Distinguishing Signal from Noise in History Matching - Analysis of Ensemble Collapse on a Synthetic Data Set

Abstract

Underestimation of posterior parameter uncertainty is one of the main problems encountered when doing history matching using ensemble based methods. In history matching results with the partial or full ensembles collapse, it is very hard to distinguish updates due to spurious correlation with noise in the data from the actual updates attributed to information in the data. History matching of porosity and permeability based on well production data using the ensemble smoother with multiple data assimilation has been performed on a synthetic data set. The presence of ensemble collapse has been evaluated by different means: by looking at the stability of the update based on the starting ensemble, by adding dummy parameters to the update which do not affect the forward model, and by examining how well the data set used to generate the production data matches the posterior distributions of the parameters. Ensemble collapse can be avoided by increasing the number of ensembles. This is however a prohibitively expensive strategy for cases with a large number of history data. Localization methods have been proposed in the literature as a way to increase the ensemble spread and hence avoid collapse, by for example limiting the analysis update to regions of influence of the data, while at the same time keeping the number of ensembles low. A local analysis was performed to reduce the problems related to ensemble collapse. The results from the localized history matching produce a posterior distribution that better matches the original data set. Since our test data set is synthetic, we may perform measures of posterior uncertainty estimation by comparing with the true solution, with and without localization.