Complex geology estimation using the iterative adaptive Gaussian mixture filter

In the past years, multi-point geostatistical simulation (MPS) geo-models have been used successfully to create realistic geological instances (facies fields). However, the conditioning of such geological deposits to production data is still a challenge, especially when an assisted history matching (AHM) model based on Bayesian inversion is used. This is hampered when we deal with complex geometry and topology and when the number of the facies types is greater than two. The estimation of the facies field is carried out combining two components: a parameterization of the facies field and a AHM method. In this study, we extend a parameterization of the facies fields, defined in a multidimensional normalized space by drawing from a marginal conditional Gaussian distribution. This is a generalization of a parameterization used in a previous study for channelized reservoirs and can be used for any type of geological layouts of the prior (in the MPS case, the training image). The parameterization ensures that the updates are always facies realization. However, traditional history matching methods tend to either destroy this topological structure or collapse into a single realization giving an unrealistic description of the uncertainty. To improve this issue, the iterative adaptive Gaussian mixture (IAGM) has been used as AHM method with a maximum of three iterations for the case studies. The method is tested for a 2D reservoir model, where four facies types are present, of which one exhibits channelized geometry. The topology is complex because two of the facies types cannot be in contact with each other. After assimilation of the production data, the IAGM was able to reduce the prior uncertainty toward an ensemble with realistic geological structure, with a good data match and predictive capacity.