Analysis of tracer tomography using temporal moments of tracer breakthrough curves

Junfeng Zhu, Xing Cai, Tian-Chyi J Yeh

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

Hydraulic/partitioning tracer tomography (HPTT) was recently developed by Yeh and Zhu [Yeh T-CJ, Zhu J. Hydraulic/partitioning tracer tomography for characterization of dense nonaqueous phase liquid source zones, Water Resour Res 2007;43:W06435. doi:10.1029/2006WR004877.] for estimating spatial distribution of dense nonaqueous phase liquids (DNAPLs) in the subsurface. Since discrete tracer concentration data are directly utilized for the estimation of DNAPLs, this approach solves the hyperbolic convection-dispersion equation. Solution to the convection-dispersion equation however demands fine temporal and spatial discretization, resulting in high computational cost for an HPTT analysis. In this work, we use temporal moments of tracer breakthrough curves instead of discrete concentration data to estimate DNAPL distribution. This approach solves time independent partial differential equations of the temporal moments, and therefore avoids solving the convection-dispersion equation using a time marching scheme, resulting in a dramatic reduction of computational cost. To reduce numerical oscillations associated with convection dominated transport problems such as in inter-well tracer tests, the approach uses a finite element solver adopting the streamline upwind Petrov-Galerkin method to calculate moments and sensitivities. We test the temporal moment approach through numerical simulations. Comparing the computational costs between utilizing moments and discrete concentrations, we find that temporal moments significantly reduce the computation time. We also find that tracer moment data collected through a tomographic survey alone are able to yield reasonable estimates of hydraulic conductivity, as indicated by a correlation of 0.588 between estimated and true hydraulic conductivity fields in the synthetic case study.

Original languageEnglish (US)
Pages (from-to)391-400
Number of pages10
JournalAdvances in Water Resources
Volume32
Issue number3
DOIs
StatePublished - Mar 2009

Fingerprint

breakthrough curve
tomography
tracer
nonaqueous phase liquid
convection
partitioning
hydraulics
hydraulic conductivity
cost
Galerkin method
analysis
oscillation
spatial distribution
simulation

Keywords

  • Hydraulic/tracer tomography
  • Parameter estimation
  • Source zone characterization
  • Temporal moments

ASJC Scopus subject areas

  • Water Science and Technology

Cite this

Analysis of tracer tomography using temporal moments of tracer breakthrough curves. / Zhu, Junfeng; Cai, Xing; Yeh, Tian-Chyi J.

In: Advances in Water Resources, Vol. 32, No. 3, 03.2009, p. 391-400.

Research output: Contribution to journalArticle

@article{6b5e26322f594b18a604afeac61563b4,
title = "Analysis of tracer tomography using temporal moments of tracer breakthrough curves",
abstract = "Hydraulic/partitioning tracer tomography (HPTT) was recently developed by Yeh and Zhu [Yeh T-CJ, Zhu J. Hydraulic/partitioning tracer tomography for characterization of dense nonaqueous phase liquid source zones, Water Resour Res 2007;43:W06435. doi:10.1029/2006WR004877.] for estimating spatial distribution of dense nonaqueous phase liquids (DNAPLs) in the subsurface. Since discrete tracer concentration data are directly utilized for the estimation of DNAPLs, this approach solves the hyperbolic convection-dispersion equation. Solution to the convection-dispersion equation however demands fine temporal and spatial discretization, resulting in high computational cost for an HPTT analysis. In this work, we use temporal moments of tracer breakthrough curves instead of discrete concentration data to estimate DNAPL distribution. This approach solves time independent partial differential equations of the temporal moments, and therefore avoids solving the convection-dispersion equation using a time marching scheme, resulting in a dramatic reduction of computational cost. To reduce numerical oscillations associated with convection dominated transport problems such as in inter-well tracer tests, the approach uses a finite element solver adopting the streamline upwind Petrov-Galerkin method to calculate moments and sensitivities. We test the temporal moment approach through numerical simulations. Comparing the computational costs between utilizing moments and discrete concentrations, we find that temporal moments significantly reduce the computation time. We also find that tracer moment data collected through a tomographic survey alone are able to yield reasonable estimates of hydraulic conductivity, as indicated by a correlation of 0.588 between estimated and true hydraulic conductivity fields in the synthetic case study.",
keywords = "Hydraulic/tracer tomography, Parameter estimation, Source zone characterization, Temporal moments",
author = "Junfeng Zhu and Xing Cai and Yeh, {Tian-Chyi J}",
year = "2009",
month = "3",
doi = "10.1016/j.advwatres.2008.12.001",
language = "English (US)",
volume = "32",
pages = "391--400",
journal = "Advances in Water Resources",
issn = "0309-1708",
publisher = "Elsevier Limited",
number = "3",

}

TY - JOUR

T1 - Analysis of tracer tomography using temporal moments of tracer breakthrough curves

AU - Zhu, Junfeng

AU - Cai, Xing

AU - Yeh, Tian-Chyi J

PY - 2009/3

Y1 - 2009/3

N2 - Hydraulic/partitioning tracer tomography (HPTT) was recently developed by Yeh and Zhu [Yeh T-CJ, Zhu J. Hydraulic/partitioning tracer tomography for characterization of dense nonaqueous phase liquid source zones, Water Resour Res 2007;43:W06435. doi:10.1029/2006WR004877.] for estimating spatial distribution of dense nonaqueous phase liquids (DNAPLs) in the subsurface. Since discrete tracer concentration data are directly utilized for the estimation of DNAPLs, this approach solves the hyperbolic convection-dispersion equation. Solution to the convection-dispersion equation however demands fine temporal and spatial discretization, resulting in high computational cost for an HPTT analysis. In this work, we use temporal moments of tracer breakthrough curves instead of discrete concentration data to estimate DNAPL distribution. This approach solves time independent partial differential equations of the temporal moments, and therefore avoids solving the convection-dispersion equation using a time marching scheme, resulting in a dramatic reduction of computational cost. To reduce numerical oscillations associated with convection dominated transport problems such as in inter-well tracer tests, the approach uses a finite element solver adopting the streamline upwind Petrov-Galerkin method to calculate moments and sensitivities. We test the temporal moment approach through numerical simulations. Comparing the computational costs between utilizing moments and discrete concentrations, we find that temporal moments significantly reduce the computation time. We also find that tracer moment data collected through a tomographic survey alone are able to yield reasonable estimates of hydraulic conductivity, as indicated by a correlation of 0.588 between estimated and true hydraulic conductivity fields in the synthetic case study.

AB - Hydraulic/partitioning tracer tomography (HPTT) was recently developed by Yeh and Zhu [Yeh T-CJ, Zhu J. Hydraulic/partitioning tracer tomography for characterization of dense nonaqueous phase liquid source zones, Water Resour Res 2007;43:W06435. doi:10.1029/2006WR004877.] for estimating spatial distribution of dense nonaqueous phase liquids (DNAPLs) in the subsurface. Since discrete tracer concentration data are directly utilized for the estimation of DNAPLs, this approach solves the hyperbolic convection-dispersion equation. Solution to the convection-dispersion equation however demands fine temporal and spatial discretization, resulting in high computational cost for an HPTT analysis. In this work, we use temporal moments of tracer breakthrough curves instead of discrete concentration data to estimate DNAPL distribution. This approach solves time independent partial differential equations of the temporal moments, and therefore avoids solving the convection-dispersion equation using a time marching scheme, resulting in a dramatic reduction of computational cost. To reduce numerical oscillations associated with convection dominated transport problems such as in inter-well tracer tests, the approach uses a finite element solver adopting the streamline upwind Petrov-Galerkin method to calculate moments and sensitivities. We test the temporal moment approach through numerical simulations. Comparing the computational costs between utilizing moments and discrete concentrations, we find that temporal moments significantly reduce the computation time. We also find that tracer moment data collected through a tomographic survey alone are able to yield reasonable estimates of hydraulic conductivity, as indicated by a correlation of 0.588 between estimated and true hydraulic conductivity fields in the synthetic case study.

KW - Hydraulic/tracer tomography

KW - Parameter estimation

KW - Source zone characterization

KW - Temporal moments

UR - http://www.scopus.com/inward/record.url?scp=61349092849&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=61349092849&partnerID=8YFLogxK

U2 - 10.1016/j.advwatres.2008.12.001

DO - 10.1016/j.advwatres.2008.12.001

M3 - Article

AN - SCOPUS:61349092849

VL - 32

SP - 391

EP - 400

JO - Advances in Water Resources

JF - Advances in Water Resources

SN - 0309-1708

IS - 3

ER -