History matching of facies distribution with varying mean lengths or different principle correlation orientations

The reservoir rock usually consists of several distinct facies. And, due to the different formation environments, the mean length of each facies could be regionally varying inside a layer or between different layers and the principle correlation orientations could be different between different facies. In this study, we investigate the history matching problem of facies distribution with varying mean lengths or different principle correlation orientations. The reparameterization scheme proposed by Chang et al. (2010) is adopted here to parameterize the facies distribution. Here we mainly investigate the establishment of the representing node system for the complex facies distribution considered and test its sensitivity. For the cases with isotropic correlation but regionally varying mean lengths, we propose a spatially non-uniform representing node system to suitably capture the regional information. For the cases with different principle correlation orientations, we propose a multiple representing node systems to suitably preserve the characteristic of each facies. Through the reparameterization, the level set function values generated for the representing nodes are the model parameters of the Ensemble Kalman filter (EnKF) and then be updated in the data assimilation process. Three synthetic cases are set up to test the performance of the proposed method, and the numerical results show that the main features of the reference fields can be captured by the realizations or the probabilistic map. The proposed method is shown to be flexible for the history matching problem of facies distribution with varying mean lengths or different principle correlation orientations.