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An efficient Bayesian inversion of a geothermal prospect using a multivariate adaptive regression spline method

Author

Listed:
  • Chen, Mingjie
  • Tompson, Andrew F.B.
  • Mellors, Robert J.
  • Ramirez, Abelardo L.
  • Dyer, Kathleen M.
  • Yang, Xianjin
  • Wagoner, Jeffrey L.

Abstract

In this study, an efficient Bayesian framework equipped with a multivariate adaptive regression spline (MARS) technique is developed to alleviate computational burdens encountered in a conventional Bayesian inversion of a geothermal prospect. Fast MARS models are developed from training dataset generated by CPU-intensive hydrothermal models and used as surrogate of high-fidelity physical models in Markov Chain Monte Carlo (MCMC) sampling. This Bayesian inference with MARS-enabled MCMC method is used to reduce prior estimates of uncertainty in structural or characteristic hydrothermal flow parameters of the model to posterior distributions. A geothermal prospect near Superstition Mountain in Imperial County of California in USA is used to illustrate the proposed framework and demonstrate the computational efficiency of MARS-based Bayesian inversion. The developed MARS models are also used to efficiently drive calculation of Sobol’ total sensitivity indices. Only top sensitive parameters are included in Bayesian inference to further improve the computational efficiency of inversion. Sensitivity analysis also confirms that water circulation through high permeable structures, rather than heat conduction through impermeable granite, is the primary heat transfer method. The presented framework is demonstrated an efficient tool to update knowledge of geothermal prospects by inversing field data. Although only thermal data is used in this study, other type of data, such as flow and transport observations, can be jointly used in this method for underground hydrocarbon reservoirs.

Suggested Citation

  • Chen, Mingjie & Tompson, Andrew F.B. & Mellors, Robert J. & Ramirez, Abelardo L. & Dyer, Kathleen M. & Yang, Xianjin & Wagoner, Jeffrey L., 2014. "An efficient Bayesian inversion of a geothermal prospect using a multivariate adaptive regression spline method," Applied Energy, Elsevier, vol. 136(C), pages 619-627.
    • Handle: RePEc:eee:appene:v:136:y:2014:i:c:p:619-627
    DOI: 10.1016/j.apenergy.2014.09.063
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    References listed on IDEAS

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    1. Regis, Rommel G. & Shoemaker, Christine A., 2007. "Parallel radial basis function methods for the global optimization of expensive functions," European Journal of Operational Research, Elsevier, vol. 182(2), pages 514-535, October.
    2. Cai, Baoping & Liu, Yonghong & Fan, Qian & Zhang, Yunwei & Liu, Zengkai & Yu, Shilin & Ji, Renjie, 2014. "Multi-source information fusion based fault diagnosis of ground-source heat pump using Bayesian network," Applied Energy, Elsevier, vol. 114(C), pages 1-9.
    3. Rommel G. Regis & Christine A. Shoemaker, 2007. "A Stochastic Radial Basis Function Method for the Global Optimization of Expensive Functions," INFORMS Journal on Computing, INFORMS, vol. 19(4), pages 497-509, November.
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    Cited by:

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    2. Anna Wachowicz-Pyzik & Anna Sowiżdżał & Leszek Pająk & Paweł Ziółkowski & Janusz Badur, 2020. "Assessment of the Effective Variants Leading to Higher Efficiency for the Geothermal Doublet, Using Numerical Analysis‒Case Study from Poland (Szczecin Trough)," Energies, MDPI, vol. 13(9), pages 1-20, May.
    3. Athens, Noah D. & Caers, Jef K., 2019. "A Monte Carlo-based framework for assessing the value of information and development risk in geothermal exploration," Applied Energy, Elsevier, vol. 256(C).
    4. Chen, Mingjie & Tompson, Andrew F.B. & Mellors, Robert J. & Abdalla, Osman, 2015. "An efficient optimization of well placement and control for a geothermal prospect under geological uncertainty," Applied Energy, Elsevier, vol. 137(C), pages 352-363.
    5. Chen, Siyuan & Zhang, Qi & Li, Hailong & Mclellan, Benjamin & Zhang, Tiantian & Tan, Zhizhou, 2019. "Investment decision on shallow geothermal heating & cooling based on compound options model: A case study of China," Applied Energy, Elsevier, vol. 254(C).

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