Multifidelity Framework For Uncertainty Quantification With Multiple Quantities Of Interest

Abstract

A systematic framework, involving flow simulation and model selection at many fidelity (resolution) levels, is introduced to accurately quantify the impact of geological uncertainty on multiple output quantities of interest (QoIs). The methodology considers large numbers of realizations (O(1000) in the case presented), though very few (O(10)) simulations are performed at the highest resolutions. We proceed from coarser to finer resolution levels, and at each stage simulation results are used to select a subset of realizations to simulate at the next (higher) fidelity level. Models are constructed at all resolution levels through upscaling of the underlying fine-scale realizations. A global transmissibility upscaling procedure is applied for this purpose. Approximate cumulative distribution functions (CDFs) are constructed for all QoIs considered. The QoI values themselves are always computed at the finest scale, but corresponding percentile values are determined using results at a "rank-preserving" (coarser) fidelity level. Detailed results are presented for oil-water flow in a channelized system. Simulations at seven different fidelity levels are used, and eight QoIs are evaluated. Results for the example considered demonstrate accurate reconstruction of fine-scale CDFs for all QoIs, with a speedup factor of about 18 relative to performing all simulations on the fine scale.