Using Evolution Strategy with Meta-models for Well Placement Optimization

Optimum implementation of non-conventional wells allows us to increase considerably hydrocarbon recovery. By considering the high drilling cost and the potential improvement in well productivity, well placement decision is an important issue in field development. Considering complex reservoir geology and high reservoir heterogeneities, stochastic optimization methods are the most suitable approaches for optimum well placement. This paper proposes an optimization methodology to determine optimal well location and trajectory based upon the Covariance Matrix Adaptation - Evolution Strategy (CMA-ES) which is a variant of Evolution Strategies recognized as one of the most powerful derivative-free optimizers for continuous optimization. To improve the optimization procedure, two new techniques are investigated: (1). Adaptive penalization with rejection is developed to handle well placement constraints. (2). A meta-model, based on locally weighted regression, is incorporated into CMA-ES using an approximate ranking procedure. Therefore, we can reduce the number of reservoir simulations, which are computationally expensive. Several examples are presented. Our new approach is compared with a Genetic Algorithm incorporating the Genocop III technique. It is shown that our approach outperforms the genetic algorithm: it leads in general to both a higher NPV and a significant reduction of the number of reservoir simulations.

[1]  Petros Koumoutsakos,et al.  Local Meta-models for Optimization Using Evolution Strategies , 2006, PPSN.

[2]  Roland N. Horne,et al.  Uncertainty Assessment of Well-Placement Optimization , 2004 .

[3]  Jan Dirk Jansen,et al.  Adjoint-Based Well-Placement Optimization Under Production Constraints , 2008 .

[4]  Z. Michalewicz,et al.  Genocop III: a co-evolutionary algorithm for numerical optimization problems with nonlinear constraints , 1995, Proceedings of 1995 IEEE International Conference on Evolutionary Computation.

[5]  Nikolaus Hansen,et al.  Evaluating the CMA Evolution Strategy on Multimodal Test Functions , 2004, PPSN.

[6]  Zbigniew Michalewicz,et al.  Evolutionary algorithms for constrained engineering problems , 1996, Computers & Industrial Engineering.

[7]  Roland N. Horne,et al.  Optimization of Well Placement , 2000 .

[8]  Petros Koumoutsakos,et al.  A Method for Handling Uncertainty in Evolutionary Optimization With an Application to Feedback Control of Combustion , 2009, IEEE Transactions on Evolutionary Computation.

[9]  Wen H. Chen,et al.  Efficient Well Placement Optimization with Gradient-based Algorithms and Adjoint Models , 2008 .

[10]  Anne Auger,et al.  Comparing results of 31 algorithms from the black-box optimization benchmarking BBOB-2009 , 2010, GECCO '10.

[11]  L. Durlofsky,et al.  Optimization of nonconventional wells under uncertainty using statistical proxies , 2006 .

[12]  Roland N. Horne,et al.  Optimization of Well Placement in a Gulf of Mexico Waterflooding Project , 2002 .

[13]  Guillermo Montes,et al.  The Use of Genetic Algorithms in Well Placement Optimization , 2001 .

[14]  Anne Auger,et al.  Investigating the Local-Meta-Model CMA-ES for Large Population Sizes , 2010, EvoApplications.

[15]  Dilza Szwarcman,et al.  Well Placement Optimization Using a Genetic Algorithm With Nonlinear Constraints , 2009 .

[16]  Louis J. Durlofsky,et al.  Optimization of Nonconventional Well Type, Location and Trajectory , 2002 .