Model and economic uncertainties in balancing short-term and long-term objectives in water-flooding optimization.

Model-based optimization of oil production has a significant scope to increase ultimate recovery or financial life-cycle performance. The Net Present Value (NPV) objective in such an optimization framework, because of its nature, focuses on the long-term gains while the short-term production is not explicitly addressed. At the same time the achievable NPV is highly uncertain due to the limited knowledge of reservoir model parameters and varying economic conditions. Different (ad-hoc) methods have been proposed to introduce short-term considerations to balance short-term and long-term objectives in a model-based approach. In this work, we address the question whether through an explicit handling of model and economic uncertainties in NPV (robust) optimization, an appropriate balance between these economic objectives is naturally obtained. A set (ensemble) of possible realizations of the reservoir models is considered as a discretized approximation of the uncertainty space, while different oil price scenarios are considered to characterize the economic uncertainty. A gradient-based optimization procedure is used where the gradient information is computed by solving adjoint equations. A robust optimization framework with an average NPV with respect to the ensemble of models and the oil price scenarios is formulated and the NPV build-up over time is studied. As robust optimization (RO) does not attempt to reduce the sensitivity of the solution to uncertainty, a mean-variance optimization (MVO) approach is implemented which maximizes the average NPV and minimizes the variance of the NPV distribution. It is shown by simulation examples that with RO, the average NPV is increased compared to the reactive strategy, with both forms of uncertainty. However, an NPV build-up over time that is considerably slower than for a reactive strategy is obtained. A faster NPV build-up compared to RO is achieved in MVO by choosing different weightings on variance in the mean-variance objective, at the price of slightly compromising on the long-term gains.