Smart fields can provide enhanced oil recovery through the combined use of optimization and data assimilation. In this paper, we focus on the dynamic optimization of injection and production rates during waterflooding. In particular, we use optimal control theory in order to find an optimal well management strategy over the life of the reservoir that maximizes an objective function (e.g. recovery or net present value). Optimal control requires the determination of a potentially large number of (groups of) well rates for a potentially large number of time periods. However, the optimal number of well groups and time steps is not known a-priori. Moreover, taking these numbers too large slows down the optimization process and increases the chance of achieving a sub-optimal solution. We investigated the use of multi-scale regularization methods to achieve grouping of the control settings of the wells in both space and time. Starting out with a very coarse grouping, the resolution is subsequently refined during the optimization. The regularization is adaptive in that the multi-scale parameterization is chosen based on the gradients of the objective function. Results for the numerical examples studied indicate that the regularization may lead to significantly different optimum strategies, but may result in a similar cumulative oil production.

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