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Title: Method of model reduction and multifidelity models for solute transport in random layered porous media

Abstract

This work presents a hierarchical model for solute transport in bounded layered porous media with random permeability. The model generalizes the Taylor-Aris dispersion theory to stochastic transport in random layered porous media with a known velocity covariance function. In the hierarchical model, we represent (random) concentration in terms of its cross-sectional average and a variation function. We derive a one-dimensional stochastic advection-dispersion-type equation for the average concentration and a stochastic Poisson equation for the variation function, as well as expressions for the effective velocity and dispersion coefficient. We observe that velocity fluctuations enhance dispersion in a non-monotonic fashion: the dispersion initially increases with correlation length λ, reaches a maximum, and decreases to zero at infinity. Maximum enhancement can be obtained at the correlation length about 0.25 the size of the porous media perpendicular to flow.

Authors:
;
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1422346
Report Number(s):
PNNL-SA-119187
Journal ID: ISSN 2470-0045; PLEEE8
DOE Contract Number:  
AC05-76RL01830
Resource Type:
Journal Article
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 96; Journal Issue: 3; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
stochastic PDE; model reduction; advection; solute transport; porous media

Citation Formats

Xu, Zhijie, and Tartakovsky, Alexandre M. Method of model reduction and multifidelity models for solute transport in random layered porous media. United States: N. p., 2017. Web. doi:10.1103/PhysRevE.96.033314.
Xu, Zhijie, & Tartakovsky, Alexandre M. Method of model reduction and multifidelity models for solute transport in random layered porous media. United States. doi:10.1103/PhysRevE.96.033314.
Xu, Zhijie, and Tartakovsky, Alexandre M. Fri . "Method of model reduction and multifidelity models for solute transport in random layered porous media". United States. doi:10.1103/PhysRevE.96.033314.
@article{osti_1422346,
title = {Method of model reduction and multifidelity models for solute transport in random layered porous media},
author = {Xu, Zhijie and Tartakovsky, Alexandre M.},
abstractNote = {This work presents a hierarchical model for solute transport in bounded layered porous media with random permeability. The model generalizes the Taylor-Aris dispersion theory to stochastic transport in random layered porous media with a known velocity covariance function. In the hierarchical model, we represent (random) concentration in terms of its cross-sectional average and a variation function. We derive a one-dimensional stochastic advection-dispersion-type equation for the average concentration and a stochastic Poisson equation for the variation function, as well as expressions for the effective velocity and dispersion coefficient. We observe that velocity fluctuations enhance dispersion in a non-monotonic fashion: the dispersion initially increases with correlation length λ, reaches a maximum, and decreases to zero at infinity. Maximum enhancement can be obtained at the correlation length about 0.25 the size of the porous media perpendicular to flow.},
doi = {10.1103/PhysRevE.96.033314},
journal = {Physical Review E},
issn = {2470-0045},
number = 3,
volume = 96,
place = {United States},
year = {2017},
month = {9}
}