Generation of a Pareto front for a bi-objective water flooding optimization problem using approximate ensemble gradients

Rahul Fonseca, Albert C. Reynolds, Jan Dirk Jansen

Research output: Contribution to journalArticleScientificpeer-review

26 Citations (Scopus)
24 Downloads (Pure)


Conflicting objectives are frequently encountered in most real-world problems. When dealing with conflicting objectives, decision makers prefer to obtain a range of possible optimal solutions from which to choose. In theory, methods exists that can produce a range of possible solutions, some of which are “Pareto Optimal”. The application of these methods to solve bi-objective production optimization problems is increasing. A recent paper introduced a method to find points on the boundary of the objective function space by solving a constrained optimization problem using adjoint gradients. In this work, we investigate the applicability of using ensemble optimization (EnOpt) (which relies on approximate ensemble gradients instead of exact adjoint-based gradients) to generate points along a “Pareto” front with acceptable computational effort.. Moreover, we investigate the applicability of this approximate gradient technique to solve constrained optimization problems using the augmented Lagrangian method. Finally, we compare the performance of this bi-objective optimization method to a traditional weighted sum method for bi-objective water flooding optimization of two different synthetic reservoir models. The two objectives used in this work are, undiscounted (0%) net present value (NPV), representing long-term targets and highly discounted (25%) NPV, representing short-term operational targets. The controls are inflow control valve (ICV) settings over time for one model and water injection rate controls for the other. The effect of different starting points and the computational efficiency of the constrained optimization method are also investigated.
Original languageEnglish
Pages (from-to)249-260
Number of pages12
JournalJournal of Petroleum Science and Engineering
Issue numberNovember
Publication statusPublished - 9 Jun 2016


  • Water flooding
  • Bi-objective optimization
  • Pareto front
  • Ensemble optimization
  • Approximate gradient
  • Augmented Lagrangian


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