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Modeling wellbore heat exchangers: Fully numerical to fully analytical solutions

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  • Tang, Hewei
  • Xu, Boyue
  • Hasan, A. Rashid
  • Sun, Zhuang
  • Killough, John

Abstract

The successful modeling of wellbore heat exchangers requires tight coupling between the formation heat conduction and the wellbore thermal dynamics. In this paper, we developed three representative solutions: a fully numerical solution that treats both formation and wellbore numerically, a semi-numerical solution that treats formation analytically and wellbore numerically and a fully analytical solution that treats both formation and wellbore analytically. The outlet temperature, pressure, and heat flow rate predicted by the three solutions are compared. The results of this comparison indicate that the fully numerical solution is the only accurate solution for the early transient time. After the system reaches quasi-steady state, temperature and heat flow estimated from all three solutions are in very good agreement. The analysis of transient fluid properties and mass flow rates revealed that constant fluid property model cannot accurately estimate the pressure loss for the system. The newly proposed fully analytical solution is applied in an economic analysis problem for calculating the optimal insulation thickness and mass flow rate to minimize the cost of generated power.

Suggested Citation

  • Tang, Hewei & Xu, Boyue & Hasan, A. Rashid & Sun, Zhuang & Killough, John, 2019. "Modeling wellbore heat exchangers: Fully numerical to fully analytical solutions," Renewable Energy, Elsevier, vol. 133(C), pages 1124-1135.
    • Handle: RePEc:eee:renene:v:133:y:2019:i:c:p:1124-1135
    DOI: 10.1016/j.renene.2018.10.094
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    5. Zhang, Jun, 2023. "Performance of high temperature steam injection in horizontal wells of heavy oil reservoirs," Energy, Elsevier, vol. 282(C).
    6. Hu, Xincheng & Banks, Jonathan & Guo, Yunting & Huang, Guangping & Liu, Wei Victor, 2021. "Effects of temperature-dependent property variations on the output capacity prediction of a deep coaxial borehole heat exchanger," Renewable Energy, Elsevier, vol. 165(P1), pages 334-349.
    7. 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.
    8. Pokhrel, Sajjan & Sasmito, Agus P. & Sainoki, Atsushi & Tosha, Toshiyuki & Tanaka, Tatsuya & Nagai, Chiaki & Ghoreishi-Madiseh, Seyed Ali, 2022. "Field-scale experimental and numerical analysis of a downhole coaxial heat exchanger for geothermal energy production," Renewable Energy, Elsevier, vol. 182(C), pages 521-535.
    9. Hu, Xincheng & Banks, Jonathan & Guo, Yunting & Liu, Wei Victor, 2021. "Retrofitting abandoned petroleum wells as doublet deep borehole heat exchangers for geothermal energy production—a numerical investigation," Renewable Energy, Elsevier, vol. 176(C), pages 115-134.

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