Well placement optimization with the covariance matrix adaptation evolution strategy and meta-models |
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Authors: | Zyed Bouzarkouna Didier Yu Ding Anne Auger |
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Institution: | 1. IFP Energies nouvelles, 1 & 4 avenue de Bois-Pr??au, 92852, Rueil-Malmaison Cedex, France 2. TAO Team, INRIA Saclay-?le-de-France, LRI, Paris-Sud University, 91405, Orsay Cedex, France
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Abstract: | The amount of hydrocarbon recovered can be considerably increased by finding optimal placement of non-conventional wells.
For that purpose, the use of optimization algorithms, where the objective function is evaluated using a reservoir simulator,
is needed. Furthermore, for complex reservoir geologies with high heterogeneities, the optimization problem requires algorithms
able to cope with the non-regularity of the objective function. In this paper, we propose an optimization methodology for
determining optimal well locations and trajectories based on the covariance matrix adaptation evolution strategy (CMA-ES)
which is recognized as one of the most powerful derivative-free optimizers for continuous optimization. In addition, to improve
the optimization procedure, two new techniques are proposed: (a) adaptive penalization with rejection in order to handle well
placement constraints and (b) incorporation of a meta-model, based on locally weighted regression, into CMA-ES, using an approximate
stochastic ranking procedure, in order to reduce the number of reservoir simulations required to evaluate the objective function.
The approach is applied to the PUNQ-S3 case and compared with a genetic algorithm (GA) incorporating the Genocop III technique
for handling constraints. To allow a fair comparison, both algorithms are used without parameter tuning on the problem, and
standard settings are used for the GA and default settings for CMA-ES. It is shown that our new approach outperforms the genetic
algorithm: It leads in general to both a higher net present value and a significant reduction in the number of reservoir simulations
needed to reach a good well configuration. Moreover, coupling CMA-ES with a meta-model leads to further improvement, which
was around 20% for the synthetic case in this study. |
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