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Solute transport in fractured rocks: Analysis of analytical solutions and determination of transport parameters
KTH, School of Engineering Sciences in Chemistry, Biotechnology and Health (CBH), Chemical Engineering. (Division of Nuclear Waste Engineering)
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 [en]
Fractured rock, Radionuclide transport, Analytical solution, Dispersion mechanisms, Electromigration.
Keywords [sv]
Sprickigt berg, Radionukidtransport, analytisk lösning, Dispersionsmekanismer, Elektromigration.
National Category
Chemical Engineering
Research subject
Chemical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-265611ISBN: 978-91-7873-412-2 (print)OAI: oai:DiVA.org:kth-265611DiVA, id: diva2:1380189
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
List of papers
1. Solute transport along a single fracture in a porous rock: a simple analytical solution and its extension for modeling velocity dispersion
Open this publication in new window or tab >>Solute transport along a single fracture in a porous rock: a simple analytical solution and its extension for modeling velocity dispersion
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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
Fractured rocks - Velocity dispersion - Mathematical model - Matrix diffusion - Taylor dispersion
National Category
Other Chemical Engineering Chemical Process Engineering
Research subject
Chemical Engineering
Identifiers
urn:nbn:se:kth:diva-213979 (URN)10.1007/s10040-017-1627-8 (DOI)000423051600020 ()2-s2.0-85026908664 (Scopus ID)
Note

QC 20170918

Available from: 2017-09-07 Created: 2017-09-07 Last updated: 2019-12-18Bibliographically approved
2. Solute transport along a single fracture with a finite extent of matrix: A new simple solution and temporal moment analysis
Open this publication in new window or tab >>Solute transport along a single fracture with a finite extent of matrix: A new simple solution and temporal moment analysis
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2018 (English)In: Journal of Hydrology, ISSN 0022-1694, E-ISSN 1879-2707, Vol. 562, p. 290-304Article in journal (Refereed) Published
Abstract [en]

A new simple and robust solution, based on uniform steady-state flow velocity, is developed for the problem of solute transport in a fracture-matrix system with a finite penetration depth of a radioactive contaminant into the rock matrix. The solution is an extension of Liu et al. (2017) to finite penetration depth and an alternative solution strategy to the problem solved by Sudicky et al. (1982). The solution takes the form of a convolution of two functions. The first function describes the probability density function of the residence time distribution of a conservative solute resulting merely from advection and Fickian dispersion. The second function is actually the impulse response of the fracture-matrix system in the case of a plug flow without any hydrodynamic dispersion. As a result, the effects of Fickian dispersion and matrix diffusion on solute transport are decoupled, and thus the resulting breakthrough curve can be analyzed in terms of those two functions. In addition to this, the derived Péclet numbers of those two functions, based on temporal moments, are also found to be associated with the derived Péclet number of the resulting breakthrough curve. By comparing the Péclet numbers of those two functions, the contribution of Fickian dispersion and matrix diffusion to solute spreading is determined in a straightforward way. This can aid to find out the dominating mechanism on solute transport, and therefore the performance of breakthrough curve.

Place, publisher, year, edition, pages
Elsevier, 2018
Keywords
Dispersion, Fractured rocks, Matrix diffusion, Péclet number, Solute transport model, Temporal moment analysis
National Category
Oceanography, Hydrology and Water Resources
Identifiers
urn:nbn:se:kth:diva-228725 (URN)10.1016/j.jhydrol.2018.05.016 (DOI)000438003000022 ()2-s2.0-85047099016 (Scopus ID)
Funder
Swedish Nuclear Fuel and Waste Management Company, SKB
Note

QC 20180529

Available from: 2018-05-29 Created: 2018-05-29 Last updated: 2019-12-18Bibliographically approved
3. A modification of the electromigration device and modelling methods for diffusion and sorption studies of radionuclides in intact crystalline rocks.
Open this publication in new window or tab >>A modification of the electromigration device and modelling methods for diffusion and sorption studies of radionuclides in intact crystalline rocks.
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2019 (English)In: Journal of Contaminant Hydrology, ISSN 0169-7722, E-ISSN 1873-6009Article in journal, Editorial material (Refereed) In press
Abstract [en]

To determine the diffusion and sorption propertiesof radionuclides in intact crystalline rocks, a newelectromigration devicewas built and tested by running with I-and Se(IV) ions. By introducing a potentiostatto impose a constant voltageover the studied rock sample, the electromigration device cangive more stable and accurateexperimental resultsthan those from the traditional electromigration devices.In addition, the variation in the pHofthe background electrolytes wasminimised by adding a small amount of NaHCO3as buffers.To interpret the experimental results with moreconfidence, anadvection-dispersion model was also developed in thisstudy, which accounts for the most important mechanisms governing ionic transport in the electromigration experiments.Data analysis of the breakthrough curves by the advection-dispersion model, instead of the traditional ideal plug-flowmodel,suggest that the effective diffusivitiesof I-and Se(IV)are (1.15±0.06) ×10-13m2/s and (3.50±0.86) ×10-14m2/s, respectively. The results also show thatI-is more mobile than Se(IV) ions when migrating through the sameintact rock sampleand that theirsorption properties are almost identical.

Keywords
Electromigration, advection-dispersion model, Se(IV), iodide, intact crystallinerock
National Category
Other Earth and Related Environmental Sciences
Identifiers
urn:nbn:se:kth:diva-265607 (URN)10.1016/j.jconhyd.2019.103585 (DOI)2-s2.0-85076970669 (Scopus ID)
Available from: 2019-12-18 Created: 2019-12-18 Last updated: 2020-03-09Bibliographically approved
4. Development and application of an advection-dispersion model for data analysis of electromigration experiments with intact rock cores
Open this publication in new window or tab >>Development and application of an advection-dispersion model for data analysis of electromigration experiments with intact rock cores
(English)Manuscript (preprint) (Other (popular science, discussion, etc.))
National Category
Other Earth and Related Environmental Sciences
Identifiers
urn:nbn:se:kth:diva-265609 (URN)
Note

QC 20191220

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

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