Joint estimation of facies boundaries and petrophysical properties in multi-facies channelized reservoirs through ensemble-based Kalman filter and level set parametrization

Ensemble-based assimilation methods are the most promising tools for dynamic characterization of reservoir models. However, because of inherent assumption of Gaussianity, these methods are not directly applicable to channelized reservoirs wherein the distribution of petrophysical properties is multimodal. Transformation of facies field to level set functions have been proposed to alleviate the problem of multimodality. Level set representation ensures that the estimated fields are facies realizations as well as no modification of the assimilation method is required. Moreover, due to the complexity of the history matching problem in the channelized reservoirs, most researchers conventionally assume that the petrophysical properties within each facies are constant and spatially uniform. In this study, an ensemble-based assimilation technique along with the level set parameterization are applied to estimate absolute and relative permeabilities jointly in the channelized reservoirs. That is, categorical facies variables together with petrophysical properties of the facies are simultaneously updated within the assimilation framework. To the best of our knowledge, the current study is the first one that investigates the simultaneous estimation of absolute permeability fields and relative permeability curves in the channelized reservoirs. The proposed method is justified by two different cases in a synthetic channelized reservoir. The first case is a two-facies reservoir, whereas the second case is more complex and contains four facies. Observation data include production rates of the producers, bottomhole pressure of the injectors, and facies types at the well locations. History matching process results in an accurate estimation of the channel structure together with monotonic reduction of the root-mean-squared error between the estimated and the true permeability field. Furthermore, relative permeability parameters are correctly estimated, history match is improved, and uncertainty of the model parameters is reduced.