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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: 2019-12-18Bibliographically 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
2. Solute transport in fractured rocks: Analysis of analytical solutions and determination of transport parameters
Open this publication in new window or tab >>Solute transport in fractured rocks: Analysis of analytical solutions and determination of transport parameters
2020 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In order to facilitate the assessment of the safety and function of deep geological repositories for radioactive waste, several models have been developed to describe water flow and transport of solutes in fractured crystalline rock. The rock around the repository is described and modelled as a network of water-bearing fractures.

The first part of the work concerns analytical solutions of the mathematical models, first developed in the 1980s to describe nuclide transport with seeping water in the fractures where the nuclides can also diffuse in and out of the pores into the rock matrix. A new simple analytical solution is described in which the interaction between matrix diffusion and hydrodynamic dispersion could be decoupled, which makes the interaction between the processes visible while making the solution more manageable. In addition, another dispersion mechanism caused by the presence of independent transport paths is easily handled with the new model. This makes it possible to treat both dispersion mechanisms with the same formalism. This makes the new model more useful in interpreting field experiments with tracer as well as for long-term simulation of nuclide migration in rock.

The second part of the work is about molecular diffusion in the rock matrix itself, which is a central mechanism in the model above. One way to measure diffusion and sorption in rock pieces is to force ions through the pores of the rock by means of electromigration. The method previously used has been improved by adding a potentiostat and a pH buffer. The experimental results become more stable.

To better interpret the results, a general model for transport in the rock matrix was developed. The model includes electromigration, electroosmosis and dispersion in the pore system. The effective pore diffusivity and matrix formation factor can be determined from the experiments. The results show that the developed electromigration method can be used to provide high quality experimental data.

Abstract [sv]

För att underlätta bedömning av säkerhet och funktion hos djupa geologiska förvar för radioaktivt avfall har flera modeller utvecklats för att beskriva vattenflöde och transport av lösta ämnen i kristallint berg med sprickor. Berget kring förvaret beskrivs och modelleras som ett nätverk av vattenförande sprickor.

Den fösta delen av arbetet handlar om analytiska lösningar av de matematiska modellerna, utvecklades på 1980-talet för att beskriva nuklidtransport med sipprande vatten i sprickorna där nukliderna även kan diffundera in och ut ur porerna in bergmatrisen. En ny enkel analytisk lösning beskrivs i vilken samverkan mellan hydrodynamisk dispersion och matrisdiffusion kunnat frikopplas, vilket gör att samverkan mellan processerna synliggörs samtidigt som lösningen är mer hanterbar. Dessutom kan en annan dispersionsmekanism orsakad av närvaron av oberoende transportvägar med lätthet hanteras med den nya modellen. Detta gör det möjligt att behandla både dispersionsmekanismer med samma formalism. Detta gör den nya lösningen mer användbar vid tolkningen av fältförsök med spårämnen liksom för långsiktig simulering av nuklidspridning i berg.

Den andra delen av arbetet handlar om molekylär diffusion i bergmatrisen vilket är en central mekanism i modellen ovan. Ett sätt att mäta diffusion och sorption i bergstycken bygger på att driva in joner i bergets porer av med hjälp elektromigration. Den tidigare använda metoden har förbättrats genom att lägga till en potentiostat och pH-buffert. De experimentella resultaten blir därvid mer stabila.

För att bättre tolka resultaten utvecklades en generell modell för transport i bergmatrisen. Modellen inbegriper elektromigration, elektroosmos och dispersion i porsystemet. Den effektiva por-diffusiviteten och matrisens formationsfaktor kan bestämmas ur experimenten. Resultaten visar att den utvecklade elektromigreringsmetoden kan användas för att ge experimentella data av hög kvalitet.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2020. p. 49
Series
TRITA-CBH-FOU ; 2020:5
Keywords
Fractured rock, Radionuclide transport, Analytical solution, Dispersion mechanisms, Electromigration., Sprickigt berg, Radionukidtransport, analytisk lösning, Dispersionsmekanismer, Elektromigration.
National Category
Chemical Engineering
Research subject
Chemical Engineering
Identifiers
urn:nbn:se:kth:diva-265611 (URN)978-91-7873-412-2 (ISBN)
Public defence
2020-02-27, Kollegiesalen, Brinellvägen 8, Stockholm, 10:00 (English)
Opponent
Supervisors
Funder
Swedish Nuclear Fuel and Waste Management Company, SKB, C7241
Note

QC 2020-01-20

Available from: 2020-01-20 Created: 2019-12-18 Last updated: 2020-01-20Bibliographically approved

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Liu, LongchengNeretnieks, IvarsMeng, Shuo

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