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Model-based dynamic optimization of the water-flooding process in oil reservoirs is a computationally complex problem and suffers from high levels of uncertainty. A traditional way of quantifying uncertainty in robust water-flooding optimization is by considering an ensemble of uncertain model realizations. These models are generally not validated with data and the resulting robust optimization strategies are mostly offline or open-loop. The main focus of this work is to develop an adaptive or online robust optimization scheme using residual analysis as a major ingredient. The models in an ensemble are confronted with data and an adapted ensemble is formed with only those models that are not invalidated. As a next step, the robust optimization is again performed (i.e., updated/adjusted) with this adapted ensemble. The adapted ensemble gives a less conservative description of uncertainty and also reduces the high computational cost involved in robust optimization. Simulation example shows that an increase in the objective function value with a reduction of uncertainty on these values is obtained with the developed adaptive robust scheme compared to an open-loop offline robust strategy with the full ensemble and an adaptive scheme using Ensemble Kalman Filter (EnKF), which is one of the most common parameter estimation methods in reservoir simulations.

An adaptive robust optimization scheme for water-flooding optimization in oil reservoirs using residual analysis