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Title: Uncertainty Quantification in Scale-Dependent Models of Flow in Porous Media

Abstract

Equations governing flow and transport in heterogeneous porous media are scale-dependent. We demonstrate that it is possible to identify a support scale $$\eta^*$$, such that the typically employed approximate formulations of Moment Equations (ME) yield accurate (statistical) moments of a target environmental state variable. Under these circumstances, the ME approach can be used as an alternative to the Monte Carlo (MC) method for Uncertainty Quantification in diverse fields of Earth and environmental sciences. MEs are directly satisfied by the leading moments of the quantities of interest and are defined on the same support scale as the governing stochastic partial differential equations (PDEs). Computable approximations of the otherwise exact MEs can be obtained through perturbation expansion of moments of the state variables in orders of the standard deviation of the random model parameters. As such, their convergence is guaranteed only for the standard deviation smaller than one. Furthermore, we demonstrate our approach in the context of steady-state groundwater flow in a porous medium with a spatially random hydraulic conductivity.

Authors:
 [1]; ORCiD logo [2];  [1]; ORCiD logo [2]
  1. Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
  2. Politecnico di Milano (Italy). Dipartimento di Ingegneria Civile e Ambientale
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1430446
Alternate Identifier(s):
OSTI ID: 1464339
Report Number(s):
[PNNL-SA-114624]
[Journal ID: ISSN 0043-1397; KJ0401000]
Grant/Contract Number:  
[AC05-76RL01830]
Resource Type:
Accepted Manuscript
Journal Name:
Water Resources Research
Additional Journal Information:
[ Journal Volume: 53; Journal Issue: 11]; Journal ID: ISSN 0043-1397
Publisher:
American Geophysical Union (AGU)
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; scale-depent analysis; uncertainty quantification; moment equations; flow in porous media; randomness; scale dependence

Citation Formats

Tartakovsky, Alexandre M., Panzeri, M., Tartakovsky, G. D., and Guadagnini, A. Uncertainty Quantification in Scale-Dependent Models of Flow in Porous Media. United States: N. p., 2017. Web. doi:10.1002/2017WR020905.
Tartakovsky, Alexandre M., Panzeri, M., Tartakovsky, G. D., & Guadagnini, A. Uncertainty Quantification in Scale-Dependent Models of Flow in Porous Media. United States. doi:10.1002/2017WR020905.
Tartakovsky, Alexandre M., Panzeri, M., Tartakovsky, G. D., and Guadagnini, A. Mon . "Uncertainty Quantification in Scale-Dependent Models of Flow in Porous Media". United States. doi:10.1002/2017WR020905. https://www.osti.gov/servlets/purl/1430446.
@article{osti_1430446,
title = {Uncertainty Quantification in Scale-Dependent Models of Flow in Porous Media},
author = {Tartakovsky, Alexandre M. and Panzeri, M. and Tartakovsky, G. D. and Guadagnini, A.},
abstractNote = {Equations governing flow and transport in heterogeneous porous media are scale-dependent. We demonstrate that it is possible to identify a support scale $\eta^*$, such that the typically employed approximate formulations of Moment Equations (ME) yield accurate (statistical) moments of a target environmental state variable. Under these circumstances, the ME approach can be used as an alternative to the Monte Carlo (MC) method for Uncertainty Quantification in diverse fields of Earth and environmental sciences. MEs are directly satisfied by the leading moments of the quantities of interest and are defined on the same support scale as the governing stochastic partial differential equations (PDEs). Computable approximations of the otherwise exact MEs can be obtained through perturbation expansion of moments of the state variables in orders of the standard deviation of the random model parameters. As such, their convergence is guaranteed only for the standard deviation smaller than one. Furthermore, we demonstrate our approach in the context of steady-state groundwater flow in a porous medium with a spatially random hydraulic conductivity.},
doi = {10.1002/2017WR020905},
journal = {Water Resources Research},
number = [11],
volume = [53],
place = {United States},
year = {2017},
month = {10}
}

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