HJDS and PSO are simulator-nonintrusive algorithms that usually perform well in optimization for oil-field operations. In these problems, which have 120 and 40 well controls and include nonlinear constraints, we observe for PO reductions in computational cost (for solutions of comparable quality) of around 30% and 50% with respect to Hooke-Jeeves Direct Search (HJDS), which, in turn, outperforms Particle Swarm Optimization (PSO). PO is tested on two waterflooding problems built upon a synthetic model previously studied in well-control optimization literature. The optimal search may be finalized earlier than at the fourth stage whenever the solution obtained is of satisfactory quality. Nonlinear (operational) constraints are handled in PO with the filter method. The final and fourth stage aims at additional improvement resorting to direct optimization of the best solution from the previous stages. MM has solid theoretical foundations and leads to efficient optimization schemes in multiple engineering disciplines. In the third stage, the precision of the proxy model is iteratively improved and the enhanced surrogate model is re-optimized via Manifold Mapping (MM), a method that combines models with different levels of accuracy. This fact is supported by the good performance in this type of optimization problems of techniques that rely strongly on linearity assumptions, such as Trajectory Piecewise Linearization, a procedure that is not always applicable due to its simulator-intrusive nature. GBCs can be especially suited to problems where nonlinearities are not strong, as is the case often for well-control optimization. This proxy is based on Generalized Barycentric Coordinates (GBCs), a generalization of the concept of barycentric coordinates used within a triangle. Thereafter, in the second stage, a fast-to-evaluate proxy model is constructed with the points considered in the experimental design. The first stage of PO consists in a global exploration of the search space using design of experiments.
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In this paper we present Progressive Optimization (PO), a simulator-nonintrusive four-stage methodology to accelerate optimal search substantially in well-control applications. However, in many practical situations the optimization algorithms used are still computationally expensive. Well-control management is nowadays frequently approached by means of mathematical optimization.