shallow subsurface—a critical view on the status quo. Groundwater 53(3):356–361

    Article  Google Scholar 

  50. Wagner V, Bayer P, Kübert M, Blum P (2012) Numerical sensitivity study of thermal response tests. Energy 41:245–253

    Google Scholar 

  51. Wang W, Kosakowski G, Kolditz O (2009) A parallel finite element scheme for thermo-hydro-mechanical (THM) coupled problems in porous media. Comput Geosci 35(8):1631–1641. doi:10.1016/j.cageo.2008.07.007

    Article  Google Scholar 

  52. Zhang C, Guo Z, Liu Y, Cong X, Peng D (2014) A review on thermal response test of ground-coupled heat pump systems. Energy Rev 40:851–867

    Google Scholar 

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The authors would gratefully like to acknowledge the funding provided by the German Ministry of Education and Research (BMBF) for the ANGUS+ project, Grant Number 03EK3022, as well as the support of the Project Management Jülich (PTJ).

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Correspondence to Anke Boockmeyer.

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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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Boockmeyer, A., Bauer, S. Efficient simulation of multiple borehole heat exchanger storage sites. Environ Earth Sci 75, 1021 (2016).

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  • Borehole thermal energy storage
  • Borehole heat exchanger
  • Numerical simulation
  • Fully discretised models
  • OpenGeoSys