Ensemble-based history matching methods have received great attention in reservoir engineering. In real applications, small ensembles are often used in reservoir simulations to reduce the computational costs. A small ensemble size may lead to ensemble collapse, a phenomenon in which the spread of the ensemble of history-matched reservoir models becomes extremely small. Ensemble collapse is not desired for an ensemble-based history matching method, because it will not only deteriorate the capacity in uncertainty quantification, but also force the ensemble-based method to stop updating reservoir models later on. In practice, distance-based localization is thus introduced to prevent ensemble collapse. Distance-based localization works well in many problems. However, one prerequisite in using distance-based localization is that the observations have associated physical locations. In certain circumstances with complex observations, this may not be true, and it thus becomes changeling to apply distance-based localization.
In this work, we propose a data driven adaptive localization scheme that does not reply on the physical locations of the observations. Instead, we use the spatial distributions of the correlations between model variables and the corresponding simulated observations. In the course of history matching, we update model variables by only using the observations that have relatively high correlations with them, while excluding those that have relatively low correlations.
We demonstrate the efficacy of the proposed localization scheme in one 2D and one 3D seismic history matching problems. In both problems, ensemble collapse is severe in the presence of large amounts of observational data, but distance-based localization is not applicable due to the lack of physical locations of the seismic data in use. In contrast, correlation-based localization not only works well to prevent ensemble collapse, and also renders good history matching results.