A new methodology for the joint optimization of economic project life 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. Use of this framework allows an operator to avoid situations where NPV continues to increase in time, but the late-time cash flows are negligible (in terms of an appropriate financial metric) relative to the capital invested in the project. 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 in the cases considered) are optimized in the inner loop. The inner-loop optimization is accomplished by use of an adjointgradient-based approach, while the outer-loop optimization entails an interpolation technique. We demonstrate the successful application of this framework for production optimization for two-and three-dimensional reservoir models under waterflood. The tradeoff between maximized NPV and rate of return is assessed, as is the impact of discount rate on optimal operations. We believe this to be the first production optimization formulation that explicitly incorporates both NPV and rate of return. As such, this approach may represent an alternative to existing treatments that entail the bi-objective optimization of long-and short-term NPV.

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