Abstract
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.
Similar content being viewed by others
Abbreviations
- a :
-
Solid compressibility (Pa−1)
- b :
-
Fluid compressibility (Pa−1)
- cρ :
-
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)
- cub:
-
Hollow cuboid
- cyl:
-
Hollow cylinder
- i :
-
Direction
- w:
-
Water
References
Abdelaziz SL, Ozudogru TY, Olgun CG, Martin JR (2014) Multilayer finite line source model for vertical heat exchangers. Geothermics 51:406–416
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
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
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
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
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
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
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
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
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
Bear J (2007) Hydraulics of groundwater. Dover Publications, Mineola
Bear J, Bachmat Y (1990) Introduction to modeling and transport phenomena in porous media. Kluwer Academic Publishers, Dortrecht
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
Beier RA (2014) Transient heat transfer in a U-tube borehole heat exchanger. Appl Therm Eng 62:256–266
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
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)
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
Carslaw HS, Jaeger JC (1959) Conduction of heat in solids, 2nd edn. Oxford University Press, New York
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
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
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
Eskilson P (1987) Thermal analysis of heat extraction boreholes. Ph.D. Thesis, University of Lund. Lund, Sweden
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
IEA (2008) Worldwide trends in energy use and efficiency. IEA/OECD, Paris
Ingersoll LR, Zoeble OJ, Ingersoll AC (1954) Heat conduction with engineering, geological and other applications. University of Wisconsin Press, Madison
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
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)
Kohl T, Brenni R, Eugster W (2002) System performance of a deep borehole heat exchanger. Geothermics 31:687–708
Kolditz O, Bauer S (2004) A process-oriented approach to computing multi-field problems in porous media. J Hydroinf 6(3):225–244
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
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
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)
Marcotte D, Pasquier P (2008) On the estimation of thermal resistance in borehole thermal conductivity test. Renew Energy 33:2407–2415
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
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
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
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
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
Rivera JA, Blum P, Bayer P (2015) Ground energy balance for borehole heat exchangers: vertical fluxes, groundwater and storage. Renew Energy 83:1341–1351
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
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
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
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)
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
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
Sørensen PA, Larsen J, Thøgersen L, Dannemand Andersen J, Østergaard C, Schmidt T (2013) Boreholes in Brædstrup. Final report
Sternberg A, Bardow A (2015) Power-to-What? Environmental assessment of energy storage systems. Energy Environ Sci 8:389–400
VDI (2010) Thermal use of the underground - fundamentals, approvals, environmental aspects. VDI 4640 Part I
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
Wagner V, Bayer P, Kübert M, Blum P (2012) Numerical sensitivity study of thermal response tests. Energy 41:245–253
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
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
Acknowledgments
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).
Author information
Authors and Affiliations
Corresponding author
Additional information
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.
Rights and permissions
About this article
Cite this article
Boockmeyer, A., Bauer, S. Efficient simulation of multiple borehole heat exchanger storage sites. Environ Earth Sci 75, 1021 (2016). https://doi.org/10.1007/s12665-016-5773-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12665-016-5773-4