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

Tartakovsky, Alexandre M.; Panzeri, M.; Tartakovsky, G. D.; Guadagnini, A.

doi:10.1002/2017WR020905

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

Journal Article · Mon Oct 16 04:00:00 EDT 2017 · Water Resources Research

DOI:https://doi.org/10.1002/2017WR020905· OSTI ID:1430446

Tartakovsky, Alexandre M. ^[1]; ^[2]; Tartakovsky, G. D. ^[1]; ^[2]

Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Politecnico di Milano (Italy). Dipartimento di Ingegneria Civile e Ambientale

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.

View Accepted Manuscript (DOE)

Research Organization:: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-76RL01830

OSTI ID:: 1430446

Alternate ID(s):: OSTI ID: 1464339

Report Number(s):: PNNL-SA--114624; KJ0401000

Journal Information:: Water Resources Research, Journal Name: Water Resources Research Journal Issue: 11 Vol. 53; ISSN 0043-1397

Publisher:: American Geophysical Union (AGU)Copyright Statement

Country of Publication:: United States

Language:: English

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