Ensemble-Level Upscaling for Efficient Estimation of Fine-Scale Production Statistics

Summary Upscaling is often needed in reservoir simulation to coarsen highly detailed geological descriptions. Most existing upscaling procedures aim to reproduce fine-scale results for a particular geological model (realization). In this work, we develop and test a new approach, ensemble-level upscaling, for efficiently generating up-scaled two-phase flow parameters (e.g., upscaled relative permeabilities) for multiple geological realizations. The ensemble-level upscaling approach aims to achieve agreement between the fine-and coarse-scale flow models at the ensemble level, rather than realization-by-realization agreement, as is the intent of existing upscaling techniques. For this purpose, flow-based upscaling calculations are combined with a statistical procedure based on a cluster analysis. This approach allows us to compute numerically the upscaled two-phase flow functions for only a small fraction of the coarse blocks. For the majority of blocks, these functions are estimated statistically on the basis of single-phase velocity information (attributes), determined when the upscaled single-phase parameters are calculated. The procedure is designed to maintain close correspondence between the cumulative distribution functions (CDFs) for the numerically computed and statistically estimated two-phase flow functions. We apply the method to 2D synthetic models of multiple realizations for uncertainty quantification. Models with different geological heterogeneity and fluid-mobility ratios are considered. It is shown that the method consistently corrects the biases evident in primitive coarse-scale predictions and can capture the ensemble statistics (e.g., P50, P10, P90) of the fine-scale results almost as accurately as the full flow-based upscaling procedures but with much less computational effort. The overall approach is flexible and can be used with any combination of upscaling procedures.