Abstract A common approach to dealing with uncertainty when optimizing the expected value of a cost function is to perform the optimization of controls over an ensemble by simulating the outcome of the controls on each model realization. For reservoir management or reservoir field development optimization, this approach is very expensive, however, as the cost of each simulation is high. In this paper, a “mean model” methodology is proposed that only requires optimization on a single model, even when the reservoir models in the ensemble are anisotropic at the reservoir scale. It is shown, however, that a tensor-valued mean model for the permeability field with effective relative permeability functions can be more suitable than a scalar mean model in this case. The effectiveness of the tensor mean-model approach is demonstrated for optimization of vertical and lateral well locations in a two-phase, three-dimensional reservoir model with 100 realizations of channelized geology.
Dean S. Oliver (2026) studied this question.