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.