Quantifying the Uncertainty in the Facies Probability Cubes Using an Ensemble Kalman Filter Methodology

The work presented here introduces a new framework in the plurigaussian simulation context, which takes into account the uncertainty in the prior probability cubes. At the end of the assimilation process, we are able to offer besides an update of the facies fields, an update of the facies probability cubes. In order to achieve that, we extend the adaptive plurigaussian simulation methodology to work with multiple realizations of facies probability cubes and afterwards condition the facies fields to the production data. We generate an ensemble of facies fields by means of an ensemble of pairs of Gaussian fields. Each pair of Gaussian fields simulates a facies field from a different family of probability cubes. In the pluri-Gaussian methodology, the Gaussian fields represent the parameterization of the facies fields and are the parameters updated by the AHM process. The updated facies fields are generated with the updated values of the Gaussian fields. In addition, we are using the updated values of the Gaussian fields for reconstruction of the updated facies probability cubes. In our example, the ensemble of the prior facies probability cubes is created by perturbing a single realization with noise that is in correlation with a given prior uncertainty.