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Solute transport along a single fracture in a porous rock: a simple analytical solution and its extension for modeling velocity dispersion
KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Chemical Engineering. (Division of Nuclear Waste Engineering)
KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Chemical Engineering. (Division of Nuclear Waste Engineering)
KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Chemical Engineering.ORCID iD: 0000-0002-6049-428X
KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Chemical Engineering.
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2017 (English)In: Hydrogeology Journal, ISSN 1431-2174, E-ISSN 1435-0157Article in journal (Refereed) Published
Abstract [en]

A simple and robust solution is developed for the problem of solute transport along a single fracture in a porous rock. The solution is referred to as the solution to the single-flow-path model and takes the form of a convolution of two functions. The first function is the probability density function of residence-time distribution of a conservative solute in the fracture-only system as if the rock matrix is impermeable. The second function is the response of the fracture-matrix system to the input source when Fickian-type dispersion is completely neglected; thus, the effects of Fickian-type dispersion and matrix diffusion have been decoupled. It is also found that the solution can be understood in a way in line with the concept of velocity dispersion in fractured rocks. The solution is therefore extended into more general cases to also account for velocity variation between the channels. This leads to a development of the multi-channel model followed by detailed statistical descriptions of channel properties and sensitivity analysis of the model upon changes in the model key parameters. The simulation results obtained by the multi-channel model in this study fairly well agree with what is often observed in field experiments—i.e. the unchanged Peclet number with distance, which cannot be predicted by the classical advection-dispersion equation. In light of the findings from the aforementioned analysis, it is suggested that forced-gradient experiments can result in considerably different estimates of dispersivity compared to what can be found in natural-gradient systems for typical channel widths.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2017.
Keywords [en]
Fractured rocks - Velocity dispersion - Mathematical model - Matrix diffusion - Taylor dispersion
National Category
Other Chemical Engineering Chemical Process Engineering
Research subject
Chemical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-213979DOI: 10.1007/s10040-017-1627-8ISI: 000423051600020Scopus ID: 2-s2.0-85026908664OAI: oai:DiVA.org:kth-213979DiVA, id: diva2:1139490
Note

QC 20170918

Available from: 2017-09-07 Created: 2017-09-07 Last updated: 2018-02-02Bibliographically approved
In thesis
1. Solute Transport in Fractured Rocks: The Effect of Stagnant Water Zones and Velocity Dispersion
Open this publication in new window or tab >>Solute Transport in Fractured Rocks: The Effect of Stagnant Water Zones and Velocity Dispersion
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The focus of this thesis is on the development of new models to improve our understanding of radionuclide transport in the repository “far-field” in fractured rocks. The proposed models contribute to the channel network concept and describe the recently developed models with stagnant water zones (STWZs) and channels with variable aperture allowing to consider their possible impacts on the overall transport of radionuclides in fractured rocks. New conceptual models are also proposed to better understand hydrodynamic dispersion in fractured rocks by taking into account velocity distribution within tapered channels, i.e., Fickian-type dispersion, and between different flow paths, i.e., velocity dispersion, as embodied in the proposed multi-channel model.

The results of both deterministic and probabilistic analyses reveal that over the long times of interest for safety assessment of high-level radioactive waste repositories, STWZs can substantially enhance the retardation of both short- and long-lived nuclides, with the exception of the non-sorbing species, i.e., 36Cl and 129I. Nevertheless, over the short time-scales the impact of STWZs is not very strong and is not expected to affect the results of short-term field experiments. It is also shown that the proposed multi-channel model can explain the apparent scale dependency of the dispersion coefficient that is often observed in tracer experiments. It is further discussed that the interpreted results of short-range tracer experiments cannot necessarily give information on what would take place over longer distances because the spreading mechanisms are expected to be entirely different. Usefulness of the continuum model to interpret tracer experiments is, thereafter, discussed and arguments are presented to support the premise that it is more physically meaningful to describe flow and transport as taking place in a three-dimensional network of channels.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2017
Series
TRITA-CHE-Report, ISSN 1654-1081 ; 37
Keywords
Channel network concept; radionuclide transport; stagnant water zones; velocity dispersion; modeling and simulation
National Category
Chemical Engineering
Research subject
Chemical Engineering
Identifiers
urn:nbn:se:kth:diva-214040 (URN)978-91-7729-523-5 (ISBN)
Public defence
2017-10-06, Kollegiesalen, Brinellvägen 8, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20170911

Available from: 2017-09-11 Created: 2017-09-10 Last updated: 2018-12-04Bibliographically approved

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