IDEAS home Printed from https://ideas.repec.org/a/gam/jsusta/v12y2020i5p2021-d329202.html
   My bibliography  Save this article

A Fast Simulation Approach to the Thermal Recovery Characteristics of Deep Borehole Heat Exchanger after Heat Extraction

Author

Listed:
  • Yazhou Zhao

    (Key Laboratory of Shale Gas and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China
    Innovation Academy for Earth Science, Chinese Academy of Sciences, Beijing 100029, China
    College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China)

  • Zhibo Ma

    (Institute of Applied Physics and Computational Mathematics, Beijing 100094, China)

  • Zhonghe Pang

    (Key Laboratory of Shale Gas and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China
    Innovation Academy for Earth Science, Chinese Academy of Sciences, Beijing 100029, China
    College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China)

Abstract

Necessary intermittence after heat extraction for a deep borehole heat exchanger (DBHE) is beneficial for sustainable operation. This paper centers on the fast simulation for thermal recovery characteristics of DBHE under intermittent condition. First of all, in view of the existing temperature gradient and multi-layer heterogeneity of rock underground that could never be ignored for DBHE, we extend the classical finite line source model based on heat source theory and superposition principle to account for the vertical heat flux distribution varying along depth and heterogeneous thermal conductivities in the multi-layer rock zone. Moreover, a fast simulation approach for heat transfer analysis inside the borehole coupled with the extended finite line source model is put forward to depict the transient thermal response and dynamic thermal recovery of rock outside borehole. To the authors’ knowledge, no such algorithm for deep BHE has yet been suggested in the previous literature. This approach has proven to be reliable and efficient enough for DBHE simulation under the intermittent condition. Simulation results show that at least 65 days of intermittence for the model in study should be spared after the heating season to achieve sustainable heat extraction in the next cyclic operation. Compared to the detailed solution based on full discretization numerical schemes, the relative error for borehole bottom temperature was 0.79%. In addition, comparison of the simulation results for thermal performance during the heating season in a three-year cyclic operation with 205 days intermittence shows that both the outflow temperature and heat extraction rate in the subsequent cycle after intermittence are in good agreement with the full 3D numerical solution in the reference (with a relative error of 6.36% for the outflow temperature and 9.3% for the heat extraction rate). Regarding the calculation speed, around a 13 times acceleration can be achieved. Finally, it is also promising to be applicable for thermal recovery simulation after heat extraction of vertical closed loop borehole heat exchangers at arbitrary length from shallow to deep.

Suggested Citation

  • Yazhou Zhao & Zhibo Ma & Zhonghe Pang, 2020. "A Fast Simulation Approach to the Thermal Recovery Characteristics of Deep Borehole Heat Exchanger after Heat Extraction," Sustainability, MDPI, vol. 12(5), pages 1-27, March.
    • Handle: RePEc:gam:jsusta:v:12:y:2020:i:5:p:2021-:d:329202
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2071-1050/12/5/2021/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2071-1050/12/5/2021/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Li, Min & Li, Ping & Chan, Vincent & Lai, Alvin C.K., 2014. "Full-scale temperature response function (G-function) for heat transfer by borehole ground heat exchangers (GHEs) from sub-hour to decades," Applied Energy, Elsevier, vol. 136(C), pages 197-205.
    2. Seama Koohi-Fayegh & Marc A. Rosen, 2012. "On Thermally Interacting Multiple Boreholes with Variable Heating Strength: Comparison between Analytical and Numerical Approaches," Sustainability, MDPI, vol. 4(8), pages 1-19, August.
    3. Li, Min & Lai, Alvin C.K., 2015. "Review of analytical models for heat transfer by vertical ground heat exchangers (GHEs): A perspective of time and space scales," Applied Energy, Elsevier, vol. 151(C), pages 178-191.
    4. Zhang, Linfeng & Zhang, Quan & Huang, Gongsheng, 2016. "A transient quasi-3D entire time scale line source model for the fluid and ground temperature prediction of vertical ground heat exchangers (GHEs)," Applied Energy, Elsevier, vol. 170(C), pages 65-75.
    5. Yang, H. & Cui, P. & Fang, Z., 2010. "Vertical-borehole ground-coupled heat pumps: A review of models and systems," Applied Energy, Elsevier, vol. 87(1), pages 16-27, January.
    6. Li, Huai & Nagano, Katsunori & Lai, Yuanxiang & Shibata, Kazuo & Fujii, Hikari, 2013. "Evaluating the performance of a large borehole ground source heat pump for greenhouses in northern Japan," Energy, Elsevier, vol. 63(C), pages 387-399.
    7. Holmberg, Henrik & Acuña, José & Næss, Erling & Sønju, Otto K., 2016. "Thermal evaluation of coaxial deep borehole heat exchangers," Renewable Energy, Elsevier, vol. 97(C), pages 65-76.
    8. Rivera, Jaime A. & Blum, Philipp & Bayer, Peter, 2015. "Ground energy balance for borehole heat exchangers: Vertical fluxes, groundwater and storage," Renewable Energy, Elsevier, vol. 83(C), pages 1341-1351.
    9. Kim, Eui-Jong & Bernier, Michel & Cauret, Odile & Roux, Jean-Jacques, 2014. "A hybrid reduced model for borehole heat exchangers over different time-scales and regions," Energy, Elsevier, vol. 77(C), pages 318-326.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alshehri, Faisal & Beck, Stephen & Ingham, Derek & Ma, Lin & Pourkashanian, Mohammed, 2021. "Sensitivity analysis of a vertical geothermal heat pump system in a hot dry climate," Renewable Energy, Elsevier, vol. 178(C), pages 785-801.
    2. Luo, Yongqiang & Xu, Guozhi & Zhang, Shicong & Cheng, Nan & Tian, Zhiyong & Yu, Jinghua, 2022. "Heat extraction and recover of deep borehole heat exchanger: Negotiating with intermittent operation mode under complex geological conditions," Energy, Elsevier, vol. 241(C).
    3. Theo Renaud & Lehua Pan & Hannah Doran & Gioia Falcone & Patrick G. Verdin, 2021. "Numerical Analysis of Enhanced Conductive Deep Borehole Heat Exchangers," Sustainability, MDPI, vol. 13(12), pages 1-21, June.
    4. Yazhou Zhao & Xiangxi Qin & Xiangyu Shi, 2022. "Heat Transfer Modeling on High-Temperature Charging and Discharging of Deep Borehole Heat Exchanger with Transient Strong Heat Flux," Sustainability, MDPI, vol. 14(15), pages 1-34, August.
    5. Chen, Wen & Zhou, Chaohui & Huang, Xinyu & Luo, Hanbin & Luo, Yongqiang & Cheng, Nan & Tian, Zhiyong & Zhang, Shicong & Fan, Jianhua & Zhang, Ling, 2024. "Study on thermal radius and capacity of multiple deep borehole heat exchangers: Analytical solution, algorithm and application based on Response Factor Matrix method (RFM)," Energy, Elsevier, vol. 296(C).
    6. Changlong Wang & Han Fang & Xin Wang & Jinli Lu & Yanhong Sun, 2022. "Study on the Influence of Borehole Heat Capacity on Deep Coaxial Borehole Heat Exchanger," Sustainability, MDPI, vol. 14(4), pages 1-11, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Javadi, Hossein & Mousavi Ajarostaghi, Seyed Soheil & Rosen, Marc A. & Pourfallah, Mohsen, 2019. "Performance of ground heat exchangers: A comprehensive review of recent advances," Energy, Elsevier, vol. 178(C), pages 207-233.
    2. Nian, Yong-Le & Cheng, Wen-Long, 2018. "Insights into geothermal utilization of abandoned oil and gas wells," Renewable and Sustainable Energy Reviews, Elsevier, vol. 87(C), pages 44-60.
    3. Rivera, Jaime A. & Blum, Philipp & Bayer, Peter, 2016. "A finite line source model with Cauchy-type top boundary conditions for simulating near surface effects on borehole heat exchangers," Energy, Elsevier, vol. 98(C), pages 50-63.
    4. Zhang, Linfeng & Zhang, Quan & Huang, Gongsheng, 2016. "A transient quasi-3D entire time scale line source model for the fluid and ground temperature prediction of vertical ground heat exchangers (GHEs)," Applied Energy, Elsevier, vol. 170(C), pages 65-75.
    5. Guo, Y. & Huang, G. & Liu, W.V., 2023. "A new semi-analytical solution addressing varying heat transfer rates for U-shaped vertical borehole heat exchangers in multilayered ground," Energy, Elsevier, vol. 274(C).
    6. Rivera, Jaime A. & Blum, Philipp & Bayer, Peter, 2016. "Influence of spatially variable ground heat flux on closed-loop geothermal systems: Line source model with nonhomogeneous Cauchy-type top boundary conditions," Applied Energy, Elsevier, vol. 180(C), pages 572-585.
    7. Zhou, Yang & Zheng, Zhi-xiang & Zhao, Guang-si, 2022. "Analytical models for heat transfer around a single ground heat exchanger in the presence of both horizontal and vertical groundwater flow considering a convective boundary condition," Energy, Elsevier, vol. 245(C).
    8. Javed, Saqib & Spitler, Jeffrey, 2017. "Accuracy of borehole thermal resistance calculation methods for grouted single U-tube ground heat exchangers," Applied Energy, Elsevier, vol. 187(C), pages 790-806.
    9. Carotenuto, Alberto & Ciccolella, Michela & Massarotti, Nicola & Mauro, Alessandro, 2016. "Models for thermo-fluid dynamic phenomena in low enthalpy geothermal energy systems: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 60(C), pages 330-355.
    10. Wang, Changlong & Sun, Wanyu & Fu, Qiang & Lu, Yuehong & Zhang, Pengyuan, 2024. "Semi-analytical and numerical modeling of U-bend deep borehole heat exchanger," Renewable Energy, Elsevier, vol. 222(C).
    11. Ma, Qijie & Wang, Peijun, 2020. "Underground solar energy storage via energy piles," Applied Energy, Elsevier, vol. 261(C).
    12. Shi, Yu & Song, Xianzhi & Wang, Gaosheng & McLennan, John & Forbes, Bryan & Li, Xiaojiang & Li, Jiacheng, 2019. "Study on wellbore fluid flow and heat transfer of a multilateral-well CO2 enhanced geothermal system," Applied Energy, Elsevier, vol. 249(C), pages 14-27.
    13. Somogyi, Viola & Sebestyén, Viktor & Nagy, Georgina, 2017. "Scientific achievements and regulation of shallow geothermal systems in six European countries – A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 68(P2), pages 934-952.
    14. Xie, Kun & Nian, Yong-Le & Cheng, Wen-Long, 2018. "Analysis and optimization of underground thermal energy storage using depleted oil wells," Energy, Elsevier, vol. 163(C), pages 1006-1016.
    15. Pan, Aiqiang & McCartney, John S. & Lu, Lin & You, Tian, 2020. "A novel analytical multilayer cylindrical heat source model for vertical ground heat exchangers installed in layered ground," Energy, Elsevier, vol. 200(C).
    16. Davide Menegazzo & Giulia Lombardo & Sergio Bobbo & Michele De Carli & Laura Fedele, 2022. "State of the Art, Perspective and Obstacles of Ground-Source Heat Pump Technology in the European Building Sector: A Review," Energies, MDPI, vol. 15(7), pages 1-25, April.
    17. Zhang, Xueping & Han, Zongwei & Ji, Qiang & Zhang, Hongzhi & Li, Xiuming, 2021. "Thermal response tests for the identification of soil thermal parameters: A review," Renewable Energy, Elsevier, vol. 173(C), pages 1123-1135.
    18. Claudia Naldi & Enzo Zanchini, 2019. "Full-Time-Scale Fluid-to-Ground Thermal Response of a Borefield with Uniform Fluid Temperature," Energies, MDPI, vol. 12(19), pages 1-18, September.
    19. Li, Min & Lai, Alvin C.K., 2015. "Review of analytical models for heat transfer by vertical ground heat exchangers (GHEs): A perspective of time and space scales," Applied Energy, Elsevier, vol. 151(C), pages 178-191.
    20. García-Gil, Alejandro & Goetzl, Gregor & Kłonowski, Maciej R. & Borovic, Staša & Boon, David P. & Abesser, Corinna & Janza, Mitja & Herms, Ignasi & Petitclerc, Estelle & Erlström, Mikael & Holecek, Ja, 2020. "Governance of shallow geothermal energy resources," Energy Policy, Elsevier, vol. 138(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jsusta:v:12:y:2020:i:5:p:2021-:d:329202. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.