Ensemble-based multiobjective optimization of on/off control devices under geological uncertainty

Abstract

We consider robust ensemble-based (EnOpt) multiobjective production optimization of on/off inflow-control devices (ICDs) for a sector model inspired by a real-field case. The use of on/off valves as optimization variables leads to a discrete control problem. We propose a reparameterization of such discrete controls in terms of switching times (i.e., we optimize the time at which a particular valve is either open or closed). This transforms the discrete control problem into a continuous control problem that can be efficiently handled with the EnOpt method. In addition, this leads to a significant reduction in the number of controls that is expected to be beneficial for gradient quality when using approximate gradients. We consider an ensemble of sector models where the uncertainty is described by different permeability, porosity, net/gross ratios, and initial water-saturation fields. The controls are the ICD settings over time in the three horizontal injection wells, with approximately 15 ICDs per well. Different optimized strategies resulting from different initial strategies were compared. We achieved a mean 4.2% increase in expected net present value (NPV) at a 10% discount rate compared with a traditional pressure-maintenance strategy. Next, we performed a sequential biobjective optimization and achieved an increase of 9.2% in the secondary objective (25% discounted NPV to emphasize shortterm production gains) for a minimal decrease of 1% in the primary objective (0% discounted NPV to emphasize long-term recovery gains), as averaged over the 100 geological realizations. The work flow was repeated for alternative numbers of ICDs, showing that having fewer control options lowers the expected value for this particular case. The results demonstrate that ensemble-based optimization work flows are able to produce improved robust recovery strategies for realistic field-sector models against acceptable computational cost.