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:
-
[2];
[2]
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
- Politecnico di Milano (Italy). Dipartimento di Ingegneria Civile e Ambientale
- Publication Date:
- Research Org.:
- Pacific Northwest National Laboratory (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. https://doi.org/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. https://doi.org/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 = {Mon Oct 16 00:00:00 EDT 2017},
month = {Mon Oct 16 00:00:00 EDT 2017}
}
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