A Bayesian mixture-modeling approach for flow-conditioned multiple-point statistical facies simulation from uncertain training images

摘要

[1] Multiple-point statistics (MPS) provides a systematic approach for pattern-based simulation of complex discrete geologic objects from a conceptual training image (TI) as prior model. The TI contains the general shape, geometry, and connectivity structures of complex patterns and encodes the related higher-order spatial statistics of the expected features. Conditioning MPS simulated facies on flow data poses a challenging nonlinear inverse problem for estimating discrete parameter fields. Additionally, the pattern-imitating nature of MPS simulation implies that the simulated facies inherit the spatial structure of the features in the TI. Since TIs are constructed from uncertain geologic information and imperfect assumptions, the resulting simulated facies may fail to predict the correct flow and transport behavior in the subsurface environment. It is, therefore, prudent to account for the full range of structural variability in describing the geologic facies distribution by considering multiple TIs. Here, we present a Bayesian mixture model for adaptive and efficient sampling of conditional facies from multiple uncertain TIs. We partition the posterior distribution of facies into individual conditional densities of the TIs and estimate the corresponding mixture weights from the likelihood function for each TI. To implement the conditional sampling, we apply a recently developed ensemble Kalman filter (EnKF)-based probability conditioning method, whereby EnKF is used to invert the flow data and obtain a facies probability map (soft data) to guide conditional facies simulation from each TI. We demonstrate the suitability of the proposed Bayesian mixture-modeling approach using several numerical experiments in fluvial formations with uncertain orientation and structural connectivity.