Computational Techniques for Closed–loop Reservoir Modeling with Application to a Realistic Reservoir

Abstract

Real-time model-based reservoir management requires efficient computational techniques for optimizing reservoir performance under uncertainty. A variety of algorithms addressing various aspects of this “closed-loop” methodology have been presented by various investigators, but substantial effort is still needed to make the entire process robust and efficient. In our recent work, we introduced an approximate feasible direction optimization algorithm for treating nonlinear path constraints (which are constraints such as maximum liquid production rate, which must be satisfied at every time step) and a new parameterization based on kernel principal component analysis (KPCA) for multipoint geostatistical models. The KPCA representation allows for the use of a gradient-based history-matching procedure that is able to maintain a higher degree of geological realism in the history-matched model. In this article, we combine these procedures with our general adjoint-based optimization technique to provide a full closed-loop capability. This integrated set of algorithms is then applied to a realistic field case. Specifically, we describe the key computational procedures and highlight the linkages required to provide the closed-loop capability. The example case considered is based on a Gulf of Mexico reservoir and involves three injection wells and four production wells operating under bottom hole pressure, total injection rate, and maximum water cut constraints. For this case, it is demonstrated that application of the closed-loop methodology provides a 25% increase in the net present value (NPV) over predictions for a realistic base case. This improvement is almost the same as that achieved using an open-loop approach, which is an idealized formulation in which the geological model is assumed to be known. These results demonstrate that the overall closed-loop procedure will indeed be applicable for practical cases with uncertain geology.