Extended Framework for Multifidelity Uncertainty Quantification in Subsurface Flow Systems

Uncertainty quantification is often performed by simulating a large number (O(1000)) of
reservoir models, which can be very computationally expensive when the models are highly resolved.
In this study, a systematic framework is presented to reduce this computational cost by using
models at multiple levels of resolution. Coarsened models are constructed using
an accurate single-phase global transmissibility upscaling approach. The multifidelity framework
proceeds from coarser to finer models and selects subsets of models from the ensemble at
each step. Models are selected such that they approximately span the uncertainty space
for multiple quantities of interest. At the final step of the procedure, only a few (O(10))
simulations are performed at the finest scale. Percentiles are
estimated for these models using either a 'rank-preserving level' or an error model
to approximate cumulative distribution functions (CDFs) for all quantities of interest. Improvements
relative to a previous multifidelity framework, in terms of model selection and percentile assignment, are
introduced and validated. Detailed results are provided for a 2D channelized system, a 2D embedded discrete
fracture model (EDFM) system, and a 3D channelized system. Seven different fidelity levels are
considered, and CDFs for up to 18 quantities of interest are estimated. Results demonstrate that we achieve
generally accurate approximations for all CDFs, with speedups ranging from a factor of 5
to 24 relative to performing all simulations on the fine scale.