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Title: Calculating Trajectories Associated With Solute Transport in a Heterogeneous Medium

Abstract

Here, we present a trajectory-based technique for calculating solute transport in a porous medium that has several advantages over existing methods. Unlike streamlines, the extended trajectories are influenced by each of the important parameters governing transport, including molecular diffusion and transverse dispersion. The approach is complete and does not require any additional techniques, such as operator splitting or particle tracking, in order to account for the full dispersion tensor. The semianalytic expressions make it clear how the flow field, the concentration distribution, and the dispersion tensor contribute to the velocity field of an injected solute. The equations are valid for an arbitrary porous medium, including those with rapid spatial variations in properties, overcoming limitations faced by previous approaches based upon asymptotic techniques. A test on a layered model with sharp boundaries indicates that the extended trajectories are compatible with the results of a numerical simulator and differ from streamlines. We also describe a new form of the dispersion tensor that incorporates a known asymmetry. The trajectories indicate that the modifications of the dispersion tensor lead to more focused transport within regions of high conductivity. The trajectories are used to define a semianalytic relationship between solute travel times and variations inmore » solute velocities along a path that may be used for tomographic imaging. In an application to the injection of a radioactive tracer into a Berea sandstone core, monitored using micropositron emission tomographic (micro-PET) observations, the sensitivities are used to map the spatial variations of permeability within the core.« less

Authors:
ORCiD logo [1];  [1]; ORCiD logo [2];  [2]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Energy Geosciences Division
  2. Stanford Univ., CA (United States). Dept. of Energy Resources Engineering
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); National Inst. of Health (NIH) (United States)
OSTI Identifier:
1479371
Grant/Contract Number:  
[AC02-05CH11231; 1S10OD018130-01]
Resource Type:
Accepted Manuscript
Journal Name:
Water Resources Research
Additional Journal Information:
[ Journal Volume: 54; Journal Issue: 9]; Journal ID: ISSN 0043-1397
Publisher:
American Geophysical Union (AGU)
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; tracer; transport; streamlines; solute transport; inverse modeling; visualization

Citation Formats

Vasco, D. W., Pride, Steven R., Zahasky, Christopher, and Benson, Sally M. Calculating Trajectories Associated With Solute Transport in a Heterogeneous Medium. United States: N. p., 2018. Web. doi:10.1029/2018WR023019.
Vasco, D. W., Pride, Steven R., Zahasky, Christopher, & Benson, Sally M. Calculating Trajectories Associated With Solute Transport in a Heterogeneous Medium. United States. doi:10.1029/2018WR023019.
Vasco, D. W., Pride, Steven R., Zahasky, Christopher, and Benson, Sally M. Wed . "Calculating Trajectories Associated With Solute Transport in a Heterogeneous Medium". United States. doi:10.1029/2018WR023019. https://www.osti.gov/servlets/purl/1479371.
@article{osti_1479371,
title = {Calculating Trajectories Associated With Solute Transport in a Heterogeneous Medium},
author = {Vasco, D. W. and Pride, Steven R. and Zahasky, Christopher and Benson, Sally M.},
abstractNote = {Here, we present a trajectory-based technique for calculating solute transport in a porous medium that has several advantages over existing methods. Unlike streamlines, the extended trajectories are influenced by each of the important parameters governing transport, including molecular diffusion and transverse dispersion. The approach is complete and does not require any additional techniques, such as operator splitting or particle tracking, in order to account for the full dispersion tensor. The semianalytic expressions make it clear how the flow field, the concentration distribution, and the dispersion tensor contribute to the velocity field of an injected solute. The equations are valid for an arbitrary porous medium, including those with rapid spatial variations in properties, overcoming limitations faced by previous approaches based upon asymptotic techniques. A test on a layered model with sharp boundaries indicates that the extended trajectories are compatible with the results of a numerical simulator and differ from streamlines. We also describe a new form of the dispersion tensor that incorporates a known asymmetry. The trajectories indicate that the modifications of the dispersion tensor lead to more focused transport within regions of high conductivity. The trajectories are used to define a semianalytic relationship between solute travel times and variations in solute velocities along a path that may be used for tomographic imaging. In an application to the injection of a radioactive tracer into a Berea sandstone core, monitored using micropositron emission tomographic (micro-PET) observations, the sensitivities are used to map the spatial variations of permeability within the core.},
doi = {10.1029/2018WR023019},
journal = {Water Resources Research},
number = [9],
volume = [54],
place = {United States},
year = {2018},
month = {8}
}

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