Trajectorybased modeling of fluid transport in a medium with smoothly varying heterogeneity
Using an asymptotic methodology, valid in the presence of smoothly varying heterogeneity and prescribed boundaries, we derive a trajectorybased solution for tracer transport. The analysis produces a HamiltonJacobi partial differential equation for the phase of the propagating tracer front. The trajectories follow from the characteristic equations that are equivalent to the HamiltonJacobi equation. The paths are determined by the fluid velocity field, the total porosity, and the dispersion tensor. Due to their dependence upon the local hydrodynamic dispersion, they differ from conventional streamlines. This difference is borne out in numerical calculations for both uniform and dipole flow fields. In an application to the computational Xray imaging of a saline tracer test, we illustrate that the trajectories may serve as the basis for a form of tracer tomography. In particular, we use the onset time of a change in attenuation for each volume element of the Xray image as a measure of the arrival time of the saline tracer. In conclusion, the arrival times are used to image the spatial variation of the effective hydraulic conductivity within the laboratory sample.
 Authors:

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 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Energy Geosciences Division
 Publication Date:
 Grant/Contract Number:
 AC0205CH11231
 Type:
 Accepted Manuscript
 Journal Name:
 Water Resources Research
 Additional Journal Information:
 Journal Volume: 52; Journal Issue: 4; Journal ID: ISSN 00431397
 Publisher:
 American Geophysical Union (AGU)
 Research Org:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 58 GEOSCIENCES; 97 MATHEMATICS AND COMPUTING; transport; tracer; dispersion; inversion
 OSTI Identifier:
 1379254
Vasco, D. W., Pride, Steven R., and Commer, Michael. Trajectorybased modeling of fluid transport in a medium with smoothly varying heterogeneity. United States: N. p.,
Web. doi:10.1002/2015WR017646.
Vasco, D. W., Pride, Steven R., & Commer, Michael. Trajectorybased modeling of fluid transport in a medium with smoothly varying heterogeneity. United States. doi:10.1002/2015WR017646.
Vasco, D. W., Pride, Steven R., and Commer, Michael. 2016.
"Trajectorybased modeling of fluid transport in a medium with smoothly varying heterogeneity". United States.
doi:10.1002/2015WR017646. https://www.osti.gov/servlets/purl/1379254.
@article{osti_1379254,
title = {Trajectorybased modeling of fluid transport in a medium with smoothly varying heterogeneity},
author = {Vasco, D. W. and Pride, Steven R. and Commer, Michael},
abstractNote = {Using an asymptotic methodology, valid in the presence of smoothly varying heterogeneity and prescribed boundaries, we derive a trajectorybased solution for tracer transport. The analysis produces a HamiltonJacobi partial differential equation for the phase of the propagating tracer front. The trajectories follow from the characteristic equations that are equivalent to the HamiltonJacobi equation. The paths are determined by the fluid velocity field, the total porosity, and the dispersion tensor. Due to their dependence upon the local hydrodynamic dispersion, they differ from conventional streamlines. This difference is borne out in numerical calculations for both uniform and dipole flow fields. In an application to the computational Xray imaging of a saline tracer test, we illustrate that the trajectories may serve as the basis for a form of tracer tomography. In particular, we use the onset time of a change in attenuation for each volume element of the Xray image as a measure of the arrival time of the saline tracer. In conclusion, the arrival times are used to image the spatial variation of the effective hydraulic conductivity within the laboratory sample.},
doi = {10.1002/2015WR017646},
journal = {Water Resources Research},
number = 4,
volume = 52,
place = {United States},
year = {2016},
month = {3}
}