Efficient Closed-loop Production Optimization Under Uncertainty

Abstract

Abstract This work discusses a closed-loop approach for efficient real-time production optimization that consists of three key elements – adjoint models for efficient parameter and control gradient calculation, polynomial chaos expansions for efficient uncertainty propagation, and Karhunen-Loeve (K-L) expansions and Bayesian inversion theory for efficient real-time model updating (history-matching). The control gradients provided by the adjoint solution are used by a gradient-based optimization algorithm to determine optimal control settings, while the parameter gradients are used for model updating. Polynomial chaos expansions provide optimal encapsulation of information contained in the input random fields and output random variables. This approach allows the forward model to be used as a black box but is much faster than standard Monte Carlo techniques. The K-L representation allows for the direct application of adjoint techniques for history matching while assuring that the two-point geostatistics of the reservoir description are maintained. The benefits and efficiency of the overall closed-loop approach are demonstrated through real-time optimizations of net present value (NPV) for synthetic reservoirs under waterflood subject to production constraints and uncertain reservoir description. The closed-loop procedure is shown to provide a substantial improvement in NPV over the base case, and the results are seen to be very close to those obtained when the reservoir description is known apriori.