A Distance Transform Method for History Matching of Discrete Geologic Facies Models

Abstract

Abstract Construction of predictive reservoir models involves subjective interpretation and interpolation of spatially limited data, often using imperfect modeling assumptions. Hence, the process can introduce significant uncertainty and bias into production predictions. In particular, the uncertainty associated with the facies distribution in complex geologic environments, such as fluvial channels, can be consequential for production forecasting and reservoir development planning. Conventional history matching techniques are mainly designed to update continuous reservoir properties, such as permeability and porosity distributions. As such, calibrating discrete facies against production history may require a parametrization approach to convert discrete facies to continuous parameters. In this paper, we present a distance transformation method for calibrating the distribution of discrete facies againts production data. Distance-based transforms are widely used in discrete image processing, where the discrete values in each image pixel are replaced with their distance (i.e., a continuous variable) to the nearest cell with a different value (i.e., facies boundary). The history matching is then performed by updating the continuous distance maps based on observed production data. Once the distances are updated, an inverse distance transform is applied to convert them back to discrete facies models. The distance transformation enables discrete facies updating with history matching techniques that are designed for continuous variables, while ensuring that the final solution remains discrete. A low-rank representation of the continuous distance maps with the truncated singular value decomposition (SVD) is also presented for problems in which large-scale facies connectivity is expected. In that case, the production data is used to update the low-rank SVD projection coefficients of the distance maps. The developed discrete transformation ensures that the solution of the facies model calibration problem remains discrete. Furthermore, the use of prior models and SVD parameterization help to preserve the connectivity in the geologic facies after dynamic data integration. Examples with two and three facies models are used to illustrate the application of the method and to evaluate it performance.