Computational Geosciences

, Volume 22, Issue 4, pp 1009–1020 | Cite as

Decision-theoretic sensitivity analysis for reservoir development under uncertainty using multilevel quasi-Monte Carlo methods

  • Takashi GodaEmail author
  • Daisuke Murakami
  • Kei Tanaka
  • Kozo Sato
Original paper


At various stages of petroleum reservoir development, we encounter a large degree of geological uncertainty under which a rational decision has to be made. In order to identify which parameter or group of parameters significantly affects the output of a decision model, we investigate decision-theoretic sensitivity analysis and its computational issues in this paper. In particular, we employ the so-called expected value of partial perfect information (EVPPI) as a sensitivity index and apply multilevel Monte Carlo (MLMC) methods to efficient estimation of EVPPI. In a recent paper by Giles and Goda, an antithetic MLMC estimator for EVPPI is proposed and its variance analysis is conducted under some assumptions on a decision model. In this paper, for an improvement on the performance of the MLMC estimator, we incorporate randomized quasi-Monte Carlo methods within the inner sampling, which results in an multilevel quasi-Monte Carlo (MLQMC) estimator. We apply both the antithetic MLMC and MLQMC estimators to a simple waterflooding decision problem under uncertainty on absolute permeability and relative permeability curves. Through numerical experiments, we compare the performances of the MLMC and MLQMC estimators and confirm a significant advantage of the MLQMC estimator.


Decision-theoretic sensitivity analysis Expected value of information Multilevel Monte Carlo Quasi-Monte Carlo 


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The authors would like to thank Jotaro Tomoeda, Eiji Fujisawa, Hirobumi Shimano, and Makoto Ogushi of JX NOEX for helpful discussions and comments, and CMG Ltd. for the software license. The first named author would like to thank Prof. Micheal B. Giles of the University of Oxford and Dr. Howard Thom of the University of Bristol for useful discussions.

Funding information

This work is financially supported by JX Nippon Oil and Gas Exploration Corporation (JX NOEX). The work of the first named author is supported by JSPS Grant-in-Aid for Young Scientists No.15K20964 and Arai Science and Technology Foundation.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of EngineeringUniversity of TokyoTokyoJapan

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