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In this work, we develop and apply a general methodology for optimal closed-loop field development (CLFD) under geological uncertainty. CLFD involves three major steps: optimizing the field-development plan on the basis of current geological knowledge; drilling new wells, and collecting hard data and production data; and updating multiple geological models on the basis of all the available data. In the optimization step, the number, type, locations, and controls for new wells (and future controls for existing wells) are optimized with a hybrid particle swarm optimization-mesh adaptive direct search algorithm. The objective here is to maximize expected (over multiple realizations) net present value (NPV) of the overall project. History matching is accomplished with an adjoint-gradient-based "randomized maximum likelihood" procedure. Because the CLFD history-matching component is fast relative to the optimization component, we generate a relatively large number of history-matched models. Optimization is then performed with a set of "representative" realizations selected from the full set of history-matched models. We introduce a systematic optimization with sample validation (OSV) procedure, in which the number of realizations used for optimization is increased if an appropriate validation criterion is not satisfied. The CLFD methodology is applied to 2D and 3D example cases. Results show that the use of CLFD increases the NPV for the "true" (synthetic) model by 10 to 70% relative to that achieved by optimizing over a large number of prior realizations. We also compare the results for CLFD with OSV to results that use a fixed number of geological realizations. These comparisons show that the use of too few realizations in the CLFD optimization step can result in lower true-model NPVs, whereas OSV provides a systematic approach for determining the proper number of realizations.

Summary A new methodology for the joint optimization of optimal economic project life (EPL) and time-varying well controls is introduced. The procedure enables the maximization of net present value (NPV) subject to satisfaction of a specified modified internal rate of return (MIRR). Knowledge of the economic project life enables the operator to plan for infill drilling or some other type of field development in the case that the lease/contract duration is longer than the optimal project life. This will enable NPV to be maximized, and the hurdle rate to be honored, over the entire duration of the lease. The optimization is formulated as a nested procedure in which economic project life is optimized in the outer loop, and the associated well settings [time-varying bottomhole pressures (BHPs) in the cases considered] are optimized in the inner loop. The inner-loop optimization is accomplished by use of an adjoint-gradient-based approach, while the outer-loop optimization entails an interpolation technique. The successful application of this framework for production optimization for 2D and 3D reservoir models under waterflood is demonstrated. The tradeoff between maximized NPV and rate of return is assessed, as is the impact of discount rate on optimal operations. In the second example, we illustrate the advantages of initiating a new project (that satisfies the hurdle rate) once the EPL is reached. Taken in total, the results in this paper demonstrate the importance of explicitly incorporating both NPV and rate of return in production-optimization formulations.