Decision-theoretic sensitivity analysis for reservoir development under uncertainty using multilevel quasi-Monte Carlo methods
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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.
KeywordsDecision-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.
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.
- 1.Bickel, J.E., Gibson, R.L., McVay, D.A., Pickering, S., Waggoner, J.: Quantifying the reliability and value of 3D land seismic. SPE Res. Eval. Eng. 11, 832–841 (2008)Google Scholar
- 2.Bratvold, R.B., Bickel, J.E., Lohne, H.P.: Value of information in the oil and gas industry: past, present, and future. SPE Res. Eval. Eng. 12, 630–638 (2009)Google Scholar
- 4.Burkholder, D.L., Davis, B., Gundy, R.F.: Integral inequalities for convex functions of operators on martingales. In: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, vol. 2, pp. 223–240. University of California Press, Berkeley (1972)Google Scholar
- 9.Giles, M.B., Goda, T.: Decision-making under uncertainty: using MLMC for efficient estimation of EVPPI. arXiv:1708.05531 (2017)
- 17.Niederreiter, H.: Random number generation and quasi-Monte Carlo methods. CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 63, SIAM, Philadelphia (1992)Google Scholar
- 20.Owen, A.B.: Randomly permuted (t, m, s)-nets and (t, s)-sequences. In: Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (H. Niederreiter and P. J.-S. Shiue, Eds.), pp. 299–317, Springer, New York (1995)Google Scholar
- 23.Sloan, I.H., Joe, S.: Lattice methods for multiple integration. Oxford University Press, Oxford (1994)Google Scholar