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Title: Direct Breakthrough Curve Prediction From Statistics of Heterogeneous Conductivity Fields

Abstract

In this paper, we present a methodology to predict the shape of solute breakthrough curves in heterogeneous aquifers at early times and/or under high degrees of heterogeneity, both cases in which the classical macrodispersion theory may not be applicable. The methodology relies on the observation that breakthrough curves in heterogeneous media are generally well described by lognormal distributions, and mean breakthrough times can be predicted analytically. The log-variance of solute arrival is thus sufficient to completely specify the breakthrough curves, and this is calibrated as a function of aquifer heterogeneity and dimensionless distance from a source plane by means of Monte Carlo analysis and statistical regression. Using the ensemble of simulated groundwater flow and solute transport realizations employed to calibrate the predictive regression, reliability estimates for the prediction are also developed. Additional theoretical contributions include heuristics for the time until an effective macrodispersion coefficient becomes applicable, and also an expression for its magnitude that applies in highly heterogeneous systems. Finally, it is seen that the results here represent a way to derive continuous time random walk transition distributions from physical considerations rather than from empirical field calibration.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [2]; ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. University of Tübingen (Germany)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1477644
Report Number(s):
LA-UR-16-22098
Journal ID: ISSN 0043-1397
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Water Resources Research
Additional Journal Information:
Journal Volume: 54; Journal Issue: 1; Journal ID: ISSN 0043-1397
Publisher:
American Geophysical Union (AGU)
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES; 97 MATHEMATICS AND COMPUTING; solute transport; heterogeneity; upscaling; predictive modeling; stochastic hydrogeology

Citation Formats

Hansen, Scott K., Haslauer, Claus P., Cirpka, Olaf A., and Vesselinov, Velimir Valentinov. Direct Breakthrough Curve Prediction From Statistics of Heterogeneous Conductivity Fields. United States: N. p., 2018. Web. doi:10.1002/2017WR020450.
Hansen, Scott K., Haslauer, Claus P., Cirpka, Olaf A., & Vesselinov, Velimir Valentinov. Direct Breakthrough Curve Prediction From Statistics of Heterogeneous Conductivity Fields. United States. doi:10.1002/2017WR020450.
Hansen, Scott K., Haslauer, Claus P., Cirpka, Olaf A., and Vesselinov, Velimir Valentinov. Thu . "Direct Breakthrough Curve Prediction From Statistics of Heterogeneous Conductivity Fields". United States. doi:10.1002/2017WR020450. https://www.osti.gov/servlets/purl/1477644.
@article{osti_1477644,
title = {Direct Breakthrough Curve Prediction From Statistics of Heterogeneous Conductivity Fields},
author = {Hansen, Scott K. and Haslauer, Claus P. and Cirpka, Olaf A. and Vesselinov, Velimir Valentinov},
abstractNote = {In this paper, we present a methodology to predict the shape of solute breakthrough curves in heterogeneous aquifers at early times and/or under high degrees of heterogeneity, both cases in which the classical macrodispersion theory may not be applicable. The methodology relies on the observation that breakthrough curves in heterogeneous media are generally well described by lognormal distributions, and mean breakthrough times can be predicted analytically. The log-variance of solute arrival is thus sufficient to completely specify the breakthrough curves, and this is calibrated as a function of aquifer heterogeneity and dimensionless distance from a source plane by means of Monte Carlo analysis and statistical regression. Using the ensemble of simulated groundwater flow and solute transport realizations employed to calibrate the predictive regression, reliability estimates for the prediction are also developed. Additional theoretical contributions include heuristics for the time until an effective macrodispersion coefficient becomes applicable, and also an expression for its magnitude that applies in highly heterogeneous systems. Finally, it is seen that the results here represent a way to derive continuous time random walk transition distributions from physical considerations rather than from empirical field calibration.},
doi = {10.1002/2017WR020450},
journal = {Water Resources Research},
issn = {0043-1397},
number = 1,
volume = 54,
place = {United States},
year = {2018},
month = {1}
}

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Free Publicly Available Full Text
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Cited by: 1 work
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Figures / Tables:

Figure 1. Figure 1.: Example realization of a single box in the case of σ2lnK = 4.

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