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Research Papers: Petroleum Engineering

Stochastic Simplex Approximate Gradient for Robust Life-Cycle Production Optimization: Applied to Brugge Field

[+] Author and Article Information
Bailian Chen

Computational Earth Science,
Los Alamos National Laboratory,
Los Alamos, NM 87544
e-mail: bailianchen@lanl.gov

Jianchun Xu

School of Petroleum Engineering,
China University of Petroleum (East China),
Qingdao, Shandong 266580, China
e-mail: 20170048@upc.edu.cn

1Corresponding authors.

Contributed by the Petroleum Division of ASME for publication in the Journal of Energy Resources Technology. Manuscript received May 17, 2018; final manuscript received March 12, 2019; published online April 4, 2019. Assoc. Editor: Fanhua Zeng.

J. Energy Resour. Technol 141(9), 092905 (Apr 04, 2019) (11 pages) Paper No: JERT-18-1350; doi: 10.1115/1.4043244 History: Received May 17, 2018; Accepted March 14, 2019

In oil and gas industry, production optimization is a viable technique to maximize the recovery or the net present value (NPV). Robust optimization is one type of production optimization techniques where the geological uncertainty of reservoir is considered. When well operating conditions, e.g., well flow rates settings of inflow control valves and bottom-hole pressures, are the optimization variables, ensemble-based optimization (EnOpt) is the most popular ensemble-based algorithm for the robust life-cycle production optimization. Recently, a superior algorithm, stochastic simplex approximate gradient (StoSAG), was proposed. Fonseca and co-workers (2016, A Stochastic Simplex Approximate Gradient (StoSAG) for Optimization Under Uncertainty, Int. J. Numer. Methods Eng., 109(13), pp. 1756–1776) provided a theoretical argument on the superiority of StoSAG over EnOpt. However, it has not drawn significant attention in the reservoir optimization community. The purpose of this study is to provide a refined theoretical discussion on why StoSAG is generally superior to EnOpt and to provide a reasonable example (Brugge field) where StoSAG generates estimates of optimal well operating conditions that give a life-cycle NPV significantly higher than the NPV obtained from EnOpt.

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Figures

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Fig. 1

The top structure of Brugge

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Fig. 2

The log-permeability distribution in the horizontal direction for realization 1. There are nine layers: L1, L2…, L9.

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Fig. 3

Four reservoir formations with their corresponding simulation model layers (i.e., layer 1 to layer 9) and the assigned ICVs (i.e., ICV 1, ICV 2, and ICV 3)

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Fig. 4

Expectation of NPV over the number of reservoir simulations for different search direction formulations: (a) initial guess 1 and (b) initial guess 3

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Fig. 5

Estimated BHP for production wells at different control steps calculated from different search direction formulations; units are psi; initial guess 2: (a) EnOpt, (b) f-StoSAG, (c) sf-StoSAG, (d) StoSAG, and (e) ss-StoSAG

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Fig. 6

Estimated rates for water injectors at different control steps computed from different search direction formulations; units are STB/day; initial guess 2: (a) EnOpt, (b) f-StoSAG, (c) sf-StoSAG, (d) StoSAG, and (e) ss-StoSAG

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Fig. 7

Estimated settings of ICV for all the producers at different perforated segments calculated from different search direction formulations on a scale from 0 (fully closed) to 1 (fully open); initial guess 2: (a) EnOpt, ICV 1, (b) EnOpt, ICV 2, (c) EnOpt, ICV 3, (d) f-StoSAG, ICV 1, (e) f-StoSAG, ICV 2, (f) f-StoSAG, ICV 3, (g) sf-StoSAG, ICV 1, (h) sf-StoSAG, ICV 2, and (i) sf-StoSAG, ICV 3

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Fig. 8

Remaining oil saturation distribution at years 7.5 and 15 calculated from EnOpt, sf-StoSAG, and ss-StoSAG; layer 6; initial guess 2: (a) initial, (b) EnOpt, 7.5 years, (c) sf-StoSAG, 7.5 years, (d) ss-StoSAG, 7.5 years, (e) EnOpt, 15 years, (f) sf-StoSAG, 15 years, and (g) ss-StoSAG, 15 years

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