Multipoint Statistical Characterization of Geologic Facies from Dynamic Data and Uncertain Training Images

Abstract

Abstract Discrete geologic features that contribute to preferential flowpaths or act as flow barriers are rarely amenable to second-order descriptions. Using a conceptual model or training image (TI), multipoint statistics (MPS) provides a systematic approach to describe the higher-order spatial statistics of discrete geologic features. Conditioning MPS facies realizations on flow data poses a challenging nonlinear inverse problem, primarily because of the nonlinear relation between facies properties and flow response measurements. Since MPS simulated facies imitate the spatial patterns in the TI, the quality of the generated facies depend on the reliability of the TI. However, given the uncertainty in the knowledge used to construct a TI, it is imperative to account for and represent the uncertainty in any given TI. One approach to account for TI uncertainty is to use multiple TIs to cover the expected range of structural variability in geologic facies. When several TIs are used to represent the uncertainty in the conceptual geologic model for a given field, flow data may be used to quantify the importance of different TIs. Here, we present a new method for adaptively sampling conditional facies from multiple uncertain TIs. By applying a fast flow-based clustering approach, we show that one can adaptively sample facies realizations from multiple TIs to honor the observed flow data. We apply a probability conditioning method (PCM) to invert the flow data to construct a facies probability map that can be included in drawing conditional facies realizations from each TI. We illustrate that the proposed adaptive sampling scheme can be used to weigh different TI s according to their performance in matching the flow data. We demonstrate the suitability of the proposed method using numerical experiments in fluvial formations where several TIs are used to account for the uncertainty in facies structural connectivity.