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An Adaptive Hierarchical Multiscale Algorithm for Estimation of Optimal Well Controls
- Diego F. Oliveira (University of Tulsa) | Albert Reynolds (University of Tulsa)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- October 2014
- Document Type
- Journal Paper
- 909 - 930
- 2014.Society of Petroleum Engineers
- 4.3.4 Scale, 1.7.5 Well Control
- Closed-loop reservoir management, Multiscale Optimization, Production Optimization
- 5 in the last 30 days
- 336 since 2007
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In determining the optimal well controls by maximizing net present value (NPV) for the remaining life of a reservoir, one typically defines the length of the control steps a priori. Moreover, these control steps are often the same for all wells. We provide a scale-splitting/merging method for adaptively selecting the number and the lengths of control steps as the overall optimization proceeds. We start with a reasonably small number of control steps and find the associated optimal controls by maximizing NPV. Both the adjoint-gradient-based steepest-ascent method and ensemble-based optimization (EnOpt) are considered as optimization algorithms. Because the correlation length used to generate the ad hoc covariance matrix indigenous to EnOpt affects the results, we implement a simple method to reduce the correlation length as the optimization proceeds. This enables EnOpt to generate a good approximation for well-control problems in which the optimal solution is bang-bang. The adaptive approach is applied to two example problems, and the results are compared with those obtained with a predetermined number of control steps.
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