@article{f89d4479c43e40fd82f3003a596a943b,
title = "Uncertainty Quantification in Scale-Dependent Models of Flow in Porous Media",
abstract = "Equations governing flow and transport in randomly heterogeneous porous media are stochastic and scale dependent. In the moment equation (ME) method, exact deterministic equations for the leading moments of state variables are obtained at the same support scale as the governing equations. Computable approximations of the MEs can be derived via perturbation expansion in orders of the standard deviation of the random model parameters. As such, their convergence is guaranteed only for standard deviation smaller than one. Here, we consider steady-state saturated flow in a porous medium with random second-order stationary conductivity field. We show it is possible to identify a support scale η *, where the typically employed approximate formulations of MEs yield accurate (statistical) moments of a target state variable. Therefore, at support scale η * and larger, MEs present an attractive alternative to slowly convergent Monte Carlo (MC) methods whenever lead-order statistical moments of a target state variable are needed. We also demonstrate that a surrogate model for statistical moments can be constructed from MC simulations at larger support scales and be used to accurately estimate moments at smaller scales, where MC simulations are expensive and the ME method is not applicable.",
keywords = "flow in porous media, randomness, scale dependence, uncertainty quantification",
author = "Tartakovsky, {A. M.} and M. Panzeri and Tartakovsky, {G. D.} and A. Guadagnini",
note = "Funding Information: Received 6 APR 2017 Accepted 10 OCT 2017 Accepted article online 16 OCT 2017 Published online 19 NOV 2017 VC 2017. American Geophysical Union. All Rights Reserved. This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05–76RL01830 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or repro duce the published form of this manu script, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of feder ally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe- public-access-plan). Funding Information: Research at Pacific Northwest National Laboratory (PNNL) was supported by the U.S. Department of Energy (DOE) Office of Advanced Scientific Computing Research (ASCR) as part of the Early Career Award {\textquoteleft}{\textquoteleft}New Dimension Reduction Methods and Scalable Algorithms for Multiscale Nonlinear Phenomena{\textquoteright}{\textquoteright} and DOE{\textquoteright}s Office of Biological and Environmental Research (BER) through the PNNL Subsurface Biogeochemical Research Scientific Focus Area project. Funding from MIUR (Italian ministry of Education, University and Research, Water JPI, WaterWorks 2014, Project: WE-NEED-Water NEEDs, availability, quality and sustainability) and from the European Union{\textquoteright}s Horizon 2020 Research and Innovation programme (Project {\textquoteleft}{\textquoteleft}Furthering the knowledge Base for Reducing the Environmental Footprint of Shale Gas Development{\textquoteright}{\textquoteright} FRACRISK - Grant Agreement No. 640979) are also acknowledged. The manuscript data can be accessed at https://sbrsfa.velo.pnnl.gov/datasets/ ?UUID5bc98365f-d106-423b-ae35- 27606ded8498. PNNL is operated by Battelle for the DOE under Contract DE-AC05–76RL01830. Publisher Copyright: {\textcopyright} 2017. American Geophysical Union. All Rights Reserved.",
year = "2017",
month = nov,
doi = "10.1002/2017WR020905",
language = "English (US)",
volume = "53",
pages = "9392--9401",
journal = "Water Resources Research",
issn = "0043-1397",
publisher = "American Geophysical Union",
number = "11",
}