In this paper we present a comparison of three parameterizations of channelized reservoirs generated using multipoint geostatistics (MPS) in combination with a training image. In a previous study, we suggested estimating the facies probability fields from an ensemble generated with MPS and linked, marginally, the facies probability fields with the standard Gaussian variables by means of the normal score transform. We have parameterized the facies fields with random fields, marginally Gaussian, using the conditional mean of the Gaussian variables. This parameterization keeps a possible dependence structure inherited from the training image, but marginally the sampling from the Gaussian distribution is discrete and bi-modal. Here, we extend this parameterization in two directions. First, we do not take into account the dependence structure and parameterize by random sampling from the conditional distribution. The second idea is to draw samples from the conditional distribution, but using the same random seed for each grid cell within each ensemble member, but different random seeds across the ensemble members. This would preserve the dependence structure within each ensemble member while increasing the variability between the ensemble members. Both parameterizations have the property that, marginally, samples correctly from the standard Gaussian distribution. We compare the behavior of the parameterizations within a history matching process assimilating the production data. The comparison has two main directions: to prove the impact of the stochastic forcing on the history matching of geological properties and to prove the stochastic forcing on the predictive power of the models. We have used the iterative adaptive Gaussian mixture filter (IAGM) for history matching because the IAGM is suited for highly nonlinear problems and has a re-sampling step that allow us to use the already existing technique of re-sampling from the training image using updated probability fields. The re-sampling step is necessary to re-position the facies geometry, lost after a cycle of data assimilation.


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