Ensemble Level Upscaling of 3D Well-driven Flow for Efficient Uncertainty Quantification

Upscaling is commonly applied to account for the effects of fine-scale permeability heterogeneity in coarse-scale simulation models. Ensemble level upscaling (EnLU) is a recently developed approach that aims to efficiently generate coarse-scale flow models capable of reproducing the ensemble statistics (e.g., P50, P10 and P90) of fine-scale flow predictions for multiple reservoir models. Often the most expensive part of standard coarsening procedures is the generation of upscaled two-phase flow functions (e.g., relative permeabilities). EnLU provides a means for efficiently generating these upscaled functions using stochastic simulation. This involves the use of coarse-block attributes that are both fast to compute and representative of the effects of fine-scale permeability on upscaled functions. In this paper, we establish improved attributes for use in EnLU, namely the coefficient of variation of the fine-scale single-phase velocity field (computed during computation of upscaled absolute permeability) and the integral range of the fine-scale permeability variogram. Geostatistical simulation methods, which account for spatial correlations of the statistically generated upscaled functions, are also applied. The overall methodology thus enables the efficient generation of coarse-scale flow models. The procedure is tested on 3D well-driven flow problems with different (Gaussian) permeability distributions and high fluid mobility ratios. EnLU is shown to capture the ensemble statistics of fine-scale flow results (flow rate and oil cut as a function of time) with similar accuracy to full flow-based methods but at a small fraction of the computational cost.