Reservoir uncertainty tolerant, proactive control of intelligent wells

Intelligent wells (I-wells) provide layer-by-layer production and injection control. This flow control flexibility relies on the real-time operation of multiple, downhole interval control valves (ICVs) installed across the well completion intervals. Proactive control of I-wells, with its ambition of creating an optimal, operational strategy of ICVs over the full well lifetime, is a high-dimensional optimization problem with a computationally demanding and uncertain objective function based on one or more simulated reservoir model(s). This paper illustrates how a stochastic search algorithm based on the simultaneous perturbation stochastic approximation (SPSA) coupled with a utility function approach to define an objective function to account for the uncertainty in the reservoir's description can efficiently solve the proactive, I-well control problem. The utility function accounts for both the expectation and variance of the net present value (NPV) by modifying the objective function to consider multiple reservoir model realizations. Simultaneous optimization of full ensemble of model realizations is prohibitively expensive. By contrast, choosing a small ensemble of model realizations is computationally less demanding, but the small ensemble has to be itself selected. We introduce the use of k-means clustering for selecting a representative ensemble of model realizations that performs in an equivalent manner to all available realizations. A distance measure, tailored to the proactive optimization application, is used to define the similarity/dissimilarity of the different realizations which is then employed to perform the clustering. Moreover, we show that this robust proactive optimization process can either focus on the specific objective of increasing the mean or of reducing the variance (this is achieved via adjustable weights in the utility function). The relative importance of these conflicting objectives has to be taken into account during the model realization selection process to ensure the near-global success of the obtained control scenario. The proposed robust optimization framework has been tested on a representative test case (PUNQ-S3). This is a small field developed with an intelligent producer in which the uncertainty in the model has been quantified by several geological realizations. Our results demonstrate the computational efficiency of employing an ensemble of systematically selected realizations rather than the traditional methods that rely on either a single model realization or a randomly selected ensemble of realizations. Our results show the success of the developed framework in identifying control scenarios that correspond to an acceptable improvement in the expected added value at a controlled risk level while substantially reducing the computation time compared to using full ensemble of model realizations.