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

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

Research output: Contribution to journalArticle

7 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)619-627
Number of pages9
JournalApplied Energy
Volume136
DOIs
Publication statusPublished - Dec 1 2014

Fingerprint

Splines
Markov chain
Computational efficiency
Markov processes
hydrocarbon reservoir
Granite
Heat conduction
Sensitivity analysis
Program processors
heat transfer
sensitivity analysis
Monte Carlo methods
granite
Hydrocarbons
inversion
method
Sampling
Heat transfer
mountain
sampling

Keywords

  • Geothermal prospect
  • Inversion
  • Sensitivity
  • Surrogate
  • Uncertainty

ASJC Scopus subject areas

  • Energy(all)
  • Civil and Structural Engineering

Cite this

An efficient Bayesian inversion of a geothermal prospect using a multivariate adaptive regression spline method. / Chen, Mingjie; Tompson, Andrew F B; Mellors, Robert J.; Ramirez, Abelardo L.; Dyer, Kathleen M.; Yang, Xianjin; Wagoner, Jeffrey L.

In: Applied Energy, Vol. 136, 01.12.2014, p. 619-627.

Research output: Contribution to journalArticle

Chen, Mingjie ; Tompson, Andrew F B ; Mellors, Robert J. ; Ramirez, Abelardo L. ; Dyer, Kathleen M. ; Yang, Xianjin ; Wagoner, Jeffrey L. / An efficient Bayesian inversion of a geothermal prospect using a multivariate adaptive regression spline method. In: Applied Energy. 2014 ; Vol. 136. pp. 619-627.
@article{5e726caf239f4a3f869eef8e8cd74c61,
title = "An efficient Bayesian inversion of a geothermal prospect using a multivariate adaptive regression spline method",
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.",
keywords = "Geothermal prospect, Inversion, Sensitivity, Surrogate, Uncertainty",
author = "Mingjie Chen and Tompson, {Andrew F B} and Mellors, {Robert J.} and Ramirez, {Abelardo L.} and Dyer, {Kathleen M.} and Xianjin Yang and Wagoner, {Jeffrey L.}",
year = "2014",
month = "12",
day = "1",
doi = "10.1016/j.apenergy.2014.09.063",
language = "English",
volume = "136",
pages = "619--627",
journal = "Applied Energy",
issn = "0306-2619",
publisher = "Elsevier BV",

}

TY - JOUR

T1 - An efficient Bayesian inversion of a geothermal prospect using a multivariate adaptive regression spline method

AU - Chen, Mingjie

AU - Tompson, Andrew F B

AU - Mellors, Robert J.

AU - Ramirez, Abelardo L.

AU - Dyer, Kathleen M.

AU - Yang, Xianjin

AU - Wagoner, Jeffrey L.

PY - 2014/12/1

Y1 - 2014/12/1

N2 - 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.

AB - 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.

KW - Geothermal prospect

KW - Inversion

KW - Sensitivity

KW - Surrogate

KW - Uncertainty

UR - http://www.scopus.com/inward/record.url?scp=84908550466&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84908550466&partnerID=8YFLogxK

U2 - 10.1016/j.apenergy.2014.09.063

DO - 10.1016/j.apenergy.2014.09.063

M3 - Article

VL - 136

SP - 619

EP - 627

JO - Applied Energy

JF - Applied Energy

SN - 0306-2619

ER -