Efficient Ensemble-Based Stochastic Gradient Methods for Optimization Under Geological Uncertainty

Jeong, Hoonyoung; Sun, Alexander Y.; Jeon, Jonghyeon; Min, Baehyun; Jeong, Daein

doi:10.3389/feart.2020.00108

Efficient Ensemble-Based Stochastic Gradient Methods for Optimization Under Geological Uncertainty

Journal Article · Wed May 27 00:00:00 EDT 2020 · Frontiers in Earth Science

DOI:https://doi.org/10.3389/feart.2020.00108· OSTI ID:1799860

Jeong, Hoonyoung ^[1]; Sun, Alexander Y. ^[2]; Jeon, Jonghyeon ^[3]; Min, Baehyun ^[4]; Jeong, Daein ^[5]

Seoul National Univ. (Korea, Republic of). Dept. of Energy Resources Engineering; Seoul National Univ. (Korea, Republic of). Research Institute of Energy and Resources; Seoul National Univ. (Korea, Republic of). Inst. of Engineering Research; OSTI
Univ. of Texas, Austin, TX (United States). Bureau of Economic Geology, Jackson School of Geosciences
Univ. of Texas, Austin, TX (United States). Dept. of Petroleum and Geosystems Engineering, Cockrell School of Engineering
Ewha Womans Univ., Seoul (South Korea). Dept. of Climate and Energy Ssytems Engineering
Schlumberger Software Integrated Solutions, Tokyo (Japan)

Ensemble-based stochastic gradient methods, such as the ensemble optimization (EnOpt) method, the simplex gradient (SG) method, and the stochastic simplex approximate gradient (StoSAG) method, approximate the gradient of an objective function using an ensemble of perturbed control vectors. These methods are increasingly used in solving reservoir optimization problems because they are not only easy to parallelize and couple with any simulator but also computationally more efficient than the conventional finite-difference method for gradient calculations. In this work, we show that EnOpt may fail to achieve sufficient improvement of the objective function when the differences between the objective function values of perturbed control variables and their ensemble mean are large. On the basis of the comparison of EnOpt and SG, we propose a hybrid gradient of EnOpt and SG to save on the computational cost of SG. We also suggest practical ways to reduce the computational cost of EnOpt and StoSAG by approximating the objective function values of unperturbed control variables using the values of perturbed ones. We first demonstrate the performance of our improved ensemble schemes using a benchmark problem. Results show that the proposed gradients saved about 30–50% of the computational cost of the same optimization by using EnOpt, SG, and StoSAG. As a real application, we consider pressure management in carbon storage reservoirs, for which brine extraction wells need to be optimally placed to reduce reservoir pressure buildup while maximizing the net present value. Results show that our improved schemes reduce the computational cost significantly.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE Office of Fossil Energy (FE)

Grant/Contract Number:: FE0026515

OSTI ID:: 1799860

Journal Information:: Frontiers in Earth Science, Journal Name: Frontiers in Earth Science Vol. 8; ISSN 2296-6463

Publisher:: Frontiers Research FoundationCopyright Statement

Country of Publication:: United States

Language:: English

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58 GEOSCIENCES
Geology
active pressure management
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hybrid simplex gradient
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stochastic gradient
stochastic simplex approximate gradient

Efficient Ensemble-Based Stochastic Gradient Methods for Optimization Under Geological Uncertainty

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