Indicator-based data assimilation with localization for updating models using limited ensemble size

Ensemble-based methods of data assimilation rely on the deduction of statistics from an ensemble of models to perform model updates. The reliability of the updates depend upon the size of ensemble being used. A modified version of indicator-based data assimilation (InDA) with localization, is presented for reliable assimilation of production data to update an ensemble of models, of limited size. This affords the benefits of InDA to handle the non-Gaussian distribution of the parameters and non-linear relationships between observed data and update parameters, while using a limited ensemble size to achieve reliable updates. The modified InDA method relies on a localization technique which limits the update of model parameters beyond a certain spatial lag away from observed data location, thus limiting the updates caused by spurious correlations which appear because of the limited size of the ensemble. The localization method weighs the information obtained from different observation data points based on their respective spatial distances to the location where updates are performed. Because of the localization scheme, the observations at larger distances from the update locations have smaller contributions to the final updates. This method can be used to reliably ascertain the residual uncertainty in model parameters, as sequential data assimilation proceeds. The knowledge of uncertainty can be used in the prediction of future state of the reservoir.