Evolutionary Proxy Tuning for Expensive Evaluation Functions: A Real-Case Application to Petroleum Reservoir Optimization
Decisions have to be made at every level of petroleum reservoir development. For many cases, optimal decisions are dependent on many nonlinearly correlated parameters, which makes intuitive judgement difficult. In such cases automated optimization is an option. Decisions should be based on the most relevant and accurate tools available. For the well placement problem a numerical simulator that computes the movement and interaction of subsurface fluids is the most accurate tool available to engineers. However, numerical simulation is most often computationally expensive making direct optimization prohibitive in terms of CPU requirements. To overcome the computational infeasibility, one can try to utilize mathematical proxies (surrogates) to replace numerical simulators. Although these proxies are very cheap to compute, they often require an initial investment in computation for calibration purposes. The magnitude of this initial computational investment is unclear. Also the calibration points, that are used to calibrate the proxy, are chosen synchronously; that is, the choice of a particular point to be simulated is independent of the others even though in real life the choice of later experiments would be based on the experience of earlier observations. In this study, an approach is proposed which employs direct optimization and proxy approaches simultaneously. The Genetic Algorithm (GA) forms the basis of the approach. The proxy ought to evolve intelligently as the GA iterates. This work investigated the design of a composite and adaptive algorithm, and tested its effectiveness in a range of artificial test problems and real field cases. Kriging was considered as the proxy. The polytope method was also utilized to help with local search. The composite algorithm was applied to the highly non-linear problem of an offshore Gulf of Mexico hydrocarbon reservoir development and significant improvement in efficiency was observed.
KeywordsGenetic algorithm Hybrid algorithm Expensive evaluation Proxy function Petroleum reservoir.
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