Keynote - Geologically Consistent History Matching Using the Ensemble based Methods

The ensemble-based data assimilation methods have shown great potential for automatic history matching after being introduced to petroleum industry a decade ago. Over the decade, this family of methods has evolved from the initial method known as the ensemble Kalman filter to the iterative ensemble smoother (perhaps the most promising one to date for history matching). The updating scheme of the ensemble-based methods relies on the covariance, which is ideal for model parameters that are typically assumed Gaussian, i.e. log transformed horizontal permeability (log-permx) and porosity for a given facies type. The geological models for most reservoirs now typically have multiple facies types, each with distinct petrophysical properties. In this case, the joint distribution of log-permx over the entire grid is no longer multi-variant Gaussian. If the gridblock log-permx is directly updated in the ensemble-based methods, facies boundaries are smeared out, and often the updated log-permx shows values that are outside of the normal range. In order to maintain geological realism of updated models and increase their predictability, different transformation and parameterization methods have been used with the ensemble-based data assimilation methods to account for the presence of multiple facies types in the model. In this talk, I will review these methods with examples and discuss the advantage and limitation of each method.