Optimization and Engineering

, Volume 16, Issue 2, pp 441–481

Adjoint-based surrogate optimization of oil reservoir water flooding

• Bjarne Foss
Article

Abstract

Maximizing economical asset of oil reservoirs is a simulation-based optimization involving large-scale simulation models. In this work we propose the use of reduced-order models for solving optimization problems in oil reservoir simulation using a Lagrangian barrier method for the treatment of nonlinear inequality constraints. The optimization with reduced-order models is done by employing a trust-region proper orthogonal decomposition (TRPOD) algorithm. In addition to the POD method, we also build a reduced-order model based on a discrete empirical interpolation method. In the algorithm, the first-order gradient of the objective function is computed by using the adjoint method, while the inverse of the second-order gradient is approximated using the BFGS method. The reduced-order models involve both the forward (state) and backward (adjoint) equations. Three optimization case examples in production optimization of oil reservoirs are used to study the method. They show that the TRPOD method works efficiently while simultaneously honoring the nonlinear constraints.

Keywords

Model order reduction Adjoint method Nonlinear constraints Production optimization Oil reservoirs

Mathematics Subject Classification

MSC 90C30 MSC 49M37 MSC 49J20

Notes

Acknowledgments

The authors gratefully acknowledge support from the Integrated Operation Centers at NTNU (www.iocenter.no). The authors would also like to thank the anonymous referees for their valuable input.

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Authors and Affiliations

1. 1.Department of EngineeringCybernetics Norwegian University Science and Technology (NTNU)TrondheimNorway
2. 2.Department of Applied MathematicsSINTEF ICTOsloNorway